TSTP Solution File: SEV452^1 by Leo-III-SAT---1.7.15
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SEV452^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 16:00:18 EDT 2024
% Result : Theorem 272.80s 45.91s
% Output : Refutation 272.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 3
% Syntax : Number of formulae : 54 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 253 ( 51 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 650 ( 61 ~; 46 |; 17 &; 526 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 111 ( 111 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 202 ( 36 ^ 166 !; 0 ?; 202 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'const/sets/INTER\'_type',type,
'\'const/sets/INTER\'':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA > $o ) ).
thf('\'const/sets/IN\'_type',type,
'\'const/sets/IN\'':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(sk1_type,type,
sk1: skt1 > $o ).
thf(sk2_type,type,
sk2: skt1 ).
thf(3,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(9,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(10,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/INTER\'' @ TA @ A @ B ) )
= ( ( '\'const/sets/IN\'' @ TA @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_INTER_') ).
thf(12,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/INTER\'' @ TA @ A @ B ) )
= ( ( '\'const/sets/IN\'' @ TA @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/INTER\'' @ TA @ A @ B ) )
= ( ( '\'const/sets/IN\'' @ TA @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(14,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/INTER\'' @ TA @ A @ B ) )
= ( ( '\'const/sets/IN\'' @ TA @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(134,plain,
! [TA: $tType,TB: $tType,E: TB,D: TB > $o,C: TB > $o,B: TA,A: TA > $o] :
( ( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( ( '\'const/sets/IN\'' @ TB @ E @ C )
& ( '\'const/sets/IN\'' @ TB @ E @ D ) ) )
| ( ( A @ B )
!= ( '\'const/sets/IN\'' @ TB @ E @ ( '\'const/sets/INTER\'' @ TB @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,14]) ).
thf(140,plain,
! [TA: $tType,TB: $tType,F: TA > TB > TB > $o,E: TA > TB > TB > $o,D: TA > TB,C: TB > $o,B: TB > $o,A: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [G: TA] :
( '\'const/sets/IN\'' @ TB @ ( D @ G )
@ ^ [H: TB] : ( '\'const/sets/INTER\'' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
= ( ( '\'const/sets/IN\'' @ TB @ ( D @ A ) @ B )
& ( '\'const/sets/IN\'' @ TB @ ( D @ A ) @ C ) ) )
| ( ( E @ A )
!= ( ^ [G: TB] : B ) )
| ( ( F @ A )
!= ( ^ [G: TB] : C ) ) ),
inference(pre_uni,[status(thm)],[134:[bind(A,$thf( ^ [I: TA] : ( '\'const/sets/IN\'' @ TB @ ( F @ I ) @ ^ [J: TB] : ( '\'const/sets/INTER\'' @ TB @ ( H @ I @ J ) @ ( I @ I @ J ) @ J ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( F @ B ))]]) ).
thf(141,plain,
! [TA: $tType,TB: $tType,F: TA > TB > TB > $o,E: TA > TB > TB > $o,D: TA > TB,C: TB > $o,B: TB > $o,A: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [G: TA] :
( '\'const/sets/IN\'' @ TB @ ( D @ G )
@ ^ [H: TB] : ( '\'const/sets/INTER\'' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
= ( ( '\'const/sets/IN\'' @ TB @ ( D @ A ) @ B )
& ( '\'const/sets/IN\'' @ TB @ ( D @ A ) @ C ) ) )
| ( ( E @ A )
!= ( ^ [G: TB] : B ) )
| ( ( F @ A )
!= ( ^ [G: TB] : C ) ) ),
inference(pre_uni,[status(thm)],[140:[]]) ).
thf(153,plain,
! [TA: $tType,TB: $tType,F: TA > TB > TB > $o,E: TA > TB > TB > $o,D: TA > TB,C: TB > $o,B: TB > $o,A: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [G: TA] :
( '\'const/sets/IN\'' @ TB @ ( D @ G )
@ ^ [H: TB] : ( '\'const/sets/INTER\'' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
= ( ( '\'const/sets/IN\'' @ TB @ ( D @ A ) @ B )
& ( '\'const/sets/IN\'' @ TB @ ( D @ A ) @ C ) ) )
| ( ( E @ A )
!= ( ^ [G: TB] : B ) )
| ( ( F @ A )
!= ( ^ [G: TB] : C ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(128,plain,
! [TA: $tType,TB: $tType,E: TB,D: TB > $o,C: TB > $o,B: TA,A: TA > $o] :
( ( ( A @ B )
= ( ( '\'const/sets/IN\'' @ TB @ E @ C )
& ( '\'const/sets/IN\'' @ TB @ E @ D ) ) )
| ( ( '\'const/sets/IN\'' @ TA @ B @ A )
!= ( '\'const/sets/IN\'' @ TB @ E @ ( '\'const/sets/INTER\'' @ TB @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,14]) ).
