TSTP Solution File: SYN259-1 by Leo-III---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.0
% Problem  : SYN259-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n022.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 29 22:44:07 EDT 2022

% Result   : Unsatisfiable 17.08s 4.23s
% Output   : Refutation 17.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  419
% Syntax   : Number of formulae    :  787 (  81 unt;  52 typ;   0 def)
%            Number of atoms       : 2101 (   0 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives : 7331 (1368   ~;1366   |;   0   &;4597   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   89 (  89   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   54 (  52 usr;   7 con; 0-3 aty)
%            Number of variables   : 1244 (   0   ^1244   !;   0   ?;1244   :)

% Comments : 
%------------------------------------------------------------------------------
thf(p1_type,type,
    p1: $i > $i > $i > $o ).

thf(d_type,type,
    d: $i ).

thf(q5_type,type,
    q5: $i > $i > $o ).

thf(q4_type,type,
    q4: $i > $i > $o ).

thf(s5_type,type,
    s5: $i > $o ).

thf(l4_type,type,
    l4: $i > $o ).

thf(r4_type,type,
    r4: $i > $o ).

thf(p5_type,type,
    p5: $i > $i > $i > $o ).

thf(s4_type,type,
    s4: $i > $o ).

thf(l2_type,type,
    l2: $i > $i > $o ).

thf(r1_type,type,
    r1: $i > $o ).

thf(a_type,type,
    a: $i ).

thf(m5_type,type,
    m5: $i > $i > $o ).

thf(r0_type,type,
    r0: $i > $o ).

thf(s1_type,type,
    s1: $i > $o ).

thf(m2_type,type,
    m2: $i > $o ).

thf(m0_type,type,
    m0: $i > $i > $i > $o ).

thf(p0_type,type,
    p0: $i > $i > $o ).

thf(n1_type,type,
    n1: $i > $i > $i > $o ).

thf(n0_type,type,
    n0: $i > $i > $o ).

thf(e_type,type,
    e: $i ).

thf(q3_type,type,
    q3: $i > $i > $o ).

thf(s2_type,type,
    s2: $i > $o ).

thf(m3_type,type,
    m3: $i > $i > $i > $o ).

thf(r2_type,type,
    r2: $i > $o ).

thf(k3_type,type,
    k3: $i > $i > $i > $o ).

thf(p2_type,type,
    p2: $i > $i > $i > $o ).

thf(q1_type,type,
    q1: $i > $i > $i > $o ).

thf(k0_type,type,
    k0: $i > $o ).

thf(l0_type,type,
    l0: $i > $o ).

thf(q0_type,type,
    q0: $i > $i > $o ).

thf(k2_type,type,
    k2: $i > $i > $o ).

thf(n2_type,type,
    n2: $i > $o ).

thf(b_type,type,
    b: $i ).

thf(c_type,type,
    c: $i ).

thf(r3_type,type,
    r3: $i > $i > $i > $o ).

thf(m1_type,type,
    m1: $i > $i > $i > $o ).

thf(p4_type,type,
    p4: $i > $i > $i > $o ).

thf(n3_type,type,
    n3: $i > $o ).

thf(p3_type,type,
    p3: $i > $i > $i > $o ).

thf(k1_type,type,
    k1: $i > $o ).

thf(q2_type,type,
    q2: $i > $i > $i > $o ).

thf(l3_type,type,
    l3: $i > $i > $o ).

thf(l1_type,type,
    l1: $i > $i > $o ).

thf(s0_type,type,
    s0: $i > $o ).

thf(n4_type,type,
    n4: $i > $i > $o ).

thf(k4_type,type,
    k4: $i > $o ).

thf(n5_type,type,
    n5: $i > $i > $o ).

thf(k5_type,type,
    k5: $i > $o ).

thf(m4_type,type,
    m4: $i > $i > $o ).

thf(r5_type,type,
    r5: $i > $i > $o ).

thf(s3_type,type,
    s3: $i > $i > $o ).

thf(355,axiom,
    ! [B: $i,A: $i] :
      ( ( q3 @ A @ A )
      | ~ ( m0 @ B @ d @ B )
      | ~ ( k1 @ A )
      | ~ ( r2 @ d )
      | ~ ( q3 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_259) ).

thf(1036,plain,
    ! [B: $i,A: $i] :
      ( ( q3 @ A @ A )
      | ~ ( m0 @ B @ d @ B )
      | ~ ( k1 @ A )
      | ~ ( r2 @ d )
      | ~ ( q3 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(232,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( r3 @ A @ A @ A )
      | ~ ( l1 @ B @ C )
      | ~ ( n1 @ C @ C @ C )
      | ~ ( r2 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_261) ).

thf(809,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( r3 @ A @ A @ A )
      | ~ ( l1 @ B @ C )
      | ~ ( n1 @ C @ C @ C )
      | ~ ( r2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(137,axiom,
    ! [A: $i] :
      ( ( r2 @ A )
      | ~ ( r1 @ A )
      | ~ ( l0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_188) ).

thf(629,plain,
    ! [A: $i] :
      ( ( r2 @ A )
      | ~ ( r1 @ A )
      | ~ ( l0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(349,axiom,
    ! [A: $i] :
      ( ( q2 @ A @ A @ A )
      | ~ ( p1 @ A @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_181) ).

thf(1024,plain,
    ! [A: $i] :
      ( ( q2 @ A @ A @ A )
      | ~ ( p1 @ A @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(59,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( q4 @ A @ B )
      | ~ ( k3 @ C @ C @ A )
      | ~ ( q2 @ D @ B @ A )
      | ~ ( m3 @ D @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_295) ).

thf(479,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( q4 @ A @ B )
      | ~ ( k3 @ C @ C @ A )
      | ~ ( q2 @ D @ B @ A )
      | ~ ( m3 @ D @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(251,axiom,
    ! [A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( m0 @ c @ A @ A )
      | ~ ( r0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_123) ).

thf(846,plain,
    ! [A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( m0 @ c @ A @ A )
      | ~ ( r0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(80,axiom,
    ! [A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( r0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_116) ).

thf(518,plain,
    ! [A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( r0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(315,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ B @ B )
      | ~ ( p1 @ A @ C @ D )
      | ~ ( l1 @ C @ D )
      | ~ ( p2 @ A @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_146) ).

thf(962,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ B @ B )
      | ~ ( p1 @ A @ C @ D )
      | ~ ( l1 @ C @ D )
      | ~ ( p2 @ A @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(303,axiom,
    ( ( p1 @ b @ b @ b )
    | ~ ( p1 @ b @ b @ b )
    | ~ ( s0 @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_076) ).

thf(941,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(60,axiom,
    ! [B: $i,A: $i] :
      ( ( l1 @ A @ A )
      | ~ ( n0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_002) ).

thf(481,plain,
    ! [B: $i,A: $i] :
      ( ( l1 @ A @ A )
      | ~ ( n0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(145,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( n3 @ A )
      | ~ ( p2 @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_240) ).

thf(645,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( n3 @ A )
      | ~ ( p2 @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(276,axiom,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( l0 @ A )
      | ~ ( l0 @ B )
      | ~ ( p0 @ B @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_026) ).

thf(892,plain,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( l0 @ A )
      | ~ ( l0 @ B )
      | ~ ( p0 @ B @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(215,axiom,
    ! [B: $i,A: $i] :
      ( ( q2 @ A @ A @ A )
      | ~ ( q1 @ B @ c @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_184) ).

thf(777,plain,
    ! [B: $i,A: $i] :
      ( ( q2 @ A @ A @ A )
      | ~ ( q1 @ B @ c @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(99,axiom,
    ! [B: $i,A: $i] :
      ( ( r5 @ A @ B )
      | ~ ( s4 @ A )
      | ~ ( k0 @ b )
      | ~ ( n3 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_327) ).

thf(555,plain,
    ! [B: $i,A: $i] :
      ( ( r5 @ A @ B )
      | ~ ( s4 @ A )
      | ~ ( k0 @ b )
      | ~ ( n3 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(323,axiom,
    ! [A: $i] :
      ( ( q1 @ e @ A @ A )
      | ~ ( m0 @ A @ d @ A )
      | ~ ( m0 @ e @ d @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_107) ).

thf(977,plain,
    ! [A: $i] :
      ( ( q1 @ e @ A @ A )
      | ~ ( m0 @ A @ d @ A )
      | ~ ( m0 @ e @ d @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(339,axiom,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( l1 @ B @ B )
      | ~ ( p0 @ A @ B )
      | ~ ( n0 @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_065) ).

thf(1005,plain,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( l1 @ B @ B )
      | ~ ( p0 @ A @ B )
      | ~ ( n0 @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(191,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( m1 @ A @ B @ B )
      | ~ ( l0 @ C )
      | ~ ( m0 @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_015) ).

thf(730,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( m1 @ A @ B @ B )
      | ~ ( l0 @ C )
      | ~ ( m0 @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(333,axiom,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( q0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_067) ).

thf(994,plain,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( q0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(129,axiom,
    ! [A: $i] :
      ( ( r3 @ a @ a @ e )
      | ~ ( k2 @ a @ a )
      | ~ ( q2 @ A @ e @ A )
      | ~ ( m2 @ b )
      | ~ ( m3 @ a @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_269) ).

thf(614,plain,
    ! [A: $i] :
      ( ( r3 @ a @ a @ e )
      | ~ ( k2 @ a @ a )
      | ~ ( q2 @ A @ e @ A )
      | ~ ( m2 @ b )
      | ~ ( m3 @ a @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(266,axiom,
    ( ( p1 @ a @ a @ a )
    | ~ ( p0 @ b @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_075) ).

thf(873,plain,
    ( ( p1 @ a @ a @ a )
    | ~ ( p0 @ b @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(44,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ B @ B )
      | ~ ( n1 @ C @ B @ C )
      | ~ ( p0 @ A @ B )
      | ~ ( p2 @ A @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_152) ).

thf(449,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ B @ B )
      | ~ ( n1 @ C @ B @ C )
      | ~ ( p0 @ A @ B )
      | ~ ( p2 @ A @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(39,axiom,
    ! [B: $i,A: $i] :
      ( ( l3 @ A @ A )
      | ~ ( s2 @ B )
      | ~ ( l1 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_220) ).

thf(440,plain,
    ! [B: $i,A: $i] :
      ( ( l3 @ A @ A )
      | ~ ( s2 @ B )
      | ~ ( l1 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(150,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ B @ B )
      | ~ ( k1 @ C )
      | ~ ( p2 @ e @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_155) ).

thf(655,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ B @ B )
      | ~ ( k1 @ C )
      | ~ ( p2 @ e @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(76,axiom,
    ! [A: $i] : ( p0 @ b @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).

thf(511,plain,
    ! [A: $i] : ( p0 @ b @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( q5 @ A @ A )
      | ~ ( l4 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_324) ).

thf(384,plain,
    ! [A: $i] :
      ( ( q5 @ A @ A )
      | ~ ( l4 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(306,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( n5 @ A @ A )
      | ~ ( p0 @ A @ B )
      | ~ ( m4 @ C @ C )
      | ~ ( k5 @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_310) ).

thf(945,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( n5 @ A @ A )
      | ~ ( p0 @ A @ B )
      | ~ ( m4 @ C @ C )
      | ~ ( k5 @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(90,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( m3 @ A @ B @ B )
      | ~ ( n2 @ A )
      | ~ ( m2 @ B )
      | ~ ( m3 @ C @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_228) ).

thf(538,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( m3 @ A @ B @ B )
      | ~ ( n2 @ A )
      | ~ ( m2 @ B )
      | ~ ( m3 @ C @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(297,axiom,
    q0 @ e @ d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).

thf(930,plain,
    q0 @ e @ d,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(159,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( m1 @ A @ B @ B )
      | ~ ( m1 @ C @ B @ A )
      | ~ ( m1 @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_016) ).

thf(670,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( m1 @ A @ B @ B )
      | ~ ( m1 @ C @ B @ A )
      | ~ ( m1 @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(242,axiom,
    p0 @ c @ b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_18) ).

thf(829,plain,
    p0 @ c @ b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(280,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( n0 @ B @ B )
      | ~ ( l0 @ C )
      | ~ ( n1 @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_080) ).

thf(898,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( n0 @ B @ B )
      | ~ ( l0 @ C )
      | ~ ( n1 @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(26,axiom,
    k0 @ b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_32) ).

thf(417,plain,
    k0 @ b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(104,axiom,
    ( ( n2 @ c )
    | ~ ( l1 @ e @ c )
    | ~ ( k0 @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_139) ).

thf(565,plain,
    ( ( n2 @ c )
    | ~ ( l1 @ e @ c )
    | ~ ( k0 @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(148,axiom,
    ! [B: $i,A: $i] :
      ( ( r3 @ A @ B @ B )
      | ~ ( s2 @ B )
      | ~ ( l2 @ c @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_260) ).

thf(651,plain,
    ! [B: $i,A: $i] :
      ( ( r3 @ A @ B @ B )
      | ~ ( s2 @ B )
      | ~ ( l2 @ c @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(321,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( r3 @ A @ A @ A )
      | ~ ( p1 @ B @ C @ A )
      | ~ ( l2 @ C @ B )
      | ~ ( r3 @ A @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_262) ).

thf(973,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( r3 @ A @ A @ A )
      | ~ ( p1 @ B @ C @ A )
      | ~ ( l2 @ C @ B )
      | ~ ( r3 @ A @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(272,axiom,
    ( ( p1 @ d @ d @ b )
    | ~ ( p0 @ d @ b )
    | ~ ( m0 @ e @ a @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_078) ).

