TSTP Solution File: CAT003-2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : CAT003-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 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 : 600s
% DateTime : Fri Jul 15 00:03:44 EDT 2022
% Result : Unsatisfiable 6.66s 6.90s
% Output : CNFRefutation 6.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of formulae : 90 ( 60 unt; 7 typ; 0 def)
% Number of atoms : 385 ( 275 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 722 ( 78 ~; 98 |; 0 &; 546 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 126 ( 0 ^ 126 !; 0 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_codomain,type,
codomain: $i > $i ).
thf(tp_compose,type,
compose: $i > $i > $i ).
thf(tp_domain,type,
domain: $i > $i ).
thf(tp_g,type,
g: $i ).
thf(tp_h,type,
h: $i ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( codomain @ Y )
!= ( domain @ Z ) )
| ( ( compose @ X @ ( compose @ Y @ Z ) )
= ( compose @ ( compose @ X @ Y ) @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_property) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( codomain @ ( compose @ X @ Y ) )
= ( codomain @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_domain2) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( domain @ ( compose @ X @ Y ) )
= ( domain @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_domain1) ).
thf(4,axiom,
! [X: $i] :
( ( compose @ X @ ( codomain @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_composition) ).
thf(5,axiom,
! [X: $i] :
( ( compose @ ( domain @ X ) @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_composition) ).
thf(6,axiom,
! [X: $i] :
( ( domain @ ( codomain @ X ) )
= ( codomain @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of_codomain_is_codomain) ).
thf(7,axiom,
! [X: $i] :
( ( codomain @ ( domain @ X ) )
= ( domain @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_domain_is_domain) ).
thf(8,axiom,
( ( compose @ b @ h )
= ( compose @ b @ g ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bh_equals_bg) ).
thf(9,axiom,
( ( codomain @ b )
= ( domain @ g ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_b_equals_domain_of_g) ).
thf(10,axiom,
( ( codomain @ b )
= ( domain @ h ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_b_equals_domain_of_h) ).
thf(11,axiom,
( ( codomain @ a )
= ( domain @ b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_a_equals_domain_of_b) ).
thf(12,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( codomain @ ( compose @ a @ b ) )
!= ( domain @ X ) )
| ( ( compose @ ( compose @ a @ b ) @ X )
!= Y )
| ( ( codomain @ ( compose @ a @ b ) )
!= ( domain @ Z ) )
| ( ( compose @ ( compose @ a @ b ) @ Z )
!= Y )
| ( X = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',endomorphism) ).
thf(13,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(14,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[13]) ).
thf(15,negated_conjecture,
g != h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_g_equals_h) ).
thf(16,plain,
$false = $false,
inference(unfold_def,[status(thm)],[14]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( codomain @ Y )
!= ( domain @ Z ) )
| ( ( compose @ X @ ( compose @ Y @ Z ) )
= ( compose @ ( compose @ X @ Y ) @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( codomain @ ( compose @ X @ Y ) )
= ( codomain @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( domain @ ( compose @ X @ Y ) )
= ( domain @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [X: $i] :
( ( compose @ X @ ( codomain @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( ! [X: $i] :
( ( compose @ ( domain @ X ) @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(22,plain,
( ( ! [X: $i] :
( ( domain @ ( codomain @ X ) )
= ( codomain @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(23,plain,
( ( ! [X: $i] :
( ( codomain @ ( domain @ X ) )
= ( domain @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(24,plain,
( ( ( compose @ b @ h )
= ( compose @ b @ g ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(25,plain,
( ( ( codomain @ b )
= ( domain @ g ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(26,plain,
( ( ( codomain @ b )
= ( domain @ h ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(27,plain,
