%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE088+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n017.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 07:43:10 AM UTC 2026
% Result : Theorem 16.43s 5.65s
% Output : Refutation 14.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 23
% Syntax : Number of formulae : 117 ( 79 unt; 0 typ; 2 def)
% Number of atoms : 173 ( 160 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 687 ( 61 ~; 40 |; 4 &; 572 @)
% ( 1 <=>; 9 =>; 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 : 13 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 136 ( 0 ^; 134 !; 0 ?; 136 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(multiplication_decl,type,
multiplication: $i > $i > $i ).
thf(domain_decl,type,
domain: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(antidomain_decl,type,
antidomain: $i > $i ).
thf(codomain_decl,type,
codomain: $i > $i ).
thf(coantidomain_decl,type,
coantidomain: $i > $i ).
thf(one_decl,type,
one: $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
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 ) )
= zero )
=> ( ( B @ antidomain @ ( A @ domain @ addition ) )
= ( B @ antidomain ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( A @ ( sk1 @ domain @ multiplication ) )
= zero )
=> ( ( A @ antidomain @ ( sk1 @ domain @ addition ) )
= ( A @ antidomain ) ) ) ) ) ).
thf(12,axiom,
! [A: $i] :
( ( A @ coantidomain @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain1) ).
thf(56,plain,
! [A: $i] :
( ( A @ coantidomain @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(35,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)],[5]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(86,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)],[22]) ).
thf(87,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)],[86]) ).
thf(88,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)],[87]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
= B )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[88]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
= B ) ),
inference(lifteq,[status(thm)],[89]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( B @ ( A @ domain @ multiplication ) )
= zero )
=> ( ( B @ antidomain @ ( A @ domain @ addition ) )
= ( B @ antidomain ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( B @ ( A @ domain @ multiplication ) )
= zero )
=> ( ( B @ antidomain @ ( A @ domain @ addition ) )
= ( B @ antidomain ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(23,plain,
~ ! [A: $i,B: $i] :
( ( ( B @ ( A @ domain @ multiplication ) )
= zero )
=> ( ( B @ antidomain @ ( A @ domain @ addition ) )
= ( B @ antidomain ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
( ( ( sk2 @ antidomain @ ( sk1 @ domain @ addition ) )
!= ( sk2 @ antidomain ) )
& ( ( sk2 @ ( sk1 @ domain @ multiplication ) )
= zero ) ),
inference(cnf,[status(esa)],[23]) ).
thf(26,plain,
( ( sk2 @ antidomain @ ( sk1 @ domain @ addition ) )
!= ( sk2 @ antidomain ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(28,plain,
( ( sk2 @ antidomain @ ( sk1 @ domain @ addition ) )
!= ( sk2 @ antidomain ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( sk2 @ antidomain @ ( sk1 @ domain @ addition ) ) )
| ( B
!= ( sk2 @ antidomain ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[91,28]) ).
thf(109,plain,
( ( ( sk2 @ antidomain )
!= ( sk2 @ antidomain ) )
| ~ ( sk2 @ antidomain @ ( sk1 @ domain @ leq ) ) ),
inference(pattern_uni,[status(thm)],[108:[bind(A,$thf( sk1 @ domain )),bind(B,$thf( sk2 @ antidomain ))]]) ).
thf(110,plain,
~ ( sk2 @ antidomain @ ( sk1 @ domain @ leq ) ),
inference(simp,[status(thm)],[109]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ antidomain @ ( A @ antidomain @ antidomain @ addition ) )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
thf(74,plain,
! [A: $i] :
( ( A @ antidomain @ ( A @ antidomain @ antidomain @ addition ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(57,plain,
! [A: $i] :
( ( A @ coantidomain @ ( A @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[56]) ).
thf(58,plain,
! [A: $i] :
( ( A @ coantidomain @ ( A @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[57]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(41,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(42,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[41]) ).
thf(43,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[42]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( ( A @ coantidomain @ ( A @ multiplication ) )
!= ( B @ ( one @ multiplication ) ) )
| ( zero = B ) ),
inference(paramod_ordered,[status(thm)],[58,43]) ).
thf(282,plain,
( ( one @ coantidomain )
= zero ),
inference(pattern_uni,[status(thm)],[281:[bind(A,$thf( one )),bind(B,$thf( one @ coantidomain ))]]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ codomain )
= ( A @ coantidomain @ coantidomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain4) ).