thf(885,plain,
    ( ( p1 @ d @ d @ b )
    | ~ ( p0 @ d @ b )
    | ~ ( m0 @ e @ a @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(360,axiom,
    ( ( m1 @ a @ a @ a )
    | ~ ( l0 @ a )
    | ~ ( s0 @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_023) ).

thf(1046,plain,
    ( ( m1 @ a @ a @ a )
    | ~ ( l0 @ a )
    | ~ ( s0 @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(219,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( p2 @ B @ C @ B )
      | ~ ( m1 @ A @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_196) ).

thf(785,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( p2 @ B @ C @ B )
      | ~ ( m1 @ A @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(3,axiom,
    ! [B: $i,A: $i] :
      ( ( s5 @ A )
      | ~ ( l4 @ A )
      | ~ ( r4 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_329) ).

thf(372,plain,
    ! [B: $i,A: $i] :
      ( ( s5 @ A )
      | ~ ( l4 @ A )
      | ~ ( r4 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(290,axiom,
    n0 @ d @ e,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).

thf(917,plain,
    n0 @ d @ e,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(308,axiom,
    ! [B: $i,A: $i] :
      ( ( q1 @ A @ A @ B )
      | ~ ( s0 @ A )
      | ~ ( p0 @ B @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_105) ).

thf(949,plain,
    ! [B: $i,A: $i] :
      ( ( q1 @ A @ A @ B )
      | ~ ( s0 @ A )
      | ~ ( p0 @ B @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(92,axiom,
    n0 @ b @ a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_37) ).

thf(542,plain,
    n0 @ b @ a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(115,axiom,
    n0 @ a @ b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_15) ).

thf(587,plain,
    n0 @ a @ b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(247,axiom,
    ! [A: $i] :
      ( ( p4 @ c @ c @ A )
      | ~ ( n3 @ a )
      | ~ ( m3 @ A @ c @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_294) ).

thf(838,plain,
    ! [A: $i] :
      ( ( p4 @ c @ c @ A )
      | ~ ( n3 @ a )
      | ~ ( m3 @ A @ c @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(101,axiom,
    ! [B: $i,A: $i] :
      ( ( k3 @ A @ A @ B )
      | ~ ( k2 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_194) ).

thf(559,plain,
    ! [B: $i,A: $i] :
      ( ( k3 @ A @ A @ B )
      | ~ ( k2 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(255,axiom,
    ! [A: $i] :
      ( ( r5 @ A @ A )
      | ~ ( k4 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_328) ).

thf(853,plain,
    ! [A: $i] :
      ( ( r5 @ A @ A )
      | ~ ( k4 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(29,axiom,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ B @ A )
      | ~ ( m0 @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_005) ).

thf(421,plain,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ B @ A )
      | ~ ( m0 @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(270,axiom,
    ( ( p1 @ a @ a @ a )
    | ~ ( l0 @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_088) ).

thf(881,plain,
    ( ( p1 @ a @ a @ a )
    | ~ ( l0 @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(236,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( q3 @ A @ A )
      | ~ ( r2 @ A )
      | ~ ( s1 @ B )
      | ~ ( l2 @ C @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_258) ).

thf(817,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( q3 @ A @ A )
      | ~ ( r2 @ A )
      | ~ ( s1 @ B )
      | ~ ( l2 @ C @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(282,axiom,
    ( ( p2 @ a @ a @ a )
    | ~ ( p1 @ e @ e @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_172) ).

thf(902,plain,
    ( ( p2 @ a @ a @ a )
    | ~ ( p1 @ e @ e @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(319,axiom,
    ( ( q2 @ d @ a @ a )
    | ~ ( q2 @ d @ c @ a )
    | ~ ( s1 @ c )
    | ~ ( q0 @ e @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_180) ).

thf(969,plain,
    ( ( q2 @ d @ a @ a )
    | ~ ( q2 @ d @ c @ a )
    | ~ ( s1 @ c )
    | ~ ( q0 @ e @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(125,axiom,
    ! [B: $i,A: $i] :
      ( ( n1 @ A @ c @ A )
      | ~ ( m0 @ B @ A @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_039) ).

thf(606,plain,
    ! [B: $i,A: $i] :
      ( ( n1 @ A @ c @ A )
      | ~ ( m0 @ B @ A @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(204,axiom,
    ! [A: $i] :
      ( ( n5 @ A @ A )
      | ~ ( s1 @ A )
      | ~ ( k4 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_315) ).

thf(756,plain,
    ! [A: $i] :
      ( ( n5 @ A @ A )
      | ~ ( s1 @ A )
      | ~ ( k4 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(41,axiom,
    ! [B: $i,A: $i] :
      ( ( p3 @ A @ A @ A )
      | ~ ( p2 @ B @ A @ A )
      | ~ ( n3 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_248) ).

thf(443,plain,
    ! [B: $i,A: $i] :
      ( ( p3 @ A @ A @ A )
      | ~ ( p2 @ B @ A @ A )
      | ~ ( n3 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(357,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( q2 @ A @ A @ A )
      | ~ ( n1 @ B @ d @ C )
      | ~ ( k1 @ A )
      | ~ ( q2 @ C @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_185) ).

thf(1040,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( q2 @ A @ A @ A )
      | ~ ( n1 @ B @ d @ C )
      | ~ ( k1 @ A )
      | ~ ( q2 @ C @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( q4 @ A @ A )
      | ~ ( r1 @ A )
      | ~ ( l4 @ B )
      | ~ ( q4 @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_296) ).

thf(376,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( q4 @ A @ A )
      | ~ ( r1 @ A )
      | ~ ( l4 @ B )
      | ~ ( q4 @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(134,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( m2 @ A )
      | ~ ( s0 @ A )
      | ~ ( l1 @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_135) ).

thf(623,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( m2 @ A )
      | ~ ( s0 @ A )
      | ~ ( l1 @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(78,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( k3 @ A @ B @ A )
      | ~ ( s1 @ B )
      | ~ ( p2 @ C @ B @ D )
      | ~ ( n0 @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_192) ).

thf(514,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( k3 @ A @ B @ A )
      | ~ ( s1 @ B )
      | ~ ( p2 @ C @ B @ D )
      | ~ ( n0 @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(301,axiom,
    ( ( n4 @ d @ d )
    | ~ ( k3 @ c @ c @ e )
    | ~ ( q1 @ d @ d @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_282) ).

thf(937,plain,
    ( ( n4 @ d @ d )
    | ~ ( k3 @ c @ c @ e )
    | ~ ( q1 @ d @ d @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(347,axiom,
    ! [A: $i] :
      ( ( p1 @ d @ d @ A )
      | ~ ( s0 @ A )
      | ~ ( n1 @ c @ d @ A )
      | ~ ( r0 @ d )
      | ~ ( n0 @ c @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_089) ).

thf(1020,plain,
    ! [A: $i] :
      ( ( p1 @ d @ d @ A )
      | ~ ( s0 @ A )
      | ~ ( n1 @ c @ d @ A )
      | ~ ( r0 @ d )
      | ~ ( n0 @ c @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(317,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( l3 @ A @ A )
      | ~ ( p1 @ A @ A @ B )
      | ~ ( p2 @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_216) ).

thf(966,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( l3 @ A @ A )
      | ~ ( p1 @ A @ A @ B )
      | ~ ( p2 @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(238,axiom,
    ! [A: $i] :
      ( ( p3 @ e @ b @ e )
      | ~ ( m3 @ e @ A @ e )
      | ~ ( q2 @ A @ A @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_254) ).

thf(821,plain,
    ! [A: $i] :
      ( ( p3 @ e @ b @ e )
      | ~ ( m3 @ e @ A @ e )
      | ~ ( q2 @ A @ A @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(57,axiom,
    ( ( m1 @ e @ e @ e )
    | ~ ( r0 @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_030) ).

thf(475,plain,
    ( ( m1 @ e @ e @ e )
    | ~ ( r0 @ e ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(294,axiom,
    ( ( p2 @ d @ b @ b )
    | ~ ( p1 @ d @ b @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_161) ).

thf(924,plain,
    ( ( p2 @ d @ b @ b )
    | ~ ( p1 @ d @ b @ e ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(62,axiom,
    s0 @ b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).

thf(485,plain,
    s0 @ b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(245,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p4 @ A @ A @ A )
      | ~ ( l4 @ A )
      | ~ ( n0 @ A @ B )
      | ~ ( p4 @ C @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_289) ).

thf(834,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p4 @ A @ A @ A )
      | ~ ( l4 @ A )
      | ~ ( n0 @ A @ B )
      | ~ ( p4 @ C @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(16,axiom,
    ! [B: $i,A: $i] :
      ( ( m3 @ A @ A @ B )
      | ~ ( r2 @ B )
      | ~ ( k3 @ A @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_235) ).

thf(397,plain,
    ! [B: $i,A: $i] :
      ( ( m3 @ A @ A @ B )
      | ~ ( r2 @ B )
      | ~ ( k3 @ A @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(268,axiom,
    ! [B: $i,A: $i] :
      ( ( r1 @ A )
      | ~ ( q0 @ A @ B )
      | ~ ( s0 @ d )
      | ~ ( q1 @ d @ B @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_124) ).

thf(877,plain,
    ! [B: $i,A: $i] :
      ( ( r1 @ A )
      | ~ ( q0 @ A @ B )
      | ~ ( s0 @ d )
      | ~ ( q1 @ d @ B @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(193,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( m5 @ A @ B )
      | ~ ( r0 @ A )
      | ~ ( p4 @ A @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_303) ).

thf(734,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( m5 @ A @ B )
      | ~ ( r0 @ A )
      | ~ ( p4 @ A @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(312,axiom,
    ( ( n1 @ d @ e @ e )
    | ~ ( p0 @ d @ d )
    | ~ ( n1 @ e @ e @ e )
    | ~ ( r0 @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_055) ).

thf(956,plain,
    ( ( n1 @ d @ e @ e )
    | ~ ( p0 @ d @ d )
    | ~ ( n1 @ e @ e @ e )
    | ~ ( r0 @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(262,axiom,
    ! [B: $i,A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( l1 @ B @ A )
      | ~ ( n0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_058) ).

thf(866,plain,
    ! [B: $i,A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( l1 @ B @ A )
      | ~ ( n0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(46,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( m0 @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_121) ).

thf(453,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( m0 @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(335,axiom,
    ( ( q1 @ d @ d @ d )
    | ~ ( k0 @ e )
    | ~ ( s0 @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_117) ).

thf(998,plain,
    ( ( q1 @ d @ d @ d )
    | ~ ( k0 @ e )
    | ~ ( s0 @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(253,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( p0 @ B @ A )
      | ~ ( k3 @ A @ A @ A )
      | ~ ( k3 @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_207) ).

thf(849,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( p0 @ B @ A )
      | ~ ( k3 @ A @ A @ A )
      | ~ ( k3 @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(74,axiom,
    ! [A: $i] :
      ( ( q1 @ A @ b @ b )
      | ~ ( s0 @ A )
      | ~ ( s0 @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_119) ).

thf(507,plain,
    ! [A: $i] :
      ( ( q1 @ A @ b @ b )
      | ~ ( s0 @ A )
      | ~ ( s0 @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(123,axiom,
    ! [A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( s0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_032) ).

thf(602,plain,
    ! [A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( s0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(325,axiom,
    ! [A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( k0 @ e )
      | ~ ( k1 @ A )
      | ~ ( l0 @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_079) ).

thf(981,plain,
    ! [A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( k0 @ e )
      | ~ ( k1 @ A )
      | ~ ( l0 @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(23,axiom,
    ! [B: $i,A: $i] :
      ( ( m3 @ A @ B @ A )
      | ~ ( r2 @ A )
      | ~ ( k2 @ c @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_231) ).

thf(411,plain,
    ! [B: $i,A: $i] :
      ( ( m3 @ A @ B @ A )
      | ~ ( r2 @ A )
      | ~ ( k2 @ c @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(329,axiom,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ b @ B )
      | ~ ( m1 @ A @ B @ b )
      | ~ ( k0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_083) ).

thf(988,plain,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ b @ B )
      | ~ ( m1 @ A @ B @ b )
      | ~ ( k0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(292,axiom,
    ( ( q1 @ d @ d @ c )
    | ~ ( m0 @ c @ b @ a )
    | ~ ( m1 @ c @ d @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_111) ).

thf(920,plain,
    ( ( q1 @ d @ d @ c )
    | ~ ( m0 @ c @ b @ a )
    | ~ ( m1 @ c @ d @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ( m5 @ A @ A )
      | ~ ( s4 @ B )
      | ~ ( r0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_306) ).

thf(380,plain,
    ! [B: $i,A: $i] :
      ( ( m5 @ A @ A )
      | ~ ( s4 @ B )
      | ~ ( r0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(163,axiom,
    ! [A: $i] :
      ( ( m5 @ A @ A )
      | ~ ( s4 @ A )
      | ~ ( m4 @ e @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_305) ).

thf(678,plain,
    ! [A: $i] :
      ( ( m5 @ A @ A )
      | ~ ( s4 @ A )
      | ~ ( m4 @ e @ e ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(153,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p4 @ A @ B @ B )
      | ~ ( r3 @ B @ B @ A )
      | ~ ( p4 @ C @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_288) ).

thf(661,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p4 @ A @ B @ B )
      | ~ ( r3 @ B @ B @ A )
      | ~ ( p4 @ C @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(207,axiom,
    ! [B: $i,A: $i] :
      ( ( n5 @ A @ A )
      | ~ ( m0 @ B @ A @ B )
      | ~ ( n5 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_308) ).

