%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CAT004-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 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 : Sun Sep 27 06:55:18 AM UTC 2026
% Result : Unsatisfiable 29.30s 7.03s
% Output : Refutation 30.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 23
% Syntax : Number of formulae : 127 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 276 ( 133 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 911 ( 129 ~; 133 |; 0 &; 649 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 161 ( 0 ^; 161 !; 0 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
thf(h_decl,type,
h: $i ).
thf(g_decl,type,
g: $i ).
thf(equivalent_decl,type,
equivalent: $i > $i > $o ).
thf(f1_decl,type,
f1: $i > $i > $i ).
thf(there_exists_decl,type,
there_exists: $i > $o ).
thf(compose_decl,type,
compose: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(domain_decl,type,
domain: $i > $i ).
thf(codomain_decl,type,
codomain: $i > $i ).
thf(b_decl,type,
b: $i ).
thf(17,axiom,
! [A: $i] :
( ( A @ there_exists )
| ~ ( A @ codomain @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_has_elements) ).
thf(68,plain,
! [A: $i] :
( ( A @ there_exists )
| ~ ( A @ codomain @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(69,plain,
! [A: $i] :
( ( A @ there_exists )
| ~ ( A @ codomain @ there_exists ) ),
inference(cnf,[status(esa)],[68]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( A @ there_exists )
| ~ ( B @ ( A @ equivalent ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence1) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( A @ there_exists )
| ~ ( B @ ( A @ equivalent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ compose ) @ ( A @ compose ) )
= ( C @ ( B @ ( A @ compose ) @ compose ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_compose) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ compose ) @ ( A @ compose ) )
= ( C @ ( B @ ( A @ compose ) @ compose ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ ( A @ codomain @ compose ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_codomain) ).
thf(74,plain,
! [A: $i] :
( ( A @ ( A @ codomain @ compose ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ f1 ) @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',indiscernibles1) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ f1 ) @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ f1 ) @ there_exists ) ),
inference(cnf,[status(esa)],[60]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f1 ) @ there_exists )
| ( A = B ) ),
inference(lifteq,[status(thm)],[61]) ).
thf(1,negated_conjecture,
h != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_h_equals_g) ).
thf(24,plain,
h != g,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(25,plain,
h != g,
inference(polarity_switch,[status(thm)],[24]) ).
thf(26,plain,
g != h,
inference(lifteq,[status(thm)],[25]) ).
thf(476,plain,
! [B: $i,A: $i] :
( ( A != g )
| ( B != h )
| ( B @ ( A @ f1 ) @ there_exists ) ),
inference(paramod_ordered,[status(thm)],[62,26]) ).
thf(477,plain,
! [A: $i] :
( ( A != h )
| ( A @ ( g @ f1 ) @ there_exists ) ),
inference(pattern_uni,[status(thm)],[476:[bind(A,$thf( g ))]]) ).
thf(568,plain,
h @ ( g @ f1 ) @ there_exists,
inference(simp,[status(thm)],[477]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ equivalent ) )
| ( A != B )
| ~ ( A @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_and_equality_implies_equivalence1) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equivalent ) )
| ( A != B )
| ~ ( A @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equivalent ) )
| ( A != B )
| ~ ( A @ there_exists ) ),
inference(cnf,[status(esa)],[36]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equivalent ) )
| ~ ( A @ there_exists )
| ( A != B ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(39,plain,
! [A: $i] :
( ( A @ ( A @ equivalent ) )
| ~ ( A @ there_exists ) ),
inference(simp,[status(thm)],[38]) ).
thf(2051,plain,
! [A: $i] :
( ( ( h @ ( g @ f1 ) @ there_exists )
!= ( A @ there_exists ) )
| ( A @ ( A @ equivalent ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[568,39]) ).
thf(2052,plain,
! [A: $i] :
( ( ( h @ ( g @ f1 ) @ there_exists )
!= ( A @ there_exists ) )
| ( A @ ( A @ equivalent ) ) ),
inference(simp,[status(thm)],[2051]) ).
thf(2053,plain,
h @ ( g @ f1 ) @ ( h @ ( g @ f1 ) @ equivalent ),
inference(pattern_uni,[status(thm)],[2052:[bind(A,$thf( h @ ( g @ f1 ) ))]]) ).
