%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET622^5 : 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 : 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 : Wed Sep 30 08:23:03 AM UTC 2026
% Result : Theorem 8.51s 3.22s
% Output : Refutation 8.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 4
% Syntax : Number of formulae : 69 ( 15 unt; 0 typ; 3 def)
% Number of atoms : 615 ( 64 equ; 0 cnn)
% Maximal formula atoms : 66 ( 8 avg)
% Number of connectives : 1278 ( 288 ~; 285 |; 189 &; 516 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 16 ^; 12 !; 0 ?; 31 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a > $o ).
thf(sk2_decl,type,
sk2: a > $o ).
thf(sk3_decl,type,
sk3: a > $o ).
thf(sk4_decl,type,
sk4: a ).
thf(sk5_decl,type,
sk5: $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > $o] :
~ ! [B: a > $o,C: a > $o] :
( ( ^ [D: a] :
( ( A @ D )
& ~ ( ( ( B @ D )
& ~ ( C @ D ) )
| ( ( C @ D )
& ~ ( B @ D ) ) ) ) )
= ( ^ [D: a] :
( ( ( A @ D )
& ~ ( ( B @ D )
| ( C @ D ) ) )
| ( ( A @ D )
& ( B @ D )
& ( C @ D ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > $o] :
~ ! [B: a > $o] :
( ( ^ [C: a] :
( ( sk1 @ C )
& ~ ( ( ( A @ C )
& ~ ( B @ C ) )
| ( ( B @ C )
& ~ ( A @ C ) ) ) ) )
= ( ^ [C: a] :
( ( ( sk1 @ C )
& ~ ( ( A @ C )
| ( B @ C ) ) )
| ( ( sk1 @ C )
& ( A @ C )
& ( B @ C ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: a > $o] :
( ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( ( ( sk2 @ B )
& ~ ( A @ B ) )
| ( ( A @ B )
& ~ ( sk2 @ B ) ) ) ) )
!= ( ^ [B: a] :
( ( ( sk1 @ B )
& ~ ( ( sk2 @ B )
| ( A @ B ) ) )
| ( ( sk1 @ B )
& ( sk2 @ B )
& ( A @ B ) ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ^ [D: a] :
( ( A @ D )
& ~ ( ( ( B @ D )
& ~ ( C @ D ) )
| ( ( C @ D )
& ~ ( B @ D ) ) ) ) )
= ( ^ [D: a] :
( ( ( A @ D )
& ~ ( ( B @ D )
| ( C @ D ) ) )
| ( ( A @ D )
& ( B @ D )
& ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_98_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o,B: a > $o,C: a > $o] :
( ( ^ [D: a] :
( ( A @ D )
& ~ ( ( ( B @ D )
& ~ ( C @ D ) )
| ( ( C @ D )
& ~ ( B @ D ) ) ) ) )
= ( ^ [D: a] :
( ( ( A @ D )
& ~ ( ( B @ D )
| ( C @ D ) ) )
| ( ( A @ D )
& ( B @ D )
& ( C @ D ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o,B: a > $o,C: a > $o] :
( ( ^ [D: a] :
( ( A @ D )
& ~ ( ( ( B @ D )
& ~ ( C @ D ) )
| ( ( C @ D )
& ~ ( B @ D ) ) ) ) )
= ( ^ [D: a] :
( ( ( A @ D )
& ~ ( ( B @ D )
| ( C @ D ) ) )
| ( ( A @ D )
& ( B @ D )
& ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( ( ( sk2 @ A )
& ~ ( sk3 @ A ) )
| ( ( sk3 @ A )
& ~ ( sk2 @ A ) ) ) ) )
!= ( ^ [A: a] :
( ( ( sk1 @ A )
& ~ ( ( sk2 @ A )
| ( sk3 @ A ) ) )
| ( ( sk1 @ A )
& ( sk2 @ A )
& ( sk3 @ A ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( ( ( sk2 @ A )
& ~ ( sk3 @ A ) )
| ( ( sk3 @ A )
& ~ ( sk2 @ A ) ) ) ) )
!= ( ^ [A: a] :
( ( ( sk1 @ A )
& ~ ( ( sk2 @ A )
| ( sk3 @ A ) ) )
| ( ( sk1 @ A )
& ( sk2 @ A )
& ( sk3 @ A ) ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
( ( ( sk1 @ sk4 )
& ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) )
!= ( ( ( sk1 @ sk4 )
& ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ) )
| ( ( sk1 @ sk4 )
& ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) ),
inference(func_ext,[status(esa)],[5]) ).