thf(761,plain,
    ! [B: $i,A: $i] :
      ( ( n5 @ A @ A )
      | ~ ( m0 @ B @ A @ B )
      | ~ ( n5 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(88,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ B @ A )
      | ~ ( l0 @ A )
      | ~ ( r0 @ C )
      | ~ ( p0 @ D @ A )
      | ~ ( q0 @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_104) ).

thf(534,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ B @ A )
      | ~ ( l0 @ A )
      | ~ ( r0 @ C )
      | ~ ( p0 @ D @ A )
      | ~ ( q0 @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(182,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( p0 @ A @ A )
      | ~ ( r1 @ B )
      | ~ ( p2 @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_164) ).

thf(714,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( p0 @ A @ A )
      | ~ ( r1 @ B )
      | ~ ( p2 @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(226,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( k4 @ A )
      | ~ ( k3 @ B @ B @ B )
      | ~ ( n0 @ C @ B )
      | ~ ( k4 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_275) ).

thf(798,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( k4 @ A )
      | ~ ( k3 @ B @ B @ B )
      | ~ ( n0 @ C @ B )
      | ~ ( k4 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(77,axiom,
    ! [B: $i,A: $i] :
      ( ( k4 @ e )
      | ~ ( q3 @ A @ A )
      | ~ ( q1 @ a @ a @ B )
      | ~ ( r3 @ A @ e @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_276) ).

thf(512,plain,
    ! [B: $i,A: $i] :
      ( ( k4 @ e )
      | ~ ( q3 @ A @ A )
      | ~ ( q1 @ a @ a @ B )
      | ~ ( r3 @ A @ e @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(304,axiom,
    m0 @ d @ e @ c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_35) ).

thf(942,plain,
    m0 @ d @ e @ c,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(38,axiom,
    m0 @ c @ b @ a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).

thf(439,plain,
    m0 @ c @ b @ a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(286,axiom,
    ( ( l3 @ d @ d )
    | ~ ( k2 @ a @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_221) ).

thf(910,plain,
    ( ( l3 @ d @ d )
    | ~ ( k2 @ a @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(277,axiom,
    p0 @ b @ d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).

thf(894,plain,
    p0 @ b @ d,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(199,axiom,
    ! [B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( n0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_100) ).

thf(746,plain,
    ! [B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( n0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(240,axiom,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ A @ c )
      | ~ ( n0 @ B @ B )
      | ~ ( l1 @ c @ c )
      | ~ ( p0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_010) ).

thf(825,plain,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ A @ c )
      | ~ ( n0 @ B @ B )
      | ~ ( l1 @ c @ c )
      | ~ ( p0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(358,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( m1 @ B @ C @ A )
      | ~ ( q0 @ C @ D )
      | ~ ( l0 @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_081) ).

thf(1042,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( m1 @ B @ C @ A )
      | ~ ( q0 @ C @ D )
      | ~ ( l0 @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(260,axiom,
    ! [B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( q0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_093) ).

thf(862,plain,
    ! [B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( q0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(121,axiom,
    ! [B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( k1 @ B )
      | ~ ( k0 @ B )
      | ~ ( l2 @ a @ B )
      | ~ ( k2 @ A @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_142) ).

thf(598,plain,
    ! [B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( k1 @ B )
      | ~ ( k0 @ B )
      | ~ ( l2 @ a @ B )
      | ~ ( k2 @ A @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(102,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ A @ A @ A )
      | ~ ( q0 @ B @ A )
      | ~ ( k2 @ C @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_252) ).

thf(561,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ A @ A @ A )
      | ~ ( q0 @ B @ A )
      | ~ ( k2 @ C @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(13,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( m0 @ B @ B @ C )
      | ~ ( n1 @ B @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_062) ).

thf(392,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( m0 @ B @ B @ C )
      | ~ ( n1 @ B @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(33,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( m0 @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_110) ).

thf(429,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( m0 @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(221,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ A @ B @ C )
      | ~ ( r2 @ B )
      | ~ ( k3 @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_242) ).

thf(788,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ A @ B @ C )
      | ~ ( r2 @ B )
      | ~ ( k3 @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(235,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( m3 @ A @ B @ A )
      | ~ ( m0 @ C @ C @ B )
      | ~ ( l2 @ D @ A )
      | ~ ( m0 @ A @ D @ D )
      | ~ ( s2 @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_225) ).

thf(815,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( m3 @ A @ B @ A )
      | ~ ( m0 @ C @ C @ B )
      | ~ ( l2 @ D @ A )
      | ~ ( m0 @ A @ D @ D )
      | ~ ( s2 @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(21,axiom,
    ! [A: $i] :
      ( ( p2 @ b @ c @ a )
      | ~ ( r0 @ e )
      | ~ ( n1 @ c @ A @ A )
      | ~ ( p0 @ b @ A )
      | ~ ( k2 @ c @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_144) ).

thf(407,plain,
    ! [A: $i] :
      ( ( p2 @ b @ c @ a )
      | ~ ( r0 @ e )
      | ~ ( n1 @ c @ A @ A )
      | ~ ( p0 @ b @ A )
      | ~ ( k2 @ c @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(171,axiom,
    ! [A: $i] :
      ( ( m3 @ A @ A @ A )
      | ~ ( l2 @ A @ A )
      | ~ ( n2 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_232) ).

thf(693,plain,
    ! [A: $i] :
      ( ( m3 @ A @ A @ A )
      | ~ ( l2 @ A @ A )
      | ~ ( n2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(53,axiom,
    ! [A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( m2 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_212) ).

thf(467,plain,
    ! [A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( m2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(353,axiom,
    ( ( m1 @ b @ b @ b )
    | ~ ( q0 @ c @ d )
    | ~ ( l1 @ a @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_027) ).

thf(1032,plain,
    ( ( m1 @ b @ b @ b )
    | ~ ( q0 @ c @ d )
    | ~ ( l1 @ a @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(135,axiom,
    ! [A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( q1 @ A @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_154) ).

thf(625,plain,
    ! [A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( q1 @ A @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(269,axiom,
    ( ( k4 @ c )
    | ~ ( n0 @ c @ d )
    | ~ ( q3 @ e @ b )
    | ~ ( n3 @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_274) ).

thf(879,plain,
    ( ( k4 @ c )
    | ~ ( n0 @ c @ d )
    | ~ ( q3 @ e @ b )
    | ~ ( n3 @ e ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(36,axiom,
    ! [B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( m0 @ A @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_122) ).

thf(435,plain,
    ! [B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( m0 @ A @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(155,axiom,
    ! [B: $i,A: $i] :
      ( ( p4 @ A @ B @ A )
      | ~ ( k3 @ A @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_287) ).

thf(665,plain,
    ! [B: $i,A: $i] :
      ( ( p4 @ A @ B @ A )
      | ~ ( k3 @ A @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(50,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p4 @ A @ A @ A )
      | ~ ( q3 @ B @ C )
      | ~ ( n4 @ C @ A )
      | ~ ( l3 @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_293) ).

thf(461,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p4 @ A @ A @ A )
      | ~ ( q3 @ B @ C )
      | ~ ( n4 @ C @ A )
      | ~ ( l3 @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(67,axiom,
    ! [B: $i,A: $i] :
      ( ( l1 @ A @ A )
      | ~ ( k1 @ A )
      | ~ ( l0 @ B )
      | ~ ( l1 @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_004) ).

thf(493,plain,
    ! [B: $i,A: $i] :
      ( ( l1 @ A @ A )
      | ~ ( k1 @ A )
      | ~ ( l0 @ B )
      | ~ ( l1 @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(165,axiom,
    ! [B: $i,A: $i] :
      ( ( p4 @ A @ A @ B )
      | ~ ( r0 @ A )
      | ~ ( r3 @ B @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_285) ).

thf(682,plain,
    ! [B: $i,A: $i] :
      ( ( p4 @ A @ A @ B )
      | ~ ( r0 @ A )
      | ~ ( r3 @ B @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(97,axiom,
    ( ( n1 @ a @ a @ a )
    | ~ ( l0 @ a )
    | ~ ( r0 @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_056) ).

thf(551,plain,
    ( ( n1 @ a @ a @ a )
    | ~ ( l0 @ a )
    | ~ ( r0 @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(180,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ A @ B )
      | ~ ( q1 @ c @ A @ C )
      | ~ ( s1 @ c )
      | ~ ( s0 @ e )
      | ~ ( p2 @ A @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_158) ).

thf(710,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ A @ B )
      | ~ ( q1 @ c @ A @ C )
      | ~ ( s1 @ c )
      | ~ ( s0 @ e )
      | ~ ( p2 @ A @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(249,axiom,
    ! [A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( n2 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_210) ).

thf(842,plain,
    ! [A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( n2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(343,axiom,
    ( ( m3 @ c @ b @ d )
    | ~ ( l1 @ d @ b )
    | ~ ( m2 @ d )
    | ~ ( q2 @ b @ c @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_230) ).

thf(1012,plain,
    ( ( m3 @ c @ b @ d )
    | ~ ( l1 @ d @ b )
    | ~ ( m2 @ d )
    | ~ ( q2 @ b @ c @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( q0 @ B @ B )
      | ~ ( m1 @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_033) ).

thf(583,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( q0 @ B @ B )
      | ~ ( m1 @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(82,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( p2 @ B @ C @ e )
      | ~ ( s1 @ B )
      | ~ ( k3 @ A @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_200) ).

thf(522,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( p2 @ B @ C @ e )
      | ~ ( s1 @ B )
      | ~ ( k3 @ A @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(243,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( r4 @ A )
      | ~ ( n3 @ A )
      | ~ ( q3 @ B @ C )
      | ~ ( p0 @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_298) ).

thf(830,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( r4 @ A )
      | ~ ( n3 @ A )
      | ~ ( q3 @ B @ C )
      | ~ ( p0 @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(197,axiom,
    ! [A: $i] :
      ( ( m3 @ A @ A @ A )
      | ~ ( p2 @ A @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_238) ).

thf(742,plain,
    ! [A: $i] :
      ( ( m3 @ A @ A @ A )
      | ~ ( p2 @ A @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(173,axiom,
    ! [A: $i] :
      ( ( l3 @ A @ A )
      | ~ ( r2 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_218) ).

thf(697,plain,
    ! [A: $i] :
      ( ( l3 @ A @ A )
      | ~ ( r2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(188,axiom,
    q0 @ b @ b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).

thf(725,plain,
    q0 @ b @ b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(19,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( k3 @ A @ A @ B )
      | ~ ( q0 @ C @ B )
      | ~ ( k2 @ A @ D )
      | ~ ( k3 @ B @ E @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_202) ).

thf(403,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( k3 @ A @ A @ B )
      | ~ ( q0 @ C @ B )
      | ~ ( k2 @ A @ D )
      | ~ ( k3 @ B @ E @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(11,axiom,
    ! [B: $i,A: $i] :
      ( ( l4 @ A )
      | ~ ( m0 @ B @ A @ A )
      | ~ ( l4 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_278) ).

thf(388,plain,
    ! [B: $i,A: $i] :
      ( ( l4 @ A )
      | ~ ( m0 @ B @ A @ A )
      | ~ ( l4 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(264,axiom,
    ! [A: $i] :
      ( ( n5 @ d @ A )
      | ~ ( k3 @ d @ A @ a )
      | ~ ( n4 @ A @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_317) ).

thf(869,plain,
    ! [A: $i] :
      ( ( n5 @ d @ A )
      | ~ ( k3 @ d @ A @ a )
      | ~ ( n4 @ A @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(127,axiom,
    ( ( k3 @ c @ c @ c )
    | ~ ( r2 @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_214) ).

thf(610,plain,
    ( ( k3 @ c @ c @ c )
    | ~ ( r2 @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(70,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( l1 @ A @ B )
      | ~ ( p0 @ C @ A )
      | ~ ( r0 @ D )
      | ~ ( m0 @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_003) ).

thf(499,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( l1 @ A @ B )
      | ~ ( p0 @ C @ A )
      | ~ ( r0 @ D )
      | ~ ( m0 @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(257,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( n1 @ A @ B @ B )
      | ~ ( l0 @ C )
      | ~ ( l1 @ C @ A )
      | ~ ( n1 @ A @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_054) ).

thf(857,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( n1 @ A @ B @ B )
      | ~ ( l0 @ C )
      | ~ ( l1 @ C @ A )
      | ~ ( n1 @ A @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(218,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( m4 @ A @ B )
      | ~ ( l2 @ C @ B )
      | ~ ( s3 @ a @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_279) ).

thf(783,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( m4 @ A @ B )
      | ~ ( l2 @ C @ B )
      | ~ ( s3 @ a @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(28,axiom,
    q0 @ b @ e,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).

thf(420,plain,
    q0 @ b @ e,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(55,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( m0 @ B @ C @ C )
      | ~ ( m0 @ C @ A @ B )
      | ~ ( n1 @ A @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_048) ).

thf(471,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( m0 @ B @ C @ C )
      | ~ ( m0 @ C @ A @ B )
      | ~ ( n1 @ A @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(351,axiom,
    ! [A: $i] :
      ( ( p3 @ A @ d @ e )
      | ~ ( l3 @ b @ e )
      | ~ ( p2 @ d @ b @ c )
      | ~ ( n3 @ A )
      | ~ ( q2 @ A @ d @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_243) ).

thf(1028,plain,
    ! [A: $i] :
      ( ( p3 @ A @ d @ e )
      | ~ ( l3 @ b @ e )
      | ~ ( p2 @ d @ b @ c )
      | ~ ( n3 @ A )
      | ~ ( q2 @ A @ d @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(64,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( l3 @ A @ A )
      | ~ ( k3 @ B @ A @ A )
      | ~ ( l2 @ C @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_222) ).

