%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV447^1 : TPTP v9.3.1. Released v7.0.0.
% 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 : n008.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 08:37:18 AM UTC 2026
% Result : Theorem 128.09s 46.93s
% Output : Refutation 128.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 8
% Syntax : Number of formulae : 70 ( 28 unt; 0 typ; 5 def)
% Number of atoms : 480 ( 137 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 658 ( 113 ~; 59 |; 0 &; 486 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 140 ( 16 ^; 106 !; 13 ?; 140 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(skt1_type,type,
skt1: $tType ).
thf('const/sets/IN_decl',type,
'const/sets/IN':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf(sk1_decl,type,
sk1: skt1 > $o ).
thf(sk2_decl,type,
sk2: skt1 > $o ).
thf(sk3_decl,type,
sk3: skt1 ).
thf(sk5_decl,type,
sk5:
!>[TA: $tType] : ( TA > skt1 ) ).
thf(sk78_decl,type,
sk78: skt1 ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1 > $o] :
~ ! [B: skt1 > $o] :
( ( A != B )
= ( ? [C: skt1] :
( ( 'const/sets/IN' @ skt1 @ C @ B )
= ( ~ ( 'const/sets/IN' @ skt1 @ C @ A ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt1 > $o] :
( ( sk1 != A )
!= ( ? [B: skt1] :
( ( 'const/sets/IN' @ skt1 @ B @ A )
= ( ~ ( 'const/sets/IN' @ skt1 @ B @ sk1 ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
= ( ~ ( 'const/sets/IN' @ skt1 @ A @ sk1 ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [TA: $tType,A: TA] :
@+[B: skt1] :
( ( 'const/sets/IN' @ skt1 @ B @ sk2 )
= ( ~ ( 'const/sets/IN' @ skt1 @ B @ sk1 ) ) ) ) ) ).
thf(sk78_def,definition,
( sk78
= ( @+[A: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ sk1 )
!= ( 'const/sets/IN' @ skt1 @ A @ sk2 ) ) ) ) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ A )
= ( 'const/sets/IN' @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/EXTENSION_') ).
thf(11,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ A )
= ( 'const/sets/IN' @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ A )
= ( 'const/sets/IN' @ TA @ C @ B ) ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ A )
= ( 'const/sets/IN' @ TA @ C @ B ) ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(3,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(8,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(113,plain,
! [TA: $tType,TB: $tType,D: TB,C: TB > $o,B: TA > $o,A: TA > $o] :
( ( ( ! [E: TA] :
( ( 'const/sets/IN' @ TA @ E @ A )
= ( 'const/sets/IN' @ TA @ E @ B ) ) )
= ( 'const/sets/IN' @ TB @ D @ C ) )
| ( ( A = B )
!= ( C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[13,10]) ).
thf(131,plain,
! [TA: $tType,TB: $tType,C: TB > TA > $o,B: TB > TA > $o,A: TB] :
( ( ! [D: TA] :
( ( 'const/sets/IN' @ TA @ D @ ( B @ A ) )
= ( 'const/sets/IN' @ TA @ D @ ( C @ A ) ) ) )
= ( 'const/sets/IN' @ TB @ A
@ ^ [D: TB] :
( ( B @ D )
= ( C @ D ) ) ) ),
inference(pre_uni,[status(thm)],[113:[bind(A,$thf( E @ D )),bind(B,$thf( F @ D )),bind(C,$thf( ^ [G: TB] : ( ( E @ G ) = ( F @ G ) ) ))]]) ).
