%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET919+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 : n015.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 08:31:20 AM UTC 2026
% Result : Theorem 87.49s 19.19s
% Output : Refutation 74.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 21
% Syntax : Number of formulae : 724 ( 216 unt; 0 typ; 11 def)
% Number of atoms : 2032 (1032 equ; 0 cnn)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 6910 (1237 ~; 846 |; 57 &;4714 @)
% ( 6 <=>; 50 =>; 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 : 21 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 1104 ( 16 ^;1073 !; 4 ?;1104 :)
% ( 0 !>; 0 ?*; 0 @-; 11 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(set_intersection2_decl,type,
set_intersection2: $i > $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $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 ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i > $o ).
thf(sk7_decl,type,
sk7: $i > $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i > $i > $o ).
thf(sk10_decl,type,
sk10: $i > $i > $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i > $i > $i ).
thf(sk12_decl,type,
sk12: $i ).
thf(sk13_decl,type,
sk13: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ in ) )
=> ! [C: $i] :
( ( ( B @ ( C @ ( A @ unordered_pair ) @ set_intersection2 ) )
= ( A @ singleton ) )
| ( ( A != C )
& ( B @ ( C @ in ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ ( sk1 @ in ) )
=> ! [B: $i] :
( ( ( A @ ( B @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
= ( sk1 @ singleton ) )
| ( ( sk1 != B )
& ( A @ ( B @ in ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( sk2 @ ( A @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
= ( sk1 @ singleton ) )
| ( ( sk1 != A )
& ( sk2 @ ( A @ in ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ( C = B ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C = B )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( A @ ( D @ in ) )
=> ( ( D = B )
| ( D = C ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( D = B )
| ( D = C ) )
=> ( A @ ( D @ in ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( A @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
& ( C @ ( D @ in ) ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( B @ ( D @ in ) )
& ( C @ ( D @ in ) ) )
=> ( A @ ( D @ in ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(7,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(49,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)],[7]) ).
thf(50,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)],[49]) ).
thf(51,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 @ sk8 ) ) @ in ) )
| ( H @ ( G @ ( F @ sk6 ) ) ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ( ( F @ ( G @ ( H @ sk8 ) ) )
= G )
| ( ( F @ ( G @ ( H @ sk8 ) ) )
= F )
| ( H @ ( G @ ( F @ sk6 ) ) ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk6 ) ) )
| ( ( F @ ( G @ ( H @ sk7 ) ) )
!= G ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk6 ) ) )
| ( ( F @ ( G @ ( H @ sk7 ) ) )
!= F ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk6 ) ) )
| ( H @ ( F @ ( G @ ( H @ sk7 ) ) @ 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)],[50]) ).
thf(59,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(cnfConj,[status(thm)],[51]) ).
thf(68,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[59]) ).
thf(69,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( B @ in ) ),
inference(simp,[status(thm)],[68]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ in ) )
=> ( ( ( B @ ( C @ ( A @ unordered_pair ) @ set_intersection2 ) )
= ( A @ singleton ) )
| ( ( A != C )
& ( B @ ( C @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ in ) )
=> ( ( ( B @ ( C @ ( A @ unordered_pair ) @ set_intersection2 ) )
= ( A @ singleton ) )
| ( ( A != C )
& ( B @ ( C @ in ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(12,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ in ) )
=> ( ( ( B @ ( C @ ( A @ unordered_pair ) @ set_intersection2 ) )
= ( A @ singleton ) )
| ( ( A != C )
& ( B @ ( C @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,plain,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ! [C: $i] :
( ( ( B @ ( C @ ( A @ unordered_pair ) @ set_intersection2 ) )
= ( A @ singleton ) )
| ( ( A != C )
& ( B @ ( C @ in ) ) ) ) ),
inference(miniscope,[status(thm)],[12]) ).
thf(14,plain,
( ( ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
!= ( sk1 @ singleton ) )
& ( ( sk1 = sk3 )
| ~ ( sk2 @ ( sk3 @ in ) ) )
& ( sk2 @ ( sk1 @ in ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
sk2 @ ( sk1 @ in ),
inference(cnfConj,[status(thm)],[14]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( A @ ( B @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,21]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( A @ ( B @ in ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(116,plain,
~ ( sk1 @ ( sk2 @ in ) ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(133,plain,
( ( ( sk1 @ ( sk2 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,116]) ).
thf(134,plain,
( ( sk1 @ ( sk2 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(136,plain,
( ( sk2 != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[134]) ).
thf(138,plain,
sk2 != sk1,
inference(simp,[status(thm)],[136]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_intersection2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(76,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_intersection2 ) ) ) )
& ( ( C
= ( B @ ( A @ set_intersection2 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(77,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ! [D: $i] :
( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_intersection2 ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_intersection2 ) ) )
=> ( ! [D: $i] :
( ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ! [D: $i] :
( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[76]) ).
thf(78,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H
= ( G @ ( F @ set_intersection2 ) ) )
| ~ ( H @ ( F @ ( G @ ( H @ sk11 ) ) @ in ) )
| ( H @ ( G @ ( F @ sk9 ) ) ) )
& ( ( H
= ( G @ ( F @ set_intersection2 ) ) )
| ( G @ ( F @ ( G @ ( H @ sk11 ) ) @ in ) )
| ( H @ ( G @ ( F @ sk9 ) ) ) )
& ( ( H
= ( G @ ( F @ set_intersection2 ) ) )
| ( F @ ( F @ ( G @ ( H @ sk11 ) ) @ in ) )
| ( H @ ( G @ ( F @ sk9 ) ) ) )
& ( ( H
= ( G @ ( F @ set_intersection2 ) ) )
| ~ ( H @ ( G @ ( F @ sk9 ) ) )
| ~ ( G @ ( F @ ( G @ ( H @ sk10 ) ) @ in ) )
| ~ ( F @ ( F @ ( G @ ( H @ sk10 ) ) @ in ) ) )
& ( ( H
= ( G @ ( F @ set_intersection2 ) ) )
| ~ ( H @ ( G @ ( F @ sk9 ) ) )
| ( H @ ( F @ ( G @ ( H @ sk10 ) ) @ in ) ) )
& ( ( C @ ( E @ in ) )
| ~ ( B @ ( E @ in ) )
| ~ ( A @ ( E @ in ) )
| ( C
!= ( B @ ( A @ set_intersection2 ) ) ) )
& ( ( B @ ( D @ in ) )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_intersection2 ) ) ) )
& ( ( A @ ( D @ in ) )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_intersection2 ) ) ) ) ),
inference(cnf,[status(esa)],[77]) ).
thf(84,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ in ) )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(cnfConj,[status(thm)],[78]) ).
thf(87,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ in ) )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(lifteq,[status(thm)],[84]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ in ) )
| ~ ( B @ ( A @ set_intersection2 ) @ ( C @ in ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ set_intersection2 ) ) )
| ( B @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk9 ) ) ) ),
inference(cnfConj,[status(thm)],[78]) ).
thf(97,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk9 ) ) )
| ( C
= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(lifteq,[status(thm)],[82]) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk9 ) ) )
| ( C
= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(103,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(104,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(cnf,[status(esa)],[103]) ).
thf(105,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(lifteq,[status(thm)],[104]) ).
thf(1908,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_intersection2 ) )
!= ( D @ ( D @ set_intersection2 ) ) )
| ( C = D )
| ( B @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk9 ) ) ) ),
inference(paramod_ordered,[status(thm)],[98,105]) ).
thf(1909,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( A @ ( A @ ( B @ sk11 ) ) @ in ) )
| ( B @ ( A @ ( A @ sk9 ) ) ) ),
inference(pattern_uni,[status(thm)],[1908:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).
