%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE024+2 : 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 07:43:01 AM UTC 2026
% Result : Theorem 15.87s 9.97s
% Output : Refutation 16.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 23
% Syntax : Number of formulae : 130 ( 71 unt; 0 typ; 4 def)
% Number of atoms : 275 ( 153 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 906 ( 88 ~; 53 |; 27 &; 701 @)
% ( 4 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 188 ( 1 ^; 178 !; 5 ?; 188 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(test_decl,type,
test: $i > $o ).
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(multiplication_decl,type,
multiplication: $i > $i > $i ).
thf(c_decl,type,
c: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(one_decl,type,
one: $i ).
thf(complement_decl,type,
complement: $i > $i > $o ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( C @ test )
& ( B @ test ) )
=> ( ( ( A @ ( B @ c @ multiplication ) @ ( C @ c @ ( A @ multiplication ) @ addition ) )
= ( A @ ( B @ c @ multiplication ) ) )
=> ( ( C @ c @ ( A @ ( B @ multiplication ) @ multiplication ) )
= zero ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( ( sk1 @ ( A @ c @ multiplication ) @ ( B @ c @ ( sk1 @ multiplication ) @ addition ) )
= ( sk1 @ ( A @ c @ multiplication ) ) )
=> ( ( B @ c @ ( sk1 @ ( A @ multiplication ) @ multiplication ) )
= zero ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( A @ test )
& ( sk2 @ test ) )
=> ( ( ( sk1 @ ( sk2 @ c @ multiplication ) @ ( A @ c @ ( sk1 @ multiplication ) @ addition ) )
= ( sk1 @ ( sk2 @ c @ multiplication ) ) )
=> ( ( A @ c @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) )
= zero ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ complement ) ) ) ) ).
thf(16,axiom,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(86,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(87,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[86]) ).
thf(88,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[87]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(56,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ test )
<=> ? [B: $i] : ( A @ ( B @ complement ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_1) ).
thf(47,plain,
! [A: $i] :
( ( ? [B: $i] : ( A @ ( B @ complement ) )
=> ( A @ test ) )
& ( ( A @ test )
=> ? [B: $i] : ( A @ ( B @ complement ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(48,plain,
( ! [A: $i] :
( ? [B: $i] : ( A @ ( B @ complement ) )
=> ( A @ test ) )
& ! [A: $i] :
( ( A @ test )
=> ? [B: $i] : ( A @ ( B @ complement ) ) ) ),
inference(miniscope,[status(thm)],[47]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ test )
| ~ ( B @ ( C @ complement ) ) )
& ( ( A @ ( A @ sk4 @ complement ) )
| ~ ( A @ test ) ) ),
inference(cnf,[status(esa)],[48]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( A @ test )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[49]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( A @ test )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ addition ) @ c )
= ( B @ c @ ( A @ c @ multiplication ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_deMorgan1) ).
thf(89,plain,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ addition ) @ c )
= ( B @ c @ ( A @ c @ multiplication ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(83,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(84,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[83]) ).
thf(85,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[84]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(53,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,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(41,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)],[7]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(98,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)],[20]) ).
thf(4,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(32,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)],[4]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(29,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(30,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[30]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( C @ test )
& ( B @ test ) )
=> ( ( ( A @ ( B @ c @ multiplication ) @ ( C @ c @ ( A @ multiplication ) @ addition ) )
= ( A @ ( B @ c @ multiplication ) ) )
=> ( ( C @ c @ ( A @ ( B @ multiplication ) @ multiplication ) )
= zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ test )
& ( B @ test ) )
=> ( ( ( A @ ( B @ c @ multiplication ) @ ( C @ c @ ( A @ multiplication ) @ addition ) )
= ( A @ ( B @ c @ multiplication ) ) )
=> ( ( C @ c @ ( A @ ( B @ multiplication ) @ multiplication ) )
= zero ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ test )
& ( B @ test ) )
=> ( ( ( A @ ( B @ c @ multiplication ) @ ( C @ c @ ( A @ multiplication ) @ addition ) )
= ( A @ ( B @ c @ multiplication ) ) )
=> ( ( C @ c @ ( A @ ( B @ multiplication ) @ multiplication ) )
= zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
( ( ( sk3 @ c @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) )
!= zero )
& ( ( sk1 @ ( sk2 @ c @ multiplication ) @ ( sk3 @ c @ ( sk1 @ multiplication ) @ addition ) )
= ( sk1 @ ( sk2 @ c @ multiplication ) ) )
& ( sk3 @ test )
& ( sk2 @ test ) ),
inference(cnf,[status(esa)],[21]) ).