thf(478,plain,
! [B: $i,A: $i] :
( ( B != g )
| ( A != h )
| ( B @ ( A @ f1 ) @ there_exists ) ),
inference(paramod_ordered,[status(thm)],[62,26]) ).
thf(479,plain,
! [A: $i] :
( ( A != h )
| ( g @ ( A @ f1 ) @ there_exists ) ),
inference(pattern_uni,[status(thm)],[478:[bind(A,$thf( A )),bind(B,$thf( g ))]]) ).
thf(569,plain,
g @ ( h @ f1 ) @ there_exists,
inference(simp,[status(thm)],[479]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B
!= ( B @ ( A @ f1 ) ) )
| ( A
!= ( B @ ( A @ f1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',indiscernibles3) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B
!= ( B @ ( A @ f1 ) ) )
| ( A
!= ( B @ ( A @ f1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B
!= ( B @ ( A @ f1 ) ) )
| ( A
!= ( B @ ( A @ f1 ) ) ) ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ f1 ) )
!= B )
| ( ( B @ ( A @ f1 ) )
!= A ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ equivalent ) )
| ( A != B )
| ~ ( B @ there_exists )
| ~ ( A @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_and_equality_implies_equivalence2) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equivalent ) )
| ( A != B )
| ~ ( B @ there_exists )
| ~ ( A @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ domain @ ( A @ compose ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_domain) ).
thf(54,plain,
! [A: $i] :
( ( A @ domain @ ( A @ compose ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(55,plain,
! [A: $i] :
( ( A @ domain @ ( A @ compose ) )
= A ),
inference(lifteq,[status(thm)],[54]) ).
thf(23,axiom,
( ( b @ ( a @ compose ) @ ( h @ compose ) )
= ( b @ ( a @ compose ) @ ( g @ compose ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_ab_equals_g_ab) ).
thf(81,plain,
( ( b @ ( a @ compose ) @ ( h @ compose ) )
= ( b @ ( a @ compose ) @ ( g @ compose ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(82,plain,
( ( b @ ( a @ compose ) @ ( g @ compose ) )
= ( b @ ( a @ compose ) @ ( h @ compose ) ) ),
inference(lifteq,[status(thm)],[81]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ compose ) @ compose ) )
= ( C @ ( B @ compose ) @ ( A @ compose ) ) ),
inference(lifteq,[status(thm)],[52]) ).
thf(340,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ ( a @ compose ) @ ( g @ compose ) )
!= ( B @ ( A @ compose ) ) )
| ( ( C @ ( b @ ( a @ compose ) @ ( h @ compose ) @ compose ) )
= ( C @ ( B @ compose ) @ ( A @ compose ) ) ) ),
inference(paramod_ordered,[status(thm)],[82,53]) ).
thf(341,plain,
! [A: $i] :
( ( A @ ( b @ ( a @ compose ) @ ( h @ compose ) @ compose ) )
= ( A @ ( b @ ( a @ compose ) @ compose ) @ ( g @ compose ) ) ),
inference(pattern_uni,[status(thm)],[340:[bind(A,$thf( g )),bind(B,$thf( b @ ( a @ compose ) )),bind(C,$thf( C ))]]) ).
thf(357,plain,
! [A: $i] :
( ( A @ ( b @ ( a @ compose ) @ ( h @ compose ) @ compose ) )
= ( A @ ( b @ ( a @ compose ) @ compose ) @ ( g @ compose ) ) ),
inference(simp,[status(thm)],[341]) ).
thf(676,plain,
! [A: $i] :
( ( A @ ( b @ ( a @ compose ) @ compose ) @ ( h @ compose ) )
= ( A @ ( b @ compose ) @ ( a @ compose ) @ ( g @ compose ) ) ),
inference(rewrite,[status(thm)],[357,53]) ).
thf(810,plain,
! [B: $i,A: $i] :
( ( ( A @ domain @ ( A @ compose ) )
!= ( B @ ( b @ compose ) ) )
| ( ( A @ ( a @ compose ) @ ( g @ compose ) )
= ( B @ ( b @ ( a @ compose ) @ compose ) @ ( h @ compose ) ) ) ),
inference(paramod_ordered,[status(thm)],[55,676]) ).
