TSTP Solution File: SEV453^1 by Leo-III-SAT---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SEV453^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n029.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 102.75s 17.01s
% Output : Refutation 102.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 4
% Syntax : Number of formulae : 67 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 286 ( 53 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 711 ( 60 ~; 49 |; 17 &; 585 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 113 ( 113 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 247 ( 57 ^ 190 !; 0 ?; 247 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'const/sets/UNIV\'_type',type,
'\'const/sets/UNIV\'':
!>[TA: $tType] : ( TA > $o ) ).
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/sandbox/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(10,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(11,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(25,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
| ~ ( A @ B ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p','thm/sets/IN_INTER_') ).
thf(15,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)],[5]) ).
thf(16,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)],[15]) ).
thf(17,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)],[16]) ).
thf(118,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)],[17]) ).
thf(167,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)],[118]) ).
thf(141,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)],[12,17]) ).
thf(147,plain,
! [TA: $tType,TB: $tType,F: TA > TB > TB > $o,E: TA > TB > TB > $o,D: TA > TB,C: TB > $o,B: TB > $o,A: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [G: TA] :
( '\'const/sets/IN\'' @ TB @ ( D @ G )
@ ^ [H: TB] : ( '\'const/sets/INTER\'' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
= ( ( '\'const/sets/IN\'' @ TB @ ( D @ A ) @ B )
& ( '\'const/sets/IN\'' @ TB @ ( D @ A ) @ C ) ) )
| ( ( E @ A )
!= ( ^ [G: TB] : B ) )
| ( ( F @ A )
!= ( ^ [G: TB] : C ) ) ),
inference(pre_uni,[status(thm)],[141:[bind(A,$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(148,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)],[147:[]]) ).
thf(163,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)],[148]) ).
thf(131,plain,
! [TA: $tType,TB: $tType,E: TB,D: TB > $o,C: TA,B: TA > $o,A: TA > $o] :
( ( ( ( '\'const/sets/IN\'' @ TA @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ C @ B ) )
= ( D @ E ) )
| ( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/INTER\'' @ TA @ A @ B ) )
!= ( '\'const/sets/IN\'' @ TB @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[17,12]) ).
thf(132,plain,
! [TB: $tType,C: TB,B: TB > $o,A: TB > $o] :
( ( ( '\'const/sets/IN\'' @ TB @ C @ A )
& ( '\'const/sets/IN\'' @ TB @ C @ B ) )
= ( '\'const/sets/INTER\'' @ TB @ A @ B @ C ) ),
inference(pattern_uni,[status(thm)],[131:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( '\'const/sets/INTER\'' @ TB @ A @ B )),bind(E,$thf( C )),bind_type(TA,$thf( TB ))]]) ).
thf(158,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/INTER\'' @ TA @ A @ B @ C ) ),
inference(simp,[status(thm)],[132]) ).
thf(6082,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)],[163,158]) ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o] :
( ( '\'const/sets/INTER\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INTER_UNIV_1') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o] :
( ( '\'const/sets/INTER\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) )
= A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [TA: $tType,A: TA > $o] :
( ( '\'const/sets/INTER\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
( ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ ( '\'const/sets/UNIV\'' @ skt1 ) )
!= sk1 ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
( ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ ( '\'const/sets/UNIV\'' @ skt1 ) )
!= sk1 ),
inference(lifteq,[status(thm)],[8]) ).
thf(21,plain,
( ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ ( '\'const/sets/UNIV\'' @ skt1 ) @ sk2 )
!= ( sk1 @ sk2 ) ),
inference(func_ext,[status(esa)],[9]) ).
thf(22,plain,
( ~ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ ( '\'const/sets/UNIV\'' @ skt1 ) @ sk2 )
| ~ ( sk1 @ sk2 ) ),
inference(bool_ext,[status(thm)],[21]) ).
thf(4,axiom,
! [TA: $tType,A: TA] : ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_UNIV_') ).
thf(13,plain,
! [TA: $tType,A: TA] : ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,plain,
! [TA: $tType,A: TA] : ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) ),
inference(cnf,[status(esa)],[13]) ).
