%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE025+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 : n007.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 12.89s 9.50s
% Output : Refutation 12.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 22
% Syntax : Number of formulae : 124 ( 66 unt; 0 typ; 3 def)
% Number of atoms : 238 ( 177 equ; 0 cnn)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 796 ( 96 ~; 52 |; 25 &; 589 @)
% ( 4 <=>; 30 =>; 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 : 13 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 166 ( 0 ^; 160 !; 3 ?; 166 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(test_decl,type,
test: $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(leq_decl,type,
leq: $i > $i > $o ).
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(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( C @ test )
& ( B @ test ) )
=> ( ( ( C @ c @ ( A @ ( B @ multiplication ) @ multiplication ) )
= zero )
=> ( ( A @ ( B @ multiplication ) )
= ( C @ ( A @ ( B @ multiplication ) @ multiplication ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( ( B @ c @ ( sk1 @ ( A @ multiplication ) @ multiplication ) )
= zero )
=> ( ( sk1 @ ( A @ multiplication ) )
= ( B @ ( sk1 @ ( A @ multiplication ) @ multiplication ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( A @ test )
& ( sk2 @ test ) )
=> ( ( ( A @ c @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) )
= zero )
=> ( ( sk1 @ ( sk2 @ multiplication ) )
= ( A @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) ) ) ) ) ) ) ).
thf(9,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(52,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)],[9]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(46,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(47,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[46]) ).
thf(48,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[47]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( C @ test )
& ( B @ test ) )
=> ( ( ( C @ c @ ( A @ ( B @ multiplication ) @ multiplication ) )
= zero )
=> ( ( A @ ( B @ multiplication ) )
= ( C @ ( A @ ( B @ multiplication ) @ multiplication ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ test )
& ( B @ test ) )
=> ( ( ( C @ c @ ( A @ ( B @ multiplication ) @ multiplication ) )
= zero )
=> ( ( A @ ( B @ multiplication ) )
= ( C @ ( A @ ( B @ multiplication ) @ multiplication ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ test )
& ( B @ test ) )
=> ( ( ( C @ c @ ( A @ ( B @ multiplication ) @ multiplication ) )
= zero )
=> ( ( A @ ( B @ multiplication ) )
= ( C @ ( A @ ( B @ multiplication ) @ multiplication ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
( ( ( sk1 @ ( sk2 @ multiplication ) )
!= ( sk3 @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) ) )
& ( ( sk3 @ c @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) )
= zero )
& ( sk3 @ test )
& ( sk2 @ test ) ),
inference(cnf,[status(esa)],[21]) ).
thf(26,plain,
( ( sk1 @ ( sk2 @ multiplication ) )
!= ( sk3 @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(28,plain,
( ( sk3 @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(116,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk3 @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) ) )
| ( ( sk1 @ ( sk2 @ multiplication ) )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[48,28]) ).
thf(120,plain,
! [A: $i] :
( ( A != sk3 )
| ( ( sk1 @ ( sk2 @ multiplication ) )
!= zero )
| ( ( sk1 @ ( sk2 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[116]) ).
thf(127,plain,
( ( sk1 @ ( sk2 @ multiplication ) )
!= zero ),
inference(simp,[status(thm)],[120]) ).
thf(158,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[48,127]) ).
thf(159,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(162,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[159]) ).
thf(164,plain,
sk2 != zero,
inference(simp,[status(thm)],[162]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(35,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(18,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(91,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(92,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[91]) ).
thf(93,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[92]) ).
thf(269,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( zero @ ( C @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[37,93]) ).
thf(270,plain,
! [A: $i] :
( ( A @ ( zero @ addition ) )
= A ),
inference(pattern_uni,[status(thm)],[269:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
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(201,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) )
| ( ( sk3 @ ( A @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[78,28]) ).
thf(224,plain,
! [A: $i] :
( ( sk1 != one )
| ( A != sk2 )
| ( sk3 != sk1 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[201]) ).
thf(229,plain,
( ( sk1 != one )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[224]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(32,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(33,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[32]) ).
