%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE060+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n018.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 07:43:07 AM UTC 2026
% Result : Theorem 37.82s 9.28s
% Output : Refutation 31.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 20
% Syntax : Number of formulae : 115 ( 71 unt; 0 typ; 2 def)
% Number of atoms : 185 ( 163 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 667 ( 97 ~; 60 |; 3 &; 502 @)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 147 ( 0 ^; 145 !; 0 ?; 147 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(domain_decl,type,
domain: $i > $i ).
thf(multiplication_decl,type,
multiplication: $i > $i > $i ).
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(one_decl,type,
one: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ domain @ multiplication ) @ domain )
= ( B @ domain @ ( A @ domain @ multiplication ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
( ( A @ ( sk1 @ domain @ multiplication ) @ domain )
!= ( A @ domain @ ( sk1 @ domain @ multiplication ) ) ) ) ) ).
thf(15,axiom,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(64,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(65,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[64]) ).
thf(66,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[65]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( B @ ( A @ domain @ multiplication ) @ domain )
= ( B @ domain @ ( A @ domain @ multiplication ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ domain @ multiplication ) @ domain )
= ( B @ domain @ ( A @ domain @ multiplication ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(20,plain,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ domain @ multiplication ) @ domain )
= ( B @ domain @ ( A @ domain @ multiplication ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,plain,
( ( sk2 @ ( sk1 @ domain @ multiplication ) @ domain )
!= ( sk2 @ domain @ ( sk1 @ domain @ multiplication ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(22,plain,
( ( sk2 @ domain @ ( sk1 @ domain @ multiplication ) )
!= ( sk2 @ ( sk1 @ domain @ multiplication ) @ domain ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(89,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ domain @ ( sk1 @ domain @ multiplication ) ) )
| ( ( sk2 @ ( sk1 @ domain @ multiplication ) @ domain )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[66,22]) ).
thf(93,plain,
! [A: $i] :
( ( ( sk2 @ domain )
!= zero )
| ( A
!= ( sk1 @ domain ) )
| ( ( sk2 @ ( sk1 @ domain @ multiplication ) @ domain )
!= zero ) ),
inference(simp,[status(thm)],[89]) ).
thf(95,plain,
( ( ( sk2 @ domain )
!= zero )
| ( ( sk2 @ ( sk1 @ domain @ multiplication ) @ domain )
!= zero ) ),
inference(simp,[status(thm)],[93]) ).
thf(343,plain,
( ( zero != zero )
| ( ( sk2 @ ( sk1 @ domain @ multiplication ) @ domain )
!= ( sk2 @ domain ) )
| ( ( sk2 @ domain )
!= zero ) ),
inference(eqfactor_ordered,[status(thm)],[95]) ).
thf(347,plain,
( ( ( sk2 @ ( sk1 @ domain @ multiplication ) )
!= sk2 )
| ( ( sk2 @ domain )
!= zero ) ),
inference(simp,[status(thm)],[343]) ).
thf(19,axiom,
! [A: $i] :
( ( one @ ( A @ domain @ addition ) )
= one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
thf(75,plain,
! [A: $i] :
( ( one @ ( A @ domain @ addition ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(76,plain,
! [A: $i] :
( ( one @ ( A @ domain @ addition ) )
= one ),
inference(cnf,[status(esa)],[75]) ).
thf(77,plain,
! [A: $i] :
( ( one @ ( A @ domain @ addition ) )
= one ),
inference(lifteq,[status(thm)],[76]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(35,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ addition ) )
= B )
=> ( B @ ( A @ leq ) ) )
& ( ( B @ ( A @ leq ) )
=> ( ( B @ ( A @ addition ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(36,plain,
( ! [A: $i,B: $i] :
( ( ( B @ ( A @ addition ) )
= B )
=> ( B @ ( A @ leq ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( ( B @ ( A @ addition ) )
= B ) ) ),
inference(miniscope,[status(thm)],[35]) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ leq ) )
| ( ( D @ ( C @ addition ) )
!= D ) )
& ( ( ( B @ ( A @ addition ) )
= B )
| ~ ( B @ ( A @ leq ) ) ) ),
inference(cnf,[status(esa)],[36]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
!= B ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
!= B ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
!= B ) ),
inference(simp,[status(thm)],[41]) ).
thf(487,plain,
! [C: $i,B: $i,A: $i] :
( ( ( one @ ( A @ domain @ addition ) )
!= ( C @ ( B @ addition ) ) )
| ( C @ ( B @ leq ) )
| ( one != C ) ),
inference(paramod_ordered,[status(thm)],[77,42]) ).
thf(488,plain,
! [A: $i] :
( ( one @ ( A @ domain @ leq ) )
| ( one != one ) ),
inference(pattern_uni,[status(thm)],[487:[bind(A,$thf( D )),bind(B,$thf( D @ domain )),bind(C,$thf( one ))]]) ).
