%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET888+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/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 08:31:16 AM UTC 2026
% Result : Theorem 159.16s 44.52s
% Output : Refutation 154.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 22
% Syntax : Number of formulae : 375 ( 159 unt; 0 typ; 8 def)
% Number of atoms : 958 ( 485 equ; 0 cnn)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 3360 ( 581 ~; 331 |; 36 &;2354 @)
% ( 6 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 704 ( 10 ^; 681 !; 5 ?; 704 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% Comments :
%------------------------------------------------------------------------------
thf(symmetric_difference_decl,type,
symmetric_difference: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $o ).
thf(sk6_decl,type,
sk6: $i > $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( A != B )
=> ( ( B @ singleton @ ( A @ singleton @ symmetric_difference ) )
= ( B @ ( A @ unordered_pair ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( sk1 != A )
=> ( ( A @ singleton @ ( sk1 @ singleton @ symmetric_difference ) )
= ( A @ ( sk1 @ unordered_pair ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ( C = B ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C = B )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( A @ ( D @ in ) )
=> ( ( D = B )
| ( D = C ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( D = B )
| ( D = C ) )
=> ( A @ ( D @ in ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( D = B )
| ( D = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(54,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( C
= ( B @ ( A @ unordered_pair ) ) )
=> ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(55,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ! [D: $i] :
( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ unordered_pair ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
=> ( ! [D: $i] :
( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ! [D: $i] :
( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(miniscope,[status(thm)],[54]) ).
thf(56,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( F @ ( G @ ( H @ sk7 ) ) @ in ) )
| ( H @ ( G @ ( F @ sk5 ) ) ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ( ( F @ ( G @ ( H @ sk7 ) ) )
= G )
| ( ( F @ ( G @ ( H @ sk7 ) ) )
= F )
| ( H @ ( G @ ( F @ sk5 ) ) ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk5 ) ) )
| ( ( F @ ( G @ ( H @ sk6 ) ) )
!= G ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk5 ) ) )
| ( ( F @ ( G @ ( H @ sk6 ) ) )
!= F ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk5 ) ) )
| ( H @ ( F @ ( G @ ( H @ sk6 ) ) @ in ) ) )
& ( ( C @ ( E @ in ) )
| ( E != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( C @ ( E @ in ) )
| ( E != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( D = B )
| ( D = A )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(60,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(69,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[60]) ).
thf(70,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( B @ in ) ),
inference(simp,[status(thm)],[69]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ( ( B
= ( A @ singleton ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(34,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
=> ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(miniscope,[status(thm)],[33]) ).
thf(35,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk4 ) @ in ) )
| ( ( E @ ( F @ sk3 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk4 ) )
= E )
| ( ( E @ ( F @ sk3 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk4 ) @ in ) )
| ( F @ ( E @ ( F @ sk3 ) @ in ) ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk4 ) )
= E )
| ( F @ ( E @ ( F @ sk3 ) @ in ) ) )
& ( ( B @ ( D @ in ) )
| ( D != A )
| ( B
!= ( A @ singleton ) ) )
& ( ( C = A )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ singleton ) ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ singleton ) ) ),
inference(cnfConj,[status(thm)],[35]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ in ) )
| ( C = A )
| ( B
!= ( A @ singleton ) ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( A @ singleton @ ( B @ in ) )
| ( B = A ) ),
inference(simp,[status(thm)],[44]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C != A )
| ( B
!= ( A @ singleton ) ) ),
inference(cnfConj,[status(thm)],[35]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C != A )
| ( B
!= ( A @ singleton ) ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(43,plain,
! [A: $i] : ( A @ singleton @ ( A @ in ) ),
inference(simp,[status(thm)],[42]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( B @ singleton @ ( A @ singleton @ symmetric_difference ) )
= ( B @ ( A @ unordered_pair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( A != B )
=> ( ( B @ singleton @ ( A @ singleton @ symmetric_difference ) )
= ( B @ ( A @ unordered_pair ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i,B: $i] :
( ( A != B )
=> ( ( B @ singleton @ ( A @ singleton @ symmetric_difference ) )
= ( B @ ( A @ unordered_pair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,plain,
( ( ( sk2 @ singleton @ ( sk1 @ singleton @ symmetric_difference ) )
!= ( sk2 @ ( sk1 @ unordered_pair ) ) )
& ( sk1 != sk2 ) ),
inference(cnf,[status(esa)],[16]) ).
thf(18,plain,
sk1 != sk2,
inference(cnfConj,[status(thm)],[17]) ).
thf(20,plain,
sk2 != sk1,
inference(lifteq,[status(thm)],[18]) ).
thf(389,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( A != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,20]) ).
thf(390,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( A @ singleton @ ( sk2 @ in ) ) ),
inference(pattern_uni,[status(thm)],[389:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(532,plain,
~ ( sk1 @ singleton @ ( sk2 @ in ) ),
inference(simp,[status(thm)],[390]) ).
thf(618,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,532]) ).
thf(619,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[618]) ).
thf(620,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[619]) ).
thf(626,plain,
( ( sk2 @ singleton )
!= ( sk1 @ singleton ) ),
inference(simp,[status(thm)],[620]) ).
thf(711,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk2 @ singleton ) )
| ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,626]) ).
thf(712,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( sk2 @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[711:[bind(A,$thf( A )),bind(B,$thf( sk2 @ singleton ))]]) ).
thf(719,plain,
~ ( sk1 @ singleton @ singleton @ ( sk2 @ singleton @ in ) ),
inference(simp,[status(thm)],[712]) ).
thf(998,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk2 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[70,719]) ).
thf(999,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk2 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[998]) ).
thf(1026,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk1 @ singleton @ singleton ) )
| ( B
!= ( sk2 @ singleton ) ) ),
inference(simp,[status(thm)],[999]) ).
thf(1030,plain,
! [A: $i] :
( ( sk2 @ singleton @ ( A @ unordered_pair ) )
!= ( sk1 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1026]) ).
thf(13,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(93,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(94,plain,
sk8 @ empty,
inference(cnf,[status(esa)],[93]) ).
thf(14,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(95,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(96,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[95]) ).
thf(97,plain,
~ ( sk9 @ empty ),
inference(cnf,[status(esa)],[96]) ).
thf(109,plain,
( ( ( sk9 @ empty )
!= ( sk8 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[94,97]) ).
