%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE008+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 07:42:56 AM UTC 2026
% Result : Theorem 65.23s 15.00s
% Output : Refutation 65.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 20
% Syntax : Number of formulae : 124 ( 59 unt; 0 typ; 3 def)
% Number of atoms : 334 ( 174 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1004 ( 144 ~; 122 |; 37 &; 667 @)
% ( 6 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 173 ( 0 ^; 167 !; 3 ?; 173 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(test_decl,type,
test: $i > $o ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(multiplication_decl,type,
multiplication: $i > $i > $i ).
thf(c_decl,type,
c: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(one_decl,type,
one: $i ).
thf(complement_decl,type,
complement: $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: $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( C @ test )
=> ( ( ( ( zero @ ( A @ ( C @ c @ multiplication ) @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( B @ ( C @ multiplication ) @ ( A @ leq ) ) )
& ( ( B @ ( C @ multiplication ) @ ( A @ leq ) )
=> ( ( zero @ ( A @ ( C @ c @ multiplication ) @ leq ) )
& ( B @ ( A @ leq ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ test )
=> ( ( ( ( zero @ ( sk1 @ ( B @ c @ multiplication ) @ leq ) )
& ( A @ ( sk1 @ leq ) ) )
=> ( A @ ( B @ multiplication ) @ ( sk1 @ leq ) ) )
& ( ( A @ ( B @ multiplication ) @ ( sk1 @ leq ) )
=> ( ( zero @ ( sk1 @ ( B @ c @ multiplication ) @ leq ) )
& ( A @ ( sk1 @ leq ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( A @ test )
=> ( ( ( ( zero @ ( sk1 @ ( A @ c @ multiplication ) @ leq ) )
& ( sk2 @ ( sk1 @ leq ) ) )
=> ( sk2 @ ( A @ multiplication ) @ ( sk1 @ leq ) ) )
& ( ( sk2 @ ( A @ multiplication ) @ ( sk1 @ leq ) )
=> ( ( zero @ ( sk1 @ ( A @ c @ multiplication ) @ leq ) )
& ( sk2 @ ( sk1 @ leq ) ) ) ) ) ) ) ) ).
thf(14,axiom,
! [A: $i] :
( ( A @ test )
<=> ? [B: $i] : ( A @ ( B @ complement ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_1) ).
thf(69,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)],[14]) ).
thf(12,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(63,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(64,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[63]) ).
thf(65,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[64]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( C @ test )
=> ( ( B @ ( C @ multiplication ) @ ( A @ leq ) )
<=> ( ( zero @ ( A @ ( C @ c @ multiplication ) @ leq ) )
& ( B @ ( A @ leq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ test )
=> ( ( B @ ( C @ multiplication ) @ ( A @ leq ) )
<=> ( ( zero @ ( A @ ( C @ c @ multiplication ) @ leq ) )
& ( B @ ( A @ leq ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ test )
=> ( ( ( ( zero @ ( A @ ( C @ c @ multiplication ) @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( B @ ( C @ multiplication ) @ ( A @ leq ) ) )
& ( ( B @ ( C @ multiplication ) @ ( A @ leq ) )
=> ( ( zero @ ( A @ ( C @ c @ multiplication ) @ leq ) )
& ( B @ ( A @ leq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
( ( ~ ( sk2 @ ( sk3 @ multiplication ) @ ( sk1 @ leq ) )
| sk4 )
& ( ( zero @ ( sk1 @ ( sk3 @ c @ multiplication ) @ leq ) )
| sk4 )
& ( ( sk2 @ ( sk1 @ leq ) )
| sk4 )
& ( ~ sk4
| ~ ( zero @ ( sk1 @ ( sk3 @ c @ multiplication ) @ leq ) )
| ~ ( sk2 @ ( sk1 @ leq ) ) )
& ( ~ sk4
| ( sk2 @ ( sk3 @ multiplication ) @ ( sk1 @ leq ) ) )
& ( sk3 @ test ) ),
inference(cnf,[status(esa)],[19]) ).
thf(23,plain,
( ( sk2 @ ( sk1 @ leq ) )
| sk4 ),
inference(cnfConj,[status(thm)],[20]) ).
thf(21,plain,
( ~ ( sk2 @ ( sk3 @ multiplication ) @ ( sk1 @ leq ) )
| sk4 ),
inference(cnfConj,[status(thm)],[20]) ).
thf(141,plain,
( ( ( sk2 @ ( sk3 @ multiplication ) @ ( sk1 @ leq ) )
!= ( sk2 @ ( sk1 @ leq ) ) )
| ~ $true
| sk4
| sk4 ),
inference(paramod_ordered,[status(thm)],[23,21]) ).