thf(26,plain,
( ( sk3 @ c @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) )
!= zero ),
inference(cnfConj,[status(thm)],[22]) ).
thf(28,plain,
( ( sk3 @ c @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) )
!= zero ),
inference(lifteq,[status(thm)],[26]) ).
thf(115,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk3 @ c @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[31,28]) ).
thf(116,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
!= ( sk3 @ c @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) ) ),
inference(simp,[status(thm)],[115]) ).
thf(120,plain,
! [A: $i] :
( ( A
!= ( sk3 @ c ) )
| ( ( sk1 @ ( sk2 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[116]) ).
thf(124,plain,
( ( sk1 @ ( sk2 @ multiplication ) )
!= zero ),
inference(simp,[status(thm)],[120]) ).
thf(225,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[34,124]) ).
thf(244,plain,
! [C: $i,B: $i,A: $i] :
( ( C != sk1 )
| ( ( B @ ( A @ multiplication ) )
!= sk2 )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[225]) ).
thf(255,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= sk2 )
| ( ( sk1 @ ( B @ multiplication ) @ ( A @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[244]) ).
thf(19,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(95,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)],[19]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[41]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(lifteq,[status(thm)],[42]) ).
thf(142,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[88,124]) ).
thf(143,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) ),
inference(simp,[status(thm)],[142]) ).
thf(147,plain,
! [A: $i] :
( ( sk1 != zero )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[143]) ).
thf(151,plain,
sk1 != zero,
inference(simp,[status(thm)],[147]) ).
thf(18,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(92,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(93,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[92]) ).
thf(94,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[93]) ).
thf(24,plain,
sk3 @ test,
inference(cnfConj,[status(thm)],[22]) ).
thf(5,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(35,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)],[5]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ addition ) @ addition ) )
= ( A @ ( B @ addition ) @ ( C @ addition ) ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(44,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(45,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[45]) ).
thf(145,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[31,124]) ).
thf(146,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) ),
inference(simp,[status(thm)],[145]) ).
thf(150,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[146]) ).
thf(152,plain,
sk2 != zero,
inference(simp,[status(thm)],[150]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_4) ).
thf(38,plain,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ test )
=> ( ( ( A @ c )
= B )
<=> ( B @ ( A @ complement ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
thf(59,plain,
! [A: $i,B: $i] :
( ( A @ test )
=> ( ( ( B @ ( A @ complement ) )
=> ( ( A @ c )
= B ) )
& ( ( ( A @ c )
= B )
=> ( B @ ( A @ complement ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(60,plain,
! [A: $i] :
( ( A @ test )
=> ( ! [B: $i] :
( ( B @ ( A @ complement ) )
=> ( ( A @ c )
= B ) )
& ! [B: $i] :
( ( ( A @ c )
= B )
=> ( B @ ( A @ complement ) ) ) ) ),
inference(miniscope,[status(thm)],[59]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ( A @ c )
= C )
| ~ ( C @ ( A @ complement ) )
| ~ ( A @ test ) )
& ( ( B @ ( A @ complement ) )
| ( ( A @ c )
!= B )
| ~ ( A @ test ) ) ),
inference(cnf,[status(esa)],[60]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ complement ) )
| ( ( A @ c )
!= B )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[61]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
!= B ) ),
inference(lifteq,[status(thm)],[62]) ).