thf(139,plain,
! [TA: $tType,TB: $tType,C: TB > TA > $o,B: TB > TA > $o,A: TB] :
( ( ! [D: TA] :
( ( 'const/sets/IN' @ TA @ D @ ( B @ A ) )
= ( 'const/sets/IN' @ TA @ D @ ( C @ A ) ) ) )
= ( 'const/sets/IN' @ TB @ A
@ ^ [D: TB] :
( ( B @ D )
= ( C @ D ) ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A != B )
= ( ? [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ B )
= ( ~ ( 'const/sets/IN' @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/NOT_EQUAL_SETS_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A != B )
= ( ? [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ B )
= ( ~ ( 'const/sets/IN' @ TA @ C @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A != B )
= ( ? [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ B )
= ( ~ ( 'const/sets/IN' @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ( sk1 != sk2 )
!= ( ? [A: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
= ( ~ ( 'const/sets/IN' @ skt1 @ A @ sk1 ) ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
( ( sk1 != sk2 )
!= ( ? [A: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
= ( ~ ( 'const/sets/IN' @ skt1 @ A @ sk1 ) ) ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(23,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( ( ~ ( 'const/sets/IN' @ TA @ B @ A ) )
!= ( ? [C: skt1] :
( ( 'const/sets/IN' @ skt1 @ C @ sk2 )
= ( ~ ( 'const/sets/IN' @ skt1 @ C @ sk1 ) ) ) ) )
| ( ( A @ B )
!= ( sk1 = sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[10,7]) ).
thf(26,plain,
! [TA: $tType,A: TA] :
( ( ~ ( 'const/sets/IN' @ TA @ A
@ ^ [B: TA] : ( sk1 = sk2 ) ) )
!= ( ? [B: skt1] :
( ( 'const/sets/IN' @ skt1 @ B @ sk2 )
= ( ~ ( 'const/sets/IN' @ skt1 @ B @ sk1 ) ) ) ) ),
inference(pre_uni,[status(thm)],[23:[bind(A,$thf( ^ [C: TA] : ( sk1 = sk2 ) )),bind(B,$thf( B ))]]) ).
thf(28,plain,
! [TA: $tType,A: TA] :
( ( ~ ( 'const/sets/IN' @ TA @ A
@ ^ [B: TA] : ( sk1 = sk2 ) ) )
!= ( ? [B: skt1] :
( ( 'const/sets/IN' @ skt1 @ B @ sk2 )
= ( ~ ( 'const/sets/IN' @ skt1 @ B @ sk1 ) ) ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(48,plain,
! [TA: $tType,A: TA] :
( ~ ( 'const/sets/IN' @ TA @ A
@ ^ [B: TA] : ( sk1 = sk2 ) )
| ? [B: skt1] :
( ( 'const/sets/IN' @ skt1 @ B @ sk2 )
= ( ~ ( 'const/sets/IN' @ skt1 @ B @ sk1 ) ) ) ),
inference(bool_ext,[status(thm)],[28]) ).
thf(58,plain,
! [TA: $tType,A: TA] :
( ~ ( 'const/sets/IN' @ TA @ A
@ ^ [B: TA] : ( sk1 = sk2 ) )
| ( ( 'const/sets/IN' @ skt1 @ ( sk5 @ TA @ A ) @ sk2 )
= ( ~ ( 'const/sets/IN' @ skt1 @ ( sk5 @ TA @ A ) @ sk1 ) ) ) ),
inference(cnf,[status(esa)],[48]) ).
thf(59,plain,
! [TA: $tType,A: TA] :
( ( ( 'const/sets/IN' @ skt1 @ ( sk5 @ TA @ A ) @ sk2 )
= ( ~ ( 'const/sets/IN' @ skt1 @ ( sk5 @ TA @ A ) @ sk1 ) ) )
| ~ ( 'const/sets/IN' @ TA @ A
@ ^ [B: TA] : ( sk1 = sk2 ) ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(14,plain,
( ~ ( ( sk1 != sk2 ) )
| ~ ? [A: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
= ( ~ ( 'const/sets/IN' @ skt1 @ A @ sk1 ) ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(16,plain,
! [A: skt1] :
( ( sk1 = sk2 )
| ( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
!= ( ~ ( 'const/sets/IN' @ skt1 @ A @ sk1 ) ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(17,plain,
! [A: skt1] :
( ( sk2 = sk1 )
| ( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
!= ( ~ ( 'const/sets/IN' @ skt1 @ A @ sk1 ) ) ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(2049,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ ( 'const/sets/IN' @ TA @ A
@ ^ [C: TA] : ( sk1 = sk2 ) )
| ( sk2 = sk1 )
| ( ( ~ ( 'const/sets/IN' @ skt1 @ ( sk5 @ TA @ A ) @ sk1 ) )
!= ( ~ ( 'const/sets/IN' @ skt1 @ B @ sk1 ) ) )
| ( ( 'const/sets/IN' @ skt1 @ ( sk5 @ TA @ A ) @ sk2 )
!= ( 'const/sets/IN' @ skt1 @ B @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[59,17]) ).