thf(34,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[33]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(38,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)],[6]) ).
thf(39,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)],[38]) ).
thf(40,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)],[39]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
!= B ) ),
inference(cnfConj,[status(thm)],[40]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
!= B ) ),
inference(lifteq,[status(thm)],[42]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
!= B ) ),
inference(simp,[status(thm)],[44]) ).
thf(388,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ addition ) )
!= ( C @ ( B @ addition ) ) )
| ( C @ ( B @ leq ) )
| ( A != C ) ),
inference(paramod_ordered,[status(thm)],[34,45]) ).
thf(389,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ( A != A ) ),
inference(pattern_uni,[status(thm)],[388:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(393,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(simp,[status(thm)],[389]) ).
thf(13,axiom,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_4) ).
thf(73,plain,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(25,plain,
( ( sk3 @ c @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) )
= zero ),
inference(cnfConj,[status(thm)],[22]) ).
thf(27,plain,
( ( sk3 @ c @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[25]) ).
thf(154,plain,
( ( ( sk3 @ c @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[27,127]) ).
thf(155,plain,
( ( sk3 @ c @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(160,plain,
( ( ( sk3 @ c )
!= sk1 )
| ( ( sk1 @ ( sk2 @ multiplication ) )
!= sk2 ) ),
inference(simp,[status(thm)],[155]) ).
thf(414,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) )
| ( ( sk3 @ c )
!= sk1 )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[78,160]) ).
thf(420,plain,
( ( sk1 != one )
| ( sk2 != sk2 )
| ( ( sk3 @ c )
!= sk1 ) ),
inference(simp,[status(thm)],[414]) ).
thf(423,plain,
( ( sk1 != one )
| ( ( sk3 @ c )
!= sk1 ) ),
inference(simp,[status(thm)],[420]) ).
thf(112,plain,
( ( sk3 != sk1 )
| ( ( sk1 @ ( sk2 @ multiplication ) )
!= sk2 ) ),
inference(simp,[status(thm)],[28]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
= B )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[40]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
= B ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(8,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(49,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)],[8]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[50]) ).
thf(202,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk3 @ ( sk1 @ ( sk2 @ multiplication ) @ multiplication ) ) )
| ( A
!= ( sk1 @ ( sk2 @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[78,28]) ).
thf(218,plain,
( ( sk3 != one )
| ( ( sk1 @ ( sk2 @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[202]) ).
thf(234,plain,
sk3 != one,
inference(simp,[status(thm)],[218]) ).
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(88,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(10,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(55,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(56,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[55]) ).
thf(57,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[56]) ).
thf(413,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) )
| ( ( sk3 @ c )
!= sk1 )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[57,160]) ).
thf(417,plain,
( ( sk2 != sk1 )
| ( sk2 != one )
| ( ( sk3 @ c )
!= sk1 ) ),
inference(simp,[status(thm)],[413]) ).
thf(24,plain,
sk3 @ test,
inference(cnfConj,[status(thm)],[22]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
thf(29,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(12,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(70,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)],[12]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) )
= ( C @ ( B @ ( A @ addition ) @ multiplication ) ) ),
inference(lifteq,[status(thm)],[53]) ).
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(20,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(103,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)],[20]) ).
thf(168,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) )
| ( ( sk3 @ ( A @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[57,28]) ).
thf(190,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk2 != one )
| ( sk3 != sk1 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[168]) ).
thf(198,plain,
( ( sk2 != sk1 )
| ( sk2 != one )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[190]) ).
thf(431,plain,
( ( sk3 @ c @ ( sk1 @ multiplication ) @ ( sk2 @ multiplication ) )
= zero ),
inference(rewrite,[status(thm)],[27,51]) ).
thf(506,plain,
( ( ( sk3 @ c @ ( sk1 @ multiplication ) @ ( sk2 @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[431,127]) ).
thf(507,plain,
( ( sk3 @ c @ ( sk1 @ multiplication ) @ ( sk2 @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) ),
inference(simp,[status(thm)],[506]) ).
