## TSTP Solution File: GRP125-1.003 by LEO-II---1.7.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n019.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  : 600s
% DateTime : Sat Jul 16 10:16:08 EDT 2022

% Result   : Unsatisfiable 0.22s 0.45s
% Output   : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   22
% Syntax   : Number of formulae    :  111 (  73 unt;   6 typ;   0 def)
%            Number of atoms       :  509 ( 130 equ;   0 cnn)
%            Maximal formula atoms :    5 (   4 avg)
%            Number of connectives :  852 ( 111   ~; 144   |;   0   &; 597   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   5 con; 0-3 aty)
%            Number of variables   :  220 (   0   ^ 220   !;   0   ?; 220   :)

%------------------------------------------------------------------------------
thf(tp_e_1,type,
e_1: \$i ).

thf(tp_e_2,type,
e_2: \$i ).

thf(tp_e_3,type,
e_3: \$i ).

thf(tp_equalish,type,
equalish: \$i > \$i > \$o ).

thf(tp_group_element,type,
group_element: \$i > \$o ).

thf(tp_product,type,
product: \$i > \$i > \$i > \$o ).

thf(1,axiom,
! [X: \$i] : ( product @ X @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).

thf(2,axiom,
! [W: \$i,Y: \$i,X: \$i,Z: \$i] :
( ~ ( product @ W @ Y @ X )
| ~ ( product @ Z @ Y @ X )
| ( equalish @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).

thf(3,axiom,
! [X: \$i,W: \$i,Y: \$i,Z: \$i] :
( ~ ( product @ X @ W @ Y )
| ~ ( product @ X @ Z @ Y )
| ( equalish @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).

thf(4,axiom,
! [X: \$i,Y: \$i,W: \$i,Z: \$i] :
( ~ ( product @ X @ Y @ W )
| ~ ( product @ X @ Y @ Z )
| ( equalish @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).

thf(5,axiom,
! [X: \$i,Y: \$i] :
( ~ ( group_element @ X )
| ~ ( group_element @ Y )
| ( product @ X @ Y @ e_1 )
| ( product @ X @ Y @ e_2 )
| ( product @ X @ Y @ e_3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).

thf(6,axiom,
~ ( equalish @ e_3 @ e_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).

thf(7,axiom,
~ ( equalish @ e_3 @ e_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).

thf(8,axiom,
~ ( equalish @ e_2 @ e_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).

thf(9,axiom,
~ ( equalish @ e_2 @ e_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).

thf(10,axiom,
~ ( equalish @ e_1 @ e_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).

thf(11,axiom,
~ ( equalish @ e_1 @ e_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).

thf(12,axiom,
group_element @ e_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).

thf(13,axiom,
group_element @ e_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).

thf(14,axiom,
group_element @ e_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).

thf(15,conjecture,
\$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(16,negated_conjecture,
\$false = \$false,
inference(negate_conjecture,[status(cth)],[15]) ).

thf(17,negated_conjecture,
! [X: \$i,Y: \$i,Z1: \$i,Z2: \$i] :
( ~ ( product @ X @ Y @ Z1 )
| ~ ( product @ Y @ X @ Z2 )
| ( product @ Z1 @ Z2 @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).

thf(18,plain,
\$false = \$false,
inference(unfold_def,[status(thm)],[16]) ).

thf(19,plain,
( ( ! [X: \$i] : ( product @ X @ X @ X ) )
= \$true ),
inference(unfold_def,[status(thm)],[1]) ).

thf(20,plain,
( ( ! [W: \$i,Y: \$i,X: \$i,Z: \$i] :
( ~ ( product @ W @ Y @ X )
| ~ ( product @ Z @ Y @ X )
| ( equalish @ W @ Z ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[2]) ).

thf(21,plain,
( ( ! [X: \$i,W: \$i,Y: \$i,Z: \$i] :
( ~ ( product @ X @ W @ Y )
| ~ ( product @ X @ Z @ Y )
| ( equalish @ W @ Z ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[3]) ).

