%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : CAT003-4 : 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 : n002.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 42.02s 7.23s
% Output : CNFRefutation 42.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 107 ( 74 unt; 0 typ; 0 def)
% Number of atoms : 447 ( 208 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 617 ( 90 ~; 102 |; 0 &; 425 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 167 ( 0 ^; 167 !; 0 ?; 167 :)
% 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_equivalent,type,
equivalent: $i > $i > $o ).
thf(tp_g,type,
g: $i ).
thf(tp_h,type,
h: $i ).
thf(tp_there_exists,type,
there_exists: $i > $o ).
thf(1,axiom,
! [X: $i] :
( ( compose @ ( codomain @ X ) @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_codomain) ).
thf(2,axiom,
! [X: $i] :
( ( compose @ X @ ( domain @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_domain) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( compose @ X @ ( compose @ Y @ Z ) )
= ( compose @ ( compose @ X @ Y ) @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_compose) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ~ ( there_exists @ ( domain @ X ) )
| ( ( domain @ X )
!= ( codomain @ Y ) )
| ( there_exists @ ( compose @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition2) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ~ ( there_exists @ ( compose @ X @ Y ) )
| ( ( domain @ X )
= ( codomain @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition1) ).
thf(6,axiom,
! [X: $i,Y: $i] :
( ~ ( there_exists @ ( compose @ X @ Y ) )
| ( there_exists @ ( domain @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_domain) ).
thf(7,axiom,
! [X: $i] :
( ~ ( there_exists @ ( codomain @ X ) )
| ( there_exists @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_has_elements) ).
thf(8,axiom,
! [X: $i] :
( ~ ( there_exists @ ( domain @ X ) )
| ( there_exists @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_has_elements) ).
thf(9,axiom,
! [X: $i,Y: $i] :
( ~ ( there_exists @ X )
| ( X != Y )
| ( equivalent @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_and_equality_implies_equivalence1) ).
thf(10,axiom,
! [X: $i,Y: $i] :
( ~ ( equivalent @ X @ Y )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence2) ).
thf(11,axiom,
! [X: $i,Y: $i] :
( ~ ( equivalent @ X @ Y )
| ( there_exists @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence1) ).
thf(12,axiom,
( ( compose @ h @ a )
= ( compose @ g @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ha_equals_ga) ).
thf(13,axiom,
there_exists @ h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_h_exists) ).
thf(14,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( compose @ X @ ( compose @ a @ b ) )
!= Y )
| ( ( compose @ Z @ ( compose @ a @ b ) )
!= Y )
| ( X = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',epimorphism) ).
thf(15,axiom,
there_exists @ ( compose @ a @ b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_ab_exists) ).
thf(16,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(17,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[16]) ).
thf(18,negated_conjecture,
g != h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_g_equals_h) ).
thf(19,plain,
$false = $false,
inference(unfold_def,[status(thm)],[17]) ).
thf(20,plain,
( ( ! [X: $i] :
( ( compose @ ( codomain @ X ) @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(21,plain,
( ( ! [X: $i] :
( ( compose @ X @ ( domain @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( compose @ X @ ( compose @ Y @ Z ) )
= ( compose @ ( compose @ X @ Y ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( there_exists @ ( domain @ X ) )
| ( ( domain @ X )
!= ( codomain @ Y ) )
| ( there_exists @ ( compose @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( there_exists @ ( compose @ X @ Y ) )
| ( ( domain @ X )
= ( codomain @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( there_exists @ ( compose @ X @ Y ) )
| ( there_exists @ ( domain @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(26,plain,
( ( ! [X: $i] :
( ~ ( there_exists @ ( codomain @ X ) )
| ( there_exists @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(27,plain,
( ( ! [X: $i] :
( ~ ( there_exists @ ( domain @ X ) )
| ( there_exists @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( there_exists @ X )
| ( X != Y )
| ( equivalent @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equivalent @ X @ Y )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equivalent @ X @ Y )