thf(110,plain,
( ( sk9 @ empty )
!= ( sk8 @ empty ) ),
inference(simp,[status(thm)],[109]) ).
thf(111,plain,
sk9 != sk8,
inference(simp,[status(thm)],[110]) ).
thf(508,plain,
! [B: $i,A: $i] :
( ( B != sk9 )
| ( A != sk8 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,111]) ).
thf(509,plain,
! [A: $i] :
( ( A != sk8 )
| ~ ( A @ singleton @ ( sk9 @ in ) ) ),
inference(pattern_uni,[status(thm)],[508:[bind(A,$thf( A )),bind(B,$thf( sk9 ))]]) ).
thf(599,plain,
~ ( sk8 @ singleton @ ( sk9 @ in ) ),
inference(simp,[status(thm)],[509]) ).
thf(672,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk8 @ singleton @ ( sk9 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,599]) ).
thf(673,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk8 @ singleton @ ( sk9 @ in ) ) ),
inference(simp,[status(thm)],[672]) ).
thf(675,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk8 @ singleton ) )
| ( A != sk9 ) ),
inference(simp,[status(thm)],[673]) ).
thf(678,plain,
( ( sk9 @ singleton )
!= ( sk8 @ singleton ) ),
inference(simp,[status(thm)],[675]) ).
thf(976,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk9 @ singleton ) )
| ( B
!= ( sk8 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,678]) ).
thf(977,plain,
! [A: $i] :
( ( A
!= ( sk8 @ singleton ) )
| ~ ( sk9 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[976:[bind(A,$thf( sk9 @ singleton )),bind(B,$thf( B ))]]) ).
thf(980,plain,
~ ( sk9 @ singleton @ singleton @ ( sk8 @ singleton @ in ) ),
inference(simp,[status(thm)],[977]) ).
thf(1130,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk9 @ singleton @ singleton @ ( sk8 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,980]) ).
thf(1131,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk9 @ singleton @ singleton @ ( sk8 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1130]) ).
thf(1132,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk9 @ singleton @ singleton ) )
| ( A
!= ( sk8 @ singleton ) ) ),
inference(simp,[status(thm)],[1131]) ).
thf(1139,plain,
( ( sk9 @ singleton @ singleton )
!= ( sk8 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1132]) ).
thf(1316,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk9 @ singleton @ singleton ) )
| ( B
!= ( sk8 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,1139]) ).
thf(1317,plain,
! [A: $i] :
( ( A
!= ( sk8 @ singleton @ singleton ) )
| ~ ( sk9 @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1316:[bind(A,$thf( sk9 @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(1322,plain,
~ ( sk9 @ singleton @ singleton @ singleton @ ( sk8 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[1317]) ).
thf(602,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[70,532]) ).
thf(603,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[602]) ).
thf(622,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk1 @ singleton ) )
| ( B != sk2 ) ),
inference(simp,[status(thm)],[603]) ).
thf(628,plain,
! [A: $i] :
( ( sk2 @ ( A @ unordered_pair ) )
!= ( sk1 @ singleton ) ),
inference(simp,[status(thm)],[622]) ).
thf(1022,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk2 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,719]) ).
thf(1023,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk2 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1022]) ).
thf(1025,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton @ singleton ) )
| ( A
!= ( sk2 @ singleton ) ) ),
inference(simp,[status(thm)],[1023]) ).
thf(1029,plain,
( ( sk2 @ singleton @ singleton )
!= ( sk1 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1025]) ).
thf(1282,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk2 @ singleton @ singleton ) )
| ( A
!= ( sk1 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,1029]) ).
thf(1283,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( sk2 @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[1282:[bind(A,$thf( A )),bind(B,$thf( sk2 @ singleton @ singleton ))]]) ).
thf(1295,plain,
~ ( sk1 @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[1283]) ).
thf(753,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( sk2 @ ( C @ unordered_pair ) ) )
| ( B
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,628]) ).
thf(754,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( sk2 @ ( B @ unordered_pair ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[753:[bind(A,$thf( sk2 @ ( D @ unordered_pair ) )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(762,plain,
! [A: $i] :
~ ( sk2 @ ( A @ unordered_pair ) @ singleton @ ( sk1 @ singleton @ in ) ),
inference(simp,[status(thm)],[754]) ).
thf(64,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(71,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[64]) ).
thf(72,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( A @ in ) ),
inference(simp,[status(thm)],[71]) ).
thf(1128,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk9 @ singleton @ singleton @ ( sk8 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72,980]) ).
thf(1129,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk9 @ singleton @ singleton @ ( sk8 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1128]) ).
thf(1134,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk9 @ singleton @ singleton ) )
| ( A
!= ( sk8 @ singleton ) ) ),
inference(simp,[status(thm)],[1129]) ).
thf(1142,plain,
! [A: $i] :
( ( A @ ( sk8 @ singleton @ unordered_pair ) )
!= ( sk9 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1134]) ).
thf(656,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk8 @ singleton @ ( sk9 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[70,599]) ).
thf(657,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk8 @ singleton @ ( sk9 @ in ) ) ),
inference(simp,[status(thm)],[656]) ).
thf(674,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk8 @ singleton ) )
| ( B != sk9 ) ),
inference(simp,[status(thm)],[657]) ).
thf(677,plain,
! [A: $i] :
( ( sk9 @ ( A @ unordered_pair ) )
!= ( sk8 @ singleton ) ),
inference(simp,[status(thm)],[674]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(186,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( D @ ( C @ in ) ) )
| ~ ( C @ ( D @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[70,23]) ).
thf(187,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( D @ ( C @ in ) ) )
| ~ ( C @ ( D @ in ) ) ),
inference(simp,[status(thm)],[186]) ).
thf(188,plain,
! [B: $i,A: $i] :
~ ( B @ ( B @ ( A @ unordered_pair ) @ in ) ),
inference(pattern_uni,[status(thm)],[187:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ unordered_pair ) ))]]) ).
thf(202,plain,
! [B: $i,A: $i] :
~ ( B @ ( B @ ( A @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[188]) ).
thf(1382,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,1295]) ).
thf(1383,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1382]) ).
thf(1385,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk2 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[1383]) ).
thf(1398,plain,
( ( sk2 @ singleton @ singleton @ singleton )
!= ( sk1 @ singleton @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1385]) ).
thf(1769,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk2 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk1 @ singleton @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,1398]) ).