thf(22,plain,
( ( ! [X: \$i,Y: \$i,W: \$i,Z: \$i] :
( ~ ( product @ X @ Y @ W )
| ~ ( product @ X @ Y @ Z )
| ( equalish @ W @ Z ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[4]) ).

thf(23,plain,
( ( ! [X: \$i,Y: \$i] :
( ~ ( group_element @ X )
| ~ ( group_element @ Y )
| ( product @ X @ Y @ e_1 )
| ( product @ X @ Y @ e_2 )
| ( product @ X @ Y @ e_3 ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[5]) ).

thf(24,plain,
( ( ~ ( equalish @ e_3 @ e_2 ) )
= \$true ),
inference(unfold_def,[status(thm)],[6]) ).

thf(25,plain,
( ( ~ ( equalish @ e_3 @ e_1 ) )
= \$true ),
inference(unfold_def,[status(thm)],[7]) ).

thf(26,plain,
( ( ~ ( equalish @ e_2 @ e_3 ) )
= \$true ),
inference(unfold_def,[status(thm)],[8]) ).

thf(27,plain,
( ( ~ ( equalish @ e_2 @ e_1 ) )
= \$true ),
inference(unfold_def,[status(thm)],[9]) ).

thf(28,plain,
( ( ~ ( equalish @ e_1 @ e_3 ) )
= \$true ),
inference(unfold_def,[status(thm)],[10]) ).

thf(29,plain,
( ( ~ ( equalish @ e_1 @ e_2 ) )
= \$true ),
inference(unfold_def,[status(thm)],[11]) ).

thf(30,plain,
( ( group_element @ e_3 )
= \$true ),
inference(unfold_def,[status(thm)],[12]) ).

thf(31,plain,
( ( group_element @ e_2 )
= \$true ),
inference(unfold_def,[status(thm)],[13]) ).

thf(32,plain,
( ( group_element @ e_1 )
= \$true ),
inference(unfold_def,[status(thm)],[14]) ).

thf(33,plain,
( ( ! [X: \$i,Y: \$i,Z1: \$i,Z2: \$i] :
( ~ ( product @ X @ Y @ Z1 )
| ~ ( product @ Y @ X @ Z2 )
| ( product @ Z1 @ Z2 @ X ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[17]) ).

thf(34,plain,
( ( ~ \$false )
= \$true ),
inference(polarity_switch,[status(thm)],[18]) ).

thf(35,plain,
( ( ! [W: \$i,Y: \$i,X: \$i] :
( ~ ( product @ W @ Y @ X )
| ! [Z: \$i] :
( ~ ( product @ Z @ Y @ X )
| ( equalish @ W @ Z ) ) ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[20]) ).

thf(36,plain,
( ( ! [X: \$i,W: \$i,Y: \$i] :
( ~ ( product @ X @ W @ Y )
| ! [Z: \$i] :
( ~ ( product @ X @ Z @ Y )
| ( equalish @ W @ Z ) ) ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[21]) ).

thf(37,plain,
( ( ! [X: \$i,Y: \$i,W: \$i] :
( ~ ( product @ X @ Y @ W )
| ! [Z: \$i] :
( ~ ( product @ X @ Y @ Z )
| ( equalish @ W @ Z ) ) ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[22]) ).

thf(38,plain,
( ( ! [X: \$i] :
( ~ ( group_element @ X )
| ! [Y: \$i] :
( ~ ( group_element @ Y )
| ( product @ X @ Y @ e_1 )
| ( product @ X @ Y @ e_2 )
| ( product @ X @ Y @ e_3 ) ) ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[23]) ).

thf(39,plain,
( ( ! [X: \$i,Y: \$i,Z1: \$i] :
( ~ ( product @ X @ Y @ Z1 )
| ! [Z2: \$i] :
( ~ ( product @ Y @ X @ Z2 )
| ( product @ Z1 @ Z2 @ X ) ) ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[33]) ).

