%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE010+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 : n009.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 07:42:57 AM UTC 2026
% Result : Theorem 69.85s 14.19s
% Output : Refutation 58.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 20
% Syntax : Number of formulae : 129 ( 61 unt; 0 typ; 3 def)
% Number of atoms : 307 ( 181 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1168 ( 130 ~; 100 |; 21 &; 891 @)
% ( 4 <=>; 22 =>; 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 : 14 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 178 ( 1 ^; 169 !; 5 ?; 178 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(test_decl,type,
test: $i > $o ).
thf(one_decl,type,
one: $i ).
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(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 > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( A @ test )
& ( B @ test ) )
=> ( one
= ( B @ c @ ( A @ c @ multiplication ) @ ( B @ ( A @ c @ multiplication ) @ ( B @ ( A @ multiplication ) @ ( A @ ( B @ c @ multiplication ) @ ( A @ ( B @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( sk1 @ test )
& ( A @ test ) )
=> ( one
= ( A @ c @ ( sk1 @ c @ multiplication ) @ ( A @ ( sk1 @ c @ multiplication ) @ ( A @ ( sk1 @ multiplication ) @ ( sk1 @ ( A @ c @ multiplication ) @ ( sk1 @ ( A @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ complement ) ) ) ) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(88,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(1,conjecture,
! [A: $i,B: $i] :
( ( ( A @ test )
& ( B @ test ) )
=> ( one
= ( B @ c @ ( A @ c @ multiplication ) @ ( B @ ( A @ c @ multiplication ) @ ( B @ ( A @ multiplication ) @ ( A @ ( B @ c @ multiplication ) @ ( A @ ( B @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( A @ test )
& ( B @ test ) )
=> ( one
= ( B @ c @ ( A @ c @ multiplication ) @ ( B @ ( A @ c @ multiplication ) @ ( B @ ( A @ multiplication ) @ ( A @ ( B @ c @ multiplication ) @ ( A @ ( B @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i] :
( ( ( A @ test )
& ( B @ test ) )
=> ( one
= ( B @ c @ ( A @ c @ multiplication ) @ ( B @ ( A @ c @ multiplication ) @ ( B @ ( A @ multiplication ) @ ( A @ ( B @ c @ multiplication ) @ ( A @ ( B @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
( ( one
!= ( sk2 @ c @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ multiplication ) @ ( sk1 @ ( sk2 @ c @ multiplication ) @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) ) )
& ( sk1 @ test )
& ( sk2 @ test ) ),
inference(cnf,[status(esa)],[19]) ).
thf(22,plain,
sk1 @ test,
inference(cnfConj,[status(thm)],[20]) ).
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(55,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(56,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)],[55]) ).
thf(57,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)],[56]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ complement ) )
| ( ( A @ c )
!= B )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[57]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
!= B ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(61,plain,
! [A: $i] :
( ( A @ c @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[60]) ).
thf(713,plain,
! [A: $i] :
( ( ( sk1 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,61]) ).
thf(714,plain,
! [A: $i] :
( ( ( sk1 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[713]) ).
thf(715,plain,
sk1 @ c @ ( sk1 @ complement ),
inference(pattern_uni,[status(thm)],[714:[bind(A,$thf( sk1 ))]]) ).
thf(16,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(82,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(83,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[82]) ).
thf(84,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[83]) ).
thf(17,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(85,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(9,axiom,
! [A: $i] :
( ( A @ test )
<=> ? [B: $i] : ( A @ ( B @ complement ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_1) ).
thf(43,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(44,plain,
( ! [A: $i] :
( ? [B: $i] : ( A @ ( B @ complement ) )
=> ( A @ test ) )
& ! [A: $i] :
( ( A @ test )
=> ? [B: $i] : ( A @ ( B @ complement ) ) ) ),
inference(miniscope,[status(thm)],[43]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ test )
| ~ ( B @ ( C @ complement ) ) )
& ( ( A @ ( A @ sk3 @ complement ) )
| ~ ( A @ test ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [A: $i] :
( ( A @ ( A @ sk3 @ complement ) )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[45]) ).
thf(677,plain,
! [A: $i] :
( ( ( sk1 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk3 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,46]) ).
thf(678,plain,
! [A: $i] :
( ( ( sk1 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk3 @ complement ) ) ),
inference(simp,[status(thm)],[677]) ).
thf(679,plain,
sk1 @ ( sk1 @ sk3 @ complement ),
inference(pattern_uni,[status(thm)],[678:[bind(A,$thf( sk1 ))]]) ).