thf(2050,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ ( 'const/sets/IN' @ TA @ A
@ ^ [C: TA] : ( sk1 = sk2 ) )
| ( sk2 = sk1 )
| ( ( 'const/sets/IN' @ skt1 @ ( sk5 @ TA @ A ) @ sk1 )
!= ( 'const/sets/IN' @ skt1 @ B @ sk1 ) )
| ( ( 'const/sets/IN' @ skt1 @ ( sk5 @ TA @ A ) @ sk2 )
!= ( 'const/sets/IN' @ skt1 @ B @ sk2 ) ) ),
inference(simp,[status(thm)],[2049]) ).
thf(2051,plain,
! [TA: $tType,A: TA] :
( ~ ( 'const/sets/IN' @ TA @ A
@ ^ [B: TA] : ( sk1 = sk2 ) )
| ( sk2 = sk1 )
| ( ( 'const/sets/IN' @ skt1 @ ( sk5 @ TA @ A ) @ sk1 )
!= ( 'const/sets/IN' @ skt1 @ ( sk5 @ TA @ A ) @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[2050:[bind(A,$thf( C )),bind(B,$thf( sk5 @ TA @ C ))]]) ).
thf(2242,plain,
! [TA: $tType,A: TA] :
( ~ ( 'const/sets/IN' @ TA @ A
@ ^ [B: TA] : ( sk1 = sk2 ) )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[2051]) ).
thf(15,plain,
( ( sk1 != sk2 )
| ? [A: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
= ( ~ ( 'const/sets/IN' @ skt1 @ A @ sk1 ) ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(18,plain,
( ( sk1 != sk2 )
| ( ( 'const/sets/IN' @ skt1 @ sk3 @ sk2 )
= ( ~ ( 'const/sets/IN' @ skt1 @ sk3 @ sk1 ) ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(19,plain,
( ( sk2 != sk1 )
| ( ( 'const/sets/IN' @ skt1 @ sk3 @ sk2 )
= ( ~ ( 'const/sets/IN' @ skt1 @ sk3 @ sk1 ) ) ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(157,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( sk2 != sk1 )
| ( ( ~ ( A @ B ) )
= ( 'const/sets/IN' @ skt1 @ sk3 @ sk2 ) )
| ( ( 'const/sets/IN' @ TA @ B @ A )
!= ( 'const/sets/IN' @ skt1 @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[10,19]) ).
thf(158,plain,
( ( sk2 != sk1 )
| ( ( ~ ( sk1 @ sk3 ) )
= ( 'const/sets/IN' @ skt1 @ sk3 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[157:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(6731,plain,
( ( sk2 != sk1 )
| ( sk2 != sk1 )
| ( ( ~ ~ ( sk1 @ sk3 ) )
= ( 'const/sets/IN' @ skt1 @ sk3 @ sk2 ) )
| ( ( 'const/sets/IN' @ skt1 @ sk3 @ sk2 )
!= ( 'const/sets/IN' @ skt1 @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[158,19]) ).
thf(6732,plain,
( ( sk2 != sk1 )
| ( ( sk1 @ sk3 )
= ( 'const/sets/IN' @ skt1 @ sk3 @ sk2 ) )
| ( ( 'const/sets/IN' @ skt1 @ sk3 @ sk2 )
!= ( 'const/sets/IN' @ skt1 @ sk3 @ sk1 ) ) ),
inference(simp,[status(thm)],[6731]) ).
thf(6750,plain,
( ( ( sk1 @ sk3 )
= ( 'const/sets/IN' @ skt1 @ sk3 @ sk2 ) )
| ( sk2 != sk1 )
| ( sk3 != sk3 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[6732]) ).
thf(6829,plain,
( ( ( sk1 @ sk3 )
= ( 'const/sets/IN' @ skt1 @ sk3 @ sk2 ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[6750]) ).
thf(8628,plain,
( ( sk2 != sk1 )
| ( sk2 != sk1 )
| ( ( ~ ( 'const/sets/IN' @ skt1 @ sk3 @ sk2 ) )
= ( 'const/sets/IN' @ skt1 @ sk3 @ sk2 ) )
| ( ( sk1 @ sk3 )
!= ( sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[6829,158]) ).