thf(488,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( l3 @ A @ A )
      | ~ ( k3 @ B @ A @ A )
      | ~ ( l2 @ C @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(299,axiom,
    ( ( n5 @ d @ d )
    | ~ ( p4 @ c @ d @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_311) ).

thf(933,plain,
    ( ( n5 @ d @ d )
    | ~ ( p4 @ c @ d @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(158,axiom,
    l0 @ a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).

thf(669,plain,
    l0 @ a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(167,axiom,
    ( ( m1 @ e @ e @ e )
    | ~ ( r0 @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_012) ).

thf(686,plain,
    ( ( m1 @ e @ e @ e )
    | ~ ( r0 @ e ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(84,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( k5 @ A )
      | ~ ( s4 @ B )
      | ~ ( r3 @ C @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_300) ).

thf(526,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( k5 @ A )
      | ~ ( s4 @ B )
      | ~ ( r3 @ C @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(141,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( l4 @ A )
      | ~ ( p3 @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_277) ).

thf(637,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( l4 @ A )
      | ~ ( p3 @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( n5 @ A @ A )
      | ~ ( p4 @ B @ A @ A )
      | ~ ( s1 @ A )
      | ~ ( p4 @ b @ b @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_316) ).

thf(547,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( n5 @ A @ A )
      | ~ ( p4 @ B @ A @ A )
      | ~ ( s1 @ A )
      | ~ ( p4 @ b @ b @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(178,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( q3 @ A @ B )
      | ~ ( q2 @ C @ A @ B )
      | ~ ( n0 @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_255) ).

thf(706,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( q3 @ A @ B )
      | ~ ( q2 @ C @ A @ B )
      | ~ ( n0 @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(345,axiom,
    ! [B: $i,A: $i] :
      ( ( p2 @ A @ A @ d )
      | ~ ( r1 @ a )
      | ~ ( m0 @ B @ A @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_149) ).

thf(1016,plain,
    ! [B: $i,A: $i] :
      ( ( p2 @ A @ A @ d )
      | ~ ( r1 @ a )
      | ~ ( m0 @ B @ A @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(117,axiom,
    ! [A: $i] :
      ( ( m1 @ c @ a @ c )
      | ~ ( r0 @ e )
      | ~ ( m0 @ a @ e @ c )
      | ~ ( r0 @ A )
      | ~ ( k0 @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_031) ).

thf(590,plain,
    ! [A: $i] :
      ( ( m1 @ c @ a @ c )
      | ~ ( r0 @ e )
      | ~ ( m0 @ a @ e @ c )
      | ~ ( r0 @ A )
      | ~ ( k0 @ e ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(133,axiom,
    k0 @ e,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_28) ).

thf(622,plain,
    k0 @ e,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(146,axiom,
    ! [B: $i,A: $i] :
      ( ( k1 @ A )
      | ~ ( n0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_001) ).

thf(647,plain,
    ! [B: $i,A: $i] :
      ( ( k1 @ A )
      | ~ ( n0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(327,axiom,
    n0 @ d @ b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).

thf(985,plain,
    n0 @ d @ b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(175,axiom,
    ! [B: $i,A: $i] :
      ( ( r3 @ A @ A @ A )
      | ~ ( l2 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_265) ).

thf(701,plain,
    ! [B: $i,A: $i] :
      ( ( r3 @ A @ A @ A )
      | ~ ( l2 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(195,axiom,
    ! [B: $i,A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( m1 @ c @ A @ B )
      | ~ ( m0 @ b @ B @ c )
      | ~ ( n1 @ B @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_051) ).

thf(738,plain,
    ! [B: $i,A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( m1 @ c @ A @ B )
      | ~ ( m0 @ b @ B @ c )
      | ~ ( n1 @ B @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(186,axiom,
    ! [B: $i,A: $i] :
      ( ( q2 @ A @ A @ A )
      | ~ ( k1 @ B )
      | ~ ( n1 @ A @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_179) ).

thf(721,plain,
    ! [B: $i,A: $i] :
      ( ( q2 @ A @ A @ A )
      | ~ ( k1 @ B )
      | ~ ( n1 @ A @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(337,axiom,
    ! [A: $i] : ( q0 @ A @ d ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).

thf(1002,plain,
    ! [A: $i] : ( q0 @ A @ d ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( q1 @ B @ C @ B )
      | ~ ( p2 @ B @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_165) ).

thf(569,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( q1 @ B @ C @ B )
      | ~ ( p2 @ B @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(216,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ A @ A @ A )
      | ~ ( n2 @ A )
      | ~ ( q2 @ B @ C @ A )
      | ~ ( s1 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_247) ).

thf(779,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ A @ A @ A )
      | ~ ( n2 @ A )
      | ~ ( q2 @ B @ C @ A )
      | ~ ( s1 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(72,axiom,
    ! [B: $i,A: $i] :
      ( ( p5 @ b @ b @ b )
      | ~ ( p4 @ A @ A @ B )
      | ~ ( k5 @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_321) ).

thf(503,plain,
    ! [B: $i,A: $i] :
      ( ( p5 @ b @ b @ b )
      | ~ ( p4 @ A @ A @ B )
      | ~ ( k5 @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(367,axiom,
    ( ( s2 @ d )
    | ~ ( s1 @ a )
    | ~ ( s0 @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_190) ).

thf(1060,plain,
    ( ( s2 @ d )
    | ~ ( s1 @ a )
    | ~ ( s0 @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(362,axiom,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ B )
      | ~ ( p0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_069) ).

thf(1050,plain,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ B )
      | ~ ( p0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(48,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( m1 @ B @ C @ A )
      | ~ ( k0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_046) ).

thf(457,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( m1 @ B @ C @ A )
      | ~ ( k0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(223,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( s1 @ A )
      | ~ ( q0 @ A @ B )
      | ~ ( s1 @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_126) ).

thf(792,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( s1 @ A )
      | ~ ( q0 @ A @ B )
      | ~ ( s1 @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(139,axiom,
    ! [B: $i,A: $i] :
      ( ( m3 @ A @ A @ A )
      | ~ ( n2 @ A )
      | ~ ( m2 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_233) ).

thf(633,plain,
    ! [B: $i,A: $i] :
      ( ( m3 @ A @ A @ A )
      | ~ ( n2 @ A )
      | ~ ( m2 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(230,axiom,
    ! [A: $i] :
      ( ( r3 @ A @ A @ A )
      | ~ ( s2 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_264) ).

thf(805,plain,
    ! [A: $i] :
      ( ( r3 @ A @ A @ A )
      | ~ ( s2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(151,axiom,
    ! [B: $i,A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( l2 @ B @ b )
      | ~ ( k1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_197) ).

thf(657,plain,
    ! [B: $i,A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( l2 @ B @ b )
      | ~ ( k1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(161,axiom,
    ! [B: $i,A: $i] :
      ( ( p2 @ A @ B @ A )
      | ~ ( m1 @ B @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_176) ).

thf(674,plain,
    ! [B: $i,A: $i] :
      ( ( p2 @ A @ B @ A )
      | ~ ( m1 @ B @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(350,axiom,
    ( ( n5 @ b @ e )
    | ~ ( r3 @ d @ b @ c )
    | ~ ( n4 @ b @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_312) ).

thf(1026,plain,
    ( ( n5 @ b @ e )
    | ~ ( r3 @ d @ b @ c )
    | ~ ( n4 @ b @ e ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(86,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( m0 @ B @ C @ B )
      | ~ ( k0 @ A )
      | ~ ( q0 @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_042) ).

thf(530,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( m0 @ B @ C @ B )
      | ~ ( k0 @ A )
      | ~ ( q0 @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(310,axiom,
    q0 @ d @ c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_33) ).

thf(953,plain,
    q0 @ d @ c,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(295,axiom,
    ! [B: $i,A: $i] :
      ( ( p2 @ e @ A @ B )
      | ~ ( r0 @ e )
      | ~ ( p1 @ A @ B @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_145) ).

thf(926,plain,
    ! [B: $i,A: $i] :
      ( ( p2 @ e @ A @ B )
      | ~ ( r0 @ e )
      | ~ ( p1 @ A @ B @ e ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(209,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( m0 @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_025) ).

thf(765,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( m0 @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(364,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p3 @ A @ B @ C )
      | ~ ( q2 @ D @ d @ A )
      | ~ ( k2 @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_241) ).

thf(1054,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p3 @ A @ B @ C )
      | ~ ( q2 @ D @ d @ A )
      | ~ ( k2 @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(213,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( r3 @ A @ A @ B )
      | ~ ( m2 @ B )
      | ~ ( m3 @ C @ b @ A )
      | ~ ( r3 @ B @ D @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_268) ).

thf(773,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( r3 @ A @ A @ B )
      | ~ ( m2 @ B )
      | ~ ( m3 @ C @ b @ A )
      | ~ ( r3 @ B @ D @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(224,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( m1 @ a @ a @ B )
      | ~ ( p2 @ a @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_160) ).

thf(794,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( m1 @ a @ a @ B )
      | ~ ( p2 @ a @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(184,axiom,
    ( ( m3 @ b @ b @ b )
    | ~ ( l2 @ a @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_239) ).

thf(718,plain,
    ( ( m3 @ b @ b @ b )
    | ~ ( l2 @ a @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(274,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( m0 @ B @ C @ b )
      | ~ ( l0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_064) ).

thf(888,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( m0 @ B @ C @ b )
      | ~ ( l0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(284,axiom,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( n0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_066) ).

thf(906,plain,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( n0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(201,axiom,
    ! [B: $i,A: $i] :
      ( ( p2 @ A @ e @ B )
      | ~ ( n1 @ e @ A @ a )
      | ~ ( q1 @ a @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_156) ).

thf(750,plain,
    ! [B: $i,A: $i] :
      ( ( p2 @ A @ e @ B )
      | ~ ( n1 @ e @ A @ a )
      | ~ ( q1 @ a @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(131,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( q2 @ A @ B @ A )
      | ~ ( r1 @ B )
      | ~ ( m0 @ C @ D @ A )
      | ~ ( k0 @ B )
      | ~ ( q2 @ B @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_187) ).

thf(618,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( q2 @ A @ B @ A )
      | ~ ( r1 @ B )
      | ~ ( m0 @ C @ D @ A )
      | ~ ( k0 @ B )
      | ~ ( q2 @ B @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(31,axiom,
    ! [B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( n1 @ B @ B @ B )
      | ~ ( p0 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_171) ).

thf(425,plain,
    ! [B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( n1 @ B @ B @ B )
      | ~ ( p0 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(108,axiom,
    ! [A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( r0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_057) ).

thf(573,plain,
    ! [A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( r0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(169,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( r1 @ A )
      | ~ ( p2 @ B @ C @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_213) ).

thf(689,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( r1 @ A )
      | ~ ( p2 @ B @ C @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(237,axiom,
    ! [A: $i] :
      ( ( r3 @ A @ A @ A )
      | ~ ( r2 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_266) ).

thf(819,plain,
    ! [A: $i] :
      ( ( r3 @ A @ A @ A )
      | ~ ( r2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(30,axiom,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ B @ A )
      | ~ ( l0 @ A )
      | ~ ( k0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_021) ).

thf(423,plain,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ B @ A )
      | ~ ( l0 @ A )
      | ~ ( k0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(340,axiom,
    n0 @ c @ d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_34) ).

thf(1007,plain,
    n0 @ c @ d,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(192,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( l2 @ A @ A )
      | ~ ( p0 @ B @ B )
      | ~ ( s1 @ C )
      | ~ ( m0 @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_133) ).

thf(732,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( l2 @ A @ A )
      | ~ ( p0 @ B @ B )
      | ~ ( s1 @ C )
      | ~ ( m0 @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(111,axiom,
    ( ( k3 @ c @ c @ c )
    | ~ ( s2 @ e )
    | ~ ( k2 @ c @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_195) ).

thf(579,plain,
    ( ( k3 @ c @ c @ c )
    | ~ ( s2 @ e )
    | ~ ( k2 @ c @ e ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(313,axiom,
    ! [B: $i,A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( s1 @ A )
      | ~ ( q2 @ d @ B @ d )
      | ~ ( s2 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_193) ).

thf(958,plain,
    ! [B: $i,A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( s1 @ A )
      | ~ ( q2 @ d @ B @ d )
      | ~ ( s2 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(94,axiom,
    ! [B: $i,A: $i] :
      ( ( q3 @ A @ A )
      | ~ ( p2 @ B @ A @ A )
      | ~ ( q3 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_256) ).

thf(545,plain,
    ! [B: $i,A: $i] :
      ( ( q3 @ A @ A )
      | ~ ( p2 @ B @ A @ A )
      | ~ ( q3 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(24,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( r3 @ A @ B @ C )
      | ~ ( k2 @ B @ C )
      | ~ ( r2 @ C )
      | ~ ( r3 @ C @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_272) ).

thf(413,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( r3 @ A @ B @ C )
      | ~ ( k2 @ B @ C )
      | ~ ( r2 @ C )
      | ~ ( r3 @ C @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(283,axiom,
    ! [A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( k0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_068) ).

thf(904,plain,
    ! [A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( k0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(322,axiom,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ B )
      | ~ ( p0 @ B @ A )
      | ~ ( r0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_074) ).

thf(975,plain,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ B )
      | ~ ( p0 @ B @ A )
      | ~ ( r0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(267,axiom,
    ! [B: $i,A: $i] :
      ( ( q2 @ A @ B @ B )
      | ~ ( k0 @ B )
      | ~ ( p1 @ A @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_177) ).