thf(129,plain,
! [TB: $tType,C: TB > $o,B: TB > $o,A: TB] :
( ( ( '\'const/sets/IN\'' @ TB @ A @ B )
& ( '\'const/sets/IN\'' @ TB @ A @ C ) )
= ( '\'const/sets/INTER\'' @ TB @ B @ C @ A ) ),
inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( '\'const/sets/INTER\'' @ TB @ C @ D )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(149,plain,
! [TA: $tType,C: TA > $o,B: TA > $o,A: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ A @ B )
& ( '\'const/sets/IN\'' @ TA @ A @ C ) )
= ( '\'const/sets/INTER\'' @ TA @ B @ C @ A ) ),
inference(simp,[status(thm)],[129]) ).
thf(8013,plain,
! [TA: $tType,TB: $tType,F: TA > TB > TB > $o,E: TA > TB > TB > $o,D: TA > TB,C: TB > $o,B: TB > $o,A: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [G: TA] :
( '\'const/sets/IN\'' @ TB @ ( D @ G )
@ ^ [H: TB] : ( '\'const/sets/INTER\'' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
= ( '\'const/sets/INTER\'' @ TB @ B @ C @ ( D @ A ) ) )
| ( ( E @ A )
!= ( ^ [G: TB] : B ) )
| ( ( F @ A )
!= ( ^ [G: TB] : C ) ) ),
inference(rewrite,[status(thm)],[153,149]) ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o] :
( ( '\'const/sets/INTER\'' @ TA @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INTER_IDEMPOT_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o] :
( ( '\'const/sets/INTER\'' @ TA @ A @ A )
= A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [TA: $tType,A: TA > $o] :
( ( '\'const/sets/INTER\'' @ TA @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
( ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 )
!= sk1 ),
inference(cnf,[status(esa)],[6]) ).
thf(8,plain,
( ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 )
!= sk1 ),
inference(lifteq,[status(thm)],[7]) ).
thf(18,plain,
( ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 @ sk2 )
!= ( sk1 @ sk2 ) ),
inference(func_ext,[status(esa)],[8]) ).
thf(20,plain,
( ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 @ sk2 )
| ( sk1 @ sk2 ) ),
inference(bool_ext,[status(thm)],[18]) ).
thf(116,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/INTER\'' @ TA @ A @ B ) )
| ~ ( ( '\'const/sets/IN\'' @ TA @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ),
inference(bool_ext,[status(thm)],[14]) ).
thf(159,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ C @ A )
| ~ ( '\'const/sets/IN\'' @ TA @ C @ B )
| ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/INTER\'' @ TA @ A @ B ) ) ),
inference(cnf,[status(esa)],[116]) ).
thf(22,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
| ~ ( A @ B ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(19,plain,
( ~ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 @ sk2 )
| ~ ( sk1 @ sk2 ) ),
inference(bool_ext,[status(thm)],[18]) ).
thf(8178,plain,
! [TA: $tType,TB: $tType,F: TA > TB > TB > $o,E: TA > TB > TB > $o,D: TA > TB,C: TB > $o,B: TB > $o,A: TA] :
( ( ( E @ A )
!= ( ^ [G: TB] : B ) )
| ( ( F @ A )
!= ( ^ [G: TB] : C ) )
| ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [G: TA] :
( '\'const/sets/IN\'' @ TB @ ( D @ G )
@ ^ [H: TB] : ( '\'const/sets/INTER\'' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
| ~ ( sk1 @ sk2 )
| ( ( '\'const/sets/INTER\'' @ TB @ B @ C @ ( D @ A ) )
!= ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[8013,19]) ).