thf(811,plain,
( ( b @ ( a @ compose ) @ ( g @ compose ) )
= ( b @ domain @ ( b @ ( a @ compose ) @ compose ) @ ( h @ compose ) ) ),
inference(pattern_uni,[status(thm)],[810:[bind(A,$thf( b )),bind(B,$thf( b @ domain ))]]) ).
thf(960,plain,
( ( b @ domain @ ( b @ compose ) @ ( a @ compose ) @ ( h @ compose ) )
= ( b @ ( a @ compose ) @ ( h @ compose ) ) ),
inference(rewrite,[status(thm)],[811,82,53]) ).
thf(2016,plain,
! [A: $i] :
( ( ( g @ ( h @ f1 ) @ there_exists )
!= ( A @ there_exists ) )
| ( A @ ( A @ equivalent ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[569,39]) ).
thf(2017,plain,
! [A: $i] :
( ( ( g @ ( h @ f1 ) @ there_exists )
!= ( A @ there_exists ) )
| ( A @ ( A @ equivalent ) ) ),
inference(simp,[status(thm)],[2016]) ).
thf(2018,plain,
g @ ( h @ f1 ) @ ( g @ ( h @ f1 ) @ equivalent ),
inference(pattern_uni,[status(thm)],[2017:[bind(A,$thf( g @ ( h @ f1 ) ))]]) ).
thf(16,axiom,
b @ ( a @ compose ) @ there_exists,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_ab_exists) ).
thf(67,plain,
b @ ( a @ compose ) @ there_exists,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(99,plain,
! [A: $i] :
( ( ( A @ domain @ ( A @ compose ) )
!= ( b @ ( a @ compose ) ) )
| ( A @ there_exists ) ),
inference(paramod_ordered,[status(thm)],[55,67]) ).
thf(109,plain,
! [A: $i] :
( ( ( A @ domain )
!= b )
| ( A != a )
| ( A @ there_exists ) ),
inference(simp,[status(thm)],[99]) ).
thf(115,plain,
( ( ( a @ domain )
!= b )
| ( a @ there_exists ) ),
inference(simp,[status(thm)],[109]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ ( A @ equivalent ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence2) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ ( A @ equivalent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ ( A @ equivalent ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equivalent ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( B != g )
| ( A != h )
| ~ ( B @ ( A @ equivalent ) ) ),
inference(paramod_ordered,[status(thm)],[29,26]) ).
thf(213,plain,
! [A: $i] :
( ( A != h )
| ~ ( g @ ( A @ equivalent ) ) ),
inference(pattern_uni,[status(thm)],[212:[bind(A,$thf( A )),bind(B,$thf( g ))]]) ).
thf(247,plain,
~ ( g @ ( h @ equivalent ) ),
inference(simp,[status(thm)],[213]) ).
thf(464,plain,
! [B: $i,A: $i] :
( ( B
!= ( a @ domain ) )
| ( A != b )
| ( a @ there_exists )
| ( B @ ( A @ f1 ) @ there_exists ) ),
inference(paramod_ordered,[status(thm)],[62,115]) ).
thf(465,plain,
! [A: $i] :
( ( A != b )
| ( a @ there_exists )
| ( a @ domain @ ( A @ f1 ) @ there_exists ) ),
inference(pattern_uni,[status(thm)],[464:[bind(A,$thf( A )),bind(B,$thf( a @ domain ))]]) ).
thf(565,plain,
( ( a @ there_exists )
| ( a @ domain @ ( b @ f1 ) @ there_exists ) ),
inference(simp,[status(thm)],[465]) ).
thf(2022,plain,
! [A: $i] :
( ( ( b @ ( a @ compose ) @ there_exists )
!= ( A @ there_exists ) )
| ( A @ ( A @ equivalent ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[67,39]) ).
thf(2023,plain,
! [A: $i] :
( ( ( b @ ( a @ compose ) @ there_exists )
!= ( A @ there_exists ) )
| ( A @ ( A @ equivalent ) ) ),
inference(simp,[status(thm)],[2022]) ).