( ( ( codomain @ a )
= ( domain @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( codomain @ ( compose @ a @ b ) )
!= ( domain @ X ) )
| ( ( compose @ ( compose @ a @ b ) @ X )
!= Y )
| ( ( codomain @ ( compose @ a @ b ) )
!= ( domain @ Z ) )
| ( ( compose @ ( compose @ a @ b ) @ Z )
!= Y )
| ( X = Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(29,plain,
( ( ( g != h ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(30,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ! [Z: $i] :
( ( ( codomain @ Y )
!= ( domain @ Z ) )
| ( ( compose @ X @ ( compose @ Y @ Z ) )
= ( compose @ ( compose @ X @ Y ) @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( codomain @ ( compose @ X @ Y ) )
= ( codomain @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( domain @ ( compose @ X @ Y ) )
= ( domain @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(34,plain,
( ( ! [X: $i] :
( ( ( codomain @ ( compose @ a @ b ) )
!= ( domain @ X ) )
| ! [Y: $i] :
( ( ( compose @ ( compose @ a @ b ) @ X )
!= Y )
| ! [Z: $i] :
( ( ( codomain @ ( compose @ a @ b ) )
!= ( domain @ Z ) )
| ( ( compose @ ( compose @ a @ b ) @ Z )
!= Y )
| ( X = Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(35,plain,
( ( ( g != h ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(36,plain,
( ( ( g != h ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(37,plain,
( ( ! [X: $i] :
( ( ( codomain @ ( compose @ a @ b ) )
!= ( domain @ X ) )
| ! [Y: $i] :
( ( ( compose @ ( compose @ a @ b ) @ X )
!= Y )
| ! [Z: $i] :
( ( ( codomain @ ( compose @ a @ b ) )
!= ( domain @ Z ) )
| ( ( compose @ ( compose @ a @ b ) @ Z )
!= Y )
| ( X = Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(38,plain,
( ( ( codomain @ a )
= ( domain @ b ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(39,plain,
( ( ( codomain @ b )
= ( domain @ h ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(40,plain,
( ( ( codomain @ b )
= ( domain @ g ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(41,plain,
( ( ( compose @ b @ h )
= ( compose @ b @ g ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(42,plain,
( ( ! [X: $i] :
( ( codomain @ ( domain @ X ) )
= ( domain @ X ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(43,plain,
( ( ! [X: $i] :
( ( domain @ ( codomain @ X ) )
= ( codomain @ X ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(44,plain,
( ( ! [X: $i] :
( ( compose @ ( domain @ X ) @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(45,plain,
( ( ! [X: $i] :
( ( compose @ X @ ( codomain @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( domain @ ( compose @ X @ Y ) )
= ( domain @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(47,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( codomain @ ( compose @ X @ Y ) )
= ( codomain @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ! [Z: $i] :
( ( ( codomain @ Y )
!= ( domain @ Z ) )
| ( ( compose @ X @ ( compose @ Y @ Z ) )
= ( compose @ ( compose @ X @ Y ) @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(49,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(50,plain,
( ( g = h )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(51,plain,
! [SV1: $i] :
( ( ( ( codomain @ ( compose @ a @ b ) )
!= ( domain @ SV1 ) )
| ! [SY14: $i] :
( ( ( compose @ ( compose @ a @ b ) @ SV1 )
!= SY14 )
| ! [SY15: $i] :
( ( ( codomain @ ( compose @ a @ b ) )
!= ( domain @ SY15 ) )
| ( ( compose @ ( compose @ a @ b ) @ SY15 )
!= SY14 )
| ( SV1 = SY15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(52,plain,
! [SV2: $i] :
( ( ( codomain @ ( domain @ SV2 ) )
= ( domain @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(53,plain,
! [SV3: $i] :
( ( ( domain @ ( codomain @ SV3 ) )
= ( codomain @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(54,plain,
! [SV4: $i] :
( ( ( compose @ ( domain @ SV4 ) @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(55,plain,
! [SV5: $i] :
( ( ( compose @ SV5 @ ( codomain @ SV5 ) )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(56,plain,
! [SV6: $i] :
( ( ! [SY16: $i] :
( ( ( codomain @ SV6 )
!= ( domain @ SY16 ) )
| ( ( domain @ ( compose @ SV6 @ SY16 ) )
= ( domain @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(57,plain,
! [SV7: $i] :
( ( ! [SY17: $i] :