thf(875,plain,
    ! [B: $i,A: $i] :
      ( ( q2 @ A @ B @ B )
      | ~ ( k0 @ B )
      | ~ ( p1 @ A @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(110,axiom,
    ! [A: $i] :
      ( ( q5 @ A @ A )
      | ~ ( m4 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_326) ).

thf(577,plain,
    ! [A: $i] :
      ( ( q5 @ A @ A )
      | ~ ( m4 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(143,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( m3 @ A @ A @ A )
      | ~ ( q0 @ B @ C )
      | ~ ( s0 @ D )
      | ~ ( s2 @ C )
      | ~ ( r2 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_227) ).

thf(641,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( m3 @ A @ A @ A )
      | ~ ( q0 @ B @ C )
      | ~ ( s0 @ D )
      | ~ ( s2 @ C )
      | ~ ( r2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(42,axiom,
    ! [B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( l1 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_175) ).

thf(445,plain,
    ! [B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( l1 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(8,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p5 @ A @ B @ A )
      | ~ ( q4 @ B @ C )
      | ~ ( s1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_320) ).

thf(382,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p5 @ A @ B @ A )
      | ~ ( q4 @ B @ C )
      | ~ ( s1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(220,axiom,
    q0 @ a @ b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_36) ).

thf(787,plain,
    q0 @ a @ b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(366,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p1 @ A @ B @ C )
      | ~ ( m0 @ C @ A @ D )
      | ~ ( p1 @ C @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_082) ).

thf(1058,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p1 @ A @ B @ C )
      | ~ ( m0 @ C @ A @ D )
      | ~ ( p1 @ C @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(307,axiom,
    ( ( p1 @ a @ b @ a )
    | ~ ( r0 @ b )
    | ~ ( p1 @ a @ a @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_087) ).

thf(947,plain,
    ( ( p1 @ a @ b @ a )
    | ~ ( r0 @ b )
    | ~ ( p1 @ a @ a @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(91,axiom,
    ( ( k3 @ a @ a @ a )
    | ~ ( r2 @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_204) ).

thf(540,plain,
    ( ( k3 @ a @ a @ a )
    | ~ ( r2 @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(160,axiom,
    ! [A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( k1 @ A )
      | ~ ( p0 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_043) ).

thf(672,plain,
    ! [A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( k1 @ A )
      | ~ ( p0 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(281,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( p0 @ B @ C )
      | ~ ( p1 @ A @ b @ b )
      | ~ ( q0 @ b @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_108) ).

thf(900,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( p0 @ B @ C )
      | ~ ( p1 @ A @ b @ b )
      | ~ ( q0 @ b @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(130,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( l2 @ A @ A )
      | ~ ( m0 @ B @ A @ C )
      | ~ ( m1 @ C @ B @ B )
      | ~ ( p0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_134) ).

thf(616,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( l2 @ A @ A )
      | ~ ( m0 @ B @ A @ C )
      | ~ ( m1 @ C @ B @ B )
      | ~ ( p0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(324,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( l0 @ A )
      | ~ ( m0 @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_086) ).

thf(979,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( l0 @ A )
      | ~ ( m0 @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(124,axiom,
    ! [A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( l0 @ A )
      | ~ ( k0 @ A )
      | ~ ( m0 @ A @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_028) ).

thf(604,plain,
    ! [A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( l0 @ A )
      | ~ ( k0 @ A )
      | ~ ( m0 @ A @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(361,axiom,
    ( ( p2 @ e @ c @ c )
    | ~ ( r1 @ d )
    | ~ ( l1 @ e @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_147) ).

thf(1048,plain,
    ( ( p2 @ e @ c @ c )
    | ~ ( r1 @ d )
    | ~ ( l1 @ e @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(194,axiom,
    ( ( k3 @ c @ c @ c )
    | ~ ( k0 @ a )
    | ~ ( r2 @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_198) ).

thf(736,plain,
    ( ( k3 @ c @ c @ c )
    | ~ ( k0 @ a )
    | ~ ( r2 @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(330,axiom,
    s0 @ d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).

thf(990,plain,
    s0 @ d,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(334,axiom,
    ( ( p1 @ c @ e @ b )
    | ~ ( m0 @ b @ c @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_077) ).

thf(996,plain,
    ( ( p1 @ c @ e @ b )
    | ~ ( m0 @ b @ c @ e ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(45,axiom,
    ( ( m1 @ c @ c @ c )
    | ~ ( l0 @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_020) ).

thf(451,plain,
    ( ( m1 @ c @ c @ c )
    | ~ ( l0 @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(105,axiom,
    ! [B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( r1 @ B )
      | ~ ( r0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_173) ).

thf(567,plain,
    ! [B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( r1 @ B )
      | ~ ( r0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(75,axiom,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ B @ B )
      | ~ ( k1 @ a )
      | ~ ( k1 @ B )
      | ~ ( q0 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_034) ).

thf(509,plain,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ B @ B )
      | ~ ( k1 @ a )
      | ~ ( k1 @ B )
      | ~ ( q0 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(147,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( s0 @ B )
      | ~ ( r0 @ B )
      | ~ ( q0 @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_009) ).

thf(649,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( s0 @ B )
      | ~ ( r0 @ B )
      | ~ ( q0 @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(275,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( q2 @ A @ B @ A )
      | ~ ( p1 @ A @ A @ C )
      | ~ ( n1 @ B @ A @ C )
      | ~ ( q2 @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_182) ).

thf(890,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( q2 @ A @ B @ A )
      | ~ ( p1 @ A @ A @ C )
      | ~ ( n1 @ B @ A @ C )
      | ~ ( q2 @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(58,axiom,
    ( ( q1 @ b @ b @ b )
    | ~ ( r0 @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_120) ).

thf(477,plain,
    ( ( q1 @ b @ b @ b )
    | ~ ( r0 @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(233,axiom,
    ! [B: $i,A: $i] :
      ( ( q1 @ A @ B @ B )
      | ~ ( p0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_095) ).

thf(811,plain,
    ! [B: $i,A: $i] :
      ( ( q1 @ A @ B @ B )
      | ~ ( p0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(138,axiom,
    ! [B: $i,A: $i] :
      ( ( k3 @ A @ B @ A )
      | ~ ( p2 @ B @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_206) ).

thf(631,plain,
    ! [B: $i,A: $i] :
      ( ( k3 @ A @ B @ A )
      | ~ ( p2 @ B @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(205,axiom,
    m0 @ a @ e @ e,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_23) ).

thf(758,plain,
    m0 @ a @ e @ e,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(119,axiom,
    ( ( m1 @ b @ b @ b )
    | ~ ( l0 @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_008) ).

thf(594,plain,
    ( ( m1 @ b @ b @ b )
    | ~ ( l0 @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(189,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( m2 @ B )
      | ~ ( l1 @ C @ D )
      | ~ ( s2 @ A )
      | ~ ( k3 @ C @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_209) ).

thf(726,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( m2 @ B )
      | ~ ( l1 @ C @ D )
      | ~ ( s2 @ A )
      | ~ ( k3 @ C @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(61,axiom,
    ! [A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( m0 @ A @ c @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_103) ).

thf(483,plain,
    ! [A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( m0 @ A @ c @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(278,axiom,
    q0 @ d @ b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_29) ).

thf(895,plain,
    q0 @ d @ b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(316,axiom,
    ( ( k3 @ d @ d @ d )
    | ~ ( p1 @ a @ d @ b )
    | ~ ( r2 @ a )
    | ~ ( l2 @ e @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_203) ).

thf(964,plain,
    ( ( k3 @ d @ d @ d )
    | ~ ( p1 @ a @ d @ b )
    | ~ ( r2 @ a )
    | ~ ( l2 @ e @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(289,axiom,
    ( ( p2 @ d @ d @ d )
    | ~ ( k1 @ d )
    | ~ ( s0 @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_151) ).

thf(915,plain,
    ( ( p2 @ d @ d @ d )
    | ~ ( k1 @ d )
    | ~ ( s0 @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(211,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( m0 @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_014) ).

thf(769,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( m0 @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(157,axiom,
    m0 @ b @ b @ e,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_31) ).

thf(668,plain,
    m0 @ b @ b @ e,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(252,axiom,
    ( ( l2 @ c @ c )
    | ~ ( l2 @ c @ c )
    | ~ ( l1 @ e @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_132) ).

thf(848,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(81,axiom,
    ! [A: $i] :
      ( ( l3 @ A @ A )
      | ~ ( n2 @ A )
      | ~ ( m2 @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_217) ).

thf(520,plain,
    ! [A: $i] :
      ( ( l3 @ A @ A )
      | ~ ( n2 @ A )
      | ~ ( m2 @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(305,axiom,
    ! [B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( p0 @ b @ d )
      | ~ ( s0 @ b )
      | ~ ( n1 @ B @ d @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_118) ).

thf(943,plain,
    ! [B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( p0 @ b @ d )
      | ~ ( s0 @ b )
      | ~ ( n1 @ B @ d @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(348,axiom,
    ! [B: $i,A: $i] :
      ( ( n2 @ e )
      | ~ ( r1 @ b )
      | ~ ( r0 @ e )
      | ~ ( p1 @ b @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_140) ).

thf(1022,plain,
    ! [B: $i,A: $i] :
      ( ( n2 @ e )
      | ~ ( r1 @ b )
      | ~ ( r0 @ e )
      | ~ ( p1 @ b @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(287,axiom,
    ( ( l3 @ d @ c )
    | ~ ( s2 @ d )
    | ~ ( k3 @ a @ c @ a )
    | ~ ( r0 @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_224) ).

thf(912,plain,
    ( ( l3 @ d @ c )
    | ~ ( s2 @ d )
    | ~ ( k3 @ a @ c @ a )
    | ~ ( r0 @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(326,axiom,
    ! [A: $i] :
      ( ( k2 @ A @ A )
      | ~ ( n1 @ e @ d @ A )
      | ~ ( m1 @ A @ e @ A )
      | ~ ( q1 @ A @ A @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_128) ).

thf(983,plain,
    ! [A: $i] :
      ( ( k2 @ A @ A )
      | ~ ( n1 @ e @ d @ A )
      | ~ ( m1 @ A @ e @ A )
      | ~ ( q1 @ A @ A @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ( p2 @ A @ a @ A )
      | ~ ( q1 @ A @ a @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_141) ).

thf(399,plain,
    ! [A: $i] :
      ( ( p2 @ A @ a @ A )
      | ~ ( q1 @ A @ a @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(241,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ A @ B )
      | ~ ( r0 @ C )
      | ~ ( m1 @ A @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_113) ).

thf(827,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ A @ B )
      | ~ ( r0 @ C )
      | ~ ( m1 @ A @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(263,axiom,
    m0 @ e @ d @ e,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).

thf(868,plain,
    m0 @ e @ d @ e,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(126,axiom,
    ! [A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( l0 @ A )
      | ~ ( r2 @ e )
      | ~ ( r0 @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_211) ).

thf(608,plain,
    ! [A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( l0 @ A )
      | ~ ( r2 @ e )
      | ~ ( r0 @ e ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(103,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( s4 @ A )
      | ~ ( p3 @ B @ C @ D )
      | ~ ( l1 @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_299) ).

thf(563,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( s4 @ A )
      | ~ ( p3 @ B @ C @ D )
      | ~ ( l1 @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(336,axiom,
    ! [B: $i,A: $i] :
      ( ( r3 @ A @ A @ A )
      | ~ ( m0 @ d @ B @ A )
      | ~ ( r3 @ A @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_263) ).

thf(1000,plain,
    ! [B: $i,A: $i] :
      ( ( r3 @ A @ A @ A )
      | ~ ( m0 @ d @ B @ A )
      | ~ ( r3 @ A @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(254,axiom,
    ! [B: $i,A: $i] :
      ( ( k3 @ A @ B @ B )
      | ~ ( l1 @ B @ A )
      | ~ ( k3 @ A @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_199) ).

thf(851,plain,
    ! [B: $i,A: $i] :
      ( ( k3 @ A @ B @ B )
      | ~ ( l1 @ B @ A )
      | ~ ( k3 @ A @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(73,axiom,
    ! [B: $i,A: $i] :
      ( ( n5 @ A @ A )
      | ~ ( n4 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_309) ).

thf(505,plain,
    ! [B: $i,A: $i] :
      ( ( n5 @ A @ A )
      | ~ ( n4 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(34,axiom,
    ! [A: $i] :
      ( ( p3 @ A @ A @ A )
      | ~ ( n2 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_244) ).

thf(431,plain,
    ! [A: $i] :
      ( ( p3 @ A @ A @ A )
      | ~ ( n2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(149,axiom,
    ( ( q1 @ b @ b @ b )
    | ~ ( l0 @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_115) ).

thf(653,plain,
    ( ( q1 @ b @ b @ b )
    | ~ ( l0 @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(293,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p4 @ A @ A @ A )
      | ~ ( k3 @ B @ C @ C )
      | ~ ( n4 @ A @ C )
      | ~ ( p1 @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_292) ).

thf(922,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p4 @ A @ A @ A )
      | ~ ( k3 @ B @ C @ C )
      | ~ ( n4 @ A @ C )
      | ~ ( p1 @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(359,axiom,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ B @ c )
      | ~ ( r0 @ c )
      | ~ ( s0 @ d )
      | ~ ( q0 @ B @ d )
      | ~ ( p0 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_019) ).

thf(1044,plain,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ B @ c )
      | ~ ( r0 @ c )
      | ~ ( s0 @ d )
      | ~ ( q0 @ B @ d )
      | ~ ( p0 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(172,axiom,
    ! [A: $i] :
      ( ( m3 @ A @ e @ e )
      | ~ ( n2 @ e )
      | ~ ( p2 @ A @ e @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_234) ).