thf(29,plain,
! [A: $i] :
( ( A @ codomain )
= ( A @ coantidomain @ coantidomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(30,plain,
! [A: $i] :
( ( A @ codomain )
= ( A @ coantidomain @ coantidomain ) ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [A: $i] :
( ( A @ coantidomain @ coantidomain )
= ( A @ codomain ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(306,plain,
! [A: $i] :
( ( ( one @ coantidomain )
!= ( A @ coantidomain ) )
| ( ( zero @ coantidomain )
= ( A @ codomain ) ) ),
inference(paramod_ordered,[status(thm)],[282,31]) ).
thf(307,plain,
( ( zero @ coantidomain )
= ( one @ codomain ) ),
inference(pattern_uni,[status(thm)],[306:[bind(A,$thf( one ))]]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ coantidomain @ coantidomain @ multiplication ) @ coantidomain @ ( B @ ( A @ multiplication ) @ coantidomain @ addition ) )
= ( B @ ( A @ coantidomain @ coantidomain @ multiplication ) @ coantidomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain2) ).
thf(65,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ coantidomain @ coantidomain @ multiplication ) @ coantidomain @ ( B @ ( A @ multiplication ) @ coantidomain @ addition ) )
= ( B @ ( A @ coantidomain @ coantidomain @ multiplication ) @ coantidomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(382,plain,
! [A: $i] :
( ( ( zero @ coantidomain )
!= ( A @ coantidomain ) )
| ( ( one @ codomain @ coantidomain )
= ( A @ codomain ) ) ),
inference(paramod_ordered,[status(thm)],[307,31]) ).
thf(383,plain,
( ( one @ codomain @ coantidomain )
= ( zero @ codomain ) ),
inference(pattern_uni,[status(thm)],[382:[bind(A,$thf( zero ))]]) ).
thf(398,plain,
! [A: $i] :
( ( ( one @ codomain @ coantidomain )
!= ( A @ coantidomain ) )
| ( ( zero @ codomain @ coantidomain )
= ( A @ codomain ) ) ),
inference(paramod_ordered,[status(thm)],[383,31]) ).
thf(399,plain,
( ( zero @ codomain @ coantidomain )
= ( one @ codomain @ codomain ) ),
inference(pattern_uni,[status(thm)],[398:[bind(A,$thf( one @ codomain ))]]) ).
thf(420,plain,
! [A: $i] :
( ( ( zero @ codomain @ coantidomain )
!= ( A @ coantidomain ) )
| ( ( one @ codomain @ codomain @ coantidomain )
= ( A @ codomain ) ) ),
inference(paramod_ordered,[status(thm)],[399,31]) ).
thf(421,plain,
( ( one @ codomain @ codomain @ coantidomain )
= ( zero @ codomain @ codomain ) ),
inference(pattern_uni,[status(thm)],[420:[bind(A,$thf( zero @ codomain ))]]) ).
thf(566,plain,
! [A: $i] :
( ( ( one @ codomain @ codomain @ coantidomain )
!= ( A @ coantidomain ) )
| ( ( zero @ codomain @ codomain @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[421,58]) ).
thf(567,plain,
( ( zero @ codomain @ codomain @ ( one @ codomain @ codomain @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[566:[bind(A,$thf( one @ codomain @ codomain ))]]) ).
thf(19,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(77,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(78,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[77]) ).
thf(79,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[78]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
thf(83,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)],[21]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( A @ antidomain @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
thf(44,plain,
! [A: $i] :
( ( A @ ( A @ antidomain @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(45,plain,
! [A: $i] :
( ( A @ ( A @ antidomain @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [A: $i] :
( ( A @ ( A @ antidomain @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[45]) ).
thf(423,plain,
! [A: $i] :
( ( ( zero @ codomain @ coantidomain )
!= ( A @ coantidomain ) )
| ( ( one @ codomain @ codomain @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[399,58]) ).
thf(424,plain,
( ( one @ codomain @ codomain @ ( zero @ codomain @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[423:[bind(A,$thf( zero @ codomain ))]]) ).
thf(11,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(53,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(54,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[53]) ).