thf(142,plain,
( ( ( sk2 @ ( sk3 @ multiplication ) @ ( sk1 @ leq ) )
!= ( sk2 @ ( sk1 @ leq ) ) )
| sk4 ),
inference(simp,[status(thm)],[141]) ).
thf(146,plain,
( ( ( sk2 @ ( sk3 @ multiplication ) )
!= sk2 )
| ( sk1 != sk1 )
| sk4 ),
inference(simp,[status(thm)],[142]) ).
thf(150,plain,
( ( ( sk2 @ ( sk3 @ multiplication ) )
!= sk2 )
| sk4 ),
inference(simp,[status(thm)],[146]) ).
thf(186,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk2 @ ( sk3 @ multiplication ) ) )
| ( A != sk2 )
| sk4 ),
inference(paramod_ordered,[status(thm)],[65,150]) ).
thf(202,plain,
( ( sk2 != one )
| ( sk3 != sk2 )
| sk4 ),
inference(simp,[status(thm)],[186]) ).
thf(13,axiom,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(66,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(67,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[66]) ).
thf(68,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[67]) ).
thf(22,plain,
( ~ sk4
| ~ ( zero @ ( sk1 @ ( sk3 @ c @ multiplication ) @ leq ) )
| ~ ( sk2 @ ( sk1 @ leq ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(116,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ ( sk3 @ c @ multiplication ) ) )
| ~ sk4
| ~ ( zero @ ( zero @ leq ) )
| ~ ( sk2 @ ( sk1 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[68,22]) ).
thf(120,plain,
! [A: $i] :
( ( sk1 != zero )
| ( A
!= ( sk3 @ c ) )
| ~ sk4
| ~ ( zero @ ( zero @ leq ) )
| ~ ( sk2 @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(125,plain,
( ( sk1 != zero )
| ~ sk4
| ~ ( zero @ ( zero @ leq ) )
| ~ ( sk2 @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(8,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(42,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)],[8]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[42]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) )
= ( C @ ( B @ ( A @ addition ) @ multiplication ) ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( D @ ( B @ multiplication ) ) )
| ( ( D @ ( C @ multiplication ) @ ( zero @ addition ) )
= ( D @ ( C @ ( B @ addition ) @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[68,44]) ).
thf(551,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( zero @ addition ) )
= ( zero @ ( B @ ( A @ addition ) @ multiplication ) ) ),
inference(pattern_uni,[status(thm)],[550:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( zero ))]]) ).
thf(561,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( zero @ addition ) )
= ( zero @ ( B @ ( A @ addition ) @ multiplication ) ) ),
inference(simp,[status(thm)],[551]) ).
thf(548,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( D @ ( C @ multiplication ) ) )
| ( ( zero @ ( D @ ( B @ multiplication ) @ addition ) )
= ( D @ ( C @ ( B @ addition ) @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[68,44]) ).
thf(549,plain,
! [B: $i,A: $i] :
( ( zero @ ( zero @ ( B @ multiplication ) @ addition ) )
= ( zero @ ( A @ ( B @ addition ) @ multiplication ) ) ),
inference(pattern_uni,[status(thm)],[548:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( zero ))]]) ).
thf(15,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(75,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(76,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[75]) ).
thf(77,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[76]) ).
thf(577,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(rewrite,[status(thm)],[549,68,77]) ).
thf(7,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(39,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)],[7]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(cnf,[status(esa)],[39]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[40]) ).
thf(584,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( D @ ( C @ ( B @ multiplication ) @ multiplication ) ) )
| ( ( D @ ( C @ multiplication ) @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[577,41]) ).
thf(585,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[584:[bind(A,$thf( F @ ( E @ multiplication ) )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( zero ))]]) ).
thf(621,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ),
inference(simp,[status(thm)],[585]) ).
thf(626,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(rewrite,[status(thm)],[621,577]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(214,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( zero @ ( C @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[35,77]) ).
thf(215,plain,
! [A: $i] :
( ( A @ ( zero @ addition ) )
= A ),
inference(pattern_uni,[status(thm)],[214:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(734,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(rewrite,[status(thm)],[561,626,215]) ).
thf(741,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( D @ ( C @ ( B @ multiplication ) @ multiplication ) ) )
| ( ( D @ ( C @ multiplication ) @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[734,41]) ).
thf(742,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[741:[bind(A,$thf( F @ ( E @ multiplication ) )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( zero ))]]) ).
thf(782,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ),
inference(simp,[status(thm)],[742]) ).