thf(31,plain,
! [TA: $tType,TB: $tType,C: TB,B: TB > $o,A: TA] :
( ( B @ C )
| ( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) )
!= ( '\'const/sets/IN\'' @ TB @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14,12]) ).
thf(32,plain,
! [TB: $tType,A: TB] : ( '\'const/sets/UNIV\'' @ TB @ A ),
inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( A )),bind(B,$thf( '\'const/sets/UNIV\'' @ TB )),bind(C,$thf( A )),bind_type(TA,$thf( TB ))]]) ).
thf(38,plain,
! [TA: $tType,A: TA] : ( '\'const/sets/UNIV\'' @ TA @ A ),
inference(simp,[status(thm)],[32]) ).
thf(177,plain,
( ~ ( '\'const/sets/INTER\'' @ skt1 @ sk1
@ ^ [A: skt1] : $true
@ sk2 )
| ~ ( sk1 @ sk2 ) ),
inference(rewrite,[status(thm)],[22,38]) ).
thf(23,plain,
( ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ ( '\'const/sets/UNIV\'' @ skt1 ) @ sk2 )
| ( sk1 @ sk2 ) ),
inference(bool_ext,[status(thm)],[21]) ).
thf(179,plain,
( ( '\'const/sets/INTER\'' @ skt1 @ sk1
@ ^ [A: skt1] : $true
@ sk2 )
| ( sk1 @ sk2 ) ),
inference(rewrite,[status(thm)],[23,38]) ).
thf(6089,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] :
( ( sk1 @ sk2 )
| ( '\'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 ) ) )
| ( ( E @ A )
!= ( ^ [G: TB] : B ) )
| ( ( F @ A )
!= ( ^ [G: TB] : C ) )
| ( ( '\'const/sets/INTER\'' @ skt1 @ sk1
@ ^ [G: skt1] : $true
@ sk2 )
!= ( '\'const/sets/INTER\'' @ TB @ B @ C @ ( D @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[179,6082]) ).
thf(6273,plain,
! [TA: $tType,C: TA > skt1 > skt1 > $o,B: TA > skt1 > skt1 > $o,A: TA] :
( ( sk1 @ sk2 )
| ( '\'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 ) ) )
| ( ( B @ A )
!= ( ^ [D: skt1] : sk1 ) )
| ( ( C @ A )
!= ( ^ [D: skt1,E: skt1] : $true ) ) ),
inference(pre_uni,[status(thm)],[6089:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( ^ [G: skt1] : $true )),bind(D,$thf( ^ [G: TA] : sk2 )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt1 ))]]) ).
thf(6274,plain,
! [TA: $tType,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] :
( '\'const/sets/IN\'' @ skt1 @ sk2
@ ( '\'const/sets/INTER\'' @ skt1 @ sk1
@ ^ [C: skt1] : $true ) ) )
| ( sk1 @ sk2 ) ),
inference(pre_uni,[status(thm)],[6273:[bind(A,$thf( (>) )),bind(B,$thf( ^ [D: TA] : ^ [E: skt1] : sk1 )),bind(C,$thf( ^ [D: TA] : ^ [E: skt1] : ^ [F: skt1] : $true ))]]) ).
thf(24,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( A @ B ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(6684,plain,
! [TA: $tType,TB: $tType,C: TB,B: TB > $o,A: TA] :
( ( sk1 @ sk2 )
| ( B @ C )
| ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] :
( '\'const/sets/IN\'' @ skt1 @ sk2
@ ( '\'const/sets/INTER\'' @ skt1 @ sk1
@ ^ [E: skt1] : $true ) ) )
!= ( '\'const/sets/IN\'' @ TB @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6274,24]) ).
thf(6685,plain,
( ( sk1 @ sk2 )
| ( '\'const/sets/IN\'' @ skt1 @ sk2
@ ( '\'const/sets/INTER\'' @ skt1 @ sk1
@ ^ [A: skt1] : $true ) ) ),
inference(pattern_uni,[status(thm)],[6684:[bind(A,$thf( A )),bind(B,$thf( ^ [D: TB] : ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ ^ [E: skt1] : $true ) ) )),bind(C,$thf( A )),bind_type(TA,$thf( TB ))]]) ).