thf(511,plain,
! [A: $i] : ( one @ ( A @ domain @ leq ) ),
inference(simp,[status(thm)],[488]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(52,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(32,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(5,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(29,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(30,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[30]) ).
thf(305,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( zero @ ( C @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[34,31]) ).
thf(306,plain,
! [A: $i] :
( ( A @ ( zero @ addition ) )
= A ),
inference(pattern_uni,[status(thm)],[305:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(678,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( zero @ addition ) )
!= ( C @ ( B @ addition ) ) )
| ( C @ ( B @ leq ) )
| ( A != C ) ),
inference(paramod_ordered,[status(thm)],[306,42]) ).
thf(679,plain,
! [A: $i] :
( ( A @ ( zero @ leq ) )
| ( A != A ) ),
inference(pattern_uni,[status(thm)],[678:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(710,plain,
! [A: $i] : ( A @ ( zero @ leq ) ),
inference(simp,[status(thm)],[679]) ).
thf(18,axiom,
( ( zero @ domain )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
thf(73,plain,
( ( zero @ domain )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(43,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(53,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[53]) ).
thf(360,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk2 @ ( sk1 @ domain @ multiplication ) ) )
| ( A != sk2 )
| ( ( sk2 @ domain )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[54,347]) ).
thf(366,plain,
( ( sk2 != sk2 )
| ( ( sk1 @ domain )
!= one )
| ( ( sk2 @ domain )
!= zero ) ),
inference(simp,[status(thm)],[360]) ).
thf(373,plain,
( ( ( sk1 @ domain )
!= one )
| ( ( sk2 @ domain )
!= zero ) ),
inference(simp,[status(thm)],[366]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
thf(23,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ addition ) @ addition ) )
= ( A @ ( B @ addition ) @ ( C @ addition ) ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(46,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(74,plain,
( ( zero @ domain )
= zero ),
inference(lifteq,[status(thm)],[73]) ).
thf(44,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[43]) ).
thf(45,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[44]) ).
thf(88,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ domain @ ( sk1 @ domain @ multiplication ) ) )
| ( ( sk2 @ ( sk1 @ domain @ multiplication ) @ domain )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[45,22]) ).
thf(92,plain,
! [A: $i] :
( ( A
!= ( sk2 @ domain ) )
| ( ( sk1 @ domain )
!= zero )
| ( ( sk2 @ ( sk1 @ domain @ multiplication ) @ domain )
!= zero ) ),
inference(simp,[status(thm)],[88]) ).
thf(94,plain,
( ( ( sk1 @ domain )
!= zero )
| ( ( sk2 @ ( sk1 @ domain @ multiplication ) @ domain )
!= zero ) ),
inference(simp,[status(thm)],[92]) ).
thf(101,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ ( sk1 @ domain @ multiplication ) ) )
| ( ( sk1 @ domain )
!= zero )
| ( ( zero @ domain )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[45,94]) ).
thf(104,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( sk1 @ domain )
!= zero )
| ( ( sk1 @ domain )
!= zero )
| ( ( zero @ domain )
!= zero ) ),
inference(simp,[status(thm)],[101]) ).
thf(111,plain,
( ( ( sk1 @ domain )
!= zero )
| ( ( zero @ domain )
!= zero ) ),
inference(simp,[status(thm)],[104]) ).
thf(117,plain,
( ( ( sk1 @ domain )
!= zero )
| ( zero != zero ) ),
inference(rewrite,[status(thm)],[111,74]) ).
thf(118,plain,
( ( sk1 @ domain )
!= zero ),
inference(simp,[status(thm)],[117]) ).
thf(119,plain,
( ( ( sk1 @ domain )
!= ( zero @ domain ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[74,118]) ).
thf(120,plain,
( ( sk1 @ domain )
!= ( zero @ domain ) ),
inference(simp,[status(thm)],[119]) ).
thf(121,plain,
sk1 != zero,
inference(simp,[status(thm)],[120]) ).
thf(334,plain,
( ( ( sk2 @ ( sk1 @ domain @ multiplication ) @ domain )
!= ( zero @ domain ) )
| ( ( sk2 @ domain )
!= zero )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[74,95]) ).
thf(335,plain,
( ( ( sk2 @ ( sk1 @ domain @ multiplication ) @ domain )
!= ( zero @ domain ) )
| ( ( sk2 @ domain )
!= zero ) ),
inference(simp,[status(thm)],[334]) ).
thf(348,plain,
( ( ( sk2 @ ( sk1 @ domain @ multiplication ) )
!= zero )
| ( ( sk2 @ domain )
!= zero ) ),
inference(simp,[status(thm)],[335]) ).