thf(2132,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( A @ ( A @ ( B @ sk11 ) ) @ in ) )
| ( B @ ( A @ ( A @ sk9 ) ) ) ),
inference(simp,[status(thm)],[1909]) ).
thf(6,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(28,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)],[6]) ).
thf(29,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)],[28]) ).
thf(30,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk5 ) @ in ) )
| ( ( E @ ( F @ sk4 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk5 ) )
= E )
| ( ( E @ ( F @ sk4 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk5 ) @ in ) )
| ( F @ ( E @ ( F @ sk4 ) @ in ) ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk5 ) )
= E )
| ( F @ ( E @ ( F @ sk4 ) @ in ) ) )
& ( ( B @ ( D @ in ) )
| ( D != A )
| ( B
!= ( A @ singleton ) ) )
& ( ( C = A )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ singleton ) ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ singleton ) ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ in ) )
| ( C = A )
| ( B
!= ( A @ singleton ) ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ~ ( A @ singleton @ ( B @ in ) )
| ( B = A ) ),
inference(simp,[status(thm)],[39]) ).
thf(734,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( B != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,138]) ).
thf(735,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( sk2 @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[734:[bind(A,$thf( sk2 ))]]) ).
thf(1042,plain,
~ ( sk2 @ singleton @ ( sk1 @ in ) ),
inference(simp,[status(thm)],[735]) ).
thf(1178,plain,
( ( ( sk2 @ singleton @ ( sk1 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,1042]) ).
thf(1179,plain,
( ( sk2 @ singleton @ ( sk1 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[1178]) ).
thf(1202,plain,
( ( ( sk2 @ singleton )
!= sk2 )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[1179]) ).
thf(1210,plain,
( ( sk2 @ singleton )
!= sk2 ),
inference(simp,[status(thm)],[1202]) ).
thf(9499,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton ) )
| ( B != sk2 )
| ( A @ ( A @ ( A @ ( B @ sk11 ) ) @ in ) )
| ( B @ ( A @ ( A @ sk9 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2132,1210]) ).
thf(9500,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk2 @ singleton @ ( sk2 @ singleton @ ( sk2 @ singleton @ ( A @ sk11 ) ) @ in ) )
| ( A @ ( sk2 @ singleton @ ( sk2 @ singleton @ sk9 ) ) ) ),
inference(pattern_uni,[status(thm)],[9499:[bind(A,$thf( sk2 @ singleton )),bind(B,$thf( B ))]]) ).
thf(10609,plain,
( ( sk2 @ singleton @ ( sk2 @ singleton @ ( sk2 @ singleton @ ( sk2 @ sk11 ) ) @ in ) )
| ( sk2 @ ( sk2 @ singleton @ ( sk2 @ singleton @ sk9 ) ) ) ),
inference(simp,[status(thm)],[9500]) ).
thf(10,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(106,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(107,plain,
sk12 @ empty,
inference(cnf,[status(esa)],[106]) ).
thf(11,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(108,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(109,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[108]) ).
thf(110,plain,
~ ( sk13 @ empty ),
inference(cnf,[status(esa)],[109]) ).
thf(111,plain,
( ( ( sk13 @ empty )
!= ( sk12 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[107,110]) ).
thf(112,plain,
( ( sk13 @ empty )
!= ( sk12 @ empty ) ),
inference(simp,[status(thm)],[111]) ).
thf(113,plain,
sk13 != sk12,
inference(simp,[status(thm)],[112]) ).
thf(897,plain,
! [B: $i,A: $i] :
( ( A != sk13 )
| ( B != sk12 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,113]) ).
thf(898,plain,
! [A: $i] :
( ( A != sk12 )
| ~ ( sk13 @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[897:[bind(A,$thf( sk13 ))]]) ).
thf(1104,plain,
~ ( sk13 @ singleton @ ( sk12 @ in ) ),
inference(simp,[status(thm)],[898]) ).
thf(1268,plain,
( ( ( sk13 @ singleton @ ( sk12 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,1104]) ).
thf(1269,plain,
( ( sk13 @ singleton @ ( sk12 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[1268]) ).
thf(1294,plain,
( ( ( sk13 @ singleton )
!= sk2 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[1269]) ).
thf(1712,plain,
! [B: $i,A: $i] :
( ( A != sk12 )
| ( ( sk13 @ singleton )
!= sk2 )
| ( B != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1294]) ).
thf(1713,plain,
! [A: $i] :
( ( ( sk13 @ singleton )
!= sk2 )
| ( A != sk1 )
| ~ ( sk12 @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1712:[bind(A,$thf( sk12 ))]]) ).
thf(1718,plain,
( ( ( sk13 @ singleton )
!= sk2 )
| ~ ( sk12 @ singleton @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[1713]) ).
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(22,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(57,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(cnfConj,[status(thm)],[51]) ).
thf(64,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(65,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( A @ in ) ),
inference(simp,[status(thm)],[64]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ ( A @ in ) ) ),
inference(eqfactor_ordered,[status(thm)],[21]) ).
thf(121,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[120:[bind(A,$thf( B ))]]) ).
thf(122,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(simp,[status(thm)],[121]) ).
thf(228,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( C @ ( C @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,122]) ).
thf(229,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( C @ ( C @ in ) ) ),
inference(simp,[status(thm)],[228]) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= C )
| ( A != C ) ),
inference(simp,[status(thm)],[229]) ).
thf(248,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) )
!= B ),
inference(simp,[status(thm)],[238]) ).
thf(522,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)],[24,248]) ).
thf(523,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) )
!= A ),
inference(pattern_uni,[status(thm)],[522:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C != A )
| ( B
!= ( A @ singleton ) ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C != A )
| ( B
!= ( A @ singleton ) ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(46,plain,
! [A: $i] : ( A @ singleton @ ( A @ in ) ),
inference(simp,[status(thm)],[45]) ).
thf(8764,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ singleton @ ( sk1 @ in ) ) )
| ( ( sk13 @ singleton )
!= sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,1718]) ).
thf(8765,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ singleton @ ( sk1 @ in ) ) )
| ( ( sk13 @ singleton )
!= sk2 ) ),
inference(simp,[status(thm)],[8764]) ).
thf(8862,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk12 @ singleton ) )
| ( A != sk1 )
| ( ( sk13 @ singleton )
!= sk2 ) ),
inference(simp,[status(thm)],[8765]) ).
thf(8883,plain,
( ( ( sk12 @ singleton )
!= ( sk1 @ singleton ) )
| ( ( sk13 @ singleton )
!= sk2 ) ),
inference(simp,[status(thm)],[8862]) ).
thf(895,plain,
! [B: $i,A: $i] :
( ( B != sk13 )
| ( A != sk12 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,113]) ).
thf(896,plain,
! [A: $i] :
( ( A != sk12 )
| ~ ( A @ singleton @ ( sk13 @ in ) ) ),
inference(pattern_uni,[status(thm)],[895:[bind(A,$thf( A )),bind(B,$thf( sk13 ))]]) ).
thf(1103,plain,
~ ( sk12 @ singleton @ ( sk13 @ in ) ),
inference(simp,[status(thm)],[896]) ).
thf(1231,plain,
( ( ( sk12 @ singleton @ ( sk13 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,1103]) ).
thf(1232,plain,
( ( sk12 @ singleton @ ( sk13 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[1231]) ).
thf(1257,plain,
( ( ( sk12 @ singleton )
!= sk2 )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[1232]) ).
thf(1561,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk12 @ singleton ) )
| ( B != sk2 )
| ( sk13 != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1257]) ).
thf(1562,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk13 != sk1 )
| ~ ( sk12 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1561:[bind(A,$thf( sk12 @ singleton )),bind(B,$thf( B ))]]) ).