thf(8,plain,
( ( ( sk1 @ sk4 )
& ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) )
| ( ( sk1 @ sk4 )
& ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ) )
| ( ( sk1 @ sk4 )
& ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(24,plain,
( ( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| sk5 )
& ( ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| sk5 )
& ( ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 )
| sk5 )
& ( ( sk1 @ sk4 )
| ~ sk5
| ( sk1 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ~ sk5
| ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ~ sk5
| ( sk3 @ sk4 ) )
& ( ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ( sk1 @ sk4 )
| sk5 )
& ( ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk2 @ sk4 )
| sk5 )
& ( ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 )
| sk5 )
& ( ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ~ sk5
| ( sk1 @ sk4 ) )
& ( ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ~ sk5
| ( sk2 @ sk4 ) )
& ( ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ~ sk5
| ( sk3 @ sk4 ) )
& ( ~ ( sk3 @ sk4 )
| ( sk2 @ sk4 )
| ( sk1 @ sk4 )
| sk5 )
& ( ~ ( sk3 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 )
| sk5 )
& ( ~ ( sk3 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 )
| sk5 )
& ( ~ ( sk3 @ sk4 )
| ( sk2 @ sk4 )
| ~ sk5
| ( sk1 @ sk4 ) )
& ( ~ ( sk3 @ sk4 )
| ( sk2 @ sk4 )
| ~ sk5
| ( sk2 @ sk4 ) )
& ( ~ ( sk3 @ sk4 )
| ( sk2 @ sk4 )
| ~ sk5
| ( sk3 @ sk4 ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(36,plain,
( ( sk1 @ sk4 )
| ~ sk5
| ( sk1 @ sk4 ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(48,plain,
( ( sk1 @ sk4 )
| ~ sk5 ),
inference(simp,[status(thm)],[36]) ).
thf(58,plain,
( ~ sk5
| ( ( $true
& ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) )
!= ( ( ( sk1 @ sk4 )
& ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ) )
| ( ( sk1 @ sk4 )
& ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[48,6]) ).
thf(59,plain,
( ~ sk5
| ( ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) )
!= ( ( ( sk1 @ sk4 )
& ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ) )
| ( ( sk1 @ sk4 )
& ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk4 ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(60,plain,
( ~ sk5
| ( ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) )
!= ( ( ( sk1 @ sk4 )
& ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ) )
| ( ( sk1 @ sk4 )
& ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[59:[]]) ).
thf(276,plain,
( ~ sk5
| ~ sk5
| ( ( ( $true
& ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ) )
| ( ( sk1 @ sk4 )
& ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) )
!= ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) ) )
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[48,60]) ).
thf(277,plain,
( ~ sk5
| ( ( ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
| ( ( sk1 @ sk4 )
& ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) )
!= ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) ) )
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk4 ) ) ),
inference(simp,[status(thm)],[276]) ).
thf(278,plain,
( ~ sk5
| ( ( ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
| ( ( sk1 @ sk4 )
& ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) )
!= ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[277:[]]) ).
thf(388,plain,
( ~ sk5
| ~ sk5
| ( ( ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
| ( $true
& ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) )
!= ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) ) )
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[48,278]) ).
