%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : CAT004-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:10:40 AM UTC 2026
% Result : Unsatisfiable 7.01s 1.48s
% Output : CNFRefutation 7.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 98 ( 64 unt; 0 typ; 0 def)
% Number of atoms : 534 ( 387 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 847 ( 119 ~; 158 |; 0 &; 570 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 171 ( 0 ^; 171 !; 0 ?; 171 :)
% 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 @ ( compose @ a @ b ) @ h )
= ( compose @ ( compose @ a @ b ) @ g ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_h_equals_ab_g) ).
thf(9,axiom,
( ( codomain @ ( compose @ a @ b ) )
= ( domain @ g ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_ab_equals_domain_of_g) ).
thf(10,axiom,
( ( codomain @ ( compose @ a @ b ) )
= ( domain @ h ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_ab_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 @ b )
!= ( domain @ X ) )
| ( ( compose @ b @ X )
!= Y )
| ( ( codomain @ b )
!= ( domain @ Z ) )
| ( ( compose @ b @ Z )
!= Y )
| ( X = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',epimorphism2) ).
thf(13,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( codomain @ a )
!= ( domain @ X ) )
| ( ( compose @ a @ X )
!= Y )
| ( ( codomain @ a )
!= ( domain @ Z ) )
| ( ( compose @ a @ Z )
!= Y )
| ( X = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',epimorphism1) ).
thf(14,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(15,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,negated_conjecture,
h != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_h_equals_g) ).
thf(17,plain,
$false = $false,
inference(unfold_def,[status(thm)],[15]) ).
thf(18,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(19,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( codomain @ ( compose @ X @ Y ) )
= ( codomain @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(20,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( domain @ ( compose @ X @ Y ) )
= ( domain @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [X: $i] :
( ( compose @ X @ ( codomain @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(22,plain,
( ( ! [X: $i] :
( ( compose @ ( domain @ X ) @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(23,plain,
( ( ! [X: $i] :
( ( domain @ ( codomain @ X ) )
= ( codomain @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(24,plain,
( ( ! [X: $i] :
( ( codomain @ ( domain @ X ) )
= ( domain @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(25,plain,
( ( ( compose @ ( compose @ a @ b ) @ h )
= ( compose @ ( compose @ a @ b ) @ g ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(26,plain,
( ( ( codomain @ ( compose @ a @ b ) )
= ( domain @ g ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(27,plain,
( ( ( codomain @ ( compose @ a @ b ) )
= ( domain @ h ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(28,plain,
( ( ( codomain @ a )
= ( domain @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( codomain @ b )
!= ( domain @ X ) )
| ( ( compose @ b @ X )
!= Y )
| ( ( codomain @ b )
!= ( domain @ Z ) )
| ( ( compose @ b @ Z )
!= Y )
| ( X = Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( codomain @ a )
!= ( domain @ X ) )
| ( ( compose @ a @ X )
!= Y )
| ( ( codomain @ a )
!= ( domain @ Z ) )
| ( ( compose @ a @ Z )
!= Y )
| ( X = Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(31,plain,
( ( h != g )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(32,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(33,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)],[18]) ).
thf(34,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( codomain @ ( compose @ X @ Y ) )