thf(139,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 @ D ) )
= ( '\'const/sets/IN\'' @ TB @ E @ ( '\'const/sets/INTER\'' @ TB @ C @ D ) ) )
| ( ( '\'const/sets/IN\'' @ TA @ B @ A )
!= ( '\'const/sets/IN\'' @ TB @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[12,17]) ).
thf(140,plain,
! [TB: $tType,C: TB > $o,B: TB,A: TB > $o] :
( ( ( A @ B )
& ( '\'const/sets/IN\'' @ TB @ B @ C ) )
= ( '\'const/sets/IN\'' @ TB @ B @ ( '\'const/sets/INTER\'' @ TB @ A @ C ) ) ),
inference(pattern_uni,[status(thm)],[139:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(161,plain,
! [TA: $tType,C: TA > $o,B: TA,A: TA > $o] :
( ( ( A @ B )
& ( '\'const/sets/IN\'' @ TA @ B @ C ) )
= ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/INTER\'' @ TA @ A @ C ) ) ),
inference(simp,[status(thm)],[140]) ).
thf(6873,plain,
! [TA: $tType,C: TA > $o,B: TA,A: TA > $o] :
( ( sk1 @ sk2 )
| ( ( A @ B )
& ( '\'const/sets/IN\'' @ TA @ B @ C ) )
| ( ( '\'const/sets/IN\'' @ skt1 @ sk2
@ ( '\'const/sets/INTER\'' @ skt1 @ sk1
@ ^ [D: skt1] : $true ) )
!= ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/INTER\'' @ TA @ A @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[6685,161]) ).
thf(6874,plain,
( ( sk1 @ sk2 )
| ( ( sk1 @ sk2 )
& ( '\'const/sets/IN\'' @ skt1 @ sk2
@ ^ [A: skt1] : $true ) ) ),
inference(pattern_uni,[status(thm)],[6873:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( ^ [D: skt1] : $true )),bind_type(TA,$thf( skt1 ))]]) ).
thf(7042,plain,
( ( sk1 @ sk2 )
| ( sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[6874]) ).
thf(7043,plain,
sk1 @ sk2,
inference(simp,[status(thm)],[7042]) ).
thf(7072,plain,
( ~ ( '\'const/sets/INTER\'' @ skt1 @ sk1
@ ^ [A: skt1] : $true
@ sk2 )
| ~ $true ),
inference(rewrite,[status(thm)],[177,7043]) ).
thf(7073,plain,
~ ( '\'const/sets/INTER\'' @ skt1 @ sk1
@ ^ [A: skt1] : $true
@ sk2 ),
inference(simp,[status(thm)],[7072]) ).
thf(7183,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
@ ^ [G: skt1] : $true
@ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[6082,7073]) ).
thf(7186,plain,
! [TA: $tType,C: TA > skt1 > skt1 > $o,B: TA > skt1 > skt1 > $o,A: TA] :
( ( ( B @ A )
!= ( ^ [D: skt1] : sk1 ) )
| ( ( C @ A )
!= ( ^ [D: skt1,E: skt1] : $true ) )
| ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] :
( '\'const/sets/IN\'' @ skt1 @ sk2
@ ^ [E: skt1] : ( '\'const/sets/INTER\'' @ skt1 @ ( B @ D @ E ) @ ( C @ D @ E ) @ E ) ) ) ),
inference(pre_uni,[status(thm)],[7183:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( ^ [G: skt1] : $true )),bind(D,$thf( ^ [G: TA] : sk2 )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt1 ))]]) ).
thf(7187,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] :
( '\'const/sets/IN\'' @ skt1 @ sk2
@ ( '\'const/sets/INTER\'' @ skt1 @ sk1
@ ^ [C: skt1] : $true ) ) ),
inference(pre_uni,[status(thm)],[7186:[bind(A,$thf( (>) )),bind(B,$thf( ^ [D: TA] : ^ [E: skt1] : sk1 )),bind(C,$thf( ^ [D: TA] : ^ [E: skt1] : ^ [F: skt1] : $true ))]]) ).