thf(2024,plain,
b @ ( a @ compose ) @ ( b @ ( a @ compose ) @ equivalent ),
inference(pattern_uni,[status(thm)],[2023:[bind(A,$thf( b @ ( a @ compose ) ))]]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( A @ codomain @ there_exists )
| ~ ( B @ ( A @ compose ) @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_codomain) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( A @ codomain @ there_exists )
| ~ ( B @ ( A @ compose ) @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( A != g )
| ( B != h )
| ~ ( B @ ( A @ equivalent ) ) ),
inference(paramod_ordered,[status(thm)],[29,26]) ).
thf(211,plain,
! [A: $i] :
( ( A != h )
| ~ ( A @ ( g @ equivalent ) ) ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( g ))]]) ).
thf(246,plain,
~ ( h @ ( g @ equivalent ) ),
inference(simp,[status(thm)],[211]) ).
thf(255,plain,
! [B: $i,A: $i] :
( ( A != h )
| ~ ( B @ ( g @ equivalent ) )
| ~ ( B @ ( A @ equivalent ) ) ),
inference(paramod_ordered,[status(thm)],[29,246]) ).
thf(256,plain,
! [A: $i] :
( ~ ( A @ ( g @ equivalent ) )
| ~ ( A @ ( h @ equivalent ) ) ),
inference(pattern_uni,[status(thm)],[255:[bind(A,$thf( h ))]]) ).
thf(261,plain,
! [A: $i] :
( ~ ( A @ ( g @ equivalent ) )
| ~ ( A @ ( h @ equivalent ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(269,plain,
! [B: $i,A: $i] :
( ( B != g )
| ~ ( A @ ( h @ equivalent ) )
| ~ ( B @ ( A @ equivalent ) ) ),
inference(paramod_ordered,[status(thm)],[29,247]) ).
thf(270,plain,
! [A: $i] :
( ~ ( A @ ( h @ equivalent ) )
| ~ ( g @ ( A @ equivalent ) ) ),
inference(pattern_uni,[status(thm)],[269:[bind(A,$thf( A )),bind(B,$thf( g ))]]) ).
thf(259,plain,
! [B: $i,A: $i] :
( ( B != h )
| ~ ( A @ ( g @ equivalent ) )
| ~ ( B @ ( A @ equivalent ) ) ),
inference(paramod_ordered,[status(thm)],[29,246]) ).
thf(260,plain,
! [A: $i] :
( ~ ( A @ ( g @ equivalent ) )
| ~ ( h @ ( A @ equivalent ) ) ),
inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( A )),bind(B,$thf( h ))]]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( b @ ( C @ compose ) )
!= B )
| ( ( b @ ( A @ compose ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_product2) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( b @ ( C @ compose ) )
!= B )
| ( ( b @ ( A @ compose ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B
= ( B @ ( A @ f1 ) ) )
| ( A
= ( B @ ( A @ f1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',indiscernibles2) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B
= ( B @ ( A @ f1 ) ) )
| ( A
= ( B @ ( A @ f1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(806,plain,
! [B: $i,A: $i] :
( ( ( A @ domain @ ( A @ compose ) )
!= ( B @ ( b @ ( a @ compose ) @ compose ) ) )
| ( ( A @ ( h @ compose ) )
= ( B @ ( b @ compose ) @ ( a @ compose ) @ ( g @ compose ) ) ) ),
inference(paramod_ordered,[status(thm)],[55,676]) ).
thf(807,plain,
( ( b @ ( a @ compose ) @ domain @ ( b @ compose ) @ ( a @ compose ) @ ( g @ compose ) )
= ( b @ ( a @ compose ) @ ( h @ compose ) ) ),
inference(pattern_uni,[status(thm)],[806:[bind(A,$thf( b @ ( a @ compose ) )),bind(B,$thf( b @ ( a @ compose ) @ domain ))]]) ).
thf(1225,plain,
! [A: $i] :
( ( ( b @ ( a @ compose ) @ domain @ ( b @ compose ) @ ( a @ compose ) @ ( g @ compose ) )
!= ( A @ ( b @ compose ) @ ( a @ compose ) @ ( g @ compose ) ) )
| ( ( A @ ( b @ ( a @ compose ) @ compose ) @ ( h @ compose ) )
= ( b @ ( a @ compose ) @ ( h @ compose ) ) ) ),
inference(paramod_ordered,[status(thm)],[807,676]) ).