thf(510,plain,
( ( ( sk3 @ c @ ( sk1 @ multiplication ) )
!= sk1 )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[507]) ).
thf(536,plain,
( ( sk3 @ c @ ( sk1 @ multiplication ) )
!= sk1 ),
inference(simp,[status(thm)],[510]) ).
thf(543,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk3 @ c @ ( sk1 @ multiplication ) ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[78,536]) ).
thf(553,plain,
( ( ( sk3 @ c )
!= one )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[543]) ).
thf(557,plain,
( ( sk3 @ c )
!= one ),
inference(simp,[status(thm)],[553]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ addition ) @ addition ) )
= ( A @ ( B @ addition ) @ ( C @ addition ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(23,plain,
sk2 @ test,
inference(cnfConj,[status(thm)],[22]) ).
thf(74,plain,
! [A: $i] :
( ( ( A @ c )
= zero )
| ( A @ test ) ),
inference(cnf,[status(esa)],[73]) ).
thf(75,plain,
! [A: $i] :
( ( A @ test )
| ( ( A @ c )
= zero ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(11,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(58,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)],[11]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ test )
<=> ? [B: $i] : ( A @ ( B @ complement ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_1) ).
thf(82,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)],[16]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( A @ test )
=> ( ( ( A @ c )
= B )
<=> ( B @ ( A @ complement ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
thf(94,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)],[19]) ).
thf(375,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( zero @ addition ) )
!= ( C @ ( B @ addition ) ) )
| ( C @ ( B @ leq ) )
| ( A != C ) ),
inference(paramod_ordered,[status(thm)],[270,45]) ).
thf(376,plain,
! [A: $i] :
( ( A @ ( zero @ leq ) )
| ( A != A ) ),
inference(pattern_uni,[status(thm)],[375:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(395,plain,
! [A: $i] : ( A @ ( zero @ leq ) ),
inference(simp,[status(thm)],[376]) ).
thf(156,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[81,127]) ).
thf(157,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ ( sk2 @ multiplication ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(161,plain,
! [A: $i] :
( ( sk1 != zero )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[157]) ).
thf(163,plain,
sk1 != zero,
inference(simp,[status(thm)],[161]) ).
thf(2146,plain,
$false,
inference(e,[status(thm)],[52,164,270,229,393,73,423,112,43,51,234,88,37,417,24,46,93,57,78,29,38,160,70,21,45,32,34,54,49,81,76,103,91,198,431,35,48,557,127,31,55,23,75,58,536,82,79,94,395,163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE025+2 : 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
% 0.19/5.46 % Computer : n007.cluster.edu
% 0.19/5.46 % Model : x86_64 x86_64
% 0.19/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.46 % Memory : 8046.5625MB
% 0.19/5.46 % OS : Linux 6.8.0-71-generic
% 0.19/5.46 % CPULimit : 300
% 0.19/5.46 % WCLimit : 300
% 0.19/5.46 % DateTime : Fri Sep 25 19:13:15 UTC 2026
% 0.19/5.47 % CPUTime :
% 0.19/5.47 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
% 0.98/6.05 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/6.26 % [INFO] Parsing done (207ms).
% 1.26/6.27 % [INFO] Running in sequential loop mode.
% 1.90/6.67 % [INFO] eprover registered as external prover.
% 1.90/6.68 % [INFO] Scanning for conjecture ...
% 2.09/6.78 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 2.25/6.85 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.25/6.88 % [INFO] Problem is first-order (TPTP FOF).
% 2.25/6.89 % [INFO] Type checking passed.
% 2.25/6.89 % [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 ...
% 12.89/9.48 % External prover 'e' found a proof!
% 12.89/9.48 % [INFO] Killing All external provers ...
% 12.89/9.48 % Time passed: 3874ms (effective reasoning time: 3206ms)
% 12.89/9.49 % 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)>
% 12.89/9.50 % 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
% 12.89/9.50 % No. of inferences in proof: 121
% 12.89/9.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3874 ms resp. 3206 ms w/o parsing
% 12.27/9.57 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.27/9.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------