thf(8629,plain,
( ( sk2 != sk1 )
| ( ( sk1 @ sk3 )
!= ( sk1 @ sk3 ) ) ),
inference(simp,[status(thm)],[8628]) ).
thf(8630,plain,
sk2 != sk1,
inference(pattern_uni,[status(thm)],[8629:[]]) ).
thf(19226,plain,
! [TA: $tType,A: TA] :
~ ( 'const/sets/IN' @ TA @ A
@ ^ [B: TA] : ( sk1 = sk2 ) ),
inference(simplifyReflect,[status(thm)],[2242,8630]) ).
thf(19293,plain,
! [TA: $tType,TB: $tType,TC: $tType,D: TC,C: TB > TA > $o,B: TB > TA > $o,A: TB] :
( ~ ! [E: TA] :
( ( 'const/sets/IN' @ TA @ E @ ( B @ A ) )
= ( 'const/sets/IN' @ TA @ E @ ( C @ A ) ) )
| ( ( 'const/sets/IN' @ TB @ A
@ ^ [E: TB] :
( ( B @ E )
= ( C @ E ) ) )
!= ( 'const/sets/IN' @ TC @ D
@ ^ [E: TC] : ( sk1 = sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[139,19226]) ).
thf(19294,plain,
~ ! [A: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ sk1 )
= ( 'const/sets/IN' @ skt1 @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[19293:[bind(A,$thf( A )),bind(B,$thf( ^ [E: TC] : sk1 )),bind(C,$thf( ^ [E: TC] : sk2 )),bind(D,$thf( A )),bind_type(TA,$thf( skt1 )),bind_type(TB,$thf( TC ))]]) ).
thf(19312,plain,
( ( 'const/sets/IN' @ skt1 @ sk78 @ sk1 )
!= ( 'const/sets/IN' @ skt1 @ sk78 @ sk2 ) ),
inference(cnf,[status(esa)],[19294]) ).
thf(19313,plain,
( ( 'const/sets/IN' @ skt1 @ sk78 @ sk2 )
!= ( 'const/sets/IN' @ skt1 @ sk78 @ sk1 ) ),
inference(lifteq,[status(thm)],[19312]) ).
thf(19334,plain,
( ( 'const/sets/IN' @ skt1 @ sk78 @ sk2 )
| ( 'const/sets/IN' @ skt1 @ sk78 @ sk1 ) ),
inference(bool_ext,[status(thm)],[19313]) ).
thf(206,plain,
! [A: skt1] :
( ( sk2 = sk1 )
| ~ ( 'const/sets/IN' @ skt1 @ A @ sk2 )
| ~ ~ ( 'const/sets/IN' @ skt1 @ A @ sk1 ) ),
inference(bool_ext,[status(thm)],[17]) ).
thf(266,plain,
! [A: skt1] :
( ( sk2 = sk1 )
| ~ ( 'const/sets/IN' @ skt1 @ A @ sk2 )
| ( 'const/sets/IN' @ skt1 @ A @ sk1 ) ),
inference(cnf,[status(esa)],[206]) ).
thf(47121,plain,
! [A: skt1] :
( ~ ( 'const/sets/IN' @ skt1 @ A @ sk2 )
| ( 'const/sets/IN' @ skt1 @ A @ sk1 ) ),
inference(simplifyReflect,[status(thm)],[266,8630]) ).
thf(47142,plain,
! [A: skt1] :
( ( 'const/sets/IN' @ skt1 @ sk78 @ sk1 )
| ~ $true
| ( 'const/sets/IN' @ skt1 @ A @ sk1 )
| ( ( 'const/sets/IN' @ skt1 @ sk78 @ sk2 )
!= ( 'const/sets/IN' @ skt1 @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[19334,47121]) ).
thf(47143,plain,
! [A: skt1] :
( ( 'const/sets/IN' @ skt1 @ sk78 @ sk1 )
| ( 'const/sets/IN' @ skt1 @ A @ sk1 )
| ( ( 'const/sets/IN' @ skt1 @ sk78 @ sk2 )
!= ( 'const/sets/IN' @ skt1 @ A @ sk2 ) ) ),
inference(simp,[status(thm)],[47142]) ).
