%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE027+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 : n019.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 38.16s 8.64s
% Output : Refutation 32.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 23
% Syntax : Number of formulae : 135 ( 68 unt; 0 typ; 6 def)
% Number of atoms : 295 ( 192 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1219 ( 132 ~; 85 |; 24 &; 949 @)
% ( 4 <=>; 25 =>; 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 : 17 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 196 ( 1 ^; 179 !; 10 ?; 196 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% 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 ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( ? [E: $i] : ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) )
= ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ? [D: $i] : ( D @ test )
& ( C @ test ) )
=> ( ( B @ ( C @ c @ multiplication ) @ ( A @ ( C @ c @ multiplication ) @ ( sk1 @ ( C @ multiplication ) @ addition ) @ ( C @ multiplication ) @ addition ) )
= ( B @ ( C @ c @ multiplication ) @ ( sk1 @ ( C @ multiplication ) @ addition ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ? [C: $i] : ( C @ test )
& ( B @ test ) )
=> ( ( A @ ( B @ c @ multiplication ) @ ( sk2 @ ( B @ c @ multiplication ) @ ( sk1 @ ( B @ multiplication ) @ addition ) @ ( B @ multiplication ) @ addition ) )
= ( A @ ( B @ c @ multiplication ) @ ( sk1 @ ( B @ multiplication ) @ addition ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ? [B: $i] : ( B @ test )
& ( A @ test ) )
=> ( ( sk3 @ ( A @ c @ multiplication ) @ ( sk2 @ ( A @ c @ multiplication ) @ ( sk1 @ ( A @ multiplication ) @ addition ) @ ( A @ multiplication ) @ addition ) )
= ( sk3 @ ( A @ c @ multiplication ) @ ( sk1 @ ( A @ multiplication ) @ addition ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] : ( A @ test ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ complement ) ) ) ) ).
thf(15,axiom,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(80,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(81,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[80]) ).
thf(82,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[81]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) )
= ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) )
= ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) )
= ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] : ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) )
= ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) ) ) ),
inference(miniscope,[status(thm)],[19]) ).
thf(21,plain,
( ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) )
& ( sk5 @ test )
& ( sk4 @ test ) ),
inference(cnf,[status(esa)],[20]) ).
thf(24,plain,
( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(25,plain,
( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(110,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) ) )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(paramod_ordered,[status(thm)],[82,25]) ).
thf(114,plain,
! [A: $i] :
( ( sk2 != zero )
| ( A
!= ( sk4 @ c ) )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( ( zero @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(146,plain,
( ( sk2 != zero )
| ( ( zero @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(16,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(83,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(84,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[83]) ).
thf(85,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[84]) ).
thf(333,plain,
( ( sk2 != zero )
| ( ( sk1 @ ( sk4 @ multiplication ) @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(rewrite,[status(thm)],[146,85]) ).
thf(4,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(29,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(339,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[82,333]) ).
thf(351,plain,
! [A: $i] :
( ( ( sk1 @ ( sk4 @ multiplication ) )
!= zero )
| ( A != sk4 )
| ( sk2 != zero )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[339]) ).
thf(376,plain,
( ( sk2 != zero )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[351]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(77,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(78,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[77]) ).
thf(79,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[78]) ).
thf(266,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) ) )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( A @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,25]) ).
thf(285,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) ) )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( A
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[266]) ).
thf(313,plain,
( ( one @ ( sk1 @ ( sk4 @ multiplication ) @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) ) ),
inference(simp,[status(thm)],[285]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(855,plain,
( ( one @ ( sk1 @ multiplication ) @ ( sk4 @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) ) ),
inference(rewrite,[status(thm)],[313,31]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ test )
=> ( ( ( A @ c )
= B )
<=> ( B @ ( A @ complement ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
thf(56,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(22,plain,
sk4 @ test,
inference(cnfConj,[status(thm)],[21]) ).
thf(57,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)],[56]) ).
thf(58,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)],[57]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ complement ) )
| ( ( A @ c )
!= B )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[58]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
!= B ) ),
inference(lifteq,[status(thm)],[59]) ).
thf(62,plain,
! [A: $i] :
( ( A @ c @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[61]) ).
thf(1208,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,62]) ).
thf(1209,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1208]) ).