thf(8206,plain,
! [TA: $tType,C: TA > skt1 > skt1 > $o,B: TA > skt1 > skt1 > $o,A: TA] :
( ( ( B @ A )
!= ( ^ [D: skt1] : sk1 ) )
| ( ( C @ A )
!= ( ^ [D: skt1] : sk1 ) )
| ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] :
( '\'const/sets/IN\'' @ skt1 @ sk2
@ ^ [E: skt1] : ( '\'const/sets/INTER\'' @ skt1 @ ( B @ D @ E ) @ ( C @ D @ E ) @ E ) ) )
| ~ ( sk1 @ sk2 ) ),
inference(pre_uni,[status(thm)],[8178:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk1 )),bind(D,$thf( ^ [G: TA] : sk2 )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt1 ))]]) ).
thf(8207,plain,
! [TA: $tType,A: TA] :
( ~ ( sk1 @ sk2 )
| ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ) ) ) ),
inference(pre_uni,[status(thm)],[8206:[bind(A,$thf( (>) )),bind(B,$thf( ^ [D: TA] : ^ [E: skt1] : sk1 )),bind(C,$thf( ^ [D: TA] : ^ [E: skt1] : sk1 ))]]) ).
thf(24732,plain,
! [TA: $tType,TB: $tType,C: TB,B: TA,A: TA > $o] :
( ~ ( A @ B )
| ~ ( sk1 @ sk2 )
| ( ( '\'const/sets/IN\'' @ TA @ B @ A )
!= ( '\'const/sets/IN\'' @ TB @ C
@ ^ [D: TB] : ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[22,8207]) ).
thf(24733,plain,
( ~ ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ) )
| ~ ( sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[24732:[bind(A,$thf( ^ [D: TB] : ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ) ) )),bind(B,$thf( B )),bind(C,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(24981,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ C @ A )
| ~ ( '\'const/sets/IN\'' @ TA @ C @ B )
| ~ ( sk1 @ sk2 )
| ( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/INTER\'' @ TA @ A @ B ) )
!= ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[159,24733]) ).
thf(24982,plain,
( ~ ( '\'const/sets/IN\'' @ skt1 @ sk2 @ sk1 )
| ~ ( '\'const/sets/IN\'' @ skt1 @ sk2 @ sk1 )
| ~ ( sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[24981:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(25012,plain,
( ~ ( '\'const/sets/IN\'' @ skt1 @ sk2 @ sk1 )
| ~ ( sk1 @ sk2 ) ),
inference(simp,[status(thm)],[24982]) ).
thf(25048,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ~ ( A @ B )
| ~ ( sk1 @ sk2 )
| ( ( '\'const/sets/IN\'' @ TA @ B @ A )
!= ( '\'const/sets/IN\'' @ skt1 @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[11,25012]) ).
thf(25049,plain,
( ~ ( sk1 @ sk2 )
| ~ ( sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[25048:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(25065,plain,
~ ( sk1 @ sk2 ),
inference(simp,[status(thm)],[25049]) ).
thf(25591,plain,
( ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 @ sk2 )
| $false ),
inference(rewrite,[status(thm)],[20,25065]) ).
thf(25592,plain,
'\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 @ sk2,
inference(simp,[status(thm)],[25591]) ).
thf(25647,plain,
! [TA: $tType,TB: $tType,F: TA > TB > TB > $o,E: TA > TB > TB > $o,D: TA > TB,C: TB > $o,B: TB > $o,A: TA] :
( ( ( E @ A )
!= ( ^ [G: TB] : B ) )
| ( ( F @ A )
!= ( ^ [G: TB] : C ) )
| ( '\'const/sets/IN\'' @ TA @ A
@ ^ [G: TA] :
( '\'const/sets/IN\'' @ TB @ ( D @ G )
@ ^ [H: TB] : ( '\'const/sets/INTER\'' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
| ( ( '\'const/sets/INTER\'' @ TB @ B @ C @ ( D @ A ) )
!= ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[8013,25592]) ).
thf(25669,plain,
! [TA: $tType,C: TA > skt1 > skt1 > $o,B: TA > skt1 > skt1 > $o,A: TA] :
( ( ( B @ A )
!= ( ^ [D: skt1] : sk1 ) )
| ( ( C @ A )
!= ( ^ [D: skt1] : sk1 ) )
| ( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] :
( '\'const/sets/IN\'' @ skt1 @ sk2
@ ^ [E: skt1] : ( '\'const/sets/INTER\'' @ skt1 @ ( B @ D @ E ) @ ( C @ D @ E ) @ E ) ) ) ),
inference(pre_uni,[status(thm)],[25647:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk1 )),bind(D,$thf( ^ [G: TA] : sk2 )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt1 ))]]) ).