thf(55,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[54]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ antidomain @ multiplication ) )
!= ( one @ ( B @ multiplication ) ) )
| ( zero = B ) ),
inference(paramod_ordered,[status(thm)],[46,55]) ).
thf(165,plain,
( ( one @ antidomain )
= zero ),
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( one )),bind(B,$thf( one @ antidomain ))]]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
thf(38,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)],[6]) ).
thf(150,plain,
! [A: $i] :
( ( ( zero @ ( A @ addition ) )
!= ( sk2 @ antidomain @ ( sk1 @ domain @ addition ) ) )
| ( A
!= ( sk2 @ antidomain ) ) ),
inference(paramod_ordered,[status(thm)],[79,28]) ).
thf(156,plain,
( ( ( sk2 @ antidomain )
!= zero )
| ( ( sk2 @ antidomain )
!= ( sk1 @ domain ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(25,plain,
( ( sk2 @ ( sk1 @ domain @ multiplication ) )
= zero ),
inference(cnfConj,[status(thm)],[24]) ).
thf(27,plain,
( ( sk2 @ ( sk1 @ domain @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[25]) ).
thf(112,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ domain @ multiplication ) )
!= ( A @ ( one @ multiplication ) ) )
| ( zero = A ) ),
inference(paramod_ordered,[status(thm)],[27,43]) ).
thf(120,plain,
! [A: $i] :
( ( sk2 != A )
| ( ( sk1 @ domain )
!= one )
| ( zero = A ) ),
inference(simp,[status(thm)],[112]) ).
thf(124,plain,
( ( ( sk1 @ domain )
!= one )
| ( sk2 = zero ) ),
inference(simp,[status(thm)],[120]) ).
thf(14,axiom,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(62,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(63,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[62]) ).
thf(64,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[63]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(32,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(33,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[32]) ).
thf(34,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[33]) ).
thf(561,plain,
! [A: $i] :
( ( ( one @ codomain @ codomain @ coantidomain )
!= ( A @ coantidomain ) )
| ( ( zero @ codomain @ codomain @ coantidomain )
= ( A @ codomain ) ) ),
inference(paramod_ordered,[status(thm)],[421,31]) ).
thf(562,plain,
( ( zero @ codomain @ codomain @ coantidomain )
= ( one @ codomain @ codomain @ codomain ) ),
inference(pattern_uni,[status(thm)],[561:[bind(A,$thf( one @ codomain @ codomain ))]]) ).
thf(401,plain,
! [A: $i] :
( ( ( one @ codomain @ coantidomain )
!= ( A @ coantidomain ) )
| ( ( zero @ codomain @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[383,58]) ).
thf(402,plain,
( ( zero @ codomain @ ( one @ codomain @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[401:[bind(A,$thf( one @ codomain ))]]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ coantidomain @ ( A @ coantidomain @ coantidomain @ addition ) )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain3) ).
thf(59,plain,
! [A: $i] :
( ( A @ coantidomain @ ( A @ coantidomain @ coantidomain @ addition ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ domain )
= ( A @ antidomain @ antidomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
thf(71,plain,
! [A: $i] :
( ( A @ domain )
= ( A @ antidomain @ antidomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ antidomain @ antidomain @ ( A @ multiplication ) @ antidomain @ ( B @ ( A @ multiplication ) @ antidomain @ addition ) )
= ( B @ antidomain @ antidomain @ ( A @ multiplication ) @ antidomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
thf(47,plain,
! [A: $i,B: $i] :
( ( B @ antidomain @ antidomain @ ( A @ multiplication ) @ antidomain @ ( B @ ( A @ multiplication ) @ antidomain @ addition ) )
= ( B @ antidomain @ antidomain @ ( A @ multiplication ) @ antidomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( B @ antidomain @ antidomain @ ( A @ multiplication ) @ antidomain @ ( B @ ( A @ multiplication ) @ antidomain @ addition ) )
= ( B @ antidomain @ antidomain @ ( A @ multiplication ) @ antidomain ) ),
inference(cnf,[status(esa)],[47]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( B @ antidomain @ antidomain @ ( A @ multiplication ) @ antidomain @ ( B @ ( A @ multiplication ) @ antidomain @ addition ) )
= ( B @ antidomain @ antidomain @ ( A @ multiplication ) @ antidomain ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(80,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(130,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk2 @ ( sk1 @ domain @ multiplication ) ) )
| ( A = zero ) ),
inference(paramod_ordered,[status(thm)],[55,27]) ).