| ( there_exists @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(31,plain,
( ( ( compose @ h @ a )
= ( compose @ g @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(32,plain,
( ( there_exists @ h )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( compose @ X @ ( compose @ a @ b ) )
!= Y )
| ( ( compose @ Z @ ( compose @ a @ b ) )
!= Y )
| ( X = Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(34,plain,
( ( there_exists @ ( compose @ a @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(35,plain,
( ( g != h )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(36,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(37,plain,
( ( g != h )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(38,plain,
( ( there_exists @ ( compose @ a @ b ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( compose @ X @ ( compose @ a @ b ) )
!= Y )
| ( ( compose @ Z @ ( compose @ a @ b ) )
!= Y )
| ( X = Z ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(40,plain,
( ( there_exists @ h )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(41,plain,
( ( ( compose @ h @ a )
= ( compose @ g @ a ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equivalent @ X @ Y )
| ( there_exists @ X ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(43,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equivalent @ X @ Y )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(44,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( there_exists @ X )
| ( X != Y )
| ( equivalent @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(45,plain,
( ( ! [X: $i] :
( ~ ( there_exists @ ( domain @ X ) )
| ( there_exists @ X ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(46,plain,
( ( ! [X: $i] :
( ~ ( there_exists @ ( codomain @ X ) )
| ( there_exists @ X ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(47,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( there_exists @ ( compose @ X @ Y ) )
| ( there_exists @ ( domain @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( there_exists @ ( compose @ X @ Y ) )
| ( ( domain @ X )
= ( codomain @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(49,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( there_exists @ ( domain @ X ) )
| ( ( domain @ X )
!= ( codomain @ Y ) )
| ( there_exists @ ( compose @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(50,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( compose @ X @ ( compose @ Y @ Z ) )
= ( compose @ ( compose @ X @ Y ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(51,plain,
( ( ! [X: $i] :
( ( compose @ X @ ( domain @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(52,plain,
( ( ! [X: $i] :
( ( compose @ ( codomain @ X ) @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(53,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[36]) ).
thf(54,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( compose @ SX0 @ ( compose @ a @ b ) )
!= SX1 )
| ( ( compose @ SX2 @ ( compose @ a @ b ) )
!= SX1 )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(55,plain,
( ( g != h )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(56,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( there_exists @ SX0 )
| ( SX0 != SX1 )
| ( equivalent @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(57,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( there_exists @ ( domain @ SX0 ) )
| ( ( domain @ SX0 )
!= ( codomain @ SX1 ) )
| ( there_exists @ ( compose @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(58,plain,
! [SV1: $i] :
( ( ! [SY22: $i] :
( ~ ( equivalent @ SV1 @ SY22 )
| ( there_exists @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(59,plain,
! [SV2: $i] :
( ( ! [SY23: $i] :
( ~ ( equivalent @ SV2 @ SY23 )
| ( SV2 = SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(60,plain,
! [SV3: $i] :
( ( ~ ( there_exists @ ( domain @ SV3 ) )
| ( there_exists @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(61,plain,
! [SV4: $i] :
( ( ~ ( there_exists @ ( codomain @ SV4 ) )
| ( there_exists @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(62,plain,
! [SV5: $i] :
( ( ! [SY24: $i] :
( ~ ( there_exists @ ( compose @ SV5 @ SY24 ) )
| ( there_exists @ ( domain @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(63,plain,
! [SV6: $i] :
( ( ! [SY25: $i] :
( ~ ( there_exists @ ( compose @ SV6 @ SY25 ) )
| ( ( domain @ SV6 )
= ( codomain @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(64,plain,