( ( ( codomain @ SV7 )
!= ( domain @ SY17 ) )
| ( ( codomain @ ( compose @ SV7 @ SY17 ) )
= ( codomain @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(58,plain,
! [SV8: $i] :
( ( ! [SY18: $i] :
( ( ( codomain @ SV8 )
!= ( domain @ SY18 ) )
| ! [SY19: $i] :
( ( ( codomain @ SY18 )
!= ( domain @ SY19 ) )
| ( ( compose @ SV8 @ ( compose @ SY18 @ SY19 ) )
= ( compose @ ( compose @ SV8 @ SY18 ) @ SY19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(59,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(60,plain,
! [SV1: $i] :
( ( ( ( ( codomain @ ( compose @ a @ b ) )
!= ( domain @ SV1 ) ) )
= $true )
| ( ( ! [SY14: $i] :
( ( ( compose @ ( compose @ a @ b ) @ SV1 )
!= SY14 )
| ! [SY15: $i] :
( ( ( codomain @ ( compose @ a @ b ) )
!= ( domain @ SY15 ) )
| ( ( compose @ ( compose @ a @ b ) @ SY15 )
!= SY14 )
| ( SV1 = SY15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(61,plain,
! [SV9: $i,SV6: $i] :
( ( ( ( codomain @ SV6 )
!= ( domain @ SV9 ) )
| ( ( domain @ ( compose @ SV6 @ SV9 ) )
= ( domain @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV10: $i,SV7: $i] :
( ( ( ( codomain @ SV7 )
!= ( domain @ SV10 ) )
| ( ( codomain @ ( compose @ SV7 @ SV10 ) )
= ( codomain @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(63,plain,
! [SV11: $i,SV8: $i] :
( ( ( ( codomain @ SV8 )
!= ( domain @ SV11 ) )
| ! [SY20: $i] :
( ( ( codomain @ SV11 )
!= ( domain @ SY20 ) )
| ( ( compose @ SV8 @ ( compose @ SV11 @ SY20 ) )
= ( compose @ ( compose @ SV8 @ SV11 ) @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(64,plain,
! [SV1: $i] :
( ( ( ( codomain @ ( compose @ a @ b ) )
= ( domain @ SV1 ) )
= $false )
| ( ( ! [SY14: $i] :
( ( ( compose @ ( compose @ a @ b ) @ SV1 )
!= SY14 )
| ! [SY15: $i] :
( ( ( codomain @ ( compose @ a @ b ) )
!= ( domain @ SY15 ) )
| ( ( compose @ ( compose @ a @ b ) @ SY15 )
!= SY14 )
| ( SV1 = SY15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV9: $i,SV6: $i] :
( ( ( ( ( codomain @ SV6 )
!= ( domain @ SV9 ) ) )
= $true )
| ( ( ( domain @ ( compose @ SV6 @ SV9 ) )
= ( domain @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV10: $i,SV7: $i] :
( ( ( ( ( codomain @ SV7 )
!= ( domain @ SV10 ) ) )
= $true )
| ( ( ( codomain @ ( compose @ SV7 @ SV10 ) )
= ( codomain @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV11: $i,SV8: $i] :
( ( ( ( ( codomain @ SV8 )
!= ( domain @ SV11 ) ) )
= $true )
| ( ( ! [SY20: $i] :
( ( ( codomain @ SV11 )
!= ( domain @ SY20 ) )
| ( ( compose @ SV8 @ ( compose @ SV11 @ SY20 ) )
= ( compose @ ( compose @ SV8 @ SV11 ) @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV12: $i,SV1: $i] :
( ( ( ( ( compose @ ( compose @ a @ b ) @ SV1 )
!= SV12 )
| ! [SY21: $i] :
( ( ( codomain @ ( compose @ a @ b ) )
!= ( domain @ SY21 ) )
| ( ( compose @ ( compose @ a @ b ) @ SY21 )
!= SV12 )
| ( SV1 = SY21 ) ) )
= $true )
| ( ( ( codomain @ ( compose @ a @ b ) )
= ( domain @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV9: $i,SV6: $i] :
( ( ( ( codomain @ SV6 )
= ( domain @ SV9 ) )
= $false )
| ( ( ( domain @ ( compose @ SV6 @ SV9 ) )
= ( domain @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV10: $i,SV7: $i] :
( ( ( ( codomain @ SV7 )
= ( domain @ SV10 ) )
= $false )
| ( ( ( codomain @ ( compose @ SV7 @ SV10 ) )
= ( codomain @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(71,plain,
! [SV11: $i,SV8: $i] :
( ( ( ( codomain @ SV8 )
= ( domain @ SV11 ) )
= $false )
| ( ( ! [SY20: $i] :
( ( ( codomain @ SV11 )
!= ( domain @ SY20 ) )
| ( ( compose @ SV8 @ ( compose @ SV11 @ SY20 ) )
= ( compose @ ( compose @ SV8 @ SV11 ) @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(72,plain,
! [SV12: $i,SV1: $i] :
( ( ( ( ( compose @ ( compose @ a @ b ) @ SV1 )
!= SV12 ) )
= $true )
| ( ( ! [SY21: $i] :
( ( ( codomain @ ( compose @ a @ b ) )
!= ( domain @ SY21 ) )
| ( ( compose @ ( compose @ a @ b ) @ SY21 )
!= SV12 )
| ( SV1 = SY21 ) ) )
= $true )
| ( ( ( codomain @ ( compose @ a @ b ) )
= ( domain @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(73,plain,
! [SV8: $i,SV13: $i,SV11: $i] :
( ( ( ( ( codomain @ SV11 )
!= ( domain @ SV13 ) )
| ( ( compose @ SV8 @ ( compose @ SV11 @ SV13 ) )
= ( compose @ ( compose @ SV8 @ SV11 ) @ SV13 ) ) )
= $true )
| ( ( ( codomain @ SV8 )
