## TSTP Solution File: LAT270-2 by Z3---4.8.9.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : LAT270-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n010.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 : Sat Sep 17 18:32:34 EDT 2022

% Result   : Unsatisfiable 0.14s 0.39s
% Output   : Proof 0.14s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   36 (  11 unt;  10 typ;   0 def)
%            Number of atoms       :  155 (   0 equ)
%            Maximal formula atoms :   16 (   5 avg)
%            Number of connectives :  226 ( 111   ~;  99   |;   0   &)
%                                         (  16 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   14 (  14 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   4   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-4 aty)
%            Number of variables   :   51 (  45   !;   0   ?;  51   :)

%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( \$i * \$i * \$i ) > \$o ).

tff(t_a_type,type,
t_a: \$i ).

tff(v_A_type,type,
v_A: \$i ).

tff(c_lessequals_type,type,
c_lessequals: ( \$i * \$i * \$i ) > \$o ).

tff(tc_set_type,type,
tc_set: \$i > \$i ).

tff(c_Tarski_Ointerval_type,type,
c_Tarski_Ointerval: ( \$i * \$i * \$i * \$i ) > \$i ).

tff(v_r_type,type,
v_r: \$i ).

tff(v_S_type,type,
v_S: \$i ).

tff(v_b_type,type,
v_b: \$i ).

tff(v_a_type,type,
v_a: \$i ).

tff(1,plain,
^ [V_S: \$i,V_b: \$i,V_a: \$i] :
refl(
( ( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) )
<=> ( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) )),
inference(bind,[status(th)],]) ).

tff(2,plain,
( ! [V_S: \$i,V_b: \$i,V_a: \$i] :
( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) )
<=> ! [V_S: \$i,V_b: \$i,V_a: \$i] :
( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) ),
inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
( ! [V_S: \$i,V_b: \$i,V_a: \$i] :
( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) )
<=> ! [V_S: \$i,V_b: \$i,V_a: \$i] :
( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) ),
inference(rewrite,[status(thm)],]) ).

tff(4,plain,
^ [V_S: \$i,V_b: \$i,V_a: \$i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a) )
<=> ( ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) )),
( ( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a)
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a)) )
<=> ( ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a)) ) )),
rewrite(
( ( ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a)) )
<=> ( ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) )),
( ( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a)
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a)) )
<=> ( ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) )),
( ( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a)
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| c_lessequals(V_S,v_A,tc_set(t_a)) )
<=> ( ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| c_lessequals(V_S,v_A,tc_set(t_a)) ) )),
rewrite(
( ( ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a)
| c_lessequals(V_S,v_A,tc_set(t_a)) )
<=> ( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) )),
( ( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a)
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| c_lessequals(V_S,v_A,tc_set(t_a)) )
<=> ( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) )),
inference(bind,[status(th)],]) ).

tff(5,plain,
( ! [V_S: \$i,V_b: \$i,V_a: \$i] :
( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a)
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| c_lessequals(V_S,v_A,tc_set(t_a)) )
<=> ! [V_S: \$i,V_b: \$i,V_a: \$i] :
( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ) ),
inference(quant_intro,[status(thm)],[4]) ).

tff(6,axiom,
! [V_S: \$i,V_b: \$i,V_a: \$i] :
( ~ c_in(V_b,v_A,t_a)
| ~ c_in(V_a,v_A,t_a)
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| c_lessequals(V_S,v_A,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0) ).

tff(7,plain,
! [V_S: \$i,V_b: \$i,V_a: \$i] :
( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ),
inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
! [V_S: \$i,V_b: \$i,V_a: \$i] :
( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ),
inference(modus_ponens,[status(thm)],[7,3]) ).

tff(9,plain,
! [V_S: \$i,V_b: \$i,V_a: \$i] :
( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ),
inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
! [V_S: \$i,V_b: \$i,V_a: \$i] :
( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) ),
inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
( ~ c_lessequals(v_S,v_A,tc_set(t_a))
<=> ~ c_lessequals(v_S,v_A,tc_set(t_a)) ),
inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
~ c_lessequals(v_S,v_A,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).

tff(13,plain,
~ c_lessequals(v_S,v_A,tc_set(t_a)),
inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
( c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
<=> c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) ),
inference(rewrite,[status(thm)],]) ).

tff(15,axiom,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

tff(16,plain,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
( c_in(v_b,v_A,t_a)
<=> c_in(v_b,v_A,t_a) ),
inference(rewrite,[status(thm)],]) ).

tff(18,axiom,
c_in(v_b,v_A,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

tff(19,plain,
c_in(v_b,v_A,t_a),
inference(modus_ponens,[status(thm)],[18,17]) ).

tff(20,plain,
( c_in(v_a,v_A,t_a)
<=> c_in(v_a,v_A,t_a) ),
inference(rewrite,[status(thm)],]) ).

tff(21,axiom,
c_in(v_a,v_A,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

tff(22,plain,
c_in(v_a,v_A,t_a),
inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
( ( ~ ! [V_S: \$i,V_b: \$i,V_a: \$i] :
( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) )
| c_lessequals(v_S,v_A,tc_set(t_a))
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ c_in(v_a,v_A,t_a)
| ~ c_in(v_b,v_A,t_a) )
<=> ( ~ ! [V_S: \$i,V_b: \$i,V_a: \$i] :
( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) )
| c_lessequals(v_S,v_A,tc_set(t_a))
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ c_in(v_a,v_A,t_a)
| ~ c_in(v_b,v_A,t_a) ) ),
inference(rewrite,[status(thm)],]) ).

tff(24,plain,
( ~ ! [V_S: \$i,V_b: \$i,V_a: \$i] :
( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) )
| c_lessequals(v_S,v_A,tc_set(t_a))
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ c_in(v_a,v_A,t_a)
| ~ c_in(v_b,v_A,t_a) ),
inference(quant_inst,[status(thm)],]) ).

tff(25,plain,
( ~ ! [V_S: \$i,V_b: \$i,V_a: \$i] :
( c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
| ~ c_in(V_a,v_A,t_a)
| ~ c_in(V_b,v_A,t_a) )
| c_lessequals(v_S,v_A,tc_set(t_a))
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ c_in(v_a,v_A,t_a)
| ~ c_in(v_b,v_A,t_a) ),
inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
\$false,
inference(unit_resolution,[status(thm)],[25,22,19,16,13,10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LAT270-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33  % Computer : n010.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 300
% 0.14/0.33  % DateTime : Thu Sep  1 12:48:58 EDT 2022
% 0.14/0.34  % CPUTime  :
% 0.14/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34  Usage: tptp [options] [-file:]file
% 0.14/0.34    -h, -?       prints this message.
% 0.14/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.34    -m, -model   generate model.
% 0.14/0.34    -p, -proof   generate proof.
% 0.14/0.34    -c, -core    generate unsat core of named formulas.
% 0.14/0.34    -st, -statistics display statistics.
% 0.14/0.34    -t:timeout   set timeout (in second).
% 0.14/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34    -<param>:<value> configuration parameter and value.
% 0.14/0.34    -o:<output-file> file to place output in.
% 0.14/0.39  % SZS status Unsatisfiable
% 0.14/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------
```