! [SV7: $i] :
( ( ! [SY26: $i,SY27: $i] :
( ( compose @ SV7 @ ( compose @ SY26 @ SY27 ) )
= ( compose @ ( compose @ SV7 @ SY26 ) @ SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(65,plain,
! [SV8: $i] :
( ( ( compose @ SV8 @ ( domain @ SV8 ) )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(66,plain,
! [SV9: $i] :
( ( ( compose @ ( codomain @ SV9 ) @ SV9 )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(67,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(68,plain,
! [SV10: $i] :
( ( ! [SY28: $i,SY29: $i] :
( ( ( compose @ SV10 @ ( compose @ a @ b ) )
!= SY28 )
| ( ( compose @ SY29 @ ( compose @ a @ b ) )
!= SY28 )
| ( SV10 = SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(69,plain,
( ( g = h )
= $false ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(70,plain,
! [SV11: $i] :
( ( ! [SY30: $i] :
( ~ ( there_exists @ SV11 )
| ( SV11 != SY30 )
| ( equivalent @ SV11 @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(71,plain,
! [SV12: $i] :
( ( ! [SY31: $i] :
( ~ ( there_exists @ ( domain @ SV12 ) )
| ( ( domain @ SV12 )
!= ( codomain @ SY31 ) )
| ( there_exists @ ( compose @ SV12 @ SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(72,plain,
! [SV13: $i,SV1: $i] :
( ( ~ ( equivalent @ SV1 @ SV13 )
| ( there_exists @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(73,plain,
! [SV14: $i,SV2: $i] :
( ( ~ ( equivalent @ SV2 @ SV14 )
| ( SV2 = SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(74,plain,
! [SV3: $i] :
( ( ( ~ ( there_exists @ ( domain @ SV3 ) ) )
= $true )
| ( ( there_exists @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(75,plain,
! [SV4: $i] :
( ( ( ~ ( there_exists @ ( codomain @ SV4 ) ) )
= $true )
| ( ( there_exists @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(76,plain,
! [SV15: $i,SV5: $i] :
( ( ~ ( there_exists @ ( compose @ SV5 @ SV15 ) )
| ( there_exists @ ( domain @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(77,plain,
! [SV16: $i,SV6: $i] :
( ( ~ ( there_exists @ ( compose @ SV6 @ SV16 ) )
| ( ( domain @ SV6 )
= ( codomain @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(78,plain,
! [SV17: $i,SV7: $i] :
( ( ! [SY32: $i] :
( ( compose @ SV7 @ ( compose @ SV17 @ SY32 ) )
= ( compose @ ( compose @ SV7 @ SV17 ) @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(79,plain,
! [SV18: $i,SV10: $i] :
( ( ! [SY33: $i] :
( ( ( compose @ SV10 @ ( compose @ a @ b ) )
!= SV18 )
| ( ( compose @ SY33 @ ( compose @ a @ b ) )
!= SV18 )
| ( SV10 = SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(80,plain,
! [SV19: $i,SV11: $i] :
( ( ~ ( there_exists @ SV11 )
| ( SV11 != SV19 )
| ( equivalent @ SV11 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(81,plain,
! [SV20: $i,SV12: $i] :
( ( ~ ( there_exists @ ( domain @ SV12 ) )
| ( ( domain @ SV12 )
!= ( codomain @ SV20 ) )
| ( there_exists @ ( compose @ SV12 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(82,plain,
! [SV13: $i,SV1: $i] :
( ( ( ~ ( equivalent @ SV1 @ SV13 ) )
= $true )
| ( ( there_exists @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(83,plain,
! [SV14: $i,SV2: $i] :
( ( ( ~ ( equivalent @ SV2 @ SV14 ) )
= $true )
| ( ( SV2 = SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(84,plain,
! [SV3: $i] :
( ( ( there_exists @ ( domain @ SV3 ) )
= $false )
| ( ( there_exists @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(85,plain,
! [SV4: $i] :
( ( ( there_exists @ ( codomain @ SV4 ) )
= $false )
| ( ( there_exists @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(86,plain,
! [SV15: $i,SV5: $i] :
( ( ( ~ ( there_exists @ ( compose @ SV5 @ SV15 ) ) )
= $true )
| ( ( there_exists @ ( domain @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(87,plain,
! [SV16: $i,SV6: $i] :
( ( ( ~ ( there_exists @ ( compose @ SV6 @ SV16 ) ) )
= $true )
| ( ( ( domain @ SV6 )
= ( codomain @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(88,plain,
! [SV21: $i,SV17: $i,SV7: $i] :
( ( ( compose @ SV7 @ ( compose @ SV17 @ SV21 ) )
= ( compose @ ( compose @ SV7 @ SV17 ) @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(89,plain,
! [SV22: $i,SV18: $i,SV10: $i] :
( ( ( ( compose @ SV10 @ ( compose @ a @ b ) )
!= SV18 )
| ( ( compose @ SV22 @ ( compose @ a @ b ) )
!= SV18 )
| ( SV10 = SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(90,plain,
! [SV19: $i,SV11: $i] :
( ( ( ~ ( there_exists @ SV11 ) )
= $true )
| ( ( ( SV11 != SV19 )
| ( equivalent @ SV11 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(91,plain,