thf(7994,plain,
! [TA: $tType,TB: $tType,C: TB,B: TA,A: TA > $o] :
( ~ ( A @ B )
| ( ( '\'const/sets/IN\'' @ TA @ B @ A )
!= ( '\'const/sets/IN\'' @ TB @ C
@ ^ [D: TB] :
( '\'const/sets/IN\'' @ skt1 @ sk2
@ ( '\'const/sets/INTER\'' @ skt1 @ sk1
@ ^ [E: skt1] : $true ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,7187]) ).
thf(7995,plain,
~ ( '\'const/sets/IN\'' @ skt1 @ sk2
@ ( '\'const/sets/INTER\'' @ skt1 @ sk1
@ ^ [A: skt1] : $true ) ),
inference(pattern_uni,[status(thm)],[7994:[bind(A,$thf( ^ [D: TB] : ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ ^ [E: skt1] : $true ) ) )),bind(B,$thf( B )),bind(C,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(8143,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 ) )
!= ( '\'const/sets/IN\'' @ skt1 @ sk2
@ ( '\'const/sets/INTER\'' @ skt1 @ sk1
@ ^ [D: skt1] : $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[167,7995]) ).
thf(8144,plain,
( ~ ( '\'const/sets/IN\'' @ skt1 @ sk2 @ sk1 )
| ~ ( '\'const/sets/IN\'' @ skt1 @ sk2
@ ^ [A: skt1] : $true ) ),
inference(pattern_uni,[status(thm)],[8143:[bind(A,$thf( sk1 )),bind(B,$thf( ^ [D: skt1] : $true )),bind(C,$thf( sk2 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(7100,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( ( sk1 @ sk2 )
!= ( A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7043,25]) ).
thf(7111,plain,
! [TA: $tType,A: TA] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : ( sk1 @ sk2 ) ),
inference(pre_uni,[status(thm)],[7100:[bind(A,$thf( ^ [C: TA] : ( sk1 @ sk2 ) )),bind(B,$thf( B ))]]) ).
thf(7131,plain,
! [TA: $tType,A: TA] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : ( sk1 @ sk2 ) ),
inference(simp,[status(thm)],[7111]) ).
thf(7200,plain,
! [TA: $tType,A: TA] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : $true ),
inference(rewrite,[status(thm)],[7131,7043]) ).
thf(8305,plain,
( ~ ( '\'const/sets/IN\'' @ skt1 @ sk2 @ sk1 )
| ~ $true ),
inference(rewrite,[status(thm)],[8144,7200]) ).
thf(8306,plain,
~ ( '\'const/sets/IN\'' @ skt1 @ sk2 @ sk1 ),
inference(simp,[status(thm)],[8305]) ).
thf(8311,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ~ ( A @ B )
| ( ( '\'const/sets/IN\'' @ TA @ B @ A )
!= ( '\'const/sets/IN\'' @ skt1 @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[25,8306]) ).
thf(8312,plain,
~ ( sk1 @ sk2 ),
inference(pattern_uni,[status(thm)],[8311:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(8328,plain,
~ $true,
inference(rewrite,[status(thm)],[8312,7043]) ).
thf(8329,plain,
$false,
inference(simp,[status(thm)],[8328]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV453^1 : TPTP v8.2.0. Released v7.0.0.
% 0.11/0.12 % Command : run_Leo-III %s %d SAT
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 19:10:55 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.84/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/0.96 % [INFO] Parsing done (106ms).
% 1.19/0.96 % [INFO] Running in sequential loop mode.
% 1.44/1.16 % [INFO] nitpick registered as external prover.
% 1.44/1.17 % [INFO] Scanning for conjecture ...
% 1.71/1.22 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.81/1.24 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.81/1.25 % [INFO] Problem is higher-order (TPTP THF).
% 1.81/1.26 % [INFO] Type checking passed.
% 1.81/1.26 % [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 ...
% 102.75/17.00 % [INFO] Killing All external provers ...
% 102.75/17.01 % Time passed: 16487ms (effective reasoning time: 16038ms)
% 102.75/17.01 % 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)>
% 102.75/17.01 % Axioms used in derivation (3): thm/sets/IN_, thm/sets/IN_INTER_, thm/sets/IN_UNIV_
% 102.75/17.01 % No. of inferences in proof: 67
% 102.75/17.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 16487 ms resp. 16038 ms w/o parsing
% 102.83/17.05 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 102.83/17.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------