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(37,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(38,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[37]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(15,axiom,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(79,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(80,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[79]) ).
thf(81,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[80]) ).
thf(593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
!= ( zero @ ( D @ multiplication ) ) )
| ( ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[39,81]) ).
thf(594,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( zero @ ( A @ multiplication ) @ addition ) )
= zero ),
inference(pattern_uni,[status(thm)],[593:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( zero )),bind(D,$thf( F @ ( E @ addition ) ))]]) ).
thf(620,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( zero @ ( A @ multiplication ) @ addition ) )
= zero ),
inference(simp,[status(thm)],[594]) ).
thf(636,plain,
( ( zero @ ( zero @ addition ) )
= zero ),
inference(rewrite,[status(thm)],[620,81]) ).
thf(21,plain,
sk2 @ test,
inference(cnfConj,[status(thm)],[20]) ).
thf(674,plain,
! [A: $i] :
( ( ( sk2 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk3 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,46]) ).
thf(675,plain,
! [A: $i] :
( ( ( sk2 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk3 @ complement ) ) ),
inference(simp,[status(thm)],[674]) ).
thf(676,plain,
sk2 @ ( sk2 @ sk3 @ complement ),
inference(pattern_uni,[status(thm)],[675:[bind(A,$thf( sk2 ))]]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(40,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(41,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[40]) ).
thf(42,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[41]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(25,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(26,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[25]) ).
thf(27,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[26]) ).
thf(23,plain,
( one
!= ( sk2 @ c @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ multiplication ) @ ( sk1 @ ( sk2 @ c @ multiplication ) @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(24,plain,
( ( sk2 @ c @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ multiplication ) @ ( sk1 @ ( sk2 @ c @ multiplication ) @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) )
!= one ),
inference(lifteq,[status(thm)],[23]) ).
thf(102,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ c @ ( sk1 @ c @ multiplication ) ) )
| ( ( zero @ ( sk2 @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ multiplication ) @ ( sk1 @ ( sk2 @ c @ multiplication ) @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) )
!= one ) ),
inference(paramod_ordered,[status(thm)],[81,24]) ).
thf(114,plain,
! [A: $i] :
( ( ( sk2 @ c )
!= zero )
| ( A
!= ( sk1 @ c ) )
| ( ( zero @ ( sk2 @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ multiplication ) @ ( sk1 @ ( sk2 @ c @ multiplication ) @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) )
!= one ) ),
inference(simp,[status(thm)],[102]) ).
thf(124,plain,
( ( ( sk2 @ c )
!= zero )
| ( ( zero @ ( sk2 @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ multiplication ) @ ( sk1 @ ( sk2 @ c @ multiplication ) @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) )
!= one ) ),
inference(simp,[status(thm)],[114]) ).
thf(137,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk2 @ c @ multiplication ) ) )
| ( ( sk2 @ c )
!= zero )
| ( ( zero @ ( sk2 @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ multiplication ) @ ( zero @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) )
!= one ) ),
inference(paramod_ordered,[status(thm)],[27,124]) ).
thf(141,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( sk2 @ c )
!= zero )
| ( ( sk2 @ c )
!= zero )
| ( ( zero @ ( sk2 @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ multiplication ) @ ( zero @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) )
!= one ) ),
inference(simp,[status(thm)],[137]) ).
thf(153,plain,
( ( ( sk2 @ c )
!= zero )
| ( ( zero @ ( sk2 @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ multiplication ) @ ( zero @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) )
!= one ) ),
inference(simp,[status(thm)],[141]) ).
thf(193,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ ( sk1 @ c @ multiplication ) ) )
| ( ( sk2 @ c )
!= zero )
| ( ( zero @ ( zero @ ( sk2 @ ( sk1 @ multiplication ) @ ( zero @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) )
!= one ) ),
inference(paramod_ordered,[status(thm)],[81,153]) ).