thf(1770,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( sk2 @ singleton @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[1769:[bind(A,$thf( A )),bind(B,$thf( sk2 @ singleton @ singleton @ singleton ))]]) ).
thf(1788,plain,
~ ( sk1 @ singleton @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[1770]) ).
thf(1310,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk9 @ singleton @ singleton ) )
| ( A
!= ( sk8 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,1139]) ).
thf(1311,plain,
! [A: $i] :
( ( A
!= ( sk8 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( sk9 @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[1310:[bind(A,$thf( A )),bind(B,$thf( sk9 @ singleton @ singleton ))]]) ).
thf(1327,plain,
~ ( sk8 @ singleton @ singleton @ singleton @ ( sk9 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[1311]) ).
thf(1631,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk9 @ singleton @ singleton @ singleton @ ( sk8 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,1322]) ).
thf(1632,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk9 @ singleton @ singleton @ singleton @ ( sk8 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1631]) ).
thf(1634,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk9 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk8 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[1632]) ).
thf(1644,plain,
( ( sk9 @ singleton @ singleton @ singleton )
!= ( sk8 @ singleton @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1634]) ).
thf(1953,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk9 @ singleton @ singleton @ singleton ) )
| ( B
!= ( sk8 @ singleton @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,1644]) ).
thf(1954,plain,
! [A: $i] :
( ( A
!= ( sk8 @ singleton @ singleton @ singleton ) )
| ~ ( sk9 @ singleton @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1953:[bind(A,$thf( sk9 @ singleton @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(1961,plain,
~ ( sk9 @ singleton @ singleton @ singleton @ singleton @ ( sk8 @ singleton @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[1954]) ).
thf(3769,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk9 @ singleton @ singleton @ singleton @ singleton @ ( sk8 @ singleton @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,1961]) ).
thf(3770,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk9 @ singleton @ singleton @ singleton @ singleton @ ( sk8 @ singleton @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[3769]) ).
thf(3815,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk9 @ singleton @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk8 @ singleton @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[3770]) ).
thf(3826,plain,
( ( sk9 @ singleton @ singleton @ singleton @ singleton )
!= ( sk8 @ singleton @ singleton @ singleton @ singleton ) ),
inference(simp,[status(thm)],[3815]) ).
thf(616,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72,532]) ).
thf(617,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[616]) ).
thf(621,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk1 @ singleton ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[617]) ).
thf(627,plain,
! [A: $i] :
( ( A @ ( sk2 @ unordered_pair ) )
!= ( sk1 @ singleton ) ),
inference(simp,[status(thm)],[621]) ).
thf(732,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ ( sk2 @ unordered_pair ) ) )
| ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,627]) ).
thf(733,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ ( sk2 @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[732:[bind(A,$thf( A )),bind(B,$thf( E @ ( sk2 @ unordered_pair ) )),bind(C,$thf( E ))]]) ).
thf(747,plain,
! [A: $i] :
~ ( sk1 @ singleton @ singleton @ ( A @ ( sk2 @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[733]) ).
thf(510,plain,
! [B: $i,A: $i] :
( ( A != sk9 )
| ( B != sk8 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,111]) ).
thf(511,plain,
! [A: $i] :
( ( A != sk8 )
| ~ ( sk9 @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[510:[bind(A,$thf( sk9 ))]]) ).
thf(601,plain,
~ ( sk9 @ singleton @ ( sk8 @ in ) ),
inference(simp,[status(thm)],[511]) ).
thf(683,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk9 @ singleton @ ( sk8 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[70,601]) ).
thf(684,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk9 @ singleton @ ( sk8 @ in ) ) ),
inference(simp,[status(thm)],[683]) ).
thf(703,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk9 @ singleton ) )
| ( B != sk8 ) ),
inference(simp,[status(thm)],[684]) ).
thf(709,plain,
! [A: $i] :
( ( sk8 @ ( A @ unordered_pair ) )
!= ( sk9 @ singleton ) ),
inference(simp,[status(thm)],[703]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(972,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk9 @ singleton ) )
| ( A
!= ( sk8 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,678]) ).
thf(973,plain,
! [A: $i] :
( ( A
!= ( sk8 @ singleton ) )
| ~ ( A @ singleton @ ( sk9 @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[972:[bind(A,$thf( A )),bind(B,$thf( sk9 @ singleton ))]]) ).
thf(983,plain,
~ ( sk8 @ singleton @ singleton @ ( sk9 @ singleton @ in ) ),
inference(simp,[status(thm)],[973]) ).
thf(1160,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk8 @ singleton @ singleton @ ( sk9 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[70,983]) ).
thf(1161,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk8 @ singleton @ singleton @ ( sk9 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1160]) ).
thf(1187,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk8 @ singleton @ singleton ) )
| ( B
!= ( sk9 @ singleton ) ) ),
inference(simp,[status(thm)],[1161]) ).
thf(1191,plain,
! [A: $i] :
( ( sk9 @ singleton @ ( A @ unordered_pair ) )
!= ( sk8 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1187]) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ~ ( B @ ( C @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,23]) ).
thf(116,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ~ ( B @ ( C @ in ) ) ),
inference(simp,[status(thm)],[115]) ).
thf(117,plain,
! [A: $i] :
~ ( A @ ( A @ singleton @ in ) ),
inference(pattern_uni,[status(thm)],[116:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ singleton ))]]) ).
thf(121,plain,
! [A: $i] :
~ ( A @ ( A @ singleton @ in ) ),
inference(simp,[status(thm)],[117]) ).
thf(165,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( C @ ( C @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[70,121]) ).
thf(166,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( C @ ( C @ singleton @ in ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(192,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= C )
| ( B
!= ( C @ singleton ) ) ),
inference(simp,[status(thm)],[166]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ unordered_pair ) )
!= B ),
inference(simp,[status(thm)],[192]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk7 ) ) )
= B )
| ( ( A @ ( B @ ( C @ sk7 ) ) )
= A )
| ( C @ ( B @ ( A @ sk5 ) ) ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ sk5 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk7 ) ) )
= B )
| ( ( A @ ( B @ ( C @ sk7 ) ) )
= A ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ sk5 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk7 ) ) )
= B )
| ( ( A @ ( B @ ( C @ sk7 ) ) )
= A ) ),
inference(simp,[status(thm)],[77]) ).
thf(254,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( C @ ( D @ in ) ) )
| ~ $true
| ~ ( D @ ( C @ in ) ) ),
inference(paramod_ordered,[status(thm)],[72,23]) ).