thf(1569,plain,
( ( sk13 != sk1 )
| ~ ( sk12 @ singleton @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[1562]) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( C @ in ) ) )
| ~ $true
| ~ ( C @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[46,21]) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( C @ in ) ) )
| ~ ( C @ ( B @ in ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(128,plain,
! [A: $i] :
~ ( A @ ( A @ singleton @ in ) ),
inference(pattern_uni,[status(thm)],[127:[bind(A,$thf( D )),bind(B,$thf( D @ singleton )),bind(C,$thf( D ))]]) ).
thf(129,plain,
! [A: $i] :
~ ( A @ ( A @ singleton @ in ) ),
inference(simp,[status(thm)],[128]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( B @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,129]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( B @ singleton @ in ) ) ),
inference(simp,[status(thm)],[196]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= B )
| ( A
!= ( B @ singleton ) ) ),
inference(simp,[status(thm)],[197]) ).
thf(202,plain,
! [A: $i] :
( ( A @ singleton @ singleton )
!= A ),
inference(simp,[status(thm)],[200]) ).
thf(732,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( A != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,138]) ).
thf(733,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( A @ singleton @ ( sk2 @ in ) ) ),
inference(pattern_uni,[status(thm)],[732:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(1041,plain,
~ ( sk1 @ singleton @ ( sk2 @ in ) ),
inference(simp,[status(thm)],[733]) ).
thf(1145,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,1041]) ).
thf(1146,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[1145]) ).
thf(1165,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[1146]) ).
thf(1173,plain,
( ( sk2 @ singleton )
!= ( sk1 @ singleton ) ),
inference(simp,[status(thm)],[1165]) ).
thf(16,plain,
( ( sk1 = sk3 )
| ~ ( sk2 @ ( sk3 @ in ) ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(18,plain,
( ~ ( sk2 @ ( sk3 @ in ) )
| ( sk3 = sk1 ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(17,plain,
( ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
!= ( sk1 @ singleton ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(19,plain,
( ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
!= ( sk1 @ singleton ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(143,plain,
( ( sk3 != sk3 )
| ( ( sk2 @ ( sk1 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
!= ( sk1 @ singleton ) )
| ~ ( sk2 @ ( sk3 @ in ) ) ),
inference(paramod_ordered,[status(thm)],[18,19]) ).
thf(144,plain,
( ( ( sk2 @ ( sk1 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
!= ( sk1 @ singleton ) )
| ~ ( sk2 @ ( sk3 @ in ) ) ),
inference(pattern_uni,[status(thm)],[143:[]]) ).
thf(160,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ ( sk3 @ in ) ) )
| ( ( sk2 @ ( sk1 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
!= ( sk1 @ singleton ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,144]) ).
thf(161,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ ( sk3 @ in ) ) )
| ( ( sk2 @ ( sk1 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(166,plain,
! [A: $i] :
( ( ( A @ singleton )
!= sk2 )
| ( A != sk3 )
| ( ( sk2 @ ( sk1 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[161]) ).
thf(168,plain,
( ( ( sk3 @ singleton )
!= sk2 )
| ( ( sk2 @ ( sk1 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[166]) ).
thf(213,plain,
! [A: $i] :
( ( ( A @ ( A @ set_intersection2 ) )
!= ( sk2 @ ( sk1 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) ) )
| ( ( sk3 @ singleton )
!= sk2 )
| ( A
!= ( sk1 @ singleton ) ) ),
inference(paramod_ordered,[status(thm)],[105,168]) ).
thf(217,plain,
( ( ( sk1 @ singleton )
!= sk2 )
| ( ( sk1 @ ( sk1 @ unordered_pair ) )
!= ( sk1 @ singleton ) )
| ( ( sk3 @ singleton )
!= sk2 ) ),
inference(simp,[status(thm)],[213]) ).
thf(9103,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( A != sk1 )
| ( A @ ( A @ ( A @ ( B @ sk11 ) ) @ in ) )
| ( B @ ( A @ ( A @ sk9 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2132,138]) ).
thf(9104,plain,
! [A: $i] :
( ( A != sk1 )
| ( A @ ( A @ ( A @ ( sk2 @ sk11 ) ) @ in ) )
| ( sk2 @ ( A @ ( A @ sk9 ) ) ) ),
inference(pattern_uni,[status(thm)],[9103:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(10832,plain,
( ( sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ sk11 ) ) @ in ) )
| ( sk2 @ ( sk1 @ ( sk1 @ sk9 ) ) ) ),
inference(simp,[status(thm)],[9104]) ).
thf(131,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ ( sk2 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,116]) ).
thf(132,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(135,plain,
! [A: $i] :
( ( ( A @ singleton )
!= sk1 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[132]) ).
thf(137,plain,
( ( sk2 @ singleton )
!= sk1 ),
inference(simp,[status(thm)],[135]) ).
thf(803,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton ) )
| ( B != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,137]) ).
thf(804,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( sk2 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[803:[bind(A,$thf( sk2 @ singleton )),bind(B,$thf( B ))]]) ).
thf(1070,plain,
~ ( sk2 @ singleton @ singleton @ ( sk1 @ in ) ),
inference(simp,[status(thm)],[804]) ).
thf(1423,plain,
( ( ( sk2 @ singleton @ singleton @ ( sk1 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,1070]) ).
thf(1424,plain,
( ( sk2 @ singleton @ singleton @ ( sk1 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[1423]) ).
thf(1459,plain,
( ( ( sk2 @ singleton @ singleton )
!= sk2 )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[1424]) ).
thf(1467,plain,
( ( sk2 @ singleton @ singleton )
!= sk2 ),
inference(simp,[status(thm)],[1459]) ).
thf(1486,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton @ singleton ) )
| ( B != sk2 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1467]) ).
thf(1487,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( sk2 @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1486:[bind(A,$thf( sk2 @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(1497,plain,
~ ( sk2 @ singleton @ singleton @ singleton @ ( sk2 @ in ) ),
inference(simp,[status(thm)],[1487]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(25,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(280,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_intersection2 ) )
!= ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) ) )
| ( ( A @ ( B @ set_intersection2 ) )
!= ( sk1 @ singleton ) ) ),
inference(paramod_ordered,[status(thm)],[27,19]) ).
thf(281,plain,
( ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) )
!= ( sk1 @ singleton ) ),
inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( sk3 @ ( sk1 @ unordered_pair ) )),bind(B,$thf( sk2 ))]]) ).
thf(821,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) ) )
| ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,281]) ).
thf(822,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[821:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) ))]]) ).
thf(1078,plain,
~ ( sk1 @ singleton @ singleton @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) @ in ) ),
inference(simp,[status(thm)],[822]) ).
thf(1280,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk13 @ singleton @ ( sk12 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,1104]) ).
thf(1281,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk13 @ singleton @ ( sk12 @ in ) ) ),
inference(simp,[status(thm)],[1280]) ).
thf(1297,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk13 @ singleton ) )
| ( A != sk12 ) ),
inference(simp,[status(thm)],[1281]) ).
thf(1303,plain,
! [A: $i] :
( ( A @ ( sk12 @ unordered_pair ) )
!= ( sk13 @ singleton ) ),
inference(simp,[status(thm)],[1297]) ).
thf(8330,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( sk12 @ unordered_pair ) ) )
| ( B
!= ( sk13 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1303]) ).
thf(8331,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk13 @ singleton ) )
| ~ ( B @ ( sk12 @ unordered_pair ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[8330:[bind(A,$thf( E @ ( sk12 @ unordered_pair ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(8342,plain,
! [A: $i] :
~ ( A @ ( sk12 @ unordered_pair ) @ singleton @ ( sk13 @ singleton @ in ) ),
inference(simp,[status(thm)],[8331]) ).