thf(40,plain,
( ( ! [X: \$i,Y: \$i,Z1: \$i] :
( ~ ( product @ X @ Y @ Z1 )
| ! [Z2: \$i] :
( ~ ( product @ Y @ X @ Z2 )
| ( product @ Z1 @ Z2 @ X ) ) ) )
= \$true ),
inference(copy,[status(thm)],[39]) ).

thf(41,plain,
( ( group_element @ e_1 )
= \$true ),
inference(copy,[status(thm)],[32]) ).

thf(42,plain,
( ( group_element @ e_2 )
= \$true ),
inference(copy,[status(thm)],[31]) ).

thf(43,plain,
( ( group_element @ e_3 )
= \$true ),
inference(copy,[status(thm)],[30]) ).

thf(44,plain,
( ( ~ ( equalish @ e_1 @ e_2 ) )
= \$true ),
inference(copy,[status(thm)],[29]) ).

thf(45,plain,
( ( ~ ( equalish @ e_1 @ e_3 ) )
= \$true ),
inference(copy,[status(thm)],[28]) ).

thf(46,plain,
( ( ~ ( equalish @ e_2 @ e_1 ) )
= \$true ),
inference(copy,[status(thm)],[27]) ).

thf(47,plain,
( ( ~ ( equalish @ e_2 @ e_3 ) )
= \$true ),
inference(copy,[status(thm)],[26]) ).

thf(48,plain,
( ( ~ ( equalish @ e_3 @ e_1 ) )
= \$true ),
inference(copy,[status(thm)],[25]) ).

thf(49,plain,
( ( ~ ( equalish @ e_3 @ e_2 ) )
= \$true ),
inference(copy,[status(thm)],[24]) ).

thf(50,plain,
( ( ! [X: \$i] :
( ~ ( group_element @ X )
| ! [Y: \$i] :
( ~ ( group_element @ Y )
| ( product @ X @ Y @ e_1 )
| ( product @ X @ Y @ e_2 )
| ( product @ X @ Y @ e_3 ) ) ) )
= \$true ),
inference(copy,[status(thm)],[38]) ).

thf(51,plain,
( ( ! [X: \$i,Y: \$i,W: \$i] :
( ~ ( product @ X @ Y @ W )
| ! [Z: \$i] :
( ~ ( product @ X @ Y @ Z )
| ( equalish @ W @ Z ) ) ) )
= \$true ),
inference(copy,[status(thm)],[37]) ).

thf(52,plain,
( ( ! [X: \$i,W: \$i,Y: \$i] :
( ~ ( product @ X @ W @ Y )
| ! [Z: \$i] :
( ~ ( product @ X @ Z @ Y )
| ( equalish @ W @ Z ) ) ) )
= \$true ),
inference(copy,[status(thm)],[36]) ).

thf(53,plain,
( ( ! [W: \$i,Y: \$i,X: \$i] :
( ~ ( product @ W @ Y @ X )
| ! [Z: \$i] :
( ~ ( product @ Z @ Y @ X )
| ( equalish @ W @ Z ) ) ) )
= \$true ),
inference(copy,[status(thm)],[35]) ).

thf(54,plain,
( ( ! [X: \$i] : ( product @ X @ X @ X ) )
= \$true ),
inference(copy,[status(thm)],[19]) ).

thf(55,plain,
( ( ~ \$false )
= \$true ),
inference(copy,[status(thm)],[34]) ).

thf(56,plain,
! [SV1: \$i] :
( ( ! [SY19: \$i,SY20: \$i] :
( ~ ( product @ SV1 @ SY19 @ SY20 )
| ! [SY21: \$i] :
( ~ ( product @ SY19 @ SV1 @ SY21 )
| ( product @ SY20 @ SY21 @ SV1 ) ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).

thf(57,plain,
( ( equalish @ e_1 @ e_2 )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).

thf(58,plain,
( ( equalish @ e_1 @ e_3 )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).

thf(59,plain,
( ( equalish @ e_2 @ e_1 )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).