= ( codomain @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(35,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( domain @ ( compose @ X @ Y ) )
= ( domain @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(36,plain,
( ( ! [X: $i] :
( ( ( codomain @ b )
!= ( domain @ X ) )
| ! [Y: $i] :
( ( ( compose @ b @ X )
!= Y )
| ! [Z: $i] :
( ( ( codomain @ b )
!= ( domain @ Z ) )
| ( ( compose @ b @ Z )
!= Y )
| ( X = Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(37,plain,
( ( ! [X: $i] :
( ( ( codomain @ a )
!= ( domain @ X ) )
| ! [Y: $i] :
( ( ( compose @ a @ X )
!= Y )
| ! [Z: $i] :
( ( ( codomain @ a )
!= ( domain @ Z ) )
| ( ( compose @ a @ Z )
!= Y )
| ( X = Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(38,plain,
( ( h != g )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(39,plain,
( ( h != g )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(40,plain,
( ( ! [X: $i] :
( ( ( codomain @ a )
!= ( domain @ X ) )
| ! [Y: $i] :
( ( ( compose @ a @ X )
!= Y )
| ! [Z: $i] :
( ( ( codomain @ a )
!= ( domain @ Z ) )
| ( ( compose @ a @ Z )
!= Y )
| ( X = Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(41,plain,
( ( ! [X: $i] :
( ( ( codomain @ b )
!= ( domain @ X ) )
| ! [Y: $i] :
( ( ( compose @ b @ X )
!= Y )
| ! [Z: $i] :
( ( ( codomain @ b )
!= ( domain @ Z ) )
| ( ( compose @ b @ Z )
!= Y )
| ( X = Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(42,plain,
( ( ( codomain @ a )
= ( domain @ b ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(43,plain,
( ( ( codomain @ ( compose @ a @ b ) )
= ( domain @ h ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(44,plain,
( ( ( codomain @ ( compose @ a @ b ) )
= ( domain @ g ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(45,plain,
( ( ( compose @ ( compose @ a @ b ) @ h )
= ( compose @ ( compose @ a @ b ) @ g ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(46,plain,
( ( ! [X: $i] :
( ( codomain @ ( domain @ X ) )
= ( domain @ X ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(47,plain,
( ( ! [X: $i] :
( ( domain @ ( codomain @ X ) )
= ( codomain @ X ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(48,plain,
( ( ! [X: $i] :
( ( compose @ ( domain @ X ) @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(49,plain,
( ( ! [X: $i] :
( ( compose @ X @ ( codomain @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(50,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( domain @ ( compose @ X @ Y ) )
= ( domain @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i] :
( ( ( codomain @ X )
!= ( domain @ Y ) )
| ( ( codomain @ ( compose @ X @ Y ) )
= ( codomain @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(52,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)],[33]) ).
thf(53,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[32]) ).
thf(54,plain,
( ( h = g )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(55,plain,
! [SV1: $i] :
( ( ( ( codomain @ a )
!= ( domain @ SV1 ) )
| ! [SY17: $i] :
( ( ( compose @ a @ SV1 )
!= SY17 )
| ! [SY18: $i] :
( ( ( codomain @ a )
!= ( domain @ SY18 ) )
| ( ( compose @ a @ SY18 )
!= SY17 )
| ( SV1 = SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(56,plain,
! [SV2: $i] :
( ( ( ( codomain @ b )
!= ( domain @ SV2 ) )
| ! [SY19: $i] :
( ( ( compose @ b @ SV2 )
!= SY19 )
| ! [SY20: $i] :
( ( ( codomain @ b )
!= ( domain @ SY20 ) )
| ( ( compose @ b @ SY20 )
!= SY19 )
| ( SV2 = SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(57,plain,
! [SV3: $i] :
( ( ( codomain @ ( domain @ SV3 ) )
= ( domain @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(58,plain,
! [SV4: $i] :
( ( ( domain @ ( codomain @ SV4 ) )
= ( codomain @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(59,plain,
! [SV5: $i] :