thf(1210,plain,
sk4 @ c @ ( sk4 @ complement ),
inference(pattern_uni,[status(thm)],[1209:[bind(A,$thf( sk4 ))]]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ test )
<=> ? [B: $i] : ( A @ ( B @ complement ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_1) ).
thf(44,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(45,plain,
( ! [A: $i] :
( ? [B: $i] : ( A @ ( B @ complement ) )
=> ( A @ test ) )
& ! [A: $i] :
( ( A @ test )
=> ? [B: $i] : ( A @ ( B @ complement ) ) ) ),
inference(miniscope,[status(thm)],[44]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ test )
| ~ ( B @ ( C @ complement ) ) )
& ( ( A @ ( A @ sk6 @ complement ) )
| ~ ( A @ test ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( A @ test )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[46]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( A @ test )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(1220,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1210,49]) ).
thf(1221,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[1220]) ).
thf(1222,plain,
sk4 @ c @ test,
inference(pattern_uni,[status(thm)],[1221:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
thf(23,plain,
sk5 @ test,
inference(cnfConj,[status(thm)],[21]) ).
thf(47,plain,
! [A: $i] :
( ( A @ ( A @ sk6 @ complement ) )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[46]) ).
thf(780,plain,
! [A: $i] :
( ( ( sk5 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,47]) ).
thf(781,plain,
! [A: $i] :
( ( ( sk5 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[780]) ).
thf(782,plain,
sk5 @ ( sk5 @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[781:[bind(A,$thf( sk5 ))]]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_4) ).
thf(35,plain,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(36,plain,
! [A: $i] :
( ( ( A @ c )
= zero )
| ( A @ test ) ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
! [A: $i] :
( ( A @ test )
| ( ( A @ c )
= zero ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(50,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(51,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[50]) ).
thf(52,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[51]) ).
thf(340,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= ( zero @ ( sk4 @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[82,333]) ).
thf(347,plain,
! [A: $i] :
( ( sk1 != zero )
| ( A != sk4 )
| ( sk2 != zero )
| ( sk1 != zero )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[340]) ).
thf(372,plain,
( ( sk2 != zero )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[347]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(89,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(103,plain,
( ( ( sk3 @ ( sk4 @ c @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(143,plain,
( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ),
inference(simp,[status(thm)],[103]) ).
thf(438,plain,
( ( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) )
!= sk1 )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[143]) ).
thf(507,plain,
( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) )
!= sk1 ),
inference(simp,[status(thm)],[438]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(26,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[27]) ).
thf(105,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) ) )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,25]) ).
thf(123,plain,
! [A: $i] :
( ( A
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) )
| ( sk4 != zero )
| ( ( sk3 @ ( sk4 @ c @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[105]) ).
thf(155,plain,
( ( sk4 != zero )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[123]) ).
thf(159,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk4 != zero )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[28,155]) ).
thf(160,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk4 != zero ) ),
inference(simp,[status(thm)],[159]) ).
thf(163,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk4 != zero )
| ( sk4 != zero ) ),
inference(simp,[status(thm)],[160]) ).
thf(165,plain,
sk4 != zero,
inference(simp,[status(thm)],[163]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
thf(38,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
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/sandbox/benchmark/theBenchmark.p',test_2) ).
thf(65,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(857,plain,
! [A: $i] :
( ( ( zero @ ( A @ addition ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) )
| ( ( A @ ( sk4 @ multiplication ) )
!= ( one @ ( sk1 @ multiplication ) @ ( sk4 @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[85,855]) ).
thf(947,plain,
! [A: $i] :
( ( ( zero @ ( A @ addition ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) )
| ( A
!= ( one @ ( sk1 @ multiplication ) ) )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[857]) ).
thf(1025,plain,
( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) )
!= ( zero @ ( one @ ( sk1 @ multiplication ) @ addition ) ) ),
inference(simp,[status(thm)],[947]) ).
thf(1060,plain,
( ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) )
!= ( one @ ( sk1 @ multiplication ) ) ),
inference(rewrite,[status(thm)],[1025,85]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(41,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(777,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,47]) ).
thf(778,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[777]) ).
thf(779,plain,
sk4 @ ( sk4 @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[778:[bind(A,$thf( sk4 ))]]) ).
thf(5,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(32,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(33,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ addition ) @ addition ) )
= ( A @ ( B @ addition ) @ ( C @ addition ) ) ),
inference(lifteq,[status(thm)],[33]) ).