thf(1559,plain,
! [B: $i,A: $i] :
( ( A != sk13 )
| ( ( sk12 @ singleton )
!= sk2 )
| ( B != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1257]) ).
thf(1560,plain,
! [A: $i] :
( ( ( sk12 @ singleton )
!= sk2 )
| ( A != sk1 )
| ~ ( sk13 @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1559:[bind(A,$thf( sk13 ))]]) ).
thf(1568,plain,
( ( ( sk12 @ singleton )
!= sk2 )
| ~ ( sk13 @ singleton @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[1560]) ).
thf(6575,plain,
( ( ( sk13 @ singleton @ ( sk1 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ( ( sk12 @ singleton )
!= sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,1568]) ).
thf(6576,plain,
( ( ( sk13 @ singleton @ ( sk1 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ( ( sk12 @ singleton )
!= sk2 ) ),
inference(simp,[status(thm)],[6575]) ).
thf(6671,plain,
( ( ( sk13 @ singleton )
!= sk2 )
| ( sk1 != sk1 )
| ( ( sk12 @ singleton )
!= sk2 ) ),
inference(simp,[status(thm)],[6576]) ).
thf(6685,plain,
( ( ( sk13 @ singleton )
!= sk2 )
| ( ( sk12 @ singleton )
!= sk2 ) ),
inference(simp,[status(thm)],[6671]) ).
thf(7175,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk12 @ singleton ) )
| ( ( sk13 @ singleton )
!= sk2 )
| ( B != sk2 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,6685]) ).
thf(7176,plain,
! [A: $i] :
( ( ( sk13 @ singleton )
!= sk2 )
| ( A != sk2 )
| ~ ( sk12 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[7175:[bind(A,$thf( sk12 @ singleton )),bind(B,$thf( B ))]]) ).
thf(7188,plain,
( ( ( sk13 @ singleton )
!= sk2 )
| ~ ( sk12 @ singleton @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[7176]) ).
thf(799,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk2 @ singleton ) )
| ( A != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,137]) ).
thf(800,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( A @ singleton @ ( sk2 @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[799:[bind(A,$thf( A )),bind(B,$thf( sk2 @ singleton ))]]) ).
thf(1069,plain,
~ ( sk1 @ singleton @ ( sk2 @ singleton @ in ) ),
inference(simp,[status(thm)],[800]) ).
thf(1328,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,1069]) ).
thf(1329,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1328]) ).
thf(1359,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton ) )
| ( A
!= ( sk2 @ singleton ) ) ),
inference(simp,[status(thm)],[1329]) ).
thf(1367,plain,
( ( sk2 @ singleton @ singleton )
!= ( sk1 @ singleton ) ),
inference(simp,[status(thm)],[1359]) ).
thf(1603,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton @ singleton ) )
| ( B
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1367]) ).
thf(1604,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( sk2 @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1603:[bind(A,$thf( sk2 @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(1609,plain,
~ ( sk2 @ singleton @ singleton @ singleton @ ( sk1 @ singleton @ in ) ),
inference(simp,[status(thm)],[1604]) ).
thf(6005,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ singleton @ ( sk1 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,1609]) ).
thf(6006,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ singleton @ ( sk1 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[6005]) ).
thf(6120,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk2 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[6006]) ).
thf(6148,plain,
( ( sk2 @ singleton @ singleton @ singleton )
!= ( sk1 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[6120]) ).
thf(6939,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk2 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk1 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,6148]) ).
thf(6940,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( sk2 @ singleton @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[6939:[bind(A,$thf( A )),bind(B,$thf( sk2 @ singleton @ singleton @ singleton ))]]) ).
thf(6964,plain,
~ ( sk1 @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[6940]) ).
thf(25020,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,6964]) ).
thf(25021,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[25020]) ).
thf(25268,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk2 @ singleton @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[25021]) ).
thf(25311,plain,
( ( sk2 @ singleton @ singleton @ singleton @ singleton )
!= ( sk1 @ singleton @ singleton @ singleton ) ),
inference(simp,[status(thm)],[25268]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk1 @ ( sk2 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,116]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk1 @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[222]) ).
thf(241,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= sk1 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[223]) ).
thf(244,plain,
! [A: $i] :
( ( A @ ( sk2 @ unordered_pair ) )
!= sk1 ),
inference(simp,[status(thm)],[241]) ).
thf(252,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ unordered_pair ) )
!= ( C @ ( sk2 @ unordered_pair ) ) )
| ( ( B @ ( A @ unordered_pair ) )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[24,244]) ).
thf(253,plain,
! [A: $i] :
( ( sk2 @ ( A @ unordered_pair ) )
!= sk1 ),
inference(pattern_uni,[status(thm)],[252:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(614,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( sk2 @ ( C @ unordered_pair ) ) )
| ( B != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,253]) ).
thf(615,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ~ ( sk2 @ ( B @ unordered_pair ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[614:[bind(A,$thf( sk2 @ ( D @ unordered_pair ) )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(1001,plain,
! [A: $i] :
~ ( sk2 @ ( A @ unordered_pair ) @ singleton @ ( sk1 @ in ) ),
inference(simp,[status(thm)],[615]) ).
thf(7335,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ unordered_pair ) @ singleton @ ( sk1 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,1001]) ).
thf(7336,plain,
! [A: $i] :
( ( sk2 @ ( A @ unordered_pair ) @ singleton @ ( sk1 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[7335]) ).
thf(7424,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ unordered_pair ) @ singleton )
!= sk2 )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[7336]) ).
thf(7431,plain,
! [A: $i] :
( ( sk2 @ ( A @ unordered_pair ) @ singleton )
!= sk2 ),
inference(simp,[status(thm)],[7424]) ).
thf(1597,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk2 @ singleton @ singleton ) )
| ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1367]) ).
thf(1598,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( sk2 @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[1597:[bind(A,$thf( A )),bind(B,$thf( sk2 @ singleton @ singleton ))]]) ).
thf(1614,plain,
~ ( sk1 @ singleton @ singleton @ ( sk2 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[1598]) ).
thf(6150,plain,
( ( ( sk1 @ singleton @ singleton @ ( sk2 @ singleton @ singleton @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,1614]) ).
thf(6151,plain,
( ( sk1 @ singleton @ singleton @ ( sk2 @ singleton @ singleton @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[6150]) ).
thf(6268,plain,
( ( ( sk1 @ singleton @ singleton )
!= sk2 )
| ( ( sk2 @ singleton @ singleton )
!= sk1 ) ),
inference(simp,[status(thm)],[6151]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ in ) )
| ( ( A @ ( B @ sk4 ) )
!= A ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk5 ) @ in ) )
| ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk4 ) )
!= A ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk5 ) @ in ) )
| ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk4 ) )
!= A ) ),
inference(simp,[status(thm)],[41]) ).
thf(1326,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,1069]) ).
thf(1327,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1326]) ).
thf(1358,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk1 @ singleton ) )
| ( B
!= ( sk2 @ singleton ) ) ),
inference(simp,[status(thm)],[1327]) ).
thf(1366,plain,
! [A: $i] :
( ( sk2 @ singleton @ ( A @ unordered_pair ) )
!= ( sk1 @ singleton ) ),
inference(simp,[status(thm)],[1358]) ).
thf(1243,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk12 @ singleton @ ( sk13 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,1103]) ).
thf(1244,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk12 @ singleton @ ( sk13 @ in ) ) ),
inference(simp,[status(thm)],[1243]) ).
thf(1259,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk12 @ singleton ) )
| ( A != sk13 ) ),
inference(simp,[status(thm)],[1244]) ).
thf(1265,plain,
! [A: $i] :
( ( A @ ( sk13 @ unordered_pair ) )
!= ( sk12 @ singleton ) ),
inference(simp,[status(thm)],[1259]) ).