thf(255,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( C @ ( D @ in ) ) )
| ~ ( D @ ( C @ in ) ) ),
inference(simp,[status(thm)],[254]) ).
thf(256,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ unordered_pair ) @ in ) ),
inference(pattern_uni,[status(thm)],[255:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ unordered_pair ) )),bind(D,$thf( E ))]]) ).
thf(261,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[256]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(27,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(84,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( B @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,121]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( B @ singleton @ in ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= B )
| ( A
!= ( B @ singleton ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(132,plain,
! [A: $i] :
( ( A @ singleton @ singleton )
!= A ),
inference(simp,[status(thm)],[131]) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
| ~ ( C @ ( B @ ( A @ sk5 ) ) )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
!= B ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk5 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
!= B ) ),
inference(lifteq,[status(thm)],[59]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk5 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
!= B ) ),
inference(simp,[status(thm)],[73]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ ( A @ in ) ) ),
inference(eqfactor_ordered,[status(thm)],[23]) ).
thf(113,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[112:[bind(A,$thf( B ))]]) ).
thf(114,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(simp,[status(thm)],[113]) ).
thf(184,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( C @ ( C @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[70,114]) ).
thf(185,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( C @ ( C @ in ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(193,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= C )
| ( B != C ) ),
inference(simp,[status(thm)],[185]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
!= B ),
inference(simp,[status(thm)],[193]) ).
thf(205,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( D @ ( C @ unordered_pair ) ) )
| ( ( A @ ( B @ unordered_pair ) )
!= D ) ),
inference(paramod_ordered,[status(thm)],[26,197]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) )
!= B ),
inference(pattern_uni,[status(thm)],[205:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(391,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( B != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,20]) ).
thf(392,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( sk2 @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[391:[bind(A,$thf( sk2 ))]]) ).
thf(534,plain,
~ ( sk2 @ singleton @ ( sk1 @ in ) ),
inference(simp,[status(thm)],[392]) ).
thf(19,plain,
( ( sk2 @ singleton @ ( sk1 @ singleton @ symmetric_difference ) )
!= ( sk2 @ ( sk1 @ unordered_pair ) ) ),
inference(cnfConj,[status(thm)],[17]) ).
thf(21,plain,
( ( sk2 @ ( sk1 @ unordered_pair ) )
!= ( sk2 @ singleton @ ( sk1 @ singleton @ symmetric_difference ) ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(2005,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ ( B @ unordered_pair ) @ singleton @ ( sk1 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,762]) ).
thf(2006,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ ( B @ unordered_pair ) @ singleton @ ( sk1 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[2005]) ).
thf(2013,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= ( sk2 @ ( B @ unordered_pair ) @ singleton ) )
| ( A
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[2006]) ).
thf(2032,plain,
! [A: $i] :
( ( sk2 @ ( A @ unordered_pair ) @ singleton )
!= ( sk1 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[2013]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ symmetric_difference ) )
= ( A @ ( B @ set_difference ) @ ( B @ ( A @ set_difference ) @ set_union2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
thf(81,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ symmetric_difference ) )
= ( A @ ( B @ set_difference ) @ ( B @ ( A @ set_difference ) @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ symmetric_difference ) )
= ( A @ ( B @ set_difference ) @ ( B @ ( A @ set_difference ) @ set_union2 ) ) ),
inference(cnf,[status(esa)],[81]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ set_difference ) @ ( B @ ( A @ set_difference ) @ set_union2 ) )
= ( B @ ( A @ symmetric_difference ) ) ),
inference(lifteq,[status(thm)],[82]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(90,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(91,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(cnf,[status(esa)],[90]) ).
thf(92,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(lifteq,[status(thm)],[91]) ).
thf(335,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ set_difference ) @ ( B @ ( A @ set_difference ) @ set_union2 ) )
!= ( C @ ( C @ set_union2 ) ) )
| ( ( B @ ( A @ symmetric_difference ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[83,92]) ).
thf(336,plain,
! [A: $i] :
( ( A @ ( A @ set_difference ) )
= ( A @ ( A @ symmetric_difference ) ) ),
inference(pattern_uni,[status(thm)],[335:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ set_difference ) ))]]) ).
thf(339,plain,
! [A: $i] :
( ( A @ ( A @ set_difference ) )
= ( A @ ( A @ symmetric_difference ) ) ),
inference(simp,[status(thm)],[336]) ).
thf(728,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ set_difference ) )
!= ( C @ ( B @ set_difference ) ) )
| ( ( B @ ( C @ set_difference ) @ ( A @ ( A @ symmetric_difference ) @ set_union2 ) )
= ( C @ ( B @ symmetric_difference ) ) ) ),
inference(paramod_ordered,[status(thm)],[339,83]) ).
thf(729,plain,
! [A: $i] :
( ( A @ ( A @ set_difference ) @ ( A @ ( A @ symmetric_difference ) @ set_union2 ) )
= ( A @ ( A @ symmetric_difference ) ) ),
inference(pattern_uni,[status(thm)],[728:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(643,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ singleton @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72,534]) ).
thf(644,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ singleton @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[643]) ).
thf(649,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[644]) ).
thf(654,plain,
! [A: $i] :
( ( A @ ( sk1 @ unordered_pair ) )
!= ( sk2 @ singleton ) ),
inference(simp,[status(thm)],[649]) ).
thf(1224,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ ( sk1 @ unordered_pair ) ) )
| ( A
!= ( sk2 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,654]) ).
thf(1225,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton ) )
| ~ ( A @ singleton @ ( B @ ( sk1 @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[1224:[bind(A,$thf( A )),bind(B,$thf( E @ ( sk1 @ unordered_pair ) )),bind(C,$thf( E ))]]) ).
thf(1238,plain,
! [A: $i] :
~ ( sk2 @ singleton @ singleton @ ( A @ ( sk1 @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[1225]) ).
thf(1945,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk9 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk8 @ singleton @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,1644]) ).
thf(1946,plain,
! [A: $i] :
( ( A
!= ( sk8 @ singleton @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( sk9 @ singleton @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[1945:[bind(A,$thf( A )),bind(B,$thf( sk9 @ singleton @ singleton @ singleton ))]]) ).
thf(1968,plain,
~ ( sk8 @ singleton @ singleton @ singleton @ singleton @ ( sk9 @ singleton @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[1946]) ).