thf(789,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(rewrite,[status(thm)],[782,734]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_4) ).
thf(60,plain,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,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(87,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)],[17]) ).
thf(24,plain,
( ( zero @ ( sk1 @ ( sk3 @ c @ multiplication ) @ leq ) )
| sk4 ),
inference(cnfConj,[status(thm)],[20]) ).
thf(25,plain,
( ~ sk4
| ( sk2 @ ( sk3 @ multiplication ) @ ( sk1 @ leq ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( A @ test )
=> ( ( ( A @ c )
= B )
<=> ( B @ ( A @ complement ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
thf(78,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)],[16]) ).
thf(3,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(27,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(28,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ addition ) @ addition ) )
= ( A @ ( B @ addition ) @ ( C @ addition ) ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(36,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(37,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[36]) ).
thf(38,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[37]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(30,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(31,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[31]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(45,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(46,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[45]) ).
thf(47,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[46]) ).
thf(154,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk2 @ ( sk3 @ multiplication ) ) )
| ( A != sk2 )
| sk4 ),
inference(paramod_ordered,[status(thm)],[47,150]) ).
thf(158,plain,
( ( sk2 != sk2 )
| ( sk3 != one )
| sk4 ),
inference(simp,[status(thm)],[154]) ).
thf(161,plain,
( ( sk3 != one )
| sk4 ),
inference(simp,[status(thm)],[158]) ).
thf(140,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ ( sk3 @ multiplication ) ) )
| ~ ( zero @ ( sk1 @ leq ) )
| sk4 ),
inference(paramod_ordered,[status(thm)],[38,21]) ).
thf(145,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk3 != zero )
| ~ ( zero @ ( sk1 @ leq ) )
| sk4 ),
inference(simp,[status(thm)],[140]) ).
thf(149,plain,
( ( sk3 != zero )
| ~ ( zero @ ( sk1 @ leq ) )
| sk4 ),
inference(simp,[status(thm)],[145]) ).
thf(155,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ ( sk3 @ multiplication ) ) )
| ( sk2 != zero )
| sk4 ),
inference(paramod_ordered,[status(thm)],[68,150]) ).
thf(159,plain,
! [A: $i] :
( ( sk2 != zero )
| ( A != sk3 )
| ( sk2 != zero )
| sk4 ),
inference(simp,[status(thm)],[155]) ).
thf(162,plain,
( ( sk2 != zero )
| sk4 ),
inference(simp,[status(thm)],[159]) ).
thf(114,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk3 @ c @ multiplication ) ) )
| ~ sk4
| ~ ( zero @ ( zero @ leq ) )
| ~ ( sk2 @ ( sk1 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[38,22]) ).
thf(118,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( sk3 @ c )
!= zero )
| ~ sk4
| ~ ( zero @ ( zero @ leq ) )
| ~ ( sk2 @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(123,plain,
( ( ( sk3 @ c )
!= zero )
| ~ sk4
| ~ ( zero @ ( zero @ leq ) )
| ~ ( sk2 @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[118]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ complement ) )
<=> ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_2) ).
thf(48,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)],[10]) ).
thf(26,plain,
sk3 @ test,
inference(cnfConj,[status(thm)],[20]) ).
thf(49,plain,
( ! [A: $i,B: $i] :
( ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) )
=> ( A @ ( B @ complement ) ) )
& ! [A: $i,B: $i] :
( ( A @ ( B @ complement ) )
=> ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) ) ) ),
inference(miniscope,[status(thm)],[48]) ).
thf(50,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ complement ) )
| ( ( D @ ( C @ addition ) )
!= one )
| ( ( C @ ( D @ multiplication ) )
!= zero )
| ( ( D @ ( C @ multiplication ) )
!= zero ) )
& ( ( ( B @ ( A @ addition ) )
= one )
| ~ ( A @ ( B @ complement ) ) )
& ( ( ( A @ ( B @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) )
& ( ( ( B @ ( A @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) ) ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[50]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ complement ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(lifteq,[status(thm)],[51]) ).
thf(126,plain,
( ~ $true
| ( ( sk2 @ ( sk1 @ leq ) )
!= ( zero @ ( zero @ leq ) ) )
| ( sk1 != zero )
| ~ sk4
| ~ ( zero @ ( zero @ leq ) ) ),
inference(eqfactor_ordered,[status(thm)],[125]) ).