( ( ( compose @ ( domain @ SV5 ) @ SV5 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(60,plain,
! [SV6: $i] :
( ( ( compose @ SV6 @ ( codomain @ SV6 ) )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(61,plain,
! [SV7: $i] :
( ( ! [SY21: $i] :
( ( ( codomain @ SV7 )
!= ( domain @ SY21 ) )
| ( ( domain @ ( compose @ SV7 @ SY21 ) )
= ( domain @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(62,plain,
! [SV8: $i] :
( ( ! [SY22: $i] :
( ( ( codomain @ SV8 )
!= ( domain @ SY22 ) )
| ( ( codomain @ ( compose @ SV8 @ SY22 ) )
= ( codomain @ SY22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(63,plain,
! [SV9: $i] :
( ( ! [SY23: $i] :
( ( ( codomain @ SV9 )
!= ( domain @ SY23 ) )
| ! [SY24: $i] :
( ( ( codomain @ SY23 )
!= ( domain @ SY24 ) )
| ( ( compose @ SV9 @ ( compose @ SY23 @ SY24 ) )
= ( compose @ ( compose @ SV9 @ SY23 ) @ SY24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(64,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(65,plain,
! [SV1: $i] :
( ( ( ( codomain @ a )
!= ( domain @ SV1 ) )
= $true )
| ( ( ! [SY17: $i] :
( ( ( compose @ a @ SV1 )
!= SY17 )
| ! [SY18: $i] :
( ( ( codomain @ a )
!= ( domain @ SY18 ) )
| ( ( compose @ a @ SY18 )
!= SY17 )
| ( SV1 = SY18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(66,plain,
! [SV2: $i] :
( ( ( ( codomain @ b )
!= ( domain @ SV2 ) )
= $true )
| ( ( ! [SY19: $i] :
( ( ( compose @ b @ SV2 )
!= SY19 )
| ! [SY20: $i] :
( ( ( codomain @ b )
!= ( domain @ SY20 ) )
| ( ( compose @ b @ SY20 )
!= SY19 )
| ( SV2 = SY20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(67,plain,
! [SV10: $i,SV7: $i] :
( ( ( ( codomain @ SV7 )
!= ( domain @ SV10 ) )
| ( ( domain @ ( compose @ SV7 @ SV10 ) )
= ( domain @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(68,plain,
! [SV11: $i,SV8: $i] :
( ( ( ( codomain @ SV8 )
!= ( domain @ SV11 ) )
| ( ( codomain @ ( compose @ SV8 @ SV11 ) )
= ( codomain @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(69,plain,
! [SV12: $i,SV9: $i] :
( ( ( ( codomain @ SV9 )
!= ( domain @ SV12 ) )
| ! [SY25: $i] :
( ( ( codomain @ SV12 )
!= ( domain @ SY25 ) )
| ( ( compose @ SV9 @ ( compose @ SV12 @ SY25 ) )
= ( compose @ ( compose @ SV9 @ SV12 ) @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(70,plain,
! [SV1: $i] :
( ( ( ( codomain @ a )
= ( domain @ SV1 ) )
= $false )
| ( ( ! [SY17: $i] :
( ( ( compose @ a @ SV1 )
!= SY17 )
| ! [SY18: $i] :
( ( ( codomain @ a )
!= ( domain @ SY18 ) )
| ( ( compose @ a @ SY18 )
!= SY17 )
| ( SV1 = SY18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(71,plain,
! [SV2: $i] :
( ( ( ( codomain @ b )
= ( domain @ SV2 ) )
= $false )
| ( ( ! [SY19: $i] :
( ( ( compose @ b @ SV2 )
!= SY19 )
| ! [SY20: $i] :
( ( ( codomain @ b )
!= ( domain @ SY20 ) )
| ( ( compose @ b @ SY20 )
!= SY19 )
| ( SV2 = SY20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(72,plain,
! [SV10: $i,SV7: $i] :
( ( ( ( codomain @ SV7 )
!= ( domain @ SV10 ) )
= $true )
| ( ( ( domain @ ( compose @ SV7 @ SV10 ) )
= ( domain @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(73,plain,
! [SV11: $i,SV8: $i] :
( ( ( ( codomain @ SV8 )
!= ( domain @ SV11 ) )
= $true )
| ( ( ( codomain @ ( compose @ SV8 @ SV11 ) )
= ( codomain @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(74,plain,
! [SV12: $i,SV9: $i] :
( ( ( ( codomain @ SV9 )
!= ( domain @ SV12 ) )
= $true )
| ( ( ! [SY25: $i] :
( ( ( codomain @ SV12 )
!= ( domain @ SY25 ) )
| ( ( compose @ SV9 @ ( compose @ SV12 @ SY25 ) )
= ( compose @ ( compose @ SV9 @ SV12 ) @ SY25 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(75,plain,
! [SV13: $i,SV1: $i] :
( ( ( ( ( compose @ a @ SV1 )
!= SV13 )
| ! [SY26: $i] :
( ( ( codomain @ a )
!= ( domain @ SY26 ) )
| ( ( compose @ a @ SY26 )
!= SV13 )
| ( SV1 = SY26 ) ) )