thf(1288,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton @ singleton ) )
| ( B
!= ( sk1 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,1029]) ).
thf(1289,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton @ singleton ) )
| ~ ( sk2 @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1288:[bind(A,$thf( sk2 @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(1296,plain,
~ ( sk2 @ singleton @ singleton @ singleton @ ( sk1 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[1289]) ).
thf(1020,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk2 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72,719]) ).
thf(1021,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk2 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1020]) ).
thf(1024,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk1 @ singleton @ singleton ) )
| ( A
!= ( sk2 @ singleton ) ) ),
inference(simp,[status(thm)],[1021]) ).
thf(1027,plain,
! [A: $i] :
( ( A @ ( sk2 @ singleton @ unordered_pair ) )
!= ( sk1 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1024]) ).
thf(1559,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( sk8 @ ( C @ unordered_pair ) ) )
| ( A
!= ( sk9 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,709]) ).
thf(1560,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk9 @ singleton ) )
| ~ ( A @ singleton @ ( sk8 @ ( B @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[1559:[bind(A,$thf( A )),bind(B,$thf( sk8 @ ( D @ unordered_pair ) )),bind(C,$thf( D ))]]) ).
thf(1573,plain,
! [A: $i] :
~ ( sk9 @ singleton @ singleton @ ( sk8 @ ( A @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[1560]) ).
thf(670,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk8 @ singleton @ ( sk9 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72,599]) ).
thf(671,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk8 @ singleton @ ( sk9 @ in ) ) ),
inference(simp,[status(thm)],[670]) ).
thf(676,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk8 @ singleton ) )
| ( A != sk9 ) ),
inference(simp,[status(thm)],[671]) ).
thf(679,plain,
! [A: $i] :
( ( A @ ( sk9 @ unordered_pair ) )
!= ( sk8 @ singleton ) ),
inference(simp,[status(thm)],[676]) ).
thf(1517,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ ( sk9 @ unordered_pair ) ) )
| ( A
!= ( sk8 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,679]) ).
thf(1518,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk8 @ singleton ) )
| ~ ( A @ singleton @ ( B @ ( sk9 @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[1517:[bind(A,$thf( A )),bind(B,$thf( E @ ( sk9 @ unordered_pair ) )),bind(C,$thf( E ))]]) ).
thf(1534,plain,
! [A: $i] :
~ ( sk8 @ singleton @ singleton @ ( A @ ( sk9 @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[1518]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk4 ) )
= A )
| ( ( A @ ( B @ sk3 ) )
!= A ) ),
inference(cnfConj,[status(thm)],[35]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk4 ) )
= A )
| ( ( A @ ( B @ sk3 ) )
!= A ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk4 ) )
= A )
| ( ( A @ ( B @ sk3 ) )
!= A ) ),
inference(simp,[status(thm)],[52]) ).
thf(3082,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,1788]) ).
thf(3083,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[3082]) ).
thf(3126,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk2 @ singleton @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[3083]) ).
thf(3141,plain,
( ( sk2 @ singleton @ singleton @ singleton @ singleton )
!= ( sk1 @ singleton @ singleton @ singleton @ singleton ) ),
inference(simp,[status(thm)],[3126]) ).
thf(429,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ ( sk1 @ unordered_pair ) ) )
| ( B
!= ( sk2 @ singleton @ ( sk1 @ singleton @ symmetric_difference ) ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,21]) ).
thf(430,plain,
! [A: $i] :
( ( A
!= ( sk2 @ singleton @ ( sk1 @ singleton @ symmetric_difference ) ) )
| ~ ( sk2 @ ( sk1 @ unordered_pair ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[429:[bind(A,$thf( sk2 @ ( sk1 @ unordered_pair ) )),bind(B,$thf( B ))]]) ).
thf(554,plain,
~ ( sk2 @ ( sk1 @ unordered_pair ) @ singleton @ ( sk2 @ singleton @ ( sk1 @ singleton @ symmetric_difference ) @ in ) ),
inference(simp,[status(thm)],[430]) ).
thf(1521,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( sk9 @ unordered_pair ) ) )
| ( B
!= ( sk8 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,679]) ).
thf(1522,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk8 @ singleton ) )
| ~ ( B @ ( sk9 @ unordered_pair ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1521:[bind(A,$thf( E @ ( sk9 @ unordered_pair ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(1530,plain,
! [A: $i] :
~ ( A @ ( sk9 @ unordered_pair ) @ singleton @ ( sk8 @ singleton @ in ) ),
inference(simp,[status(thm)],[1522]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ symmetric_difference ) @ ( A @ in ) )
<=> ~ ( ( B @ ( A @ in ) )
<=> ( C @ ( A @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_0) ).
thf(98,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( ( ( C @ ( A @ in ) )
=> ( B @ ( A @ in ) ) )
& ( ( B @ ( A @ in ) )
=> ( C @ ( A @ in ) ) ) )
=> ( C @ ( B @ symmetric_difference ) @ ( A @ in ) ) )
& ( ( C @ ( B @ symmetric_difference ) @ ( A @ in ) )
=> ~ ( ( ( C @ ( A @ in ) )
=> ( B @ ( A @ in ) ) )
& ( ( B @ ( A @ in ) )
=> ( C @ ( A @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(99,plain,
( ! [A: $i,B: $i,C: $i] :
( ~ ( ( ( C @ ( A @ in ) )
=> ( B @ ( A @ in ) ) )
& ( ( B @ ( A @ in ) )
=> ( C @ ( A @ in ) ) ) )
=> ( C @ ( B @ symmetric_difference ) @ ( A @ in ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ symmetric_difference ) @ ( A @ in ) )
=> ~ ( ( ( C @ ( A @ in ) )
=> ( B @ ( A @ in ) ) )
& ( ( B @ ( A @ in ) )
=> ( C @ ( A @ in ) ) ) ) ) ),
inference(miniscope,[status(thm)],[98]) ).