thf(389,plain,
( ~ sk5
| ( ( ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
| ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) )
!= ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) ) )
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk4 ) ) ),
inference(simp,[status(thm)],[388]) ).
thf(390,plain,
( ~ sk5
| ( ( ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
| ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) )
!= ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[389:[]]) ).
thf(27,plain,
( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| sk5 ),
inference(cnfConj,[status(thm)],[24]) ).
thf(44,plain,
( ( sk1 @ sk4 )
| sk5 ),
inference(simp,[status(thm)],[27]) ).
thf(7,plain,
( ~ ( ( sk1 @ sk4 )
& ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) )
| ~ ( ( ( sk1 @ sk4 )
& ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ) )
| ( ( sk1 @ sk4 )
& ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(14,plain,
( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(18,plain,
( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ),
inference(simp,[status(thm)],[14]) ).
thf(88,plain,
( sk5
| ~ $true
| ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[44,18]) ).
thf(89,plain,
( sk5
| ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk4 ) ) ),
inference(simp,[status(thm)],[88]) ).
thf(90,plain,
( sk5
| ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[89:[]]) ).
thf(39,plain,
( ~ ( sk3 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 )
| sk5 ),
inference(cnfConj,[status(thm)],[24]) ).
thf(45,plain,
( ~ ( sk3 @ sk4 )
| ( sk2 @ sk4 )
| sk5 ),
inference(simp,[status(thm)],[39]) ).
thf(641,plain,
( sk5
| ( sk2 @ sk4 )
| ~ $true
| ( sk2 @ sk4 )
| sk5
| ( ( sk3 @ sk4 )
!= ( sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[90,45]) ).
thf(642,plain,
( sk5
| ( sk2 @ sk4 )
| ( ( sk3 @ sk4 )
!= ( sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[641]) ).
thf(643,plain,
( sk5
| ( sk2 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[642:[]]) ).
thf(49,plain,
( sk5
| ( ( $true
& ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) )
!= ( ( ( sk1 @ sk4 )
& ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ) )
| ( ( sk1 @ sk4 )
& ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[44,6]) ).
thf(50,plain,
( sk5
| ( ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) )
!= ( ( ( sk1 @ sk4 )
& ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ) )
| ( ( sk1 @ sk4 )
& ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk4 ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(51,plain,
( sk5
| ( ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) )
!= ( ( ( sk1 @ sk4 )
& ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ) )
| ( ( sk1 @ sk4 )
& ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[50:[]]) ).
thf(102,plain,
( sk5
| sk5
| ( ( ( ( sk1 @ sk4 )
& ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ) )
| ( $true
& ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) )
!= ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) ) )
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[44,51]) ).
thf(103,plain,
( sk5
| ( ( ( ( sk1 @ sk4 )
& ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ) )
| ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) )
!= ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) ) )
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk4 ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(104,plain,
( sk5
| ( ( ( ( sk1 @ sk4 )
& ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ) )
| ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) )
!= ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[103:[]]) ).
thf(674,plain,
( sk5
| sk5
| ( ( ( ( sk1 @ sk4 )
& ~ ( $true
| ( sk3 @ sk4 ) ) )
| ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) )
!= ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) ) )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[643,104]) ).
thf(675,plain,
( sk5
| ( ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) )
!= ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) ) )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[674]) ).
thf(676,plain,
( sk5
| ( ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) )
!= ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[675:[]]) ).
thf(757,plain,
( sk5
| sk5
| ( ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ $true ) ) )
!= ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[643,676]) ).
thf(758,plain,
( sk5
| ( ( ~ ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) ) )
!= ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[757]) ).
thf(759,plain,
( sk5
| ( ( ~ ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) ) )
!= ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[758:[]]) ).
thf(786,plain,
( sk5
| sk5
| ( ( ~ ( $true
& ~ ( sk3 @ sk4 ) ) )
!= ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[643,759]) ).