thf(14,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(61,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(26,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[27]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ ( A @ domain @ multiplication ) @ ( A @ addition ) )
= ( A @ ( A @ domain @ multiplication ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
thf(70,plain,
! [A: $i] :
( ( A @ ( A @ domain @ multiplication ) @ ( A @ addition ) )
= ( A @ ( A @ domain @ multiplication ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(361,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ ( sk1 @ domain @ multiplication ) ) )
| ( sk2 != zero )
| ( ( sk2 @ domain )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[66,347]) ).
thf(364,plain,
! [A: $i] :
( ( sk2 != zero )
| ( A
!= ( sk1 @ domain ) )
| ( sk2 != zero )
| ( ( sk2 @ domain )
!= zero ) ),
inference(simp,[status(thm)],[361]) ).
thf(372,plain,
( ( sk2 != zero )
| ( ( sk2 @ domain )
!= zero ) ),
inference(simp,[status(thm)],[364]) ).
thf(421,plain,
( ( ( sk2 @ domain )
!= ( zero @ domain ) )
| ( sk2 != zero )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[74,372]) ).
thf(422,plain,
( ( ( sk2 @ domain )
!= ( zero @ domain ) )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[421]) ).
thf(423,plain,
( ( sk2 != zero )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[422]) ).
thf(424,plain,
sk2 != zero,
inference(simp,[status(thm)],[423]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
thf(49,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(287,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( one @ ( C @ domain @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[34,77]) ).
thf(288,plain,
! [A: $i] :
( ( A @ domain @ ( one @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[287:[bind(A,$thf( D @ domain )),bind(B,$thf( one )),bind(C,$thf( D ))]]) ).
thf(318,plain,
! [A: $i] :
( ( A @ domain @ ( one @ addition ) )
= one ),
inference(simp,[status(thm)],[288]) ).
thf(498,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ addition ) )
!= ( C @ ( B @ addition ) ) )
| ( C @ ( B @ leq ) )
| ( A != C ) ),
inference(paramod_ordered,[status(thm)],[28,42]) ).
thf(499,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ( A != A ) ),
inference(pattern_uni,[status(thm)],[498:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(509,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(simp,[status(thm)],[499]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(cnf,[status(esa)],[46]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[47]) ).
thf(62,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[61]) ).
thf(63,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[62]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) @ domain )
= ( B @ domain @ ( A @ domain @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain5) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) @ domain )
= ( B @ domain @ ( A @ domain @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(363,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk2 @ ( sk1 @ domain @ multiplication ) ) )
| ( A != sk2 )
| ( ( sk2 @ domain )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[63,347]) ).
thf(370,plain,
( ( sk2 != one )
| ( ( sk1 @ domain )
!= sk2 )
| ( ( sk2 @ domain )
!= zero ) ),
inference(simp,[status(thm)],[363]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
= B )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
= B ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
thf(55,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ multiplication ) @ domain )
= ( B @ domain @ ( A @ multiplication ) @ domain ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ multiplication ) @ domain )
= ( B @ domain @ ( A @ multiplication ) @ domain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(14563,plain,
$false,
inference(e,[status(thm)],[347,511,52,710,77,73,66,43,373,42,25,20,46,29,121,348,61,74,28,70,424,45,64,32,34,22,118,54,49,318,509,306,35,48,63,95,67,370,31,40,26,55,23,75,58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE060+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40 % Computer : n018.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Fri Sep 25 19:21:21 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.24/1.29 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.56/1.48 % [INFO] Parsing done (186ms).
% 1.56/1.49 % [INFO] Running in sequential loop mode.
% 2.24/1.89 % [INFO] eprover registered as external prover.
% 2.42/1.90 % [INFO] Scanning for conjecture ...
% 2.42/1.99 % [INFO] Found a conjecture (or negated_conjecture) and 17 axioms. Running axiom selection ...
% 2.63/2.05 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 2.63/2.08 % [INFO] Problem is first-order (TPTP FOF).
% 2.63/2.09 % [INFO] Type checking passed.
% 2.63/2.10 % [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 ...
% 37.82/9.28 % External prover 'e' found a proof!
% 37.82/9.28 % [INFO] Killing All external provers ...
% 37.82/9.28 % Time passed: 8658ms (effective reasoning time: 7778ms)
% 37.82/9.28 % Solved by 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)>
% 37.82/9.28 % Axioms used in derivation (17): additive_identity, domain4, domain5, domain3, left_annihilation, multiplicative_right_identity, right_annihilation, multiplicative_left_identity, domain1, additive_idempotence, additive_associativity, right_distributivity, domain2, order, additive_commutativity, multiplicative_associativity, left_distributivity
% 37.82/9.28 % No. of inferences in proof: 113
% 37.82/9.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8658 ms resp. 7778 ms w/o parsing
% 31.69/9.35 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 31.69/9.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------