thf(60,plain,
( ( equalish @ e_2 @ e_3 )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(61,plain,
( ( equalish @ e_3 @ e_1 )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(62,plain,
( ( equalish @ e_3 @ e_2 )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).

thf(63,plain,
! [SV2: \$i] :
( ( ~ ( group_element @ SV2 )
| ! [SY22: \$i] :
( ~ ( group_element @ SY22 )
| ( product @ SV2 @ SY22 @ e_1 )
| ( product @ SV2 @ SY22 @ e_2 )
| ( product @ SV2 @ SY22 @ e_3 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(64,plain,
! [SV3: \$i] :
( ( ! [SY23: \$i,SY24: \$i] :
( ~ ( product @ SV3 @ SY23 @ SY24 )
| ! [SY25: \$i] :
( ~ ( product @ SV3 @ SY23 @ SY25 )
| ( equalish @ SY24 @ SY25 ) ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(65,plain,
! [SV4: \$i] :
( ( ! [SY26: \$i,SY27: \$i] :
( ~ ( product @ SV4 @ SY26 @ SY27 )
| ! [SY28: \$i] :
( ~ ( product @ SV4 @ SY28 @ SY27 )
| ( equalish @ SY26 @ SY28 ) ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(66,plain,
! [SV5: \$i] :
( ( ! [SY29: \$i,SY30: \$i] :
( ~ ( product @ SV5 @ SY29 @ SY30 )
| ! [SY31: \$i] :
( ~ ( product @ SY31 @ SY29 @ SY30 )
| ( equalish @ SV5 @ SY31 ) ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(67,plain,
! [SV6: \$i] :
( ( product @ SV6 @ SV6 @ SV6 )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(68,plain,
\$false = \$false,
inference(extcnf_not_pos,[status(thm)],[55]) ).

thf(69,plain,
! [SV7: \$i,SV1: \$i] :
( ( ! [SY32: \$i] :
( ~ ( product @ SV1 @ SV7 @ SY32 )
| ! [SY33: \$i] :
( ~ ( product @ SV7 @ SV1 @ SY33 )
| ( product @ SY32 @ SY33 @ SV1 ) ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(70,plain,
! [SV2: \$i] :
( ( ( ~ ( group_element @ SV2 ) )
= \$true )
| ( ( ! [SY22: \$i] :
( ~ ( group_element @ SY22 )
| ( product @ SV2 @ SY22 @ e_1 )
| ( product @ SV2 @ SY22 @ e_2 )
| ( product @ SV2 @ SY22 @ e_3 ) ) )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).

thf(71,plain,
! [SV8: \$i,SV3: \$i] :
( ( ! [SY34: \$i] :
( ~ ( product @ SV3 @ SV8 @ SY34 )
| ! [SY35: \$i] :
( ~ ( product @ SV3 @ SV8 @ SY35 )
| ( equalish @ SY34 @ SY35 ) ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(72,plain,
! [SV9: \$i,SV4: \$i] :
( ( ! [SY36: \$i] :
( ~ ( product @ SV4 @ SV9 @ SY36 )
| ! [SY37: \$i] :
( ~ ( product @ SV4 @ SY37 @ SY36 )
| ( equalish @ SV9 @ SY37 ) ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(73,plain,
! [SV10: \$i,SV5: \$i] :
( ( ! [SY38: \$i] :
( ~ ( product @ SV5 @ SV10 @ SY38 )
| ! [SY39: \$i] :
( ~ ( product @ SY39 @ SV10 @ SY38 )
| ( equalish @ SV5 @ SY39 ) ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(74,plain,
! [SV11: \$i,SV7: \$i,SV1: \$i] :
( ( ~ ( product @ SV1 @ SV7 @ SV11 )
| ! [SY40: \$i] :
( ~ ( product @ SV7 @ SV1 @ SY40 )
| ( product @ SV11 @ SY40 @ SV1 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).