thf(47144,plain,
( ( 'const/sets/IN' @ skt1 @ sk78 @ sk1 )
| ( 'const/sets/IN' @ skt1 @ sk78 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[47143:[bind(A,$thf( sk78 ))]]) ).
thf(47203,plain,
'const/sets/IN' @ skt1 @ sk78 @ sk1,
inference(simp,[status(thm)],[47144]) ).
thf(207,plain,
! [A: skt1] :
( ( sk2 = sk1 )
| ( 'const/sets/IN' @ skt1 @ A @ sk2 )
| ~ ( 'const/sets/IN' @ skt1 @ A @ sk1 ) ),
inference(bool_ext,[status(thm)],[17]) ).
thf(267,plain,
! [A: skt1] :
( ( sk2 = sk1 )
| ( 'const/sets/IN' @ skt1 @ A @ sk2 )
| ~ ( 'const/sets/IN' @ skt1 @ A @ sk1 ) ),
inference(cnf,[status(esa)],[207]) ).
thf(47855,plain,
! [A: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
| ~ ( 'const/sets/IN' @ skt1 @ A @ sk1 ) ),
inference(simplifyReflect,[status(thm)],[267,8630]) ).
thf(47982,plain,
! [A: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
| ~ $true
| ( ( 'const/sets/IN' @ skt1 @ sk78 @ sk1 )
!= ( 'const/sets/IN' @ skt1 @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[47203,47855]) ).
thf(47983,plain,
! [A: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
| ( ( 'const/sets/IN' @ skt1 @ sk78 @ sk1 )
!= ( 'const/sets/IN' @ skt1 @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[47982]) ).
thf(47984,plain,
'const/sets/IN' @ skt1 @ sk78 @ sk2,
inference(pattern_uni,[status(thm)],[47983:[bind(A,$thf( sk78 ))]]) ).
thf(19333,plain,
( ~ ( 'const/sets/IN' @ skt1 @ sk78 @ sk2 )
| ~ ( 'const/sets/IN' @ skt1 @ sk78 @ sk1 ) ),
inference(bool_ext,[status(thm)],[19313]) ).
thf(47222,plain,
( ~ ( 'const/sets/IN' @ skt1 @ sk78 @ sk2 )
| ~ $true ),
inference(rewrite,[status(thm)],[19333,47203]) ).
thf(47223,plain,
~ ( 'const/sets/IN' @ skt1 @ sk78 @ sk2 ),
inference(simp,[status(thm)],[47222]) ).
thf(48700,plain,
$false,
inference(rewrite,[status(thm)],[47984,47223]) ).
thf(48701,plain,
$false,
inference(simp,[status(thm)],[48700]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV447^1 : TPTP v9.3.1. Released v7.0.0.
% 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
% 0.12/0.22 % Computer : n008.cluster.edu
% 0.12/0.22 % Model : x86_64 x86_64
% 0.12/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.22 % Memory : 8046.5625MB
% 0.12/0.22 % OS : Linux 6.8.0-71-generic
% 0.12/0.22 % CPULimit : 300
% 0.12/0.22 % WCLimit : 300
% 0.12/0.22 % DateTime : Tue Sep 29 15:49:08 UTC 2026
% 0.12/0.22 % CPUTime :
% 0.12/0.22 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
% 0.98/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.16/1.00 % [INFO] Parsing done (189ms).
% 1.16/1.02 % [INFO] Running in sequential loop mode.
% 1.89/1.40 % [INFO] eprover registered as external prover.
% 1.89/1.41 % [INFO] Scanning for conjecture ...
% 2.06/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.06/1.54 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.06/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.06/1.56 % [INFO] Type checking passed.
% 2.06/1.56 % [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 ...
% 128.09/46.93 % [INFO] Killing All external provers ...
% 128.09/46.93 % Time passed: 46560ms (effective reasoning time: 45905ms)
% 128.09/46.93 % 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)>
% 128.09/46.93 % Axioms used in derivation (2): thm/sets/EXTENSION_, thm/sets/IN_
% 128.09/46.93 % No. of inferences in proof: 65
% 128.09/46.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 46560 ms resp. 45905 ms w/o parsing
% 128.09/46.97 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 128.09/46.97 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------