thf(1226,plain,
( ( b @ ( a @ compose ) @ domain @ ( b @ ( a @ compose ) @ compose ) @ ( h @ compose ) )
= ( b @ ( a @ compose ) @ ( h @ compose ) ) ),
inference(pattern_uni,[status(thm)],[1225:[bind(A,$thf( b @ ( a @ compose ) @ domain ))]]) ).
thf(1350,plain,
( ( b @ ( a @ compose ) @ domain @ ( b @ compose ) @ ( a @ compose ) @ ( h @ compose ) )
= ( b @ ( a @ compose ) @ ( h @ compose ) ) ),
inference(rewrite,[status(thm)],[1226,53]) ).
thf(733,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ compose ) @ compose ) )
!= ( D @ ( b @ ( a @ compose ) @ compose ) ) )
| ( ( C @ ( B @ compose ) @ ( A @ compose ) @ ( h @ compose ) )
= ( D @ ( b @ compose ) @ ( a @ compose ) @ ( g @ compose ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,676]) ).
thf(734,plain,
! [A: $i] :
( ( A @ ( b @ compose ) @ ( a @ compose ) @ ( g @ compose ) )
= ( A @ ( b @ compose ) @ ( a @ compose ) @ ( h @ compose ) ) ),
inference(pattern_uni,[status(thm)],[733:[bind(A,$thf( a )),bind(B,$thf( b )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(948,plain,
! [A: $i] :
( ( A @ ( b @ compose ) @ ( a @ compose ) @ ( g @ compose ) )
= ( A @ ( b @ compose ) @ ( a @ compose ) @ ( h @ compose ) ) ),
inference(simp,[status(thm)],[734]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( ( A @ domain )
= ( B @ codomain ) )
| ~ ( B @ ( A @ compose ) @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition1) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( ( A @ domain )
= ( B @ codomain ) )
| ~ ( B @ ( A @ compose ) @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(84,plain,
( ( ( b @ ( a @ compose ) @ ( g @ compose ) )
!= ( b @ ( a @ compose ) ) )
| ( b @ ( a @ compose ) @ ( h @ compose ) @ there_exists ) ),
inference(paramod_ordered,[status(thm)],[82,67]) ).
thf(86,plain,
( ( ( b @ ( a @ compose ) )
!= b )
| ( a != g )
| ( b @ ( a @ compose ) @ ( h @ compose ) @ there_exists ) ),
inference(simp,[status(thm)],[84]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ there_exists )
| ~ ( A @ domain @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_has_elements) ).
thf(76,plain,
! [A: $i] :
( ( A @ there_exists )
| ~ ( A @ domain @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(460,plain,
! [B: $i,A: $i] :
( ( A
!= ( a @ domain ) )
| ( B != b )
| ( a @ there_exists )
| ( B @ ( A @ f1 ) @ there_exists ) ),
inference(paramod_ordered,[status(thm)],[62,115]) ).
thf(461,plain,
! [A: $i] :
( ( A != b )
| ( a @ there_exists )
| ( A @ ( a @ domain @ f1 ) @ there_exists ) ),
inference(pattern_uni,[status(thm)],[460:[bind(A,$thf( a @ domain )),bind(B,$thf( B ))]]) ).
thf(563,plain,
( ( a @ there_exists )
| ( b @ ( a @ domain @ f1 ) @ there_exists ) ),
inference(simp,[status(thm)],[461]) ).
thf(22,axiom,
h @ there_exists,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_h_exists) ).
thf(80,plain,
h @ there_exists,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B
= ( B @ ( A @ f1 ) ) )
| ( A
= ( B @ ( A @ f1 ) ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ f1 ) )
= B )
| ( ( B @ ( A @ f1 ) )
= A ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( A @ domain @ there_exists )
| ~ ( B @ ( A @ compose ) @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_domain) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( A @ domain @ there_exists )
| ~ ( B @ ( A @ compose ) @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2042,plain,
! [A: $i] :
( ( ( h @ there_exists )
!= ( A @ there_exists ) )
| ( A @ ( A @ equivalent ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[80,39]) ).