thf(75,plain,
! [SV2: \$i] :
( ( ( group_element @ SV2 )
= \$false )
| ( ( ! [SY22: \$i] :
( ~ ( group_element @ SY22 )
| ( product @ SV2 @ SY22 @ e_1 )
| ( product @ SV2 @ SY22 @ e_2 )
| ( product @ SV2 @ SY22 @ e_3 ) ) )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).

thf(76,plain,
! [SV12: \$i,SV8: \$i,SV3: \$i] :
( ( ~ ( product @ SV3 @ SV8 @ SV12 )
| ! [SY41: \$i] :
( ~ ( product @ SV3 @ SV8 @ SY41 )
| ( equalish @ SV12 @ SY41 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).

thf(77,plain,
! [SV13: \$i,SV9: \$i,SV4: \$i] :
( ( ~ ( product @ SV4 @ SV9 @ SV13 )
| ! [SY42: \$i] :
( ~ ( product @ SV4 @ SY42 @ SV13 )
| ( equalish @ SV9 @ SY42 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).

thf(78,plain,
! [SV14: \$i,SV10: \$i,SV5: \$i] :
( ( ~ ( product @ SV5 @ SV10 @ SV14 )
| ! [SY43: \$i] :
( ~ ( product @ SY43 @ SV10 @ SV14 )
| ( equalish @ SV5 @ SY43 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(79,plain,
! [SV11: \$i,SV7: \$i,SV1: \$i] :
( ( ( ~ ( product @ SV1 @ SV7 @ SV11 ) )
= \$true )
| ( ( ! [SY40: \$i] :
( ~ ( product @ SV7 @ SV1 @ SY40 )
| ( product @ SV11 @ SY40 @ SV1 ) ) )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).

thf(80,plain,
! [SV2: \$i,SV15: \$i] :
( ( ( ~ ( group_element @ SV15 )
| ( product @ SV2 @ SV15 @ e_1 )
| ( product @ SV2 @ SV15 @ e_2 )
| ( product @ SV2 @ SV15 @ e_3 ) )
= \$true )
| ( ( group_element @ SV2 )
= \$false ) ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(81,plain,
! [SV12: \$i,SV8: \$i,SV3: \$i] :
( ( ( ~ ( product @ SV3 @ SV8 @ SV12 ) )
= \$true )
| ( ( ! [SY41: \$i] :
( ~ ( product @ SV3 @ SV8 @ SY41 )
| ( equalish @ SV12 @ SY41 ) ) )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).

thf(82,plain,
! [SV13: \$i,SV9: \$i,SV4: \$i] :
( ( ( ~ ( product @ SV4 @ SV9 @ SV13 ) )
= \$true )
| ( ( ! [SY42: \$i] :
( ~ ( product @ SV4 @ SY42 @ SV13 )
| ( equalish @ SV9 @ SY42 ) ) )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).

thf(83,plain,
! [SV14: \$i,SV10: \$i,SV5: \$i] :
( ( ( ~ ( product @ SV5 @ SV10 @ SV14 ) )
= \$true )
| ( ( ! [SY43: \$i] :
( ~ ( product @ SY43 @ SV10 @ SV14 )
| ( equalish @ SV5 @ SY43 ) ) )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).

thf(84,plain,
! [SV11: \$i,SV7: \$i,SV1: \$i] :
( ( ( product @ SV1 @ SV7 @ SV11 )
= \$false )
| ( ( ! [SY40: \$i] :
( ~ ( product @ SV7 @ SV1 @ SY40 )
| ( product @ SV11 @ SY40 @ SV1 ) ) )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).

thf(85,plain,
! [SV2: \$i,SV15: \$i] :
( ( ( ~ ( group_element @ SV15 ) )
= \$true )
| ( ( ( product @ SV2 @ SV15 @ e_1 )
| ( product @ SV2 @ SV15 @ e_2 )
| ( product @ SV2 @ SV15 @ e_3 ) )
= \$true )
| ( ( group_element @ SV2 )
= \$false ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).