thf(205,plain,
! [A: $i] :
( ( sk2 != zero )
| ( A
!= ( sk1 @ c ) )
| ( ( sk2 @ c )
!= zero )
| ( ( zero @ ( zero @ ( sk2 @ ( sk1 @ multiplication ) @ ( zero @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) )
!= one ) ),
inference(simp,[status(thm)],[193]) ).
thf(217,plain,
( ( sk2 != zero )
| ( ( sk2 @ c )
!= zero )
| ( ( zero @ ( zero @ ( sk2 @ ( sk1 @ multiplication ) @ ( zero @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) )
!= one ) ),
inference(simp,[status(thm)],[205]) ).
thf(220,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ ( sk1 @ multiplication ) ) )
| ( sk2 != zero )
| ( ( sk2 @ c )
!= zero )
| ( ( zero @ ( zero @ ( zero @ ( zero @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) )
!= one ) ),
inference(paramod_ordered,[status(thm)],[81,217]) ).
thf(227,plain,
! [A: $i] :
( ( sk2 != zero )
| ( A != sk1 )
| ( sk2 != zero )
| ( ( sk2 @ c )
!= zero )
| ( ( zero @ ( zero @ ( zero @ ( zero @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) )
!= one ) ),
inference(simp,[status(thm)],[220]) ).
thf(233,plain,
( ( sk2 != zero )
| ( ( sk2 @ c )
!= zero )
| ( ( zero @ ( zero @ ( zero @ ( zero @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) @ addition ) @ addition ) @ addition ) )
!= one ) ),
inference(simp,[status(thm)],[227]) ).
thf(392,plain,
( ( sk2 != zero )
| ( ( sk2 @ c )
!= zero )
| ( ( zero @ ( zero @ ( zero @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) @ addition ) @ addition ) )
!= one ) ),
inference(rewrite,[status(thm)],[233,84]) ).
thf(394,plain,
! [A: $i] :
( ( ( zero @ ( A @ addition ) )
!= ( zero @ ( zero @ ( zero @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) @ addition ) @ addition ) ) )
| ( sk2 != zero )
| ( ( sk2 @ c )
!= zero )
| ( A != one ) ),
inference(paramod_ordered,[status(thm)],[84,392]) ).
thf(395,plain,
( ( sk2 != zero )
| ( ( sk2 @ c )
!= zero )
| ( ( zero @ ( zero @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) @ addition ) )
!= one ) ),
inference(pattern_uni,[status(thm)],[394:[bind(A,$thf( zero @ ( zero @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) @ addition ) ))]]) ).
thf(414,plain,
( ( sk2 != zero )
| ( ( sk2 @ c )
!= zero )
| ( ( zero @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) )
!= one ) ),
inference(rewrite,[status(thm)],[395,84]) ).
thf(416,plain,
! [A: $i] :
( ( ( zero @ ( A @ addition ) )
!= ( zero @ ( sk1 @ ( sk2 @ multiplication ) @ addition ) ) )
| ( sk2 != zero )
| ( ( sk2 @ c )
!= zero )
| ( A != one ) ),
inference(paramod_ordered,[status(thm)],[84,414]) ).
thf(417,plain,
( ( sk2 != zero )
| ( ( sk2 @ c )
!= zero )
| ( ( sk1 @ ( sk2 @ multiplication ) )
!= one ) ),
inference(pattern_uni,[status(thm)],[416:[bind(A,$thf( sk1 @ ( sk2 @ multiplication ) ))]]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(710,plain,
! [A: $i] :
( ( ( sk2 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,61]) ).
thf(711,plain,
! [A: $i] :
( ( ( sk2 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[710]) ).
thf(712,plain,
sk2 @ c @ ( sk2 @ complement ),
inference(pattern_uni,[status(thm)],[711:[bind(A,$thf( sk2 ))]]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( A @ test )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[45]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( A @ test )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(722,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[712,48]) ).
thf(723,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[722]) ).
thf(724,plain,
sk2 @ c @ test,
inference(pattern_uni,[status(thm)],[723:[bind(A,$thf( sk2 @ c )),bind(B,$thf( sk2 ))]]) ).
thf(14,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(76,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(77,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[76]) ).
thf(78,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[77]) ).