thf(787,plain,
( sk5
| ( ( sk3 @ sk4 )
!= ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[786]) ).
thf(788,plain,
( sk5
| ( ( sk3 @ sk4 )
!= ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[787:[]]) ).
thf(809,plain,
( sk5
| sk5
| ( ( $true
& ( sk3 @ sk4 ) )
!= ( sk3 @ sk4 ) )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[643,788]) ).
thf(810,plain,
( sk5
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[809]) ).
thf(811,plain,
sk5,
inference(pattern_uni,[status(thm)],[810:[]]) ).
thf(894,plain,
( ~ $true
| ( ( ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
| ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) )
!= ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) ) ) ),
inference(rewrite,[status(thm)],[390,811]) ).
thf(895,plain,
( ( ~ ( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
| ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) )
!= ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ ( sk2 @ sk4 ) ) ) ) ),
inference(simp,[status(thm)],[894]) ).
thf(898,plain,
( ( sk1 @ sk4 )
| ~ $true ),
inference(rewrite,[status(thm)],[48,811]) ).
thf(899,plain,
sk1 @ sk4,
inference(simp,[status(thm)],[898]) ).
thf(910,plain,
( ~ $true
| ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ),
inference(rewrite,[status(thm)],[18,899]) ).
thf(911,plain,
( ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ),
inference(simp,[status(thm)],[910]) ).
thf(29,plain,
( ~ ( sk3 @ sk4 )
| ( sk2 @ sk4 )
| ~ sk5
| ( sk2 @ sk4 ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(43,plain,
( ~ ( sk3 @ sk4 )
| ( sk2 @ sk4 )
| ~ sk5 ),
inference(simp,[status(thm)],[29]) ).
thf(904,plain,
( ~ ( sk3 @ sk4 )
| ( sk2 @ sk4 )
| ~ $true ),
inference(rewrite,[status(thm)],[43,811]) ).
thf(905,plain,
( ~ ( sk3 @ sk4 )
| ( sk2 @ sk4 ) ),
inference(simp,[status(thm)],[904]) ).
thf(964,plain,
( ( sk2 @ sk4 )
| ~ $true
| ( sk2 @ sk4 )
| ( ( sk3 @ sk4 )
!= ( sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[911,905]) ).
thf(965,plain,
( ( sk2 @ sk4 )
| ( ( sk3 @ sk4 )
!= ( sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[964]) ).
thf(966,plain,
sk2 @ sk4,
inference(pattern_uni,[status(thm)],[965:[]]) ).
thf(969,plain,
( ( ~ ( $true
| ( sk3 @ sk4 ) )
| ( $true
& ( sk3 @ sk4 ) ) )
!= ( ~ ( ( $true
& ~ ( sk3 @ sk4 ) )
| ( ( sk3 @ sk4 )
& ~ $true ) ) ) ),
inference(rewrite,[status(thm)],[895,966]) ).
thf(970,plain,
$false,
inference(simp,[status(thm)],[969]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET622^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.10/0.22 % Computer : n009.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 13:39:45 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 0.89/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.98 % [INFO] Parsing done (185ms).
% 1.23/0.99 % [INFO] Running in sequential loop mode.
% 1.84/1.38 % [INFO] eprover registered as external prover.
% 1.84/1.39 % [INFO] Scanning for conjecture ...
% 2.04/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.21/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.21/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.21/1.52 % [INFO] Type checking passed.
% 2.21/1.53 % [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 ...
% 8.51/3.21 % [INFO] Killing All external provers ...
% 8.51/3.22 % Time passed: 2856ms (effective reasoning time: 2217ms)
% 8.51/3.22 % 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)>
% 8.51/3.22 % Axioms used in derivation (0):
% 8.51/3.22 % No. of inferences in proof: 66
% 8.51/3.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2856 ms resp. 2217 ms w/o parsing
% 8.51/3.29 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.51/3.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------