thf(144,plain,
! [A: $i] :
( ( sk2 != one )
| ( A
!= ( sk1 @ domain ) )
| ( A = zero ) ),
inference(simp,[status(thm)],[130]) ).
thf(146,plain,
( ( sk2 != one )
| ( ( sk1 @ domain )
= zero ) ),
inference(simp,[status(thm)],[144]) ).
thf(194,plain,
( ( ( sk2 @ antidomain )
!= ( one @ antidomain ) )
| ( zero != zero )
| ( ( sk2 @ antidomain )
!= ( sk1 @ domain ) ) ),
inference(paramod_ordered,[status(thm)],[165,156]) ).
thf(195,plain,
( ( ( sk2 @ antidomain )
!= ( one @ antidomain ) )
| ( ( sk2 @ antidomain )
!= ( sk1 @ domain ) ) ),
inference(simp,[status(thm)],[194]) ).
thf(200,plain,
( ( sk2 != one )
| ( ( sk2 @ antidomain )
!= ( sk1 @ domain ) ) ),
inference(simp,[status(thm)],[195]) ).
thf(409,plain,
( ( ( sk2 @ antidomain )
!= ( one @ antidomain ) )
| ( sk2 != one )
| ( ( sk1 @ domain )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[165,200]) ).
thf(410,plain,
( ( sk2 != one )
| ( sk2 != one )
| ( ( sk1 @ domain )
!= zero ) ),
inference(simp,[status(thm)],[409]) ).
thf(411,plain,
( ( sk2 != one )
| ( ( sk1 @ domain )
!= zero ) ),
inference(simp,[status(thm)],[410]) ).
thf(412,plain,
( ( ( sk1 @ domain )
!= ( sk1 @ domain ) )
| ( sk2 != one )
| ( zero != zero )
| ( sk2 != one ) ),
inference(paramod_ordered,[status(thm)],[146,411]) ).
thf(413,plain,
( ( ( sk1 @ domain )
!= ( sk1 @ domain ) )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[412]) ).
thf(414,plain,
sk2 != one,
inference(pattern_uni,[status(thm)],[413:[]]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
thf(50,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)],[10]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) )
= ( C @ ( B @ ( A @ addition ) @ multiplication ) ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(68,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1297,plain,
$false,
inference(e,[status(thm)],[56,37,110,74,307,65,41,567,91,43,79,83,421,46,29,424,165,28,38,156,53,124,77,64,32,34,562,402,44,59,27,71,49,86,399,80,35,282,414,50,31,40,55,23,58,383,47,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE088+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.10 % 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
% 0.18/0.46 % Computer : n017.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Fri Sep 25 19:16:03 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 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
% 1.32/1.22 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.82/1.53 % [INFO] Parsing done (309ms).
% 1.82/1.56 % [INFO] Running in sequential loop mode.
% 3.09/2.19 % [INFO] eprover registered as external prover.
% 3.15/2.20 % [INFO] Scanning for conjecture ...
% 3.31/2.34 % [INFO] Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ...
% 3.44/2.45 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 3.65/2.51 % [INFO] Problem is first-order (TPTP FOF).
% 3.65/2.52 % [INFO] Type checking passed.
% 3.65/2.53 % [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 ...
% 16.43/5.64 % External prover 'e' found a proof!
% 16.43/5.64 % [INFO] Killing All external provers ...
% 16.43/5.64 % Time passed: 5032ms (effective reasoning time: 4076ms)
% 16.43/5.65 % 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)>
% 16.43/5.65 % Axioms used in derivation (20): additive_identity, domain4, codomain4, domain3, multiplicative_right_identity, codomain2, right_annihilation, domain1, left_annihilation, codomain1, additive_idempotence, additive_associativity, right_distributivity, domain2, order, additive_commutativity, multiplicative_left_identity, codomain3, multiplicative_associativity, left_distributivity
% 16.43/5.65 % No. of inferences in proof: 115
% 16.43/5.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5032 ms resp. 4076 ms w/o parsing
% 14.88/5.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.88/5.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------