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(28,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(727,plain,
! [A: $i] :
( ( ( sk2 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[724,61]) ).
thf(728,plain,
! [A: $i] :
( ( ( sk2 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[727]) ).
thf(729,plain,
sk2 @ c @ c @ ( sk2 @ c @ complement ),
inference(pattern_uni,[status(thm)],[728:[bind(A,$thf( sk2 @ c ))]]) ).
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(31,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(32,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(cnf,[status(esa)],[31]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ addition ) @ addition ) )
= ( A @ ( B @ addition ) @ ( C @ addition ) ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(449,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) )
| ( sk2 != zero )
| ( ( sk2 @ c )
!= zero )
| ( zero != one ) ),
inference(paramod_ordered,[status(thm)],[27,417]) ).
thf(454,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk2 != zero )
| ( sk2 != zero )
| ( ( sk2 @ c )
!= zero )
| ( zero != one ) ),
inference(simp,[status(thm)],[449]) ).
thf(461,plain,
( ( sk2 != zero )
| ( ( sk2 @ c )
!= zero )
| ( zero != one ) ),
inference(simp,[status(thm)],[454]) ).
thf(448,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) )
| ( sk2 != zero )
| ( ( sk2 @ c )
!= zero )
| ( A != one ) ),
inference(paramod_ordered,[status(thm)],[42,417]) ).
thf(456,plain,
( ( sk1 != one )
| ( sk2 != one )
| ( sk2 != zero )
| ( ( sk2 @ c )
!= zero ) ),
inference(simp,[status(thm)],[448]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_4) ).
thf(34,plain,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
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(64,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(53,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(49,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(735,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ ( sk1 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[715,48]) ).
thf(736,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ ( sk1 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[735]) ).
thf(737,plain,
sk1 @ c @ test,
inference(pattern_uni,[status(thm)],[736:[bind(A,$thf( sk1 @ c )),bind(B,$thf( sk1 ))]]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( ( A @ c )
= B )
| ~ ( B @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[57]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
= B ) ),
inference(lifteq,[status(thm)],[59]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
= B ) ),
inference(simp,[status(thm)],[62]) ).
thf(501,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( zero @ ( C @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[54,84]) ).
thf(502,plain,
! [A: $i] :
( ( A @ ( zero @ addition ) )
= A ),
inference(pattern_uni,[status(thm)],[501:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(35,plain,
! [A: $i] :
( ( ( A @ c )
= zero )
| ( A @ test ) ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
! [A: $i] :
( ( A @ test )
| ( ( A @ c )
= zero ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(cnf,[status(esa)],[28]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(50,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[50]) ).
thf(13539,plain,
$false,
inference(e,[status(thm)],[88,715,84,61,85,679,636,43,82,79,676,42,417,37,25,52,724,46,78,28,21,729,33,461,456,34,64,22,27,54,49,81,76,737,39,48,712,63,414,502,31,40,55,36,30,51,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE010+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.10 % 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
% 0.21/0.46 % Computer : n009.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % OS : Linux 6.8.0-71-generic
% 0.21/0.46 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Fri Sep 25 19:12:29 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 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
% 0.97/1.01 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.65/1.20 % [INFO] Parsing done (183ms).
% 1.65/1.21 % [INFO] Running in sequential loop mode.
% 2.24/1.54 % [INFO] eprover registered as external prover.
% 2.24/1.55 % [INFO] Scanning for conjecture ...
% 2.51/1.64 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.78/1.70 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.78/1.73 % [INFO] Problem is first-order (TPTP FOF).
% 2.78/1.73 % [INFO] Type checking passed.
% 2.78/1.74 % [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 ...
% 69.85/14.18 % External prover 'e' found a proof!
% 69.85/14.19 % [INFO] Killing All external provers ...
% 69.85/14.19 % Time passed: 13535ms (effective reasoning time: 12974ms)
% 69.85/14.19 % 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)>
% 69.85/14.19 % 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
% 69.85/14.19 % No. of inferences in proof: 126
% 69.85/14.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 13535 ms resp. 12974 ms w/o parsing
% 58.79/14.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 58.79/14.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------