! [SV20: $i,SV12: $i] :
( ( ( ~ ( there_exists @ ( domain @ SV12 ) ) )
= $true )
| ( ( ( ( domain @ SV12 )
!= ( codomain @ SV20 ) )
| ( there_exists @ ( compose @ SV12 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(92,plain,
! [SV13: $i,SV1: $i] :
( ( ( equivalent @ SV1 @ SV13 )
= $false )
| ( ( there_exists @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(93,plain,
! [SV14: $i,SV2: $i] :
( ( ( equivalent @ SV2 @ SV14 )
= $false )
| ( ( SV2 = SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(94,plain,
! [SV15: $i,SV5: $i] :
( ( ( there_exists @ ( compose @ SV5 @ SV15 ) )
= $false )
| ( ( there_exists @ ( domain @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(95,plain,
! [SV16: $i,SV6: $i] :
( ( ( there_exists @ ( compose @ SV6 @ SV16 ) )
= $false )
| ( ( ( domain @ SV6 )
= ( codomain @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(96,plain,
! [SV22: $i,SV18: $i,SV10: $i] :
( ( ( ( compose @ SV10 @ ( compose @ a @ b ) )
!= SV18 )
= $true )
| ( ( ( ( compose @ SV22 @ ( compose @ a @ b ) )
!= SV18 )
| ( SV10 = SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(97,plain,
! [SV19: $i,SV11: $i] :
( ( ( there_exists @ SV11 )
= $false )
| ( ( ( SV11 != SV19 )
| ( equivalent @ SV11 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(98,plain,
! [SV20: $i,SV12: $i] :
( ( ( there_exists @ ( domain @ SV12 ) )
= $false )
| ( ( ( ( domain @ SV12 )
!= ( codomain @ SV20 ) )
| ( there_exists @ ( compose @ SV12 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(99,plain,
! [SV22: $i,SV18: $i,SV10: $i] :
( ( ( ( compose @ SV10 @ ( compose @ a @ b ) )
= SV18 )
= $false )
| ( ( ( ( compose @ SV22 @ ( compose @ a @ b ) )
!= SV18 )
| ( SV10 = SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(100,plain,
! [SV19: $i,SV11: $i] :
( ( ( SV11 != SV19 )
= $true )
| ( ( equivalent @ SV11 @ SV19 )
= $true )
| ( ( there_exists @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(101,plain,
! [SV20: $i,SV12: $i] :
( ( ( ( domain @ SV12 )
!= ( codomain @ SV20 ) )
= $true )
| ( ( there_exists @ ( compose @ SV12 @ SV20 ) )
= $true )
| ( ( there_exists @ ( domain @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(102,plain,
! [SV10: $i,SV18: $i,SV22: $i] :
( ( ( ( compose @ SV22 @ ( compose @ a @ b ) )
!= SV18 )
= $true )
| ( ( SV10 = SV22 )
= $true )
| ( ( ( compose @ SV10 @ ( compose @ a @ b ) )
= SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(103,plain,
! [SV19: $i,SV11: $i] :
( ( ( SV11 = SV19 )
= $false )
| ( ( equivalent @ SV11 @ SV19 )
= $true )
| ( ( there_exists @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(104,plain,
! [SV20: $i,SV12: $i] :
( ( ( ( domain @ SV12 )
= ( codomain @ SV20 ) )
= $false )
| ( ( there_exists @ ( compose @ SV12 @ SV20 ) )
= $true )
| ( ( there_exists @ ( domain @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(105,plain,
! [SV10: $i,SV18: $i,SV22: $i] :
( ( ( ( compose @ SV22 @ ( compose @ a @ b ) )
= SV18 )
= $false )
| ( ( SV10 = SV22 )
= $true )
| ( ( ( compose @ SV10 @ ( compose @ a @ b ) )
= SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(106,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[38,105,104,103,95,94,93,92,88,85,84,69,67,66,65,41,40]) ).
thf(107,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT003-4 : 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
% 0.07/0.17 % Computer : n002.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 18:31:57 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 42.02/7.23
% 42.02/7.23 No.of.Axioms: 16
% 42.02/7.23
% 42.02/7.23 Length.of.Defs: 0
% 42.02/7.23
% 42.02/7.23 Contains.Choice.Funs: false
% 42.02/7.23 ..
% 42.02/7.23
% 42.02/7.23 ********************************
% 42.02/7.23 * All subproblems solved! *
% 42.02/7.23 ********************************
% 42.02/7.23 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:16,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:106,loop_count:0,foatp_calls:1,translation:fof_full)
% 42.02/7.23
% 42.02/7.23 %**** Beginning of derivation protocol ****
% 42.02/7.23 % SZS output start CNFRefutation
% See solution above
% 42.02/7.23
% 42.02/7.23 %**** End of derivation protocol ****
% 42.02/7.23 %**** no. of clauses in derivation: 107 ****
% 42.02/7.23 %**** clause counter: 106 ****
% 42.02/7.23
% 42.02/7.23 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:16,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:106,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------