thf(25670,plain,
! [TA: $tType,A: TA] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ) ) ),
inference(pre_uni,[status(thm)],[25669:[bind(A,$thf( (>) )),bind(B,$thf( ^ [D: TA] : ^ [E: skt1] : sk1 )),bind(C,$thf( ^ [D: TA] : ^ [E: skt1] : sk1 ))]]) ).
thf(21,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( A @ B ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(26237,plain,
! [TA: $tType,TB: $tType,C: TB,B: TB > $o,A: TA] :
( ( B @ C )
| ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ) ) )
!= ( '\'const/sets/IN\'' @ TB @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[25670,21]) ).
thf(26238,plain,
'\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ),
inference(pattern_uni,[status(thm)],[26237:[bind(A,$thf( A )),bind(B,$thf( ^ [D: TB] : ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ) ) )),bind(C,$thf( A )),bind_type(TA,$thf( TB ))]]) ).
thf(130,plain,
! [TA: $tType,TB: $tType,E: TB,D: TB > $o,C: TB > $o,B: TA,A: TA > $o] :
( ( ( ( '\'const/sets/IN\'' @ TB @ E @ C )
& ( A @ B ) )
= ( '\'const/sets/IN\'' @ TB @ E @ ( '\'const/sets/INTER\'' @ TB @ C @ D ) ) )
| ( ( '\'const/sets/IN\'' @ TA @ B @ A )
!= ( '\'const/sets/IN\'' @ TB @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[11,14]) ).
thf(131,plain,
! [TB: $tType,C: TB > $o,B: TB,A: TB > $o] :
( ( ( '\'const/sets/IN\'' @ TB @ B @ C )
& ( A @ B ) )
= ( '\'const/sets/IN\'' @ TB @ B @ ( '\'const/sets/INTER\'' @ TB @ C @ A ) ) ),
inference(pattern_uni,[status(thm)],[130:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(150,plain,
! [TA: $tType,C: TA > $o,B: TA,A: TA > $o] :
( ( ( '\'const/sets/IN\'' @ TA @ B @ C )
& ( A @ B ) )
= ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/INTER\'' @ TA @ C @ A ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(26368,plain,
! [TA: $tType,C: TA > $o,B: TA,A: TA > $o] :
( ( ( '\'const/sets/IN\'' @ TA @ B @ C )
& ( A @ B ) )
| ( ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ) )
!= ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/INTER\'' @ TA @ C @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[26238,150]) ).
thf(26369,plain,
( ( '\'const/sets/IN\'' @ skt1 @ sk2 @ sk1 )
& ( sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[26368:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(26397,plain,
sk1 @ sk2,
inference(cnf,[status(esa)],[26369]) ).
thf(26418,plain,
$false,
inference(rewrite,[status(thm)],[26397,25065]) ).
thf(26419,plain,
$false,
inference(simp,[status(thm)],[26418]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV452^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d SAT
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 21 19:11:40 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.83/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.15/0.96 % [INFO] Parsing done (102ms).
% 1.15/0.97 % [INFO] Running in sequential loop mode.
% 1.43/1.16 % [INFO] nitpick registered as external prover.
% 1.43/1.17 % [INFO] Scanning for conjecture ...
% 1.73/1.21 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.73/1.23 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.85/1.24 % [INFO] Problem is higher-order (TPTP THF).
% 1.85/1.25 % [INFO] Type checking passed.
% 1.85/1.25 % [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 ...
% 272.80/45.91 % [INFO] Killing All external provers ...
% 272.80/45.91 % Time passed: 45380ms (effective reasoning time: 44935ms)
% 272.80/45.91 % 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)>
% 272.80/45.91 % Axioms used in derivation (2): thm/sets/IN_, thm/sets/IN_INTER_
% 272.80/45.91 % No. of inferences in proof: 54
% 272.80/45.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 45380 ms resp. 44935 ms w/o parsing
% 272.81/45.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 272.81/45.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------