thf(128,plain,
( ( sk2 != zero )
| ( sk1 != zero )
| ( sk1 != zero )
| ~ sk4
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(129,plain,
( ( sk2 != zero )
| ( sk1 != zero )
| ~ sk4
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(294,plain,
( ( ( sk2 @ ( sk3 @ multiplication ) @ ( sk1 @ leq ) )
!= ( zero @ ( zero @ leq ) ) )
| ( sk2 != zero )
| ( sk1 != zero )
| ~ sk4
| ~ $true
| ~ sk4 ),
inference(paramod_ordered,[status(thm)],[25,129]) ).
thf(295,plain,
( ( ( sk2 @ ( sk3 @ multiplication ) @ ( sk1 @ leq ) )
!= ( zero @ ( zero @ leq ) ) )
| ( sk2 != zero )
| ( sk1 != zero )
| ~ sk4 ),
inference(simp,[status(thm)],[294]) ).
thf(321,plain,
( ( ( sk2 @ ( sk3 @ multiplication ) )
!= zero )
| ( sk1 != zero )
| ( sk2 != zero )
| ( sk1 != zero )
| ~ sk4 ),
inference(simp,[status(thm)],[295]) ).
thf(327,plain,
( ( ( sk2 @ ( sk3 @ multiplication ) )
!= zero )
| ( sk2 != zero )
| ( sk1 != zero )
| ~ sk4 ),
inference(simp,[status(thm)],[321]) ).
thf(489,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ ( sk3 @ multiplication ) ) )
| ( zero != zero )
| ( sk2 != zero )
| ( sk1 != zero )
| ~ sk4 ),
inference(paramod_ordered,[status(thm)],[68,327]) ).
thf(490,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ ( sk3 @ multiplication ) ) )
| ( sk2 != zero )
| ( sk1 != zero )
| ~ sk4 ),
inference(simp,[status(thm)],[489]) ).
thf(497,plain,
! [A: $i] :
( ( sk2 != zero )
| ( A != sk3 )
| ( sk2 != zero )
| ( sk1 != zero )
| ~ sk4 ),
inference(simp,[status(thm)],[490]) ).
thf(499,plain,
( ( sk2 != zero )
| ( sk1 != zero )
| ~ sk4 ),
inference(simp,[status(thm)],[497]) ).
thf(508,plain,
( ( sk4 != sk4 )
| ( sk2 != zero )
| ( sk1 != zero )
| ~ $true
| ( sk2 != zero ) ),
inference(paramod_ordered,[status(thm)],[162,499]) ).
thf(509,plain,
( ( sk4 != sk4 )
| ( sk1 != zero )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[508]) ).
thf(510,plain,
( ( sk1 != zero )
| ( sk2 != zero ) ),
inference(pattern_uni,[status(thm)],[509:[]]) ).
thf(61,plain,
! [A: $i] :
( ( ( A @ c )
= zero )
| ( A @ test ) ),
inference(cnf,[status(esa)],[60]) ).
thf(62,plain,
! [A: $i] :
( ( A @ test )
| ( ( A @ c )
= zero ) ),
inference(lifteq,[status(thm)],[61]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(90,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)],[18]) ).
thf(30506,plain,
$false,
inference(e,[status(thm)],[69,202,125,789,60,65,77,41,39,66,35,87,42,24,25,78,29,38,21,33,32,45,161,149,22,44,27,162,123,48,63,150,26,55,23,75,510,36,30,19,47,62,90,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE008+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n017.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 : Fri Sep 25 19:06:49 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
% 0.87/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.19 % [INFO] Parsing done (202ms).
% 1.46/1.20 % [INFO] Running in sequential loop mode.
% 2.21/1.61 % [INFO] eprover registered as external prover.
% 2.21/1.62 % [INFO] Scanning for conjecture ...
% 2.39/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.59/1.80 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.59/1.83 % [INFO] Problem is first-order (TPTP FOF).
% 2.59/1.84 % [INFO] Type checking passed.
% 2.59/1.85 % [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 ...
% 65.23/14.99 % External prover 'e' found a proof!
% 65.23/14.99 % [INFO] Killing All external provers ...
% 65.23/14.99 % Time passed: 14462ms (effective reasoning time: 13784ms)
% 65.23/14.99 % 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)>
% 65.23/15.00 % Axioms used in derivation (16): additive_identity, test_3, test_4, left_annihilation, right_distributivity, multiplicative_right_identity, test_1, right_annihilation, additive_idempotence, additive_associativity, order, additive_commutativity, test_2, multiplicative_left_identity, multiplicative_associativity, left_distributivity
% 65.23/15.00 % No. of inferences in proof: 121
% 65.23/15.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 14462 ms resp. 13784 ms w/o parsing
% 65.89/15.07 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 65.89/15.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------