thf(86,plain,
! [SV12: \$i,SV8: \$i,SV3: \$i] :
( ( ( product @ SV3 @ SV8 @ SV12 )
= \$false )
| ( ( ! [SY41: \$i] :
( ~ ( product @ SV3 @ SV8 @ SY41 )
| ( equalish @ SV12 @ SY41 ) ) )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).

thf(87,plain,
! [SV13: \$i,SV9: \$i,SV4: \$i] :
( ( ( product @ SV4 @ SV9 @ SV13 )
= \$false )
| ( ( ! [SY42: \$i] :
( ~ ( product @ SV4 @ SY42 @ SV13 )
| ( equalish @ SV9 @ SY42 ) ) )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).

thf(88,plain,
! [SV14: \$i,SV10: \$i,SV5: \$i] :
( ( ( product @ SV5 @ SV10 @ SV14 )
= \$false )
| ( ( ! [SY43: \$i] :
( ~ ( product @ SY43 @ SV10 @ SV14 )
| ( equalish @ SV5 @ SY43 ) ) )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).

thf(89,plain,
! [SV11: \$i,SV16: \$i,SV1: \$i,SV7: \$i] :
( ( ( ~ ( product @ SV7 @ SV1 @ SV16 )
| ( product @ SV11 @ SV16 @ SV1 ) )
= \$true )
| ( ( product @ SV1 @ SV7 @ SV11 )
= \$false ) ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(90,plain,
! [SV2: \$i,SV15: \$i] :
( ( ( group_element @ SV15 )
= \$false )
| ( ( ( product @ SV2 @ SV15 @ e_1 )
| ( product @ SV2 @ SV15 @ e_2 )
| ( product @ SV2 @ SV15 @ e_3 ) )
= \$true )
| ( ( group_element @ SV2 )
= \$false ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).

thf(91,plain,
! [SV12: \$i,SV17: \$i,SV8: \$i,SV3: \$i] :
( ( ( ~ ( product @ SV3 @ SV8 @ SV17 )
| ( equalish @ SV12 @ SV17 ) )
= \$true )
| ( ( product @ SV3 @ SV8 @ SV12 )
= \$false ) ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).

thf(92,plain,
! [SV9: \$i,SV13: \$i,SV18: \$i,SV4: \$i] :
( ( ( ~ ( product @ SV4 @ SV18 @ SV13 )
| ( equalish @ SV9 @ SV18 ) )
= \$true )
| ( ( product @ SV4 @ SV9 @ SV13 )
= \$false ) ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(93,plain,
! [SV5: \$i,SV14: \$i,SV10: \$i,SV19: \$i] :
( ( ( ~ ( product @ SV19 @ SV10 @ SV14 )
| ( equalish @ SV5 @ SV19 ) )
= \$true )
| ( ( product @ SV5 @ SV10 @ SV14 )
= \$false ) ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(94,plain,
! [SV11: \$i,SV16: \$i,SV1: \$i,SV7: \$i] :
( ( ( ~ ( product @ SV7 @ SV1 @ SV16 ) )
= \$true )
| ( ( product @ SV11 @ SV16 @ SV1 )
= \$true )
| ( ( product @ SV1 @ SV7 @ SV11 )
= \$false ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).

thf(95,plain,
! [SV15: \$i,SV2: \$i] :
( ( ( product @ SV2 @ SV15 @ e_1 )
= \$true )
| ( ( ( product @ SV2 @ SV15 @ e_2 )
| ( product @ SV2 @ SV15 @ e_3 ) )
= \$true )
| ( ( group_element @ SV15 )
= \$false )
| ( ( group_element @ SV2 )
= \$false ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).

thf(96,plain,
! [SV12: \$i,SV17: \$i,SV8: \$i,SV3: \$i] :
( ( ( ~ ( product @ SV3 @ SV8 @ SV17 ) )
= \$true )
| ( ( equalish @ SV12 @ SV17 )
= \$true )
| ( ( product @ SV3 @ SV8 @ SV12 )
= \$false ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).