= $true )
| ( ( ( codomain @ a )
= ( domain @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV14: $i,SV2: $i] :
( ( ( ( ( compose @ b @ SV2 )
!= SV14 )
| ! [SY27: $i] :
( ( ( codomain @ b )
!= ( domain @ SY27 ) )
| ( ( compose @ b @ SY27 )
!= SV14 )
| ( SV2 = SY27 ) ) )
= $true )
| ( ( ( codomain @ b )
= ( domain @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV10: $i,SV7: $i] :
( ( ( ( codomain @ SV7 )
= ( domain @ SV10 ) )
= $false )
| ( ( ( domain @ ( compose @ SV7 @ SV10 ) )
= ( domain @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(78,plain,
! [SV11: $i,SV8: $i] :
( ( ( ( codomain @ SV8 )
= ( domain @ SV11 ) )
= $false )
| ( ( ( codomain @ ( compose @ SV8 @ SV11 ) )
= ( codomain @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(79,plain,
! [SV12: $i,SV9: $i] :
( ( ( ( codomain @ SV9 )
= ( domain @ SV12 ) )
= $false )
| ( ( ! [SY25: $i] :
( ( ( codomain @ SV12 )
!= ( domain @ SY25 ) )
| ( ( compose @ SV9 @ ( compose @ SV12 @ SY25 ) )
= ( compose @ ( compose @ SV9 @ SV12 ) @ SY25 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(80,plain,
! [SV13: $i,SV1: $i] :
( ( ( ( compose @ a @ SV1 )
!= SV13 )
= $true )
| ( ( ! [SY26: $i] :
( ( ( codomain @ a )
!= ( domain @ SY26 ) )
| ( ( compose @ a @ SY26 )
!= SV13 )
| ( SV1 = SY26 ) ) )
= $true )
| ( ( ( codomain @ a )
= ( domain @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(81,plain,
! [SV14: $i,SV2: $i] :
( ( ( ( compose @ b @ SV2 )
!= SV14 )
= $true )
| ( ( ! [SY27: $i] :
( ( ( codomain @ b )
!= ( domain @ SY27 ) )
| ( ( compose @ b @ SY27 )
!= SV14 )
| ( SV2 = SY27 ) ) )
= $true )
| ( ( ( codomain @ b )
= ( domain @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(82,plain,
! [SV9: $i,SV15: $i,SV12: $i] :
( ( ( ( ( codomain @ SV12 )
!= ( domain @ SV15 ) )
| ( ( compose @ SV9 @ ( compose @ SV12 @ SV15 ) )
= ( compose @ ( compose @ SV9 @ SV12 ) @ SV15 ) ) )
= $true )
| ( ( ( codomain @ SV9 )
= ( domain @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(83,plain,
! [SV13: $i,SV1: $i] :
( ( ( ( compose @ a @ SV1 )
= SV13 )
= $false )
| ( ( ! [SY26: $i] :
( ( ( codomain @ a )
!= ( domain @ SY26 ) )
| ( ( compose @ a @ SY26 )
!= SV13 )
| ( SV1 = SY26 ) ) )
= $true )
| ( ( ( codomain @ a )
= ( domain @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(84,plain,
! [SV14: $i,SV2: $i] :
( ( ( ( compose @ b @ SV2 )
= SV14 )
= $false )
| ( ( ! [SY27: $i] :
( ( ( codomain @ b )
!= ( domain @ SY27 ) )
| ( ( compose @ b @ SY27 )
!= SV14 )
| ( SV2 = SY27 ) ) )
= $true )
| ( ( ( codomain @ b )
= ( domain @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(85,plain,
! [SV9: $i,SV15: $i,SV12: $i] :
( ( ( ( codomain @ SV12 )
!= ( domain @ SV15 ) )
= $true )
| ( ( ( compose @ SV9 @ ( compose @ SV12 @ SV15 ) )
= ( compose @ ( compose @ SV9 @ SV12 ) @ SV15 ) )
= $true )
| ( ( ( codomain @ SV9 )
= ( domain @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(86,plain,
! [SV1: $i,SV13: $i,SV16: $i] :
( ( ( ( ( codomain @ a )
!= ( domain @ SV16 ) )
| ( ( compose @ a @ SV16 )
!= SV13 )
| ( SV1 = SV16 ) )
= $true )
| ( ( ( compose @ a @ SV1 )
= SV13 )
= $false )
| ( ( ( codomain @ a )
= ( domain @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(87,plain,
! [SV2: $i,SV14: $i,SV17: $i] :
( ( ( ( ( codomain @ b )
!= ( domain @ SV17 ) )
| ( ( compose @ b @ SV17 )
!= SV14 )
| ( SV2 = SV17 ) )
= $true )
| ( ( ( compose @ b @ SV2 )
= SV14 )
= $false )
| ( ( ( codomain @ b )
= ( domain @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(88,plain,
! [SV9: $i,SV15: $i,SV12: $i] :
( ( ( ( codomain @ SV12 )
= ( domain @ SV15 ) )
= $false )
| ( ( ( compose @ SV9 @ ( compose @ SV12 @ SV15 ) )
= ( compose @ ( compose @ SV9 @ SV12 ) @ SV15 ) )
= $true )
| ( ( ( codomain @ SV9 )
= ( domain @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(89,plain,