thf(695,plain,
    ! [A: $i] :
      ( ( m3 @ A @ e @ e )
      | ~ ( n2 @ e )
      | ~ ( p2 @ A @ e @ e ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(47,axiom,
    ( ( n4 @ e @ e )
    | ~ ( l3 @ b @ a )
    | ~ ( p3 @ b @ e @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_283) ).

thf(455,plain,
    ( ( n4 @ e @ e )
    | ~ ( l3 @ b @ a )
    | ~ ( p3 @ b @ e @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(271,axiom,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( m0 @ b @ B @ b )
      | ~ ( l1 @ A @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_084) ).

thf(883,plain,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( m0 @ b @ B @ b )
      | ~ ( l1 @ A @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(14,axiom,
    n0 @ e @ e,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_30) ).

thf(394,plain,
    n0 @ e @ e,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(328,axiom,
    ! [A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( k1 @ A )
      | ~ ( q0 @ A @ b )
      | ~ ( p1 @ b @ b @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_101) ).

thf(986,plain,
    ! [A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( k1 @ A )
      | ~ ( q0 @ A @ b )
      | ~ ( p1 @ b @ b @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(56,axiom,
    ! [B: $i,A: $i] :
      ( ( n5 @ A @ A )
      | ~ ( q4 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_313) ).

thf(473,plain,
    ! [B: $i,A: $i] :
      ( ( n5 @ A @ A )
      | ~ ( q4 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(354,axiom,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( s0 @ A )
      | ~ ( q0 @ B @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_017) ).

thf(1034,plain,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( s0 @ A )
      | ~ ( q0 @ B @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(65,axiom,
    l0 @ c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).

thf(490,plain,
    l0 @ c,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(164,axiom,
    ! [B: $i,A: $i] :
      ( ( p4 @ A @ A @ A )
      | ~ ( p3 @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_291) ).

thf(680,plain,
    ! [B: $i,A: $i] :
      ( ( p4 @ A @ A @ A )
      | ~ ( p3 @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(154,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ A @ A @ A )
      | ~ ( l1 @ B @ B )
      | ~ ( l3 @ B @ A )
      | ~ ( p3 @ C @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_245) ).

thf(663,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ A @ A @ A )
      | ~ ( l1 @ B @ B )
      | ~ ( l3 @ B @ A )
      | ~ ( p3 @ C @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ( p5 @ A @ A @ B )
      | ~ ( s4 @ B )
      | ~ ( l2 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_318) ).

thf(374,plain,
    ! [B: $i,A: $i] :
      ( ( p5 @ A @ A @ B )
      | ~ ( s4 @ B )
      | ~ ( l2 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(79,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p4 @ A @ A @ A )
      | ~ ( m3 @ B @ C @ A )
      | ~ ( p4 @ A @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_290) ).

thf(516,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p4 @ A @ A @ A )
      | ~ ( m3 @ B @ C @ A )
      | ~ ( p4 @ A @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(302,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( k3 @ A @ A @ B )
      | ~ ( p1 @ B @ C @ A )
      | ~ ( m2 @ D )
      | ~ ( m2 @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_201) ).

thf(939,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( k3 @ A @ A @ B )
      | ~ ( p1 @ B @ C @ A )
      | ~ ( m2 @ D )
      | ~ ( m2 @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(346,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( q0 @ B @ C )
      | ~ ( k1 @ D )
      | ~ ( n1 @ B @ A @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_091) ).

thf(1018,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( q0 @ B @ C )
      | ~ ( k1 @ D )
      | ~ ( n1 @ B @ A @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(203,axiom,
    ( ( q1 @ b @ e @ e )
    | ~ ( s0 @ e )
    | ~ ( k0 @ b )
    | ~ ( l0 @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_094) ).

thf(754,plain,
    ( ( q1 @ b @ e @ e )
    | ~ ( s0 @ e )
    | ~ ( k0 @ b )
    | ~ ( l0 @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(98,axiom,
    ! [B: $i,A: $i] :
      ( ( n4 @ A @ B )
      | ~ ( p3 @ A @ B @ B )
      | ~ ( n4 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_281) ).

thf(553,plain,
    ! [B: $i,A: $i] :
      ( ( n4 @ A @ B )
      | ~ ( p3 @ A @ B @ B )
      | ~ ( n4 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(246,axiom,
    ! [B: $i,A: $i] :
      ( ( k2 @ A @ A )
      | ~ ( q1 @ B @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_129) ).

thf(836,plain,
    ! [B: $i,A: $i] :
      ( ( k2 @ A @ A )
      | ~ ( q1 @ B @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(318,axiom,
    m0 @ e @ d @ a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).

thf(968,plain,
    m0 @ e @ d @ a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(239,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( m1 @ A @ a @ B )
      | ~ ( m0 @ a @ C @ a )
      | ~ ( q0 @ A @ B )
      | ~ ( m1 @ B @ c @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_024) ).

thf(823,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( m1 @ A @ a @ B )
      | ~ ( m0 @ a @ C @ a )
      | ~ ( q0 @ A @ B )
      | ~ ( m1 @ B @ c @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(256,axiom,
    ! [B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( m0 @ A @ A @ B )
      | ~ ( k0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_114) ).

thf(855,plain,
    ! [B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( m0 @ A @ A @ B )
      | ~ ( k0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(177,axiom,
    n0 @ e @ b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).

thf(705,plain,
    n0 @ e @ b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(273,axiom,
    n0 @ d @ c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_26) ).

thf(887,plain,
    n0 @ d @ c,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(320,axiom,
    ( ( p1 @ c @ c @ c )
    | ~ ( p0 @ a @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_070) ).

thf(971,plain,
    ( ( p1 @ c @ c @ c )
    | ~ ( p0 @ a @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(311,axiom,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( p0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_085) ).

thf(954,plain,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( p0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(22,axiom,
    ! [B: $i,A: $i] :
      ( ( l2 @ A @ B )
      | ~ ( s1 @ A )
      | ~ ( n0 @ e @ B )
      | ~ ( l2 @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_131) ).

thf(409,plain,
    ! [B: $i,A: $i] :
      ( ( l2 @ A @ B )
      | ~ ( s1 @ A )
      | ~ ( n0 @ e @ B )
      | ~ ( l2 @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(332,axiom,
    ! [B: $i,A: $i] : ( m0 @ A @ d @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).

thf(993,plain,
    ! [B: $i,A: $i] : ( m0 @ A @ d @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(181,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( m1 @ A @ B @ A )
      | ~ ( p0 @ C @ B )
      | ~ ( r0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_007) ).

thf(712,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( m1 @ A @ B @ A )
      | ~ ( p0 @ C @ B )
      | ~ ( r0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(100,axiom,
    ( ( q4 @ b @ b )
    | ~ ( k3 @ c @ e @ b )
    | ~ ( l1 @ b @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_297) ).

thf(557,plain,
    ( ( q4 @ b @ b )
    | ~ ( k3 @ c @ e @ b )
    | ~ ( l1 @ b @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(338,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( q1 @ B @ B @ B )
      | ~ ( p1 @ A @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_169) ).

thf(1003,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( q1 @ B @ B @ B )
      | ~ ( p1 @ A @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(248,axiom,
    ( ( p3 @ b @ c @ b )
    | ~ ( k2 @ c @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_253) ).

thf(840,plain,
    ( ( p3 @ b @ c @ b )
    | ~ ( k2 @ c @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(51,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ A @ B )
      | ~ ( p0 @ C @ C )
      | ~ ( q0 @ B @ A )
      | ~ ( k1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_109) ).

thf(463,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ A @ B )
      | ~ ( p0 @ C @ C )
      | ~ ( q0 @ B @ A )
      | ~ ( k1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(309,axiom,
    ! [A: $i] :
      ( ( n1 @ a @ A @ b )
      | ~ ( p0 @ A @ d )
      | ~ ( p0 @ a @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_053) ).

thf(951,plain,
    ! [A: $i] :
      ( ( n1 @ a @ A @ b )
      | ~ ( p0 @ A @ d )
      | ~ ( p0 @ a @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(144,axiom,
    ! [B: $i,A: $i] :
      ( ( q2 @ A @ A @ B )
      | ~ ( l1 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_186) ).

thf(643,plain,
    ! [B: $i,A: $i] :
      ( ( q2 @ A @ A @ B )
      | ~ ( l1 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(356,axiom,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ B )
      | ~ ( n0 @ d @ A )
      | ~ ( k0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_063) ).

thf(1038,plain,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ B )
      | ~ ( n0 @ d @ A )
      | ~ ( k0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(114,axiom,
    ! [A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( n0 @ A @ A )
      | ~ ( q0 @ a @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_038) ).

thf(585,plain,
    ! [A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( n0 @ A @ A )
      | ~ ( q0 @ a @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(2,axiom,
    ! [A: $i] :
      ( ( q5 @ A @ A )
      | ~ ( q4 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_325) ).

thf(370,plain,
    ! [A: $i] :
      ( ( q5 @ A @ A )
      | ~ ( q4 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(198,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( q0 @ B @ C )
      | ~ ( q0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_018) ).

thf(744,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( q0 @ B @ C )
      | ~ ( q0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(176,axiom,
    ! [B: $i,A: $i] :
      ( ( n1 @ A @ e @ e )
      | ~ ( m0 @ A @ B @ e )
      | ~ ( k1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_040) ).

thf(703,plain,
    ! [B: $i,A: $i] :
      ( ( n1 @ A @ e @ e )
      | ~ ( m0 @ A @ B @ e )
      | ~ ( k1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(122,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( l3 @ A @ A )
      | ~ ( n2 @ B )
      | ~ ( l1 @ C @ A )
      | ~ ( l3 @ C @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_219) ).

thf(600,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( l3 @ A @ A )
      | ~ ( n2 @ B )
      | ~ ( l1 @ C @ A )
      | ~ ( l3 @ C @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(363,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( n2 @ A )
      | ~ ( p1 @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_137) ).

thf(1052,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( n2 @ A )
      | ~ ( p1 @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(261,axiom,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( m0 @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_006) ).

thf(864,plain,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( m0 @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ( q5 @ A @ B )
      | ~ ( s4 @ A )
      | ~ ( m2 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_322) ).

thf(386,plain,
    ! [B: $i,A: $i] :
      ( ( q5 @ A @ B )
      | ~ ( s4 @ A )
      | ~ ( m2 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(341,axiom,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( s0 @ B )
      | ~ ( s0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_072) ).

thf(1008,plain,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( s0 @ B )
      | ~ ( s0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( m1 @ B @ C @ A )
      | ~ ( p2 @ B @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_148) ).

thf(571,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( m1 @ B @ C @ A )
      | ~ ( p2 @ B @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(128,axiom,
    ! [A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( s1 @ A )
      | ~ ( k1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_167) ).

thf(612,plain,
    ! [A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( s1 @ A )
      | ~ ( k1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(69,axiom,
    ! [A: $i] :
      ( ( m3 @ A @ c @ A )
      | ~ ( s2 @ c )
      | ~ ( q2 @ A @ c @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_237) ).

thf(497,plain,
    ! [A: $i] :
      ( ( m3 @ A @ c @ A )
      | ~ ( s2 @ c )
      | ~ ( q2 @ A @ c @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(258,axiom,
    m0 @ e @ b @ c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_27) ).

thf(859,plain,
    m0 @ e @ b @ c,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(331,axiom,
    ! [B: $i,A: $i] :
      ( ( n1 @ A @ d @ B )
      | ~ ( p0 @ B @ B )
      | ~ ( r0 @ A )
      | ~ ( l1 @ B @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_047) ).

thf(991,plain,
    ! [B: $i,A: $i] :
      ( ( n1 @ A @ d @ B )
      | ~ ( p0 @ B @ B )
      | ~ ( r0 @ A )
      | ~ ( l1 @ B @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(52,axiom,
    ! [B: $i,A: $i] :
      ( ( n4 @ A @ A )
      | ~ ( k4 @ B )
      | ~ ( m3 @ A @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_284) ).

thf(465,plain,
    ! [B: $i,A: $i] :
      ( ( n4 @ A @ A )
      | ~ ( k4 @ B )
      | ~ ( m3 @ A @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(136,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( n1 @ A @ A @ B )
      | ~ ( m0 @ C @ D @ D )
      | ~ ( m0 @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_059) ).

thf(627,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( n1 @ A @ A @ B )
      | ~ ( m0 @ C @ D @ D )
      | ~ ( m0 @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(298,axiom,
    ( ( n1 @ d @ d @ d )
    | ~ ( q0 @ d @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_045) ).

thf(931,plain,
    ( ( n1 @ d @ d @ d )
    | ~ ( q0 @ d @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(168,axiom,
    r0 @ e,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).

thf(688,plain,
    r0 @ e,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(68,axiom,
    ! [A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( n2 @ A )
      | ~ ( k1 @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_174) ).

thf(495,plain,
    ! [A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( n2 @ A )
      | ~ ( k1 @ e ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(206,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( r3 @ A @ A @ A )
      | ~ ( p3 @ B @ A @ C )
      | ~ ( r3 @ B @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_271) ).

thf(759,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( r3 @ A @ A @ A )
      | ~ ( p3 @ B @ A @ C )
      | ~ ( r3 @ B @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(342,axiom,
    ( ( n2 @ a )
    | ~ ( m1 @ b @ a @ e )
    | ~ ( k1 @ c )
    | ~ ( n1 @ e @ a @ e )
    | ~ ( q1 @ c @ a @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_138) ).

thf(1010,plain,
    ( ( n2 @ a )
    | ~ ( m1 @ b @ a @ e )
    | ~ ( k1 @ c )
    | ~ ( n1 @ e @ a @ e )
    | ~ ( q1 @ c @ a @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(212,axiom,
    ! [A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( k1 @ A )
      | ~ ( s0 @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_112) ).