thf(1235,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ singleton @ ( sk13 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,1103]) ).
thf(1236,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ singleton @ ( sk13 @ in ) ) ),
inference(simp,[status(thm)],[1235]) ).
thf(1260,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk12 @ singleton ) )
| ( A != sk13 ) ),
inference(simp,[status(thm)],[1236]) ).
thf(1266,plain,
( ( sk13 @ singleton )
!= ( sk12 @ singleton ) ),
inference(simp,[status(thm)],[1260]) ).
thf(1415,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk13 @ singleton ) )
| ( B
!= ( sk12 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1266]) ).
thf(1416,plain,
! [A: $i] :
( ( A
!= ( sk12 @ singleton ) )
| ~ ( sk13 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1415:[bind(A,$thf( sk13 @ singleton )),bind(B,$thf( B ))]]) ).
thf(1421,plain,
~ ( sk13 @ singleton @ singleton @ ( sk12 @ singleton @ in ) ),
inference(simp,[status(thm)],[1416]) ).
thf(2289,plain,
( ( ( sk13 @ singleton @ singleton @ ( sk12 @ singleton @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,1421]) ).
thf(2290,plain,
( ( sk13 @ singleton @ singleton @ ( sk12 @ singleton @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[2289]) ).
thf(2339,plain,
( ( ( sk13 @ singleton @ singleton )
!= sk2 )
| ( ( sk12 @ singleton )
!= sk1 ) ),
inference(simp,[status(thm)],[2290]) ).
thf(1233,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk12 @ singleton @ ( sk13 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,1103]) ).
thf(1234,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk12 @ singleton @ ( sk13 @ in ) ) ),
inference(simp,[status(thm)],[1233]) ).
thf(1258,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk12 @ singleton ) )
| ( B != sk13 ) ),
inference(simp,[status(thm)],[1234]) ).
thf(1264,plain,
! [A: $i] :
( ( sk13 @ ( A @ unordered_pair ) )
!= ( sk12 @ singleton ) ),
inference(simp,[status(thm)],[1258]) ).
thf(9841,plain,
! [B: $i,A: $i] :
( ( A != sk13 )
| ( B != sk12 )
| ( A @ ( A @ ( A @ ( B @ sk11 ) ) @ in ) )
| ( B @ ( A @ ( A @ sk9 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2132,113]) ).
thf(9842,plain,
! [A: $i] :
( ( A != sk12 )
| ( sk13 @ ( sk13 @ ( sk13 @ ( A @ sk11 ) ) @ in ) )
| ( A @ ( sk13 @ ( sk13 @ sk9 ) ) ) ),
inference(pattern_uni,[status(thm)],[9841:[bind(A,$thf( sk13 ))]]) ).
thf(10719,plain,
( ( sk13 @ ( sk13 @ ( sk13 @ ( sk12 @ sk11 ) ) @ in ) )
| ( sk12 @ ( sk13 @ ( sk13 @ sk9 ) ) ) ),
inference(simp,[status(thm)],[9842]) ).
thf(1411,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk13 @ singleton ) )
| ( A
!= ( sk12 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1266]) ).
thf(1412,plain,
! [A: $i] :
( ( A
!= ( sk12 @ singleton ) )
| ~ ( A @ singleton @ ( sk13 @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[1411:[bind(A,$thf( A )),bind(B,$thf( sk13 @ singleton ))]]) ).
thf(1420,plain,
~ ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ in ) ),
inference(simp,[status(thm)],[1412]) ).
thf(2223,plain,
( ( ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,1420]) ).
thf(2224,plain,
( ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[2223]) ).
thf(2274,plain,
( ( ( sk12 @ singleton @ singleton )
!= sk2 )
| ( ( sk13 @ singleton )
!= sk1 ) ),
inference(simp,[status(thm)],[2224]) ).
thf(8200,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ ( sk13 @ unordered_pair ) ) )
| ( A
!= ( sk12 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1265]) ).
thf(8201,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk12 @ singleton ) )
| ~ ( A @ singleton @ ( B @ ( sk13 @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[8200:[bind(A,$thf( A )),bind(B,$thf( E @ ( sk13 @ unordered_pair ) )),bind(C,$thf( E ))]]) ).
thf(8214,plain,
! [A: $i] :
~ ( sk12 @ singleton @ singleton @ ( A @ ( sk13 @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[8201]) ).
thf(1311,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk2 @ singleton ) )
| ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1173]) ).
thf(1312,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( sk2 @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[1311:[bind(A,$thf( A )),bind(B,$thf( sk2 @ singleton ))]]) ).
thf(1319,plain,
~ ( sk1 @ singleton @ singleton @ ( sk2 @ singleton @ in ) ),
inference(simp,[status(thm)],[1312]) ).
thf(8544,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( sk2 @ ( C @ unordered_pair ) @ singleton ) )
| ( A != sk2 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,7431]) ).
thf(8545,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ~ ( A @ singleton @ ( sk2 @ ( B @ unordered_pair ) @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[8544:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( E @ unordered_pair ) @ singleton )),bind(C,$thf( E ))]]) ).
thf(8571,plain,
! [A: $i] :
~ ( sk2 @ singleton @ ( sk2 @ ( A @ unordered_pair ) @ singleton @ in ) ),
inference(simp,[status(thm)],[8545]) ).
thf(1223,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton ) )
| ( B != sk2 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1210]) ).
thf(1224,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( sk2 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1223:[bind(A,$thf( sk2 @ singleton )),bind(B,$thf( B ))]]) ).
thf(1229,plain,
~ ( sk2 @ singleton @ singleton @ ( sk2 @ in ) ),
inference(simp,[status(thm)],[1224]) ).
thf(1504,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ ( sk2 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,1229]) ).
thf(1505,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[1504]) ).
thf(1537,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk2 @ singleton @ singleton ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[1505]) ).
thf(1539,plain,
( ( sk2 @ singleton @ singleton )
!= ( sk2 @ singleton ) ),
inference(simp,[status(thm)],[1537]) ).
thf(1631,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton @ singleton ) )
| ( B
!= ( sk2 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1539]) ).
thf(1632,plain,
! [A: $i] :
( ( A
!= ( sk2 @ singleton ) )
| ~ ( sk2 @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1631:[bind(A,$thf( sk2 @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(1637,plain,
~ ( sk2 @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ in ) ),
inference(simp,[status(thm)],[1632]) ).
thf(6303,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,1637]) ).
thf(6304,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[6303]) ).
thf(6416,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk2 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk2 @ singleton ) ) ),
inference(simp,[status(thm)],[6304]) ).
thf(6428,plain,
( ( sk2 @ singleton @ singleton @ singleton )
!= ( sk2 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[6416]) ).
thf(7035,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton @ singleton @ singleton ) )
| ( B
!= ( sk2 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,6428]) ).
thf(7036,plain,
! [A: $i] :
( ( A
!= ( sk2 @ singleton @ singleton ) )
| ~ ( sk2 @ singleton @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[7035:[bind(A,$thf( sk2 @ singleton @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(7059,plain,
~ ( sk2 @ singleton @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[7036]) ).
thf(25655,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,7059]) ).
thf(25656,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[25655]) ).
thf(25905,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk2 @ singleton @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk2 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[25656]) ).
thf(25929,plain,
( ( sk2 @ singleton @ singleton @ singleton @ singleton )
!= ( sk2 @ singleton @ singleton @ singleton ) ),
inference(simp,[status(thm)],[25905]) ).
thf(7096,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( sk13 @ ( C @ unordered_pair ) ) )
| ( B
!= ( sk12 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1264]) ).