thf(65,plain,
! [A: $i] :
( ( A @ c @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[64]) ).
thf(212,plain,
( ( sk3 @ c @ ( sk1 @ multiplication ) @ ( sk2 @ multiplication ) )
!= zero ),
inference(rewrite,[status(thm)],[28,34]) ).
thf(23,plain,
sk2 @ test,
inference(cnfConj,[status(thm)],[22]) ).
thf(670,plain,
! [A: $i] :
( ( ( sk2 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,65]) ).
thf(671,plain,
! [A: $i] :
( ( ( sk2 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[670]) ).
thf(672,plain,
sk2 @ c @ ( sk2 @ complement ),
inference(pattern_uni,[status(thm)],[671:[bind(A,$thf( sk2 ))]]) ).
thf(687,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[672,52]) ).
thf(688,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[687]) ).
thf(689,plain,
sk2 @ c @ test,
inference(pattern_uni,[status(thm)],[688:[bind(A,$thf( sk2 @ c )),bind(B,$thf( sk2 ))]]) ).
thf(262,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk3 @ c @ ( sk1 @ multiplication ) @ ( sk2 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[88,212]) ).
thf(263,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
!= ( sk3 @ c @ ( sk1 @ multiplication ) @ ( sk2 @ multiplication ) ) ),
inference(simp,[status(thm)],[262]) ).
thf(281,plain,
! [A: $i] :
( ( ( sk3 @ c @ ( sk1 @ multiplication ) )
!= zero )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[263]) ).
thf(291,plain,
( ( sk3 @ c @ ( sk1 @ multiplication ) )
!= zero ),
inference(simp,[status(thm)],[281]) ).
thf(25,plain,
( ( sk1 @ ( sk2 @ c @ multiplication ) @ ( sk3 @ c @ ( sk1 @ multiplication ) @ addition ) )
= ( sk1 @ ( sk2 @ c @ multiplication ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(27,plain,
( ( sk1 @ ( sk2 @ c @ multiplication ) @ ( sk3 @ c @ ( sk1 @ multiplication ) @ addition ) )
= ( sk1 @ ( sk2 @ c @ multiplication ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(50,plain,
! [A: $i] :
( ( A @ ( A @ sk4 @ complement ) )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[49]) ).
thf(481,plain,
! [A: $i] :
( ( ( sk3 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk4 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,50]) ).
thf(482,plain,
! [A: $i] :
( ( ( sk3 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk4 @ complement ) ) ),
inference(simp,[status(thm)],[481]) ).
thf(483,plain,
sk3 @ ( sk3 @ sk4 @ complement ),
inference(pattern_uni,[status(thm)],[482:[bind(A,$thf( sk3 ))]]) ).
thf(175,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) )
| ( ( sk3 @ c @ ( A @ multiplication ) )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[85,28]) ).
thf(194,plain,
! [A: $i] :
( ( sk1 != one )
| ( A != sk2 )
| ( ( sk3 @ c @ ( A @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[175]) ).
thf(198,plain,
( ( sk1 != one )
| ( ( sk3 @ c @ ( sk2 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[194]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(cnf,[status(esa)],[56]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(562,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( zero @ ( C @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[58,94]) ).
thf(563,plain,
! [A: $i] :
( ( A @ ( zero @ addition ) )
= A ),
inference(pattern_uni,[status(thm)],[562:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ multiplication ) @ c )
= ( B @ c @ ( A @ c @ addition ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_deMorgan2) ).
thf(80,plain,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ multiplication ) @ c )
= ( B @ c @ ( A @ c @ addition ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(39,plain,
! [A: $i] :
( ( ( A @ c )
= zero )
| ( A @ test ) ),
inference(cnf,[status(esa)],[38]) ).
thf(40,plain,
! [A: $i] :
( ( A @ test )
| ( ( A @ c )
= zero ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(54,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[53]) ).
thf(55,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[54]) ).