thf(2043,plain,
! [A: $i] :
( ( ( h @ there_exists )
!= ( A @ there_exists ) )
| ( A @ ( A @ equivalent ) ) ),
inference(simp,[status(thm)],[2042]) ).
thf(2044,plain,
h @ ( h @ equivalent ),
inference(pattern_uni,[status(thm)],[2043:[bind(A,$thf( h ))]]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( a @ ( C @ compose ) )
!= B )
| ( ( a @ ( A @ compose ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_product1) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( a @ ( C @ compose ) )
!= B )
| ( ( a @ ( A @ compose ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ( B != g )
| ~ ( h @ ( A @ equivalent ) )
| ~ ( B @ ( A @ equivalent ) ) ),
inference(paramod_ordered,[status(thm)],[29,246]) ).
thf(258,plain,
! [A: $i] :
( ~ ( h @ ( A @ equivalent ) )
| ~ ( g @ ( A @ equivalent ) ) ),
inference(pattern_uni,[status(thm)],[257:[bind(A,$thf( A )),bind(B,$thf( g ))]]) ).
thf(75,plain,
! [A: $i] :
( ( A @ ( A @ codomain @ compose ) )
= A ),
inference(lifteq,[status(thm)],[74]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( B @ there_exists )
| ~ ( B @ ( A @ equivalent ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence3) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( B @ there_exists )
| ~ ( B @ ( A @ equivalent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1692,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ f1 ) )
!= ( g @ ( h @ f1 ) ) )
| ( B @ there_exists )
| ( A = B )
| ( ( B @ ( A @ f1 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[35,569]) ).
thf(1693,plain,
( ( g @ there_exists )
| ( g = h )
| ( ( g @ ( h @ f1 ) )
= h ) ),
inference(pattern_uni,[status(thm)],[1692:[bind(A,$thf( h )),bind(B,$thf( g ))]]) ).
thf(2467,plain,
( ( g @ there_exists )
| ( ( g @ ( h @ f1 ) )
= h ) ),
inference(simplifyReflect,[status(thm)],[1693,26]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ compose ) @ there_exists )
| ( ( A @ domain )
!= ( B @ codomain ) )
| ~ ( A @ domain @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition2) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ compose ) @ there_exists )
| ( ( A @ domain )
!= ( B @ codomain ) )
| ~ ( A @ domain @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(8825,plain,
$false,
inference(e,[status(thm)],[69,56,52,74,2053,569,32,63,960,2018,115,247,24,565,2024,78,261,29,60,270,260,70,33,1350,948,53,44,27,54,86,81,76,39,563,80,35,50,67,2044,40,26,258,55,75,568,58,246,82,36,30,2467,47,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39 % Computer : n002.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 22:51:07 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.89/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.30/1.19 % [INFO] Parsing done (202ms).
% 1.47/1.20 % [INFO] Running in sequential loop mode.
% 2.19/1.61 % [INFO] eprover registered as external prover.
% 2.19/1.62 % [INFO] Scanning for conjecture ...
% 2.38/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 22 axioms. Running axiom selection ...
% 2.38/1.79 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 2.58/1.83 % [INFO] Problem is propositional (TPTP CNF).
% 2.58/1.84 % [INFO] Type checking passed.
% 2.58/1.84 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 29.30/7.03 % External prover 'e' found a proof!
% 29.30/7.03 % [INFO] Killing All external provers ...
% 29.30/7.03 % Time passed: 6493ms (effective reasoning time: 5819ms)
% 29.30/7.03 % Axioms used in derivation (22): equivalence_implies_existence3, assume_ab_exists, existence_and_equality_implies_equivalence2, compose_codomain, indiscernibles3, domain_codomain_composition2, compose_domain, composition_implies_codomain, cancellation_for_product1, equivalence_implies_existence1, indiscernibles1, h_ab_equals_g_ab, assume_h_exists, equivalence_implies_existence2, codomain_has_elements, associativity_of_compose, cancellation_for_product2, domain_codomain_composition1, composition_implies_domain, domain_has_elements, existence_and_equality_implies_equivalence1, indiscernibles2
% 29.30/7.03 % No. of inferences in proof: 127
% 29.30/7.03 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 6493 ms resp. 5819 ms w/o parsing
% 30.00/7.10 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 30.00/7.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------