thf(100,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ symmetric_difference ) @ ( D @ in ) )
| ( E @ ( D @ in ) )
| ~ ( F @ ( D @ in ) ) )
& ( ( F @ ( E @ symmetric_difference ) @ ( D @ in ) )
| ( F @ ( D @ in ) )
| ~ ( E @ ( D @ in ) ) )
& ( ~ ( B @ ( A @ in ) )
| ~ ( C @ ( A @ in ) )
| ~ ( C @ ( B @ symmetric_difference ) @ ( A @ in ) ) )
& ( ( C @ ( A @ in ) )
| ~ ( C @ ( A @ in ) )
| ~ ( C @ ( B @ symmetric_difference ) @ ( A @ in ) ) )
& ( ~ ( B @ ( A @ in ) )
| ( B @ ( A @ in ) )
| ~ ( C @ ( B @ symmetric_difference ) @ ( A @ in ) ) )
& ( ( C @ ( A @ in ) )
| ( B @ ( A @ in ) )
| ~ ( C @ ( B @ symmetric_difference ) @ ( A @ in ) ) ) ),
inference(cnf,[status(esa)],[99]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ in ) )
| ~ ( C @ ( A @ in ) )
| ~ ( C @ ( B @ symmetric_difference ) @ ( A @ in ) ) ),
inference(cnfConj,[status(thm)],[100]) ).
thf(715,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton ) )
| ( B
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,626]) ).
thf(716,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( sk2 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[715:[bind(A,$thf( sk2 @ singleton )),bind(B,$thf( B ))]]) ).
thf(720,plain,
~ ( sk2 @ singleton @ singleton @ ( sk1 @ singleton @ in ) ),
inference(simp,[status(thm)],[716]) ).
thf(1074,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ ( sk1 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72,720]) ).
thf(1075,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ ( sk1 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1074]) ).
thf(1078,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton ) )
| ( A
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[1075]) ).
thf(1086,plain,
! [A: $i] :
( ( A @ ( sk1 @ singleton @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1078]) ).
thf(230,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( C @ ( C @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72,121]) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( C @ ( C @ singleton @ in ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(260,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= C )
| ( A
!= ( C @ singleton ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(266,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ singleton @ unordered_pair ) )
!= B ),
inference(simp,[status(thm)],[260]) ).
thf(749,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( sk2 @ ( C @ unordered_pair ) ) )
| ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,628]) ).
thf(750,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( sk2 @ ( B @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[749:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( D @ unordered_pair ) )),bind(C,$thf( D ))]]) ).
thf(765,plain,
! [A: $i] :
~ ( sk1 @ singleton @ singleton @ ( sk2 @ ( A @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[750]) ).
thf(736,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( sk2 @ unordered_pair ) ) )
| ( B
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,627]) ).
thf(737,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( B @ ( sk2 @ unordered_pair ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[736:[bind(A,$thf( E @ ( sk2 @ unordered_pair ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(744,plain,
! [A: $i] :
~ ( A @ ( sk2 @ unordered_pair ) @ singleton @ ( sk1 @ singleton @ in ) ),
inference(simp,[status(thm)],[737]) ).
thf(1830,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( sk2 @ unordered_pair ) @ singleton @ ( sk1 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,744]) ).
thf(1831,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( sk2 @ unordered_pair ) @ singleton @ ( sk1 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1830]) ).
thf(1836,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= ( B @ ( sk2 @ unordered_pair ) @ singleton ) )
| ( A
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[1831]) ).
thf(1846,plain,
! [A: $i] :
( ( A @ ( sk2 @ unordered_pair ) @ singleton )
!= ( sk1 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1836]) ).
thf(1496,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( sk9 @ ( C @ unordered_pair ) ) )
| ( A
!= ( sk8 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,677]) ).
thf(1497,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk8 @ singleton ) )
| ~ ( A @ singleton @ ( sk9 @ ( B @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[1496:[bind(A,$thf( A )),bind(B,$thf( sk9 @ ( D @ unordered_pair ) )),bind(C,$thf( D ))]]) ).
thf(1510,plain,
! [A: $i] :
~ ( sk8 @ singleton @ singleton @ ( sk9 @ ( A @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[1497]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ symmetric_difference ) )
= ( A @ ( B @ symmetric_difference ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
thf(30,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ symmetric_difference ) )
= ( A @ ( B @ symmetric_difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ symmetric_difference ) )
= ( A @ ( B @ symmetric_difference ) ) ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ symmetric_difference ) )
= ( A @ ( B @ symmetric_difference ) ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ in ) )
| ( ( A @ ( B @ sk3 ) )
!= A ) ),
inference(cnfConj,[status(thm)],[35]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk4 ) @ in ) )
| ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk3 ) )
!= A ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk4 ) @ in ) )
| ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk3 ) )
!= A ) ),
inference(simp,[status(thm)],[48]) ).
thf(85,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ~ ? [B: $i] : ( B @ ( A @ set_union2 ) @ empty ) ),
inference(miniscope,[status(thm)],[84]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ set_union2 ) @ empty )
| ( A @ empty ) ),
inference(cnf,[status(esa)],[85]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
| ~ ( C @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk5 ) ) ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk5 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[63]) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk5 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ unordered_pair ) )
!= ( D @ ( C @ unordered_pair ) ) )
| ( ( B @ ( A @ unordered_pair ) )
!= D ) ),
inference(paramod_ordered,[status(thm)],[26,197]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
!= A ),
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(423,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk2 @ ( sk1 @ unordered_pair ) ) )
| ( A
!= ( sk2 @ singleton @ ( sk1 @ singleton @ symmetric_difference ) ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,21]) ).
thf(424,plain,
! [A: $i] :
( ( A
!= ( sk2 @ singleton @ ( sk1 @ singleton @ symmetric_difference ) ) )
| ~ ( A @ singleton @ ( sk2 @ ( sk1 @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[423:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ unordered_pair ) ))]]) ).
thf(553,plain,
~ ( sk2 @ singleton @ ( sk1 @ singleton @ symmetric_difference ) @ singleton @ ( sk2 @ ( sk1 @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[424]) ).
thf(2159,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ ( sk1 @ singleton @ symmetric_difference ) @ singleton @ ( sk2 @ ( sk1 @ unordered_pair ) @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,553]) ).
thf(2160,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ ( sk1 @ singleton @ symmetric_difference ) @ singleton @ ( sk2 @ ( sk1 @ unordered_pair ) @ in ) ) ),
inference(simp,[status(thm)],[2159]) ).
thf(2165,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk2 @ singleton @ ( sk1 @ singleton @ symmetric_difference ) @ singleton ) )
| ( A
!= ( sk2 @ ( sk1 @ unordered_pair ) ) ) ),
inference(simp,[status(thm)],[2160]) ).