thf(7097,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk12 @ singleton ) )
| ~ ( sk13 @ ( B @ unordered_pair ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[7096:[bind(A,$thf( sk13 @ ( D @ unordered_pair ) )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(7112,plain,
! [A: $i] :
~ ( sk13 @ ( A @ unordered_pair ) @ singleton @ ( sk12 @ singleton @ in ) ),
inference(simp,[status(thm)],[7097]) ).
thf(164,plain,
( ( ( sk2 @ ( sk3 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ( ( sk2 @ ( sk1 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
!= ( sk1 @ singleton ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,144]) ).
thf(165,plain,
( ( ( sk2 @ ( sk3 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ( ( sk2 @ ( sk1 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[164]) ).
thf(167,plain,
( ( sk2 != sk2 )
| ( sk3 != sk1 )
| ( ( sk2 @ ( sk1 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(169,plain,
( ( sk3 != sk1 )
| ( ( sk2 @ ( sk1 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[167]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_intersection2 ) )
!= ( sk2 @ ( sk1 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) ) )
| ( sk3 != sk1 )
| ( ( A @ ( B @ set_intersection2 ) )
!= ( sk1 @ singleton ) ) ),
inference(paramod_ordered,[status(thm)],[27,169]) ).
thf(261,plain,
( ( sk3 != sk1 )
| ( ( sk1 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) )
!= ( sk1 @ singleton ) ) ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( sk1 @ ( sk1 @ unordered_pair ) )),bind(B,$thf( sk2 ))]]) ).
thf(1425,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ singleton @ singleton @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,1070]) ).
thf(1426,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ singleton @ singleton @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[1425]) ).
thf(1457,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton ) )
| ( B != sk1 ) ),
inference(simp,[status(thm)],[1426]) ).
thf(1465,plain,
! [A: $i] :
( ( sk1 @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1457]) ).
thf(1270,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk13 @ singleton @ ( sk12 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,1104]) ).
thf(1271,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk13 @ singleton @ ( sk12 @ in ) ) ),
inference(simp,[status(thm)],[1270]) ).
thf(1296,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk13 @ singleton ) )
| ( B != sk12 ) ),
inference(simp,[status(thm)],[1271]) ).
thf(1302,plain,
! [A: $i] :
( ( sk12 @ ( A @ unordered_pair ) )
!= ( sk13 @ singleton ) ),
inference(simp,[status(thm)],[1296]) ).
thf(174,plain,
! [A: $i] :
( ( ( A @ ( A @ set_intersection2 ) )
!= ( sk2 @ ( sk1 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) ) )
| ( A
!= ( sk1 @ singleton ) )
| ~ ( sk2 @ ( sk3 @ in ) ) ),
inference(paramod_ordered,[status(thm)],[105,144]) ).
thf(179,plain,
( ( ( sk1 @ singleton )
!= sk2 )
| ( ( sk1 @ ( sk1 @ unordered_pair ) )
!= ( sk1 @ singleton ) )
| ~ ( sk2 @ ( sk3 @ in ) ) ),
inference(simp,[status(thm)],[174]) ).
thf(724,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ in ) )
!= ( A @ singleton @ ( B @ in ) ) )
| ~ $true
| ( B = A ) ),
inference(paramod_ordered,[status(thm)],[15,40]) ).
thf(725,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ in ) )
!= ( A @ singleton @ ( B @ in ) ) )
| ( B = A ) ),
inference(simp,[status(thm)],[724]) ).
thf(991,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= sk2 )
| ( sk1 != B )
| ( B = A ) ),
inference(simp,[status(thm)],[725]) ).
thf(1136,plain,
! [A: $i] :
( ( ( A @ singleton )
!= sk2 )
| ( sk1 = A ) ),
inference(simp,[status(thm)],[991]) ).
thf(139,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ ( sk3 @ in ) ) )
| ~ $true
| ( sk3 = sk1 ) ),
inference(paramod_ordered,[status(thm)],[46,18]) ).
thf(140,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ ( sk3 @ in ) ) )
| ( sk3 = sk1 ) ),
inference(simp,[status(thm)],[139]) ).
thf(147,plain,
! [A: $i] :
( ( ( A @ singleton )
!= sk2 )
| ( A != sk3 )
| ( sk3 = sk1 ) ),
inference(simp,[status(thm)],[140]) ).
thf(149,plain,
( ( ( sk3 @ singleton )
!= sk2 )
| ( sk3 = sk1 ) ),
inference(simp,[status(thm)],[147]) ).
thf(668,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk3 @ singleton ) )
| ( B != sk2 )
| ( sk3 = sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,149]) ).
thf(669,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk3 = sk1 )
| ~ ( sk3 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[668:[bind(A,$thf( sk3 @ singleton )),bind(B,$thf( B ))]]) ).
thf(1020,plain,
( ( sk3 = sk1 )
| ~ ( sk3 @ singleton @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[669]) ).
thf(2225,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,1420]) ).
thf(2226,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[2225]) ).
thf(2275,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk12 @ singleton @ singleton ) )
| ( B
!= ( sk13 @ singleton ) ) ),
inference(simp,[status(thm)],[2226]) ).
thf(2281,plain,
! [A: $i] :
( ( sk13 @ singleton @ ( A @ unordered_pair ) )
!= ( sk12 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[2275]) ).
thf(1176,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ singleton @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,1042]) ).
thf(1177,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ singleton @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[1176]) ).
thf(1204,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[1177]) ).
thf(1212,plain,
! [A: $i] :
( ( A @ ( sk1 @ unordered_pair ) )
!= ( sk2 @ singleton ) ),
inference(simp,[status(thm)],[1204]) ).
thf(2629,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ ( sk1 @ unordered_pair ) ) )
| ( A
!= ( sk2 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1212]) ).
thf(2630,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton ) )
| ~ ( A @ singleton @ ( B @ ( sk1 @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[2629:[bind(A,$thf( A )),bind(B,$thf( E @ ( sk1 @ unordered_pair ) )),bind(C,$thf( E ))]]) ).
thf(2639,plain,
! [A: $i] :
~ ( sk2 @ singleton @ singleton @ ( A @ ( sk1 @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[2630]) ).
thf(1645,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk2 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,1319]) ).
thf(1646,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk2 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1645]) ).
thf(1688,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk1 @ singleton @ singleton ) )
| ( B
!= ( sk2 @ singleton ) ) ),
inference(simp,[status(thm)],[1646]) ).
thf(1696,plain,
! [A: $i] :
( ( sk2 @ singleton @ ( A @ unordered_pair ) )
!= ( sk1 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1688]) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
| ~ ( C @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk6 ) ) ) ),
inference(cnfConj,[status(thm)],[51]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk6 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[56]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( C @ sk8 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk6 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ ( sk3 @ in ) ) )
| ( ( sk2 @ ( sk1 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
!= ( sk1 @ singleton ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,144]) ).
thf(237,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ ( sk3 @ in ) ) )
| ( ( sk2 @ ( sk1 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[236]) ).
thf(240,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= sk2 )
| ( A != sk3 )
| ( ( sk2 @ ( sk1 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(243,plain,
! [A: $i] :
( ( ( A @ ( sk3 @ unordered_pair ) )
!= sk2 )
| ( ( sk2 @ ( sk1 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[240]) ).
thf(811,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ ( sk2 @ unordered_pair ) ) )
| ( A != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,244]) ).
thf(812,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ~ ( A @ singleton @ ( B @ ( sk2 @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[811:[bind(A,$thf( A )),bind(B,$thf( E @ ( sk2 @ unordered_pair ) )),bind(C,$thf( E ))]]) ).
thf(1074,plain,
! [A: $i] :
~ ( sk1 @ singleton @ ( A @ ( sk2 @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[812]) ).