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(86,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(39,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(624,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)],[40,82]) ).
thf(625,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( zero @ ( A @ multiplication ) @ addition ) )
= zero ),
inference(pattern_uni,[status(thm)],[624:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( zero )),bind(D,$thf( F @ ( E @ addition ) ))]]) ).
thf(712,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( zero @ ( A @ multiplication ) @ addition ) )
= zero ),
inference(simp,[status(thm)],[625]) ).
thf(720,plain,
( ( zero @ ( zero @ addition ) )
= zero ),
inference(rewrite,[status(thm)],[712,82]) ).
thf(726,plain,
! [C: $i,B: $i,A: $i] :
( ( ( zero @ ( zero @ addition ) )
!= ( B @ ( C @ addition ) ) )
| ( ( A @ ( zero @ addition ) )
= ( A @ ( B @ addition ) @ ( C @ addition ) ) ) ),
inference(paramod_ordered,[status(thm)],[720,34]) ).
thf(727,plain,
! [A: $i] :
( ( A @ ( zero @ addition ) @ ( zero @ addition ) )
= ( A @ ( zero @ addition ) ) ),
inference(pattern_uni,[status(thm)],[726:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( zero ))]]) ).
thf(42,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[41]) ).
thf(43,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[42]) ).
thf(338,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ( ( A @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[43,333]) ).
thf(361,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk4 != one )
| ( sk2 != zero )
| ( A != sk1 )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[338]) ).
thf(386,plain,
( ( sk4 != one )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[361]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(lifteq,[status(thm)],[54]) ).
thf(342,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk2 != zero )
| ( ( A @ ( sk4 @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,333]) ).
thf(358,plain,
! [A: $i] :
( ( sk1 != one )
| ( A != sk4 )
| ( sk2 != zero )
| ( A != sk1 )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[342]) ).
thf(383,plain,
( ( sk1 != one )
| ( sk4 != sk1 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[358]) ).
thf(334,plain,
( ( sk2 != zero )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= sk1 )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[333]) ).
thf(369,plain,
( ( sk2 != zero )
| ( ( sk1 @ ( sk4 @ multiplication ) )
!= sk1 ) ),
inference(simp,[status(thm)],[334]) ).
thf(7841,plain,
$false,
inference(e,[status(thm)],[333,29,376,85,53,77,855,19,83,56,1222,782,37,25,52,372,89,507,165,28,38,65,1210,1060,41,779,32,34,22,44,49,86,80,35,50,31,727,386,143,43,40,26,55,23,383,82,79,720,47,62,369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE027+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.24/0.49 % Computer : n019.cluster.edu
% 0.24/0.49 % Model : x86_64 x86_64
% 0.24/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.49 % Memory : 8046.5625MB
% 0.24/0.49 % OS : Linux 6.8.0-71-generic
% 0.24/0.49 % CPULimit : 300
% 0.24/0.49 % WCLimit : 300
% 0.24/0.49 % DateTime : Fri Sep 25 19:15:04 UTC 2026
% 0.24/0.49 % CPUTime :
% 0.24/0.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.43/1.31 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.68/1.45 % [INFO] Parsing done (132ms).
% 1.68/1.46 % [INFO] Running in sequential loop mode.
% 2.48/1.76 % [INFO] eprover registered as external prover.
% 2.48/1.77 % [INFO] Scanning for conjecture ...
% 2.70/1.89 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.91/1.93 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.91/1.95 % [INFO] Problem is first-order (TPTP FOF).
% 2.91/1.95 % [INFO] Type checking passed.
% 2.91/1.95 % [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 ...
% 38.16/8.64 % External prover 'e' found a proof!
% 38.16/8.64 % [INFO] Killing All external provers ...
% 38.16/8.64 % Time passed: 7939ms (effective reasoning time: 7179ms)
% 38.16/8.64 % 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)>
% 38.16/8.64 % 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
% 38.16/8.64 % No. of inferences in proof: 129
% 38.16/8.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7939 ms resp. 7179 ms w/o parsing
% 32.74/8.73 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 32.74/8.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------