= ( domain @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(74,plain,
! [SV12: $i,SV1: $i] :
( ( ( ( compose @ ( compose @ a @ b ) @ SV1 )
= SV12 )
= $false )
| ( ( ! [SY21: $i] :
( ( ( codomain @ ( compose @ a @ b ) )
!= ( domain @ SY21 ) )
| ( ( compose @ ( compose @ a @ b ) @ SY21 )
!= SV12 )
| ( SV1 = SY21 ) ) )
= $true )
| ( ( ( codomain @ ( compose @ a @ b ) )
= ( domain @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(75,plain,
! [SV8: $i,SV13: $i,SV11: $i] :
( ( ( ( ( codomain @ SV11 )
!= ( domain @ SV13 ) ) )
= $true )
| ( ( ( compose @ SV8 @ ( compose @ SV11 @ SV13 ) )
= ( compose @ ( compose @ SV8 @ SV11 ) @ SV13 ) )
= $true )
| ( ( ( codomain @ SV8 )
= ( domain @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(76,plain,
! [SV1: $i,SV12: $i,SV14: $i] :
( ( ( ( ( codomain @ ( compose @ a @ b ) )
!= ( domain @ SV14 ) )
| ( ( compose @ ( compose @ a @ b ) @ SV14 )
!= SV12 )
| ( SV1 = SV14 ) )
= $true )
| ( ( ( compose @ ( compose @ a @ b ) @ SV1 )
= SV12 )
= $false )
| ( ( ( codomain @ ( compose @ a @ b ) )
= ( domain @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(77,plain,
! [SV8: $i,SV13: $i,SV11: $i] :
( ( ( ( codomain @ SV11 )
= ( domain @ SV13 ) )
= $false )
| ( ( ( compose @ SV8 @ ( compose @ SV11 @ SV13 ) )
= ( compose @ ( compose @ SV8 @ SV11 ) @ SV13 ) )
= $true )
| ( ( ( codomain @ SV8 )
= ( domain @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(78,plain,
! [SV1: $i,SV12: $i,SV14: $i] :
( ( ( ( ( codomain @ ( compose @ a @ b ) )
!= ( domain @ SV14 ) ) )
= $true )
| ( ( ( ( compose @ ( compose @ a @ b ) @ SV14 )
!= SV12 )
| ( SV1 = SV14 ) )
= $true )
| ( ( ( compose @ ( compose @ a @ b ) @ SV1 )
= SV12 )
= $false )
| ( ( ( codomain @ ( compose @ a @ b ) )
= ( domain @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(79,plain,
! [SV1: $i,SV12: $i,SV14: $i] :
( ( ( ( codomain @ ( compose @ a @ b ) )
= ( domain @ SV14 ) )
= $false )
| ( ( ( ( compose @ ( compose @ a @ b ) @ SV14 )
!= SV12 )
| ( SV1 = SV14 ) )
= $true )
| ( ( ( compose @ ( compose @ a @ b ) @ SV1 )
= SV12 )
= $false )
| ( ( ( codomain @ ( compose @ a @ b ) )
= ( domain @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(80,plain,
! [SV1: $i,SV12: $i,SV14: $i] :
( ( ( ( ( compose @ ( compose @ a @ b ) @ SV14 )
!= SV12 ) )
= $true )
| ( ( SV1 = SV14 )
= $true )
| ( ( ( codomain @ ( compose @ a @ b ) )
= ( domain @ SV14 ) )
= $false )
| ( ( ( compose @ ( compose @ a @ b ) @ SV1 )
= SV12 )
= $false )
| ( ( ( codomain @ ( compose @ a @ b ) )
= ( domain @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(81,plain,
! [SV1: $i,SV12: $i,SV14: $i] :
( ( ( ( compose @ ( compose @ a @ b ) @ SV14 )
= SV12 )
= $false )
| ( ( SV1 = SV14 )
= $true )
| ( ( ( codomain @ ( compose @ a @ b ) )
= ( domain @ SV14 ) )
= $false )
| ( ( ( compose @ ( compose @ a @ b ) @ SV1 )
= SV12 )
= $false )
| ( ( ( codomain @ ( compose @ a @ b ) )
= ( domain @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(82,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[38,81,77,70,69,59,55,54,53,52,50,41,40,39]) ).
thf(83,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : CAT003-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun May 29 17:20:23 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 13
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.36 (rf:0,axioms:13,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:15,loop_count:0,foatp_calls:0,translation:fof_full)....
% 6.66/6.90
% 6.66/6.90 ********************************
% 6.66/6.90 * All subproblems solved! *
% 6.66/6.90 ********************************
% 6.66/6.90 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,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:82,loop_count:0,foatp_calls:1,translation:fof_full)
% 6.66/6.90
% 6.66/6.90 %**** Beginning of derivation protocol ****
% 6.66/6.90 % SZS output start CNFRefutation
% See solution above
% 6.66/6.90
% 6.66/6.90 %**** End of derivation protocol ****
% 6.66/6.90 %**** no. of clauses in derivation: 83 ****
% 6.66/6.90 %**** clause counter: 82 ****
% 6.66/6.90
% 6.66/6.90 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,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:82,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------