thf(8490,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk2 @ ( C @ unordered_pair ) ) )
| ( ( A @ ( B @ unordered_pair ) @ singleton )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[24,7431]) ).
thf(8491,plain,
! [A: $i] :
( ( A @ ( sk2 @ unordered_pair ) @ singleton )
!= sk2 ),
inference(pattern_uni,[status(thm)],[8490:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(8646,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( sk2 @ unordered_pair ) @ singleton ) )
| ( B != sk2 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,8491]) ).
thf(8647,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ~ ( B @ ( sk2 @ unordered_pair ) @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[8646:[bind(A,$thf( F @ ( sk2 @ unordered_pair ) @ singleton )),bind(B,$thf( B )),bind(C,$thf( F ))]]) ).
thf(8655,plain,
! [A: $i] :
~ ( A @ ( sk2 @ unordered_pair ) @ singleton @ singleton @ ( sk2 @ in ) ),
inference(simp,[status(thm)],[8647]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ set_intersection2 ) ) )
| ~ ( C @ ( B @ ( A @ sk9 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) ) ),
inference(cnfConj,[status(thm)],[78]) ).
thf(91,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk9 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) )
| ( C
= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk9 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) )
| ( C
= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(16345,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ ( sk13 @ ( sk13 @ sk9 ) ) )
!= ( C @ ( B @ ( A @ sk9 ) ) ) )
| ~ $true
| ( C @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) )
| ( C
= ( B @ ( A @ set_intersection2 ) ) )
| ( sk13 @ ( sk13 @ ( sk13 @ ( sk12 @ sk11 ) ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[10719,92]) ).
thf(16346,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk12 @ ( sk13 @ ( sk13 @ sk9 ) ) )
!= ( C @ ( B @ ( A @ sk9 ) ) ) )
| ( C @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) )
| ( C
= ( B @ ( A @ set_intersection2 ) ) )
| ( sk13 @ ( sk13 @ ( sk13 @ ( sk12 @ sk11 ) ) @ in ) ) ),
inference(simp,[status(thm)],[16345]) ).
thf(16347,plain,
( ( sk12 @ ( sk13 @ ( sk13 @ ( sk12 @ sk10 ) ) @ in ) )
| ( ( sk13 @ ( sk13 @ set_intersection2 ) )
= sk12 )
| ( sk13 @ ( sk13 @ ( sk13 @ ( sk12 @ sk11 ) ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[16346:[bind(A,$thf( sk13 )),bind(B,$thf( sk13 )),bind(C,$thf( sk12 ))]]) ).
thf(39638,plain,
( ( sk12 @ ( sk13 @ ( sk13 @ ( sk12 @ sk10 ) ) @ in ) )
| ( sk13 = sk12 )
| ( sk13 @ ( sk13 @ ( sk13 @ ( sk12 @ sk11 ) ) @ in ) ) ),
inference(rewrite,[status(thm)],[16347,105]) ).
thf(39639,plain,
( ( sk12 @ ( sk13 @ ( sk13 @ ( sk12 @ sk10 ) ) @ in ) )
| ( sk13 @ ( sk13 @ ( sk13 @ ( sk12 @ sk11 ) ) @ in ) ) ),
inference(simplifyReflect,[status(thm)],[39638,113]) ).
thf(2360,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ singleton @ ( sk2 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,1497]) ).
thf(2361,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[2360]) ).
thf(2405,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk2 @ singleton @ singleton @ singleton ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[2361]) ).
thf(2415,plain,
( ( sk2 @ singleton @ singleton @ singleton )
!= ( sk2 @ singleton ) ),
inference(simp,[status(thm)],[2405]) ).
thf(3177,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton @ singleton @ singleton ) )
| ( B
!= ( sk2 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,2415]) ).
thf(3178,plain,
! [A: $i] :
( ( A
!= ( sk2 @ singleton ) )
| ~ ( sk2 @ singleton @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[3177:[bind(A,$thf( sk2 @ singleton @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(3186,plain,
~ ( sk2 @ singleton @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ in ) ),
inference(simp,[status(thm)],[3178]) ).
thf(7171,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk13 @ singleton ) )
| ( A != sk2 )
| ( ( sk12 @ singleton )
!= sk2 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,6685]) ).
thf(7172,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( sk12 @ singleton )
!= sk2 )
| ~ ( A @ singleton @ ( sk13 @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[7171:[bind(A,$thf( A )),bind(B,$thf( sk13 @ singleton ))]]) ).
thf(7187,plain,
( ( ( sk12 @ singleton )
!= sk2 )
| ~ ( sk2 @ singleton @ ( sk13 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[7172]) ).
thf(27568,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ ( sk13 @ singleton @ in ) ) )
| ( ( sk12 @ singleton )
!= sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,7187]) ).
thf(27569,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ ( sk13 @ singleton @ in ) ) )
| ( ( sk12 @ singleton )
!= sk2 ) ),
inference(simp,[status(thm)],[27568]) ).
thf(27761,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk2 @ singleton ) )
| ( A
!= ( sk13 @ singleton ) )
| ( ( sk12 @ singleton )
!= sk2 ) ),
inference(simp,[status(thm)],[27569]) ).
thf(27813,plain,
( ( ( sk13 @ singleton @ singleton )
!= ( sk2 @ singleton ) )
| ( ( sk12 @ singleton )
!= sk2 ) ),
inference(simp,[status(thm)],[27761]) ).
thf(1555,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk12 @ singleton ) )
| ( A != sk2 )
| ( sk13 != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1257]) ).
thf(1556,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk13 != sk1 )
| ~ ( A @ singleton @ ( sk12 @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[1555:[bind(A,$thf( A )),bind(B,$thf( sk12 @ singleton ))]]) ).
thf(1567,plain,
( ( sk13 != sk1 )
| ~ ( sk2 @ singleton @ ( sk12 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1556]) ).
thf(6453,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ ( sk12 @ singleton @ in ) ) )
| ( sk13 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,1567]) ).
thf(6454,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ ( sk12 @ singleton @ in ) ) )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[6453]) ).
thf(6548,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk2 @ singleton ) )
| ( A
!= ( sk12 @ singleton ) )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[6454]) ).
thf(6560,plain,
( ( ( sk12 @ singleton @ singleton )
!= ( sk2 @ singleton ) )
| ( sk13 != sk1 ) ),
inference(simp,[status(thm)],[6548]) ).
thf(2633,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( sk1 @ unordered_pair ) ) )
| ( B
!= ( sk2 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1212]) ).
thf(2634,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton ) )
| ~ ( B @ ( sk1 @ unordered_pair ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[2633:[bind(A,$thf( E @ ( sk1 @ unordered_pair ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(2641,plain,
! [A: $i] :
~ ( A @ ( sk1 @ unordered_pair ) @ singleton @ ( sk2 @ singleton @ in ) ),
inference(simp,[status(thm)],[2634]) ).
thf(83,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ~ ( B @ ( D @ in ) )
| ~ ( A @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(cnfConj,[status(thm)],[78]) ).
thf(101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ~ ( B @ ( D @ in ) )
| ~ ( A @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(lifteq,[status(thm)],[83]) ).
thf(102,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ set_intersection2 ) @ ( C @ in ) )
| ~ ( B @ ( C @ in ) )
| ~ ( A @ ( C @ in ) ) ),
inference(simp,[status(thm)],[101]) ).
thf(315,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ ( sk3 @ in ) ) )
| ~ $true
| ( sk3 = sk1 ) ),
inference(paramod_ordered,[status(thm)],[69,18]) ).
thf(316,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ ( sk3 @ in ) ) )
| ( sk3 = sk1 ) ),
inference(simp,[status(thm)],[315]) ).