! [SV1: $i,SV13: $i,SV16: $i] :
( ( ( ( codomain @ a )
!= ( domain @ SV16 ) )
= $true )
| ( ( ( ( compose @ a @ SV16 )
!= SV13 )
| ( SV1 = SV16 ) )
= $true )
| ( ( ( compose @ a @ SV1 )
= SV13 )
= $false )
| ( ( ( codomain @ a )
= ( domain @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(90,plain,
! [SV2: $i,SV14: $i,SV17: $i] :
( ( ( ( codomain @ b )
!= ( domain @ SV17 ) )
= $true )
| ( ( ( ( compose @ b @ SV17 )
!= SV14 )
| ( SV2 = SV17 ) )
= $true )
| ( ( ( compose @ b @ SV2 )
= SV14 )
= $false )
| ( ( ( codomain @ b )
= ( domain @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(91,plain,
! [SV1: $i,SV13: $i,SV16: $i] :
( ( ( ( codomain @ a )
= ( domain @ SV16 ) )
= $false )
| ( ( ( ( compose @ a @ SV16 )
!= SV13 )
| ( SV1 = SV16 ) )
= $true )
| ( ( ( compose @ a @ SV1 )
= SV13 )
= $false )
| ( ( ( codomain @ a )
= ( domain @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(92,plain,
! [SV2: $i,SV14: $i,SV17: $i] :
( ( ( ( codomain @ b )
= ( domain @ SV17 ) )
= $false )
| ( ( ( ( compose @ b @ SV17 )
!= SV14 )
| ( SV2 = SV17 ) )
= $true )
| ( ( ( compose @ b @ SV2 )
= SV14 )
= $false )
| ( ( ( codomain @ b )
= ( domain @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(93,plain,
! [SV1: $i,SV13: $i,SV16: $i] :
( ( ( ( compose @ a @ SV16 )
!= SV13 )
= $true )
| ( ( SV1 = SV16 )
= $true )
| ( ( ( codomain @ a )
= ( domain @ SV16 ) )
= $false )
| ( ( ( compose @ a @ SV1 )
= SV13 )
= $false )
| ( ( ( codomain @ a )
= ( domain @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(94,plain,
! [SV2: $i,SV14: $i,SV17: $i] :
( ( ( ( compose @ b @ SV17 )
!= SV14 )
= $true )
| ( ( SV2 = SV17 )
= $true )
| ( ( ( codomain @ b )
= ( domain @ SV17 ) )
= $false )
| ( ( ( compose @ b @ SV2 )
= SV14 )
= $false )
| ( ( ( codomain @ b )
= ( domain @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(95,plain,
! [SV1: $i,SV13: $i,SV16: $i] :
( ( ( ( compose @ a @ SV16 )
= SV13 )
= $false )
| ( ( SV1 = SV16 )
= $true )
| ( ( ( codomain @ a )
= ( domain @ SV16 ) )
= $false )
| ( ( ( compose @ a @ SV1 )
= SV13 )
= $false )
| ( ( ( codomain @ a )
= ( domain @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(96,plain,
! [SV2: $i,SV14: $i,SV17: $i] :
( ( ( ( compose @ b @ SV17 )
= SV14 )
= $false )
| ( ( SV2 = SV17 )
= $true )
| ( ( ( codomain @ b )
= ( domain @ SV17 ) )
= $false )
| ( ( ( compose @ b @ SV2 )
= SV14 )
= $false )
| ( ( ( codomain @ b )
= ( domain @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(97,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[42,96,95,88,78,77,64,60,59,58,57,54,45,44,43]) ).
thf(98,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.18 % Computer : n005.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 18:27:44 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.01/1.48
% 7.01/1.48 No.of.Axioms: 14
% 7.01/1.48
% 7.01/1.48 Length.of.Defs: 0
% 7.01/1.48
% 7.01/1.48 Contains.Choice.Funs: false
% 7.01/1.48 ..
% 7.01/1.48
% 7.01/1.48 ********************************
% 7.01/1.48 * All subproblems solved! *
% 7.01/1.48 ********************************
% 7.01/1.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:14,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:97,loop_count:0,foatp_calls:1,translation:fof_full)
% 7.01/1.48
% 7.01/1.48 %**** Beginning of derivation protocol ****
% 7.01/1.48 % SZS output start CNFRefutation
% See solution above
% 7.01/1.48
% 7.01/1.48 %**** End of derivation protocol ****
% 7.01/1.48 %**** no. of clauses in derivation: 98 ****
% 7.01/1.48 %**** clause counter: 97 ****
% 7.01/1.48
% 7.01/1.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:14,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:97,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------