thf(2180,plain,
( ( sk2 @ ( sk1 @ unordered_pair ) @ singleton )
!= ( sk2 @ singleton @ ( sk1 @ singleton @ symmetric_difference ) @ singleton ) ),
inference(simp,[status(thm)],[2165]) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
| ~ ( C @ ( B @ ( A @ sk5 ) ) )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
!= A ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk5 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
!= A ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk5 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
!= A ) ),
inference(simp,[status(thm)],[65]) ).
thf(62,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ( D = A )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(79,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ in ) )
| ( D = B )
| ( D = A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[62]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ unordered_pair ) @ ( C @ in ) )
| ( C = B )
| ( C = A ) ),
inference(simp,[status(thm)],[79]) ).
thf(629,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ singleton @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[70,534]) ).
thf(630,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ singleton @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[629]) ).
thf(648,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton ) )
| ( B != sk1 ) ),
inference(simp,[status(thm)],[630]) ).
thf(653,plain,
! [A: $i] :
( ( sk1 @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton ) ),
inference(simp,[status(thm)],[648]) ).
thf(697,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk9 @ singleton @ ( sk8 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72,601]) ).
thf(698,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk9 @ singleton @ ( sk8 @ in ) ) ),
inference(simp,[status(thm)],[697]) ).
thf(701,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk9 @ singleton ) )
| ( A != sk8 ) ),
inference(simp,[status(thm)],[698]) ).
thf(707,plain,
! [A: $i] :
( ( A @ ( sk8 @ unordered_pair ) )
!= ( sk9 @ singleton ) ),
inference(simp,[status(thm)],[701]) ).
thf(1538,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ ( sk8 @ unordered_pair ) ) )
| ( A
!= ( sk9 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,707]) ).
thf(1539,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk9 @ singleton ) )
| ~ ( A @ singleton @ ( B @ ( sk8 @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[1538:[bind(A,$thf( A )),bind(B,$thf( E @ ( sk8 @ unordered_pair ) )),bind(C,$thf( E ))]]) ).
thf(1551,plain,
! [A: $i] :
~ ( sk9 @ singleton @ singleton @ ( A @ ( sk8 @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[1539]) ).
thf(1207,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( sk1 @ ( C @ unordered_pair ) ) )
| ( B
!= ( sk2 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,653]) ).
thf(1208,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton ) )
| ~ ( sk1 @ ( B @ unordered_pair ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1207:[bind(A,$thf( sk1 @ ( D @ unordered_pair ) )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(1218,plain,
! [A: $i] :
~ ( sk1 @ ( A @ unordered_pair ) @ singleton @ ( sk2 @ singleton @ in ) ),
inference(simp,[status(thm)],[1208]) ).
thf(1106,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk9 @ singleton @ singleton @ ( sk8 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[70,980]) ).
thf(1107,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk9 @ singleton @ singleton @ ( sk8 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1106]) ).
thf(1133,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk9 @ singleton @ singleton ) )
| ( B
!= ( sk8 @ singleton ) ) ),
inference(simp,[status(thm)],[1107]) ).
thf(1141,plain,
! [A: $i] :
( ( sk8 @ singleton @ ( A @ unordered_pair ) )
!= ( sk9 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1133]) ).
thf(1228,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( sk1 @ unordered_pair ) ) )
| ( B
!= ( sk2 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,654]) ).
thf(1229,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton ) )
| ~ ( B @ ( sk1 @ unordered_pair ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1228:[bind(A,$thf( E @ ( sk1 @ unordered_pair ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(1240,plain,
! [A: $i] :
~ ( A @ ( sk1 @ unordered_pair ) @ singleton @ ( sk2 @ singleton @ in ) ),
inference(simp,[status(thm)],[1229]) ).
thf(726,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ set_difference ) )
!= ( B @ ( C @ set_difference ) ) )
| ( ( A @ ( A @ symmetric_difference ) @ ( C @ ( B @ set_difference ) @ set_union2 ) )
= ( C @ ( B @ symmetric_difference ) ) ) ),
inference(paramod_ordered,[status(thm)],[339,83]) ).
thf(727,plain,
! [A: $i] :
( ( A @ ( A @ symmetric_difference ) @ ( A @ ( A @ set_difference ) @ set_union2 ) )
= ( A @ ( A @ symmetric_difference ) ) ),
inference(pattern_uni,[status(thm)],[726:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(1203,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( sk1 @ ( C @ unordered_pair ) ) )
| ( A
!= ( sk2 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,653]) ).
thf(1204,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton ) )
| ~ ( A @ singleton @ ( sk1 @ ( B @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[1203:[bind(A,$thf( A )),bind(B,$thf( sk1 @ ( D @ unordered_pair ) )),bind(C,$thf( D ))]]) ).
thf(1216,plain,
! [A: $i] :
~ ( sk2 @ singleton @ singleton @ ( sk1 @ ( A @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[1204]) ).
thf(1182,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk8 @ singleton @ singleton @ ( sk9 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72,983]) ).
thf(1183,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk8 @ singleton @ singleton @ ( sk9 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1182]) ).
thf(1186,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk8 @ singleton @ singleton ) )
| ( A
!= ( sk9 @ singleton ) ) ),
inference(simp,[status(thm)],[1183]) ).
thf(1189,plain,
! [A: $i] :
( ( A @ ( sk9 @ singleton @ unordered_pair ) )
!= ( sk8 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1186]) ).
thf(1563,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( sk8 @ ( C @ unordered_pair ) ) )
| ( B
!= ( sk9 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,709]) ).
thf(1564,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk9 @ singleton ) )
| ~ ( sk8 @ ( B @ unordered_pair ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1563:[bind(A,$thf( sk8 @ ( D @ unordered_pair ) )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(1575,plain,
! [A: $i] :
~ ( sk8 @ ( A @ unordered_pair ) @ singleton @ ( sk9 @ singleton @ in ) ),
inference(simp,[status(thm)],[1564]) ).
thf(1542,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( sk8 @ unordered_pair ) ) )
| ( B
!= ( sk9 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,707]) ).
thf(1543,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk9 @ singleton ) )
| ~ ( B @ ( sk8 @ unordered_pair ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1542:[bind(A,$thf( E @ ( sk8 @ unordered_pair ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(1553,plain,
! [A: $i] :
~ ( A @ ( sk8 @ unordered_pair ) @ singleton @ ( sk9 @ singleton @ in ) ),
inference(simp,[status(thm)],[1543]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(87,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( D @ ( B @ in ) ) )
| ~ ( C @ ( B @ in ) )
| ~ $true
| ~ ( D @ ( C @ symmetric_difference ) @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[43,105]) ).