thf(771,plain,
    ! [A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( k1 @ A )
      | ~ ( s0 @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(83,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( n1 @ A @ B @ A )
      | ~ ( p0 @ A @ A )
      | ~ ( p0 @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_044) ).

thf(524,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( n1 @ A @ B @ A )
      | ~ ( p0 @ A @ A )
      | ~ ( p0 @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(112,axiom,
    ! [A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( s0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_097) ).

thf(581,plain,
    ! [A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( s0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(1,negated_conjecture,
    ! [A: $i] :
      ~ ( p1 @ A @ d @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

thf(368,plain,
    ! [A: $i] :
      ~ ( p1 @ A @ d @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(250,axiom,
    ( ( k2 @ e @ e )
    | ~ ( l1 @ e @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_130) ).

thf(844,plain,
    ( ( k2 @ e @ e )
    | ~ ( l1 @ e @ e ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(234,axiom,
    ! [B: $i,A: $i] :
      ( ( n1 @ A @ A @ B )
      | ~ ( m0 @ b @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_036) ).

thf(813,plain,
    ! [B: $i,A: $i] :
      ( ( n1 @ A @ A @ B )
      | ~ ( m0 @ b @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ( s1 @ A )
      | ~ ( p0 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_125) ).

thf(390,plain,
    ! [A: $i] :
      ( ( s1 @ A )
      | ~ ( p0 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(18,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ B @ B )
      | ~ ( k0 @ C )
      | ~ ( l0 @ A )
      | ~ ( q1 @ B @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_099) ).

thf(401,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ B @ B )
      | ~ ( k0 @ C )
      | ~ ( l0 @ A )
      | ~ ( q1 @ B @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(27,axiom,
    ( ( n1 @ c @ c @ c )
    | ~ ( l0 @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_049) ).

thf(418,plain,
    ( ( n1 @ c @ c @ c )
    | ~ ( l0 @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(217,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( k2 @ A @ B )
      | ~ ( m1 @ C @ B @ A )
      | ~ ( k1 @ D )
      | ~ ( k2 @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_127) ).

thf(781,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( k2 @ A @ B )
      | ~ ( m1 @ C @ B @ A )
      | ~ ( k1 @ D )
      | ~ ( k2 @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(116,axiom,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( q0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_013) ).

thf(588,plain,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ A @ A )
      | ~ ( q0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(174,axiom,
    ! [A: $i] :
      ( ( m5 @ A @ A )
      | ~ ( k4 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_304) ).

thf(699,plain,
    ! [A: $i] :
      ( ( m5 @ A @ A )
      | ~ ( k4 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(279,axiom,
    ! [A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( l1 @ A @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_157) ).

thf(896,plain,
    ! [A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( l1 @ A @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(200,axiom,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ B @ A )
      | ~ ( r0 @ A )
      | ~ ( l0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_035) ).

thf(748,plain,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ B @ A )
      | ~ ( r0 @ A )
      | ~ ( l0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(352,axiom,
    ( ( p2 @ a @ c @ b )
    | ~ ( l1 @ e @ c )
    | ~ ( l2 @ e @ b )
    | ~ ( r1 @ e )
    | ~ ( m1 @ d @ a @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_168) ).

thf(1030,plain,
    ( ( p2 @ a @ c @ b )
    | ~ ( l1 @ e @ c )
    | ~ ( l2 @ e @ b )
    | ~ ( r1 @ e )
    | ~ ( m1 @ d @ a @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(35,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ A @ A @ A )
      | ~ ( k1 @ A )
      | ~ ( q2 @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_250) ).

thf(433,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ A @ A @ A )
      | ~ ( k1 @ A )
      | ~ ( q2 @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(156,axiom,
    p0 @ b @ c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_22) ).

thf(667,plain,
    p0 @ b @ c,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(208,axiom,
    ! [B: $i,A: $i] :
      ( ( m4 @ A @ A )
      | ~ ( p3 @ B @ B @ B )
      | ~ ( m3 @ A @ A @ B )
      | ~ ( m4 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_280) ).

thf(763,plain,
    ! [B: $i,A: $i] :
      ( ( m4 @ A @ A )
      | ~ ( p3 @ B @ B @ B )
      | ~ ( m3 @ A @ A @ B )
      | ~ ( m4 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(96,axiom,
    ! [B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( q1 @ B @ c @ B )
      | ~ ( k2 @ A @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_163) ).

thf(549,plain,
    ! [B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( q1 @ B @ c @ B )
      | ~ ( k2 @ A @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(89,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( n5 @ A @ B )
      | ~ ( q4 @ C @ D )
      | ~ ( n4 @ A @ D )
      | ~ ( p4 @ E @ E @ B )
      | ~ ( n5 @ E @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_307) ).

thf(536,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( n5 @ A @ B )
      | ~ ( q4 @ C @ D )
      | ~ ( n4 @ A @ D )
      | ~ ( p4 @ E @ E @ B )
      | ~ ( n5 @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(288,axiom,
    q0 @ d @ d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_25) ).

thf(914,plain,
    q0 @ d @ d,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(6,axiom,
    ( ( q5 @ a @ a )
    | ~ ( r4 @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_323) ).

thf(378,plain,
    ( ( q5 @ a @ a )
    | ~ ( r4 @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(244,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( s3 @ A @ B )
      | ~ ( q2 @ C @ A @ C )
      | ~ ( s2 @ A )
      | ~ ( m0 @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_273) ).

thf(832,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( s3 @ A @ B )
      | ~ ( q2 @ C @ A @ C )
      | ~ ( s2 @ A )
      | ~ ( m0 @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(166,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p3 @ A @ B @ B )
      | ~ ( m3 @ B @ C @ D )
      | ~ ( p2 @ A @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_251) ).

thf(684,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p3 @ A @ B @ B )
      | ~ ( m3 @ B @ C @ D )
      | ~ ( p2 @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(183,axiom,
    ( ( m3 @ b @ b @ b )
    | ~ ( q2 @ a @ b @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_229) ).

thf(716,plain,
    ( ( m3 @ b @ b @ b )
    | ~ ( q2 @ a @ b @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(227,axiom,
    ! [A: $i] : ( m0 @ a @ A @ a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).

thf(800,plain,
    ! [A: $i] : ( m0 @ a @ A @ a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(132,axiom,
    ( ( m2 @ b )
    | ~ ( k1 @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_136) ).

thf(620,plain,
    ( ( m2 @ b )
    | ~ ( k1 @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(202,axiom,
    ! [A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( k1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_159) ).

thf(752,plain,
    ! [A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( k1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( s0 @ A )
      | ~ ( m0 @ B @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_098) ).

thf(447,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( s0 @ A )
      | ~ ( m0 @ B @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ( m3 @ A @ A @ A )
      | ~ ( n2 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_236) ).

thf(405,plain,
    ! [A: $i] :
      ( ( m3 @ A @ A @ A )
      | ~ ( n2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(222,axiom,
    ! [A: $i] :
      ( ( n5 @ A @ A )
      | ~ ( r4 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_314) ).

thf(790,plain,
    ! [A: $i] :
      ( ( n5 @ A @ A )
      | ~ ( r4 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(231,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( n1 @ B @ C @ C )
      | ~ ( p0 @ B @ D )
      | ~ ( m1 @ A @ C @ B )
      | ~ ( q1 @ D @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_096) ).

thf(807,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( n1 @ B @ C @ C )
      | ~ ( p0 @ B @ D )
      | ~ ( m1 @ A @ C @ B )
      | ~ ( q1 @ D @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(37,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( r3 @ A @ B @ A )
      | ~ ( p2 @ A @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_267) ).

thf(437,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( r3 @ A @ B @ A )
      | ~ ( p2 @ A @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(210,axiom,
    ! [A: $i] :
      ( ( n1 @ e @ e @ A )
      | ~ ( s0 @ b )
      | ~ ( m1 @ b @ A @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_041) ).

thf(767,plain,
    ! [A: $i] :
      ( ( n1 @ e @ e @ A )
      | ~ ( s0 @ b )
      | ~ ( m1 @ b @ A @ e ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(365,axiom,
    ( ( p1 @ e @ e @ e )
    | ~ ( r0 @ e )
    | ~ ( k0 @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_090) ).

thf(1056,plain,
    ( ( p1 @ e @ e @ e )
    | ~ ( r0 @ e )
    | ~ ( k0 @ e ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(87,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p5 @ A @ B @ B )
      | ~ ( l2 @ A @ C )
      | ~ ( p5 @ A @ C @ A )
      | ~ ( m4 @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_319) ).

thf(532,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p5 @ A @ B @ B )
      | ~ ( l2 @ A @ C )
      | ~ ( p5 @ A @ C @ A )
      | ~ ( m4 @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(185,axiom,
    m0 @ b @ a @ a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_38) ).

thf(720,plain,
    m0 @ b @ a @ a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(225,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ B @ A )
      | ~ ( n0 @ C @ B )
      | ~ ( p0 @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_092) ).

thf(796,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( q1 @ A @ B @ A )
      | ~ ( n0 @ C @ B )
      | ~ ( p0 @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(291,axiom,
    ! [A: $i] :
      ( ( p2 @ b @ c @ c )
      | ~ ( p1 @ A @ b @ b )
      | ~ ( n1 @ e @ e @ A )
      | ~ ( q1 @ e @ c @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_162) ).

thf(918,plain,
    ! [A: $i] :
      ( ( p2 @ b @ c @ c )
      | ~ ( p1 @ A @ b @ b )
      | ~ ( n1 @ e @ e @ A )
      | ~ ( q1 @ e @ c @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(228,axiom,
    ! [A: $i] :
      ( ( r3 @ A @ b @ A )
      | ~ ( r0 @ A )
      | ~ ( p2 @ b @ A @ b )
      | ~ ( l2 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_270) ).

thf(801,plain,
    ! [A: $i] :
      ( ( r3 @ A @ b @ A )
      | ~ ( r0 @ A )
      | ~ ( p2 @ b @ A @ b )
      | ~ ( l2 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(314,axiom,
    ! [A: $i] :
      ( ( p2 @ a @ A @ d )
      | ~ ( n0 @ A @ d )
      | ~ ( m1 @ a @ A @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_166) ).

thf(960,plain,
    ! [A: $i] :
      ( ( p2 @ a @ A @ d )
      | ~ ( n0 @ A @ d )
      | ~ ( m1 @ a @ A @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(140,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( m0 @ B @ B @ B )
      | ~ ( k1 @ A )
      | ~ ( s0 @ A )
      | ~ ( p0 @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_052) ).

thf(635,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( m0 @ B @ B @ B )
      | ~ ( k1 @ A )
      | ~ ( s0 @ A )
      | ~ ( p0 @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(296,axiom,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( n0 @ e @ b )
      | ~ ( k0 @ b )
      | ~ ( k0 @ A )
      | ~ ( k1 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_073) ).

thf(928,plain,
    ! [B: $i,A: $i] :
      ( ( p1 @ A @ A @ A )
      | ~ ( n0 @ e @ b )
      | ~ ( k0 @ b )
      | ~ ( k0 @ A )
      | ~ ( k1 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(25,axiom,
    ! [B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( k0 @ A )
      | ~ ( l0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_102) ).

thf(415,plain,
    ! [B: $i,A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( k0 @ A )
      | ~ ( l0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(15,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( q3 @ A @ B )
      | ~ ( n1 @ C @ A @ B )
      | ~ ( s2 @ A )
      | ~ ( q3 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_257) ).

thf(395,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( q3 @ A @ B )
      | ~ ( n1 @ C @ A @ B )
      | ~ ( s2 @ A )
      | ~ ( q3 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(109,axiom,
    ! [A: $i] :
      ( ( s2 @ A )
      | ~ ( q2 @ b @ A @ b )
      | ~ ( s1 @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_189) ).

thf(575,plain,
    ! [A: $i] :
      ( ( s2 @ A )
      | ~ ( q2 @ b @ A @ b )
      | ~ ( s1 @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(32,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( p4 @ A @ A @ A )
      | ~ ( q3 @ B @ C )
      | ~ ( n3 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_286) ).

thf(427,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p4 @ A @ A @ A )
      | ~ ( q3 @ B @ C )
      | ~ ( n3 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(259,axiom,
    ( ( p2 @ c @ e @ e )
    | ~ ( l1 @ c @ b )
    | ~ ( q1 @ e @ e @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_143) ).

thf(860,plain,
    ( ( p2 @ c @ e @ e )
    | ~ ( l1 @ c @ b )
    | ~ ( q1 @ e @ e @ e ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(120,axiom,
    ( ( k5 @ b )
    | ~ ( s4 @ e )
    | ~ ( n1 @ b @ b @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_301) ).

thf(596,plain,
    ( ( k5 @ b )
    | ~ ( s4 @ e )
    | ~ ( n1 @ b @ b @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(85,axiom,
    ! [B: $i,A: $i] :
      ( ( n1 @ A @ B @ A )
      | ~ ( s0 @ b )
      | ~ ( l0 @ A )
      | ~ ( p0 @ b @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_050) ).

thf(528,plain,
    ! [B: $i,A: $i] :
      ( ( n1 @ A @ B @ A )
      | ~ ( s0 @ b )
      | ~ ( l0 @ A )
      | ~ ( p0 @ b @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(49,axiom,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ A @ B )
      | ~ ( k0 @ A )
      | ~ ( n0 @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_011) ).

thf(459,plain,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ A @ B )
      | ~ ( k0 @ A )
      | ~ ( n0 @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(285,axiom,
    ( ( s2 @ d )
    | ~ ( r1 @ d )
    | ~ ( s1 @ d ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_191) ).