thf(665,plain,
! [A: $i] :
( ( ( sk3 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,65]) ).
thf(666,plain,
! [A: $i] :
( ( ( sk3 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[665]) ).
thf(667,plain,
sk3 @ c @ ( sk3 @ complement ),
inference(pattern_uni,[status(thm)],[666:[bind(A,$thf( sk3 ))]]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ complement ) )
<=> ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).
thf(68,plain,
! [A: $i,B: $i] :
( ( ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) )
=> ( A @ ( B @ complement ) ) )
& ( ( A @ ( B @ complement ) )
=> ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(484,plain,
! [A: $i] :
( ( ( sk2 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk4 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,50]) ).
thf(485,plain,
! [A: $i] :
( ( ( sk2 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk4 @ complement ) ) ),
inference(simp,[status(thm)],[484]) ).
thf(486,plain,
sk2 @ ( sk2 @ sk4 @ complement ),
inference(pattern_uni,[status(thm)],[485:[bind(A,$thf( sk2 ))]]) ).
thf(112,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk3 @ c @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[88,28]) ).
thf(113,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
!= ( sk3 @ c @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(118,plain,
! [A: $i] :
( ( ( sk3 @ c )
!= zero )
| ( A
!= ( sk1 @ ( sk2 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[113]) ).
thf(122,plain,
( ( sk3 @ c )
!= zero ),
inference(simp,[status(thm)],[118]) ).
thf(674,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ ( sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[667,52]) ).
thf(675,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ ( sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[674]) ).
thf(676,plain,
sk3 @ c @ test,
inference(pattern_uni,[status(thm)],[675:[bind(A,$thf( sk3 @ c )),bind(B,$thf( sk3 ))]]) ).
thf(2925,plain,
$false,
inference(e,[status(thm)],[88,56,52,89,85,53,41,98,255,95,43,151,94,24,37,46,152,29,38,21,92,65,124,212,689,32,34,44,291,59,27,86,672,483,198,563,80,35,50,31,40,55,23,58,667,47,68,486,122,83,676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE024+2 : 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
% 0.14/5.42 % Computer : n018.cluster.edu
% 0.14/5.42 % Model : x86_64 x86_64
% 0.14/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.42 % Memory : 8046.5625MB
% 0.14/5.42 % OS : Linux 6.8.0-71-generic
% 0.14/5.43 % CPULimit : 300
% 0.14/5.43 % WCLimit : 300
% 0.14/5.43 % DateTime : Fri Sep 25 19:16:57 UTC 2026
% 0.14/5.43 % CPUTime :
% 0.14/5.43 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
% 0.19/6.02 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.35/6.23 % [INFO] Parsing done (213ms).
% 1.35/6.25 % [INFO] Running in sequential loop mode.
% 2.08/6.65 % [INFO] eprover registered as external prover.
% 2.08/6.66 % [INFO] Scanning for conjecture ...
% 2.30/6.76 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 2.45/6.83 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.45/6.87 % [INFO] Problem is first-order (TPTP FOF).
% 2.45/6.87 % [INFO] Type checking passed.
% 2.45/6.88 % [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 ...
% 15.87/9.96 % External prover 'e' found a proof!
% 15.87/9.97 % [INFO] Killing All external provers ...
% 15.87/9.97 % Time passed: 4393ms (effective reasoning time: 3714ms)
% 15.87/9.97 % 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)>
% 15.87/9.97 % Axioms used in derivation (18): test_3, test_4, left_annihilation, right_distributivity, multiplicative_right_identity, test_1, test_deMorgan2, additive_identity, additive_idempotence, additive_associativity, order, additive_commutativity, right_annihilation, test_deMorgan1, test_2, multiplicative_left_identity, multiplicative_associativity, left_distributivity
% 15.87/9.97 % No. of inferences in proof: 126
% 15.87/9.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4393 ms resp. 3714 ms w/o parsing
% 16.59/10.05 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.59/10.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------