thf(136,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( D @ ( B @ in ) ) )
| ~ ( C @ ( B @ in ) )
| ~ ( D @ ( C @ symmetric_difference ) @ ( B @ in ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ~ ( B @ singleton @ ( A @ symmetric_difference ) @ ( B @ in ) ) ),
inference(pattern_uni,[status(thm)],[136:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( E @ singleton ))]]) ).
thf(151,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ~ ( B @ singleton @ ( A @ symmetric_difference ) @ ( B @ in ) ) ),
inference(simp,[status(thm)],[137]) ).
thf(1500,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( sk9 @ ( C @ unordered_pair ) ) )
| ( B
!= ( sk8 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,677]) ).
thf(1501,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk8 @ singleton ) )
| ~ ( sk9 @ ( B @ unordered_pair ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1500:[bind(A,$thf( sk9 @ ( D @ unordered_pair ) )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(1512,plain,
! [A: $i] :
~ ( sk9 @ ( A @ unordered_pair ) @ singleton @ ( sk8 @ singleton @ in ) ),
inference(simp,[status(thm)],[1501]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk4 ) )
= A )
| ( B @ ( A @ ( B @ sk3 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[35]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk3 ) @ in ) )
| ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk4 ) )
= A ) ),
inference(lifteq,[status(thm)],[40]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk3 ) @ in ) )
| ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk4 ) )
= A ) ),
inference(simp,[status(thm)],[50]) ).
thf(209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( C @ ( D @ unordered_pair ) ) )
| ( ( A @ ( B @ unordered_pair ) )
!= D ) ),
inference(paramod_ordered,[status(thm)],[26,206]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) )
!= A ),
inference(pattern_uni,[status(thm)],[209:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(123,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( B @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,114]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( B @ in ) ) ),
inference(simp,[status(thm)],[123]) ).
thf(125,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[124]) ).
thf(126,plain,
! [A: $i] :
( ( A @ singleton )
!= A ),
inference(simp,[status(thm)],[125]) ).
thf(1777,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton @ singleton @ singleton ) )
| ( B
!= ( sk1 @ singleton @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[45,1398]) ).
thf(1778,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton @ singleton @ singleton ) )
| ~ ( sk2 @ singleton @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1777:[bind(A,$thf( sk2 @ singleton @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(1789,plain,
~ ( sk2 @ singleton @ singleton @ singleton @ singleton @ ( sk1 @ singleton @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[1778]) ).
thf(282,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( D @ ( C @ unordered_pair ) ) )
| ~ ( D @ ( A @ ( B @ unordered_pair ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[26,202]) ).
thf(283,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( B @ unordered_pair ) @ in ) ),
inference(pattern_uni,[status(thm)],[282:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ in ) )
| ( B @ ( A @ ( B @ sk3 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[35]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk4 ) @ in ) )
| ( B @ ( A @ ( B @ sk3 ) @ in ) )
| ( B
= ( A @ singleton ) ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk4 ) @ in ) )
| ( B @ ( A @ ( B @ sk3 ) @ in ) )
| ( B
= ( A @ singleton ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
| ~ ( C @ ( B @ ( A @ sk5 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk6 ) ) @ in ) ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk5 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk6 ) ) @ in ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[61]) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk5 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk6 ) ) @ in ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(1052,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ singleton @ singleton @ ( sk1 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[70,720]) ).
thf(1053,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ singleton @ singleton @ ( sk1 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1052]) ).
thf(1079,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton ) )
| ( B
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[1053]) ).
thf(1088,plain,
! [A: $i] :
( ( sk1 @ singleton @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1079]) ).
thf(100025,plain,
$false,
inference(e,[status(thm)],[1030,1322,628,1295,762,1142,677,202,1788,1327,3826,747,709,24,719,1191,196,20,93,1398,78,261,29,121,84,132,74,206,678,534,70,21,2032,729,33,1238,92,197,1968,97,1296,1027,1573,1534,980,53,3141,339,554,1644,679,1530,654,105,1086,266,765,1846,1510,32,45,601,22,27,1139,54,49,86,81,76,98,208,599,2180,66,1029,626,983,80,653,553,1551,1961,707,95,16,1218,744,1141,43,1240,727,72,627,1216,1189,1575,1553,87,26,114,23,151,1512,30,51,210,126,1789,532,720,94,283,47,68,83,1088,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET888+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.24/5.70 % Computer : n019.cluster.edu
% 0.24/5.70 % Model : x86_64 x86_64
% 0.24/5.70 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/5.70 % Memory : 8046.5625MB
% 0.24/5.70 % OS : Linux 6.8.0-71-generic
% 0.24/5.70 % CPULimit : 300
% 0.24/5.70 % WCLimit : 300
% 0.24/5.70 % DateTime : Sat Sep 26 08:24:41 UTC 2026
% 0.24/5.71 % CPUTime :
% 0.24/5.71 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.22/6.33 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.77/6.61 % [INFO] Parsing done (277ms).
% 1.77/6.63 % [INFO] Running in sequential loop mode.
% 2.49/7.10 % [INFO] eprover registered as external prover.
% 2.49/7.11 % [INFO] Scanning for conjecture ...
% 2.80/7.26 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 2.98/7.32 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 2.98/7.36 % [INFO] Problem is first-order (TPTP FOF).
% 2.98/7.37 % [INFO] Type checking passed.
% 2.98/7.38 % [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 ...
% 159.16/44.52 % External prover 'e' found a proof!
% 159.16/44.52 % [INFO] Killing All external provers ...
% 159.16/44.52 % Time passed: 38604ms (effective reasoning time: 37879ms)
% 159.16/44.52 % 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)>
% 159.16/44.52 % Axioms used in derivation (13): d1_tarski, commutativity_k2_xboole_0, fc3_xboole_0, commutativity_k2_tarski, d6_xboole_0, rc1_xboole_0, idempotence_k2_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, d2_tarski, fc2_xboole_0, t1_xboole_0, commutativity_k5_xboole_0
% 159.16/44.52 % No. of inferences in proof: 367
% 159.16/44.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 38604 ms resp. 37879 ms w/o parsing
% 154.14/44.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 154.14/44.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------