thf(908,plain,
    ( ( s2 @ d )
    | ~ ( r1 @ d )
    | ~ ( s1 @ d ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(187,axiom,
    ! [B: $i,A: $i] :
      ( ( q2 @ A @ c @ B )
      | ~ ( k1 @ B )
      | ~ ( l0 @ c )
      | ~ ( l2 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_183) ).

thf(723,plain,
    ! [B: $i,A: $i] :
      ( ( q2 @ A @ c @ B )
      | ~ ( k1 @ B )
      | ~ ( l0 @ c )
      | ~ ( l2 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(170,axiom,
    ! [A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( r2 @ c )
      | ~ ( l1 @ b @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_208) ).

thf(691,plain,
    ! [A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( r2 @ c )
      | ~ ( l1 @ b @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(40,axiom,
    r0 @ b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).

thf(442,plain,
    r0 @ b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(265,axiom,
    ! [A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( n1 @ d @ d @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_153) ).

thf(871,plain,
    ! [A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( n1 @ d @ d @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(71,axiom,
    ( ( l3 @ c @ c )
    | ~ ( k2 @ b @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_223) ).

thf(501,plain,
    ( ( l3 @ c @ c )
    | ~ ( k2 @ b @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(190,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( m3 @ A @ A @ A )
      | ~ ( k2 @ B @ C )
      | ~ ( m3 @ A @ C @ A )
      | ~ ( n0 @ C @ a )
      | ~ ( l2 @ a @ a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_226) ).

thf(728,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( m3 @ A @ A @ A )
      | ~ ( k2 @ B @ C )
      | ~ ( m3 @ A @ C @ A )
      | ~ ( n0 @ C @ a )
      | ~ ( l2 @ a @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(196,axiom,
    ! [A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( k0 @ A )
      | ~ ( s0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_061) ).

thf(740,plain,
    ! [A: $i] :
      ( ( n1 @ A @ A @ A )
      | ~ ( k0 @ A )
      | ~ ( s0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( q2 @ A @ A @ A )
      | ~ ( q0 @ B @ A )
      | ~ ( n1 @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_178) ).

thf(486,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( q2 @ A @ A @ A )
      | ~ ( q0 @ B @ A )
      | ~ ( n1 @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(229,axiom,
    ( ( m1 @ e @ e @ e )
    | ~ ( s0 @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_022) ).

thf(803,plain,
    ( ( m1 @ e @ e @ e )
    | ~ ( s0 @ e ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(54,axiom,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ B @ A )
      | ~ ( p0 @ A @ B )
      | ~ ( s0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_029) ).

thf(469,plain,
    ! [B: $i,A: $i] :
      ( ( m1 @ A @ B @ A )
      | ~ ( p0 @ A @ B )
      | ~ ( s0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(300,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p1 @ A @ B @ A )
      | ~ ( l0 @ C )
      | ~ ( p1 @ B @ D @ A )
      | ~ ( s0 @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_071) ).

thf(935,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p1 @ A @ B @ A )
      | ~ ( l0 @ C )
      | ~ ( p1 @ B @ D @ A )
      | ~ ( s0 @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(152,axiom,
    ! [A: $i] :
      ( ( p3 @ A @ A @ A )
      | ~ ( l2 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_246) ).

thf(659,plain,
    ! [A: $i] :
      ( ( p3 @ A @ A @ A )
      | ~ ( l2 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(93,axiom,
    ! [B: $i,A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( p2 @ B @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_205) ).

thf(543,plain,
    ! [B: $i,A: $i] :
      ( ( k3 @ A @ A @ A )
      | ~ ( p2 @ B @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(214,axiom,
    ! [B: $i,A: $i] :
      ( ( l3 @ A @ B )
      | ~ ( r0 @ A )
      | ~ ( p2 @ A @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_215) ).

thf(775,plain,
    ! [B: $i,A: $i] :
      ( ( l3 @ A @ B )
      | ~ ( r0 @ A )
      | ~ ( p2 @ A @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(142,axiom,
    ! [A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( s0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_106) ).

thf(639,plain,
    ! [A: $i] :
      ( ( q1 @ A @ A @ A )
      | ~ ( s0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(162,axiom,
    ! [A: $i] :
      ( ( p2 @ A @ e @ A )
      | ~ ( n1 @ A @ e @ e ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_170) ).

thf(676,plain,
    ! [A: $i] :
      ( ( p2 @ A @ e @ A )
      | ~ ( n1 @ A @ e @ e ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(66,axiom,
    ! [B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( m1 @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_150) ).

thf(491,plain,
    ! [B: $i,A: $i] :
      ( ( p2 @ A @ A @ A )
      | ~ ( m1 @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(118,axiom,
    ! [A: $i] :
      ( ( p3 @ A @ A @ A )
      | ~ ( k1 @ A )
      | ~ ( n2 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_249) ).

thf(592,plain,
    ! [A: $i] :
      ( ( p3 @ A @ A @ A )
      | ~ ( k1 @ A )
      | ~ ( n2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(179,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( n1 @ A @ B @ A )
      | ~ ( p0 @ C @ A )
      | ~ ( l0 @ B )
      | ~ ( r0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_037) ).

thf(708,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( n1 @ A @ B @ A )
      | ~ ( p0 @ C @ A )
      | ~ ( l0 @ B )
      | ~ ( r0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(344,axiom,
    ( ( n1 @ d @ d @ b )
    | ~ ( q0 @ b @ e )
    | ~ ( m1 @ d @ e @ e )
    | ~ ( k0 @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_060) ).

thf(1014,plain,
    ( ( n1 @ d @ d @ b )
    | ~ ( q0 @ b @ e )
    | ~ ( m1 @ d @ e @ e )
    | ~ ( k0 @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(1767,plain,
    $false,
    inference(cvc4,[status(thm)],[1036,809,629,1024,479,846,518,962,941,481,645,892,777,555,977,1005,730,994,614,873,449,440,655,511,384,945,538,930,670,829,898,417,565,651,973,885,1046,785,372,917,949,542,587,838,559,853,421,881,817,902,969,606,756,443,1040,376,623,514,937,1020,966,821,475,924,485,834,397,877,734,956,866,453,998,849,507,602,981,411,988,920,380,678,661,761,534,714,798,512,942,439,910,894,746,825,1042,862,598,561,392,429,788,815,407,693,467,1032,625,879,435,665,461,493,682,551,710,842,1012,583,522,830,742,697,725,403,388,869,610,499,857,783,420,471,1028,488,933,669,686,526,637,547,706,1016,590,622,647,985,701,738,721,1002,569,779,503,1060,1050,457,792,633,805,657,674,1026,530,953,926,765,1054,773,794,718,888,906,750,618,425,573,689,819,423,1007,732,579,958,545,413,904,975,875,577,641,445,382,787,1058,947,540,672,900,616,979,604,1048,736,990,996,451,567,509,649,890,477,811,631,758,594,726,483,895,964,915,769,668,848,520,943,1022,912,983,399,827,868,608,563,1000,851,505,431,653,922,1044,695,455,883,394,986,473,1034,490,680,663,374,516,939,1018,754,553,836,968,823,855,705,887,971,954,409,993,712,557,1003,840,463,951,643,1038,585,370,744,703,600,1052,864,386,1008,571,612,497,859,991,465,627,931,688,495,759,1010,771,524,581,368,844,813,390,401,418,781,588,699,896,748,1030,433,667,763,549,536,914,378,832,684,716,800,620,752,447,405,790,807,437,767,1056,532,720,796,918,801,960,635,928,415,395,575,427,860,596,528,459,908,723,691,442,871,501,728,740,486,803,469,935,659,543,775,639,676,491,592,708,1014]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN259-1 : TPTP v8.1.0. Released v1.1.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n022.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Mon Sep  5 02:18:39 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.83/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.53/1.03  % [INFO] 	 Parsing done (196ms). 
% 1.53/1.04  % [INFO] 	 Running in sequential loop mode. 
% 2.18/1.25  % [INFO] 	 eprover registered as external prover. 
% 2.18/1.25  % [INFO] 	 cvc4 registered as external prover. 
% 2.18/1.25  % [INFO] 	 Scanning for conjecture ... 
% 2.44/1.33  % [INFO] 	 Found a conjecture and 368 axioms. Running axiom selection ... 
% 2.69/1.43  % [INFO] 	 Axiom selection finished. Selected 366 axioms (removed 2 axioms). 
% 3.19/1.54  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 3.19/1.55  % [INFO] 	 Type checking passed. 
% 3.19/1.55  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 17.08/4.22  % External prover 'cvc4' found a proof!
% 17.08/4.22  % [INFO] 	 Killing All external provers ... 
% 17.08/4.22  % Time passed: 3728ms (effective reasoning time: 3179ms)
% 17.08/4.22  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 17.08/4.23  % Axioms used in derivation (366): axiom_7, axiom_26, rule_220, rule_161, rule_082, rule_135, rule_056, rule_142, rule_226, rule_231, rule_124, rule_153, rule_207, axiom_33, rule_093, axiom_10, rule_114, rule_294, rule_311, rule_046, rule_243, rule_232, rule_165, rule_146, rule_215, rule_085, axiom_22, rule_131, rule_179, rule_120, rule_319, rule_300, rule_078, rule_157, rule_288, rule_324, rule_327, rule_190, rule_103, rule_067, rule_205, rule_298, rule_237, rule_158, rule_008, rule_089, rule_175, rule_291, rule_259, rule_042, rule_248, rule_071, rule_059, rule_200, rule_276, rule_102, axiom_15, rule_147, rule_060, rule_317, rule_113, rule_063, rule_281, rule_221, rule_254, rule_139, rule_074, rule_328, rule_272, rule_052, rule_128, rule_136, rule_125, axiom_19, rule_283, axiom_21, rule_086, rule_197, rule_198, axiom_38, rule_186, rule_265, rule_210, rule_097, rule_019, rule_242, rule_081, rule_172, rule_229, rule_227, axiom_2, rule_011, rule_115, rule_160, rule_112, rule_299, rule_218, rule_101, rule_187, rule_117, rule_005, rule_076, rule_079, rule_068, rule_241, rule_253, rule_309, axiom_27, rule_194, rule_162, rule_289, rule_129, rule_208, rule_183, rule_264, rule_295, rule_159, axiom_6, rule_275, rule_238, rule_263, rule_306, rule_176, rule_022, rule_092, rule_104, axiom_32, rule_009, rule_047, rule_216, rule_033, rule_148, rule_032, rule_285, rule_057, rule_166, rule_014, rule_016, rule_141, rule_260, rule_152, rule_271, rule_003, rule_043, rule_316, rule_048, rule_249, rule_027, axiom_16, rule_284, rule_134, rule_193, rule_182, rule_036, rule_053, rule_145, axiom_3, rule_126, rule_075, rule_106, rule_308, rule_322, rule_199, rule_156, rule_171, rule_064, rule_130, rule_280, rule_098, rule_070, rule_025, rule_123, rule_290, rule_137, axiom_20, rule_087, rule_230, rule_313, rule_107, rule_149, rule_209, rule_240, rule_017, rule_192, axiom_31, rule_188, rule_268, rule_251, rule_195, rule_296, rule_279, rule_099, rule_039, rule_069, axiom_24, rule_040, axiom_1, rule_234, rule_167, rule_119, rule_320, rule_246, rule_224, rule_173, rule_088, rule_031, rule_282, rule_305, rule_111, rule_315, rule_184, rule_212, axiom_35, axiom_28, rule_105, rule_177, rule_058, rule_257, rule_044, rule_100, rule_219, rule_020, rule_006, rule_116, rule_163, rule_262, rule_170, rule_138, rule_122, rule_286, rule_155, rule_035, rule_301, axiom_8, axiom_36, rule_267, rule_091, rule_325, rule_307, rule_002, rule_239, rule_256, rule_274, rule_054, axiom_17, rule_021, rule_144, rule_127, rule_024, rule_213, rule_013, rule_133, rule_080, rule_151, rule_065, rule_312, rule_252, rule_108, rule_223, rule_235, rule_028, rule_010, rule_066, rule_245, rule_321, rule_278, rule_077, rule_217, axiom_13, rule_178, rule_202, rule_140, rule_228, rule_118, rule_181, axiom_5, rule_029, rule_214, rule_062, rule_038, rule_030, axiom_25, rule_206, rule_236, rule_051, rule_287, rule_026, rule_185, rule_083, axiom_34, rule_037, rule_174, rule_310, rule_045, rule_073, rule_323, rule_018, rule_094, rule_261, rule_233, rule_191, axiom_29, axiom_11, rule_049, rule_015, rule_055, rule_292, rule_204, rule_196, rule_318, rule_270, rule_303, rule_189, axiom_23, rule_007, rule_250, rule_110, rule_329, rule_314, axiom_30, rule_090, rule_225, rule_004, rule_169, rule_247, axiom_18, rule_096, rule_132, rule_061, rule_121, rule_201, axiom_12, rule_211, rule_326, rule_168, rule_180, rule_266, rule_012, axiom_9, rule_109, rule_293, rule_269, rule_273, rule_154, rule_304, axiom_14, rule_072, rule_244, rule_034, rule_095, rule_164, rule_255, rule_023, rule_203, rule_222, rule_143, rule_297, rule_001, rule_150, rule_084, rule_277, axiom_4, axiom_37, rule_041, rule_258, rule_050
% 17.08/4.23  % No. of inferences in proof: 735
% 17.08/4.23  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3728 ms resp. 3179 ms w/o parsing
% 17.63/4.34  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.63/4.34  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------