thf(97,plain,
! [SV9: \$i,SV13: \$i,SV18: \$i,SV4: \$i] :
( ( ( ~ ( product @ SV4 @ SV18 @ SV13 ) )
= \$true )
| ( ( equalish @ SV9 @ SV18 )
= \$true )
| ( ( product @ SV4 @ SV9 @ SV13 )
= \$false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).

thf(98,plain,
! [SV5: \$i,SV14: \$i,SV10: \$i,SV19: \$i] :
( ( ( ~ ( product @ SV19 @ SV10 @ SV14 ) )
= \$true )
| ( ( equalish @ SV5 @ SV19 )
= \$true )
| ( ( product @ SV5 @ SV10 @ SV14 )
= \$false ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).

thf(99,plain,
! [SV11: \$i,SV16: \$i,SV1: \$i,SV7: \$i] :
( ( ( product @ SV7 @ SV1 @ SV16 )
= \$false )
| ( ( product @ SV11 @ SV16 @ SV1 )
= \$true )
| ( ( product @ SV1 @ SV7 @ SV11 )
= \$false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).

thf(100,plain,
! [SV15: \$i,SV2: \$i] :
( ( ( product @ SV2 @ SV15 @ e_2 )
= \$true )
| ( ( product @ SV2 @ SV15 @ e_3 )
= \$true )
| ( ( product @ SV2 @ SV15 @ e_1 )
= \$true )
| ( ( group_element @ SV15 )
= \$false )
| ( ( group_element @ SV2 )
= \$false ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).

thf(101,plain,
! [SV12: \$i,SV17: \$i,SV8: \$i,SV3: \$i] :
( ( ( product @ SV3 @ SV8 @ SV17 )
= \$false )
| ( ( equalish @ SV12 @ SV17 )
= \$true )
| ( ( product @ SV3 @ SV8 @ SV12 )
= \$false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).

thf(102,plain,
! [SV9: \$i,SV13: \$i,SV18: \$i,SV4: \$i] :
( ( ( product @ SV4 @ SV18 @ SV13 )
= \$false )
| ( ( equalish @ SV9 @ SV18 )
= \$true )
| ( ( product @ SV4 @ SV9 @ SV13 )
= \$false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).

thf(103,plain,
! [SV5: \$i,SV14: \$i,SV10: \$i,SV19: \$i] :
( ( ( product @ SV19 @ SV10 @ SV14 )
= \$false )
| ( ( equalish @ SV5 @ SV19 )
= \$true )
| ( ( product @ SV5 @ SV10 @ SV14 )
= \$false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).

thf(104,plain,
\$false = \$true,
inference(fo_atp_e,[status(thm)],[41,103,102,101,100,99,68,67,62,61,60,59,58,57,43,42]) ).

thf(105,plain,
\$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[104]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.13/0.15  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.37  % Computer : n019.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 600
% 0.15/0.37  % DateTime : Mon Jun 13 23:18:24 EDT 2022
% 0.15/0.37  % CPUTime  :
% 0.15/0.38
% 0.15/0.38   No.of.Axioms: 15
% 0.15/0.38
% 0.15/0.38   Length.of.Defs: 0
% 0.15/0.38
% 0.15/0.38   Contains.Choice.Funs: false
% 0.15/0.39  (rf:0,axioms:15,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:17,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.22/0.45
% 0.22/0.45  ********************************
% 0.22/0.45  *   All subproblems solved!    *
% 0.22/0.45  ********************************
% 0.22/0.45  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:104,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.22/0.46
% 0.22/0.46  %**** Beginning of derivation protocol ****
% 0.22/0.46  % SZS output start CNFRefutation
% See solution above
% 0.22/0.46
% 0.22/0.46  %**** End of derivation protocol ****
% 0.22/0.46  %**** no. of clauses in derivation: 105 ****
% 0.22/0.46  %**** clause counter: 104 ****
% 0.22/0.46
% 0.22/0.46  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:104,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------
```