thf(327,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= sk2 )
| ( B != sk3 )
| ( sk3 = sk1 ) ),
inference(simp,[status(thm)],[316]) ).
thf(334,plain,
! [A: $i] :
( ( ( sk3 @ ( A @ unordered_pair ) )
!= sk2 )
| ( sk3 = sk1 ) ),
inference(simp,[status(thm)],[327]) ).
thf(1708,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk13 @ singleton ) )
| ( A != sk2 )
| ( sk12 != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1294]) ).
thf(1709,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk12 != sk1 )
| ~ ( A @ singleton @ ( sk13 @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[1708:[bind(A,$thf( A )),bind(B,$thf( sk13 @ singleton ))]]) ).
thf(1723,plain,
( ( sk12 != sk1 )
| ~ ( sk2 @ singleton @ ( sk13 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1709]) ).
thf(1647,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk2 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,1319]) ).
thf(1648,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk2 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1647]) ).
thf(1687,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton @ singleton ) )
| ( A
!= ( sk2 @ singleton ) ) ),
inference(simp,[status(thm)],[1648]) ).
thf(1695,plain,
( ( sk2 @ singleton @ singleton )
!= ( sk1 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1687]) ).
thf(3095,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk2 @ singleton @ singleton ) )
| ( A
!= ( sk1 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1695]) ).
thf(3096,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( sk2 @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[3095:[bind(A,$thf( A )),bind(B,$thf( sk2 @ singleton @ singleton ))]]) ).
thf(3111,plain,
~ ( sk1 @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[3096]) ).
thf(11388,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,3111]) ).
thf(11389,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[11388]) ).
thf(11560,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk2 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[11389]) ).
thf(11587,plain,
( ( sk2 @ singleton @ singleton @ singleton )
!= ( sk1 @ singleton @ singleton @ singleton ) ),
inference(simp,[status(thm)],[11560]) ).
thf(610,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( sk2 @ ( C @ unordered_pair ) ) )
| ( A != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,253]) ).
thf(611,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ~ ( A @ singleton @ ( sk2 @ ( B @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[610:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( D @ unordered_pair ) )),bind(C,$thf( D ))]]) ).
thf(999,plain,
! [A: $i] :
~ ( sk1 @ singleton @ ( sk2 @ ( A @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[611]) ).
thf(7215,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ ( B @ unordered_pair ) @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,999]) ).
thf(7216,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ ( B @ unordered_pair ) @ in ) ) ),
inference(simp,[status(thm)],[7215]) ).
thf(7297,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton ) )
| ( A
!= ( sk2 @ ( B @ unordered_pair ) ) ) ),
inference(simp,[status(thm)],[7216]) ).
thf(7301,plain,
! [A: $i] :
( ( sk2 @ ( A @ unordered_pair ) @ singleton )
!= ( sk1 @ singleton ) ),
inference(simp,[status(thm)],[7297]) ).
thf(1143,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,1041]) ).
thf(1144,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[1143]) ).
thf(1166,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk1 @ singleton ) )
| ( B != sk2 ) ),
inference(simp,[status(thm)],[1144]) ).
thf(1174,plain,
! [A: $i] :
( ( sk2 @ ( A @ unordered_pair ) )
!= ( sk1 @ singleton ) ),
inference(simp,[status(thm)],[1166]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ in ) )
| ( B @ ( A @ ( B @ sk4 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk5 ) @ in ) )
| ( B @ ( A @ ( B @ sk4 ) @ in ) )
| ( B
= ( A @ singleton ) ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk5 ) @ in ) )
| ( B @ ( A @ ( B @ sk4 ) @ in ) )
| ( B
= ( A @ singleton ) ) ),
inference(simp,[status(thm)],[37]) ).
thf(9953,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk2 @ singleton @ singleton ) )
| ( A != sk2 )
| ( A @ ( A @ ( A @ ( B @ sk11 ) ) @ in ) )
| ( B @ ( A @ ( A @ sk9 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2132,1467]) ).
thf(9954,plain,
! [A: $i] :
( ( A != sk2 )
| ( A @ ( A @ ( A @ ( sk2 @ singleton @ singleton @ sk11 ) ) @ in ) )
| ( sk2 @ singleton @ singleton @ ( A @ ( A @ sk9 ) ) ) ),
inference(pattern_uni,[status(thm)],[9953:[bind(A,$thf( A )),bind(B,$thf( sk2 @ singleton @ singleton ))]]) ).
thf(10756,plain,
( ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ singleton @ singleton @ sk11 ) ) @ in ) )
| ( sk2 @ singleton @ singleton @ ( sk2 @ ( sk2 @ sk9 ) ) ) ),
inference(simp,[status(thm)],[9954]) ).
thf(1180,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ singleton @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,1042]) ).
thf(1181,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ singleton @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[1180]) ).
thf(1205,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton ) )
| ( B != sk1 ) ),
inference(simp,[status(thm)],[1181]) ).
thf(1213,plain,
! [A: $i] :
( ( sk1 @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton ) ),
inference(simp,[status(thm)],[1205]) ).
thf(2658,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( sk1 @ ( C @ unordered_pair ) ) )
| ( B
!= ( sk2 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1213]) ).
thf(2659,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton ) )
| ~ ( sk1 @ ( B @ unordered_pair ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[2658:[bind(A,$thf( sk1 @ ( D @ unordered_pair ) )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(2663,plain,
! [A: $i] :
~ ( sk1 @ ( A @ unordered_pair ) @ singleton @ ( sk2 @ singleton @ in ) ),
inference(simp,[status(thm)],[2659]) ).
thf(2148,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( sk2 @ ( C @ unordered_pair ) ) )
| ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1174]) ).
thf(2149,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( sk2 @ ( B @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[2148:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( D @ unordered_pair ) )),bind(C,$thf( D ))]]) ).
thf(2157,plain,
! [A: $i] :
~ ( sk1 @ singleton @ singleton @ ( sk2 @ ( A @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[2149]) ).
thf(8326,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ ( sk12 @ unordered_pair ) ) )
| ( A
!= ( sk13 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1303]) ).
thf(8327,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk13 @ singleton ) )
| ~ ( A @ singleton @ ( B @ ( sk12 @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[8326:[bind(A,$thf( A )),bind(B,$thf( E @ ( sk12 @ unordered_pair ) )),bind(C,$thf( E ))]]) ).
thf(8339,plain,
! [A: $i] :
~ ( sk13 @ singleton @ singleton @ ( A @ ( sk12 @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[8327]) ).
thf(1714,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk13 @ singleton ) )
| ( B != sk2 )
| ( sk12 != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1294]) ).
thf(1715,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk12 != sk1 )
| ~ ( sk13 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1714:[bind(A,$thf( sk13 @ singleton )),bind(B,$thf( B ))]]) ).
thf(1719,plain,
( ( sk12 != sk1 )
| ~ ( sk13 @ singleton @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[1715]) ).
thf(2227,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,1420]) ).
thf(2228,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[2227]) ).
thf(2272,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk12 @ singleton @ singleton ) )
| ( A
!= ( sk13 @ singleton ) ) ),
inference(simp,[status(thm)],[2228]) ).
thf(2278,plain,
( ( sk13 @ singleton @ singleton )
!= ( sk12 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[2272]) ).
thf(3135,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk13 @ singleton @ singleton ) )
| ( B
!= ( sk12 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,2278]) ).
thf(3136,plain,
! [A: $i] :
( ( A
!= ( sk12 @ singleton @ singleton ) )
| ~ ( sk13 @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[3135:[bind(A,$thf( sk13 @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(3141,plain,
~ ( sk13 @ singleton @ singleton @ singleton @ ( sk12 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[3136]) ).
thf(2358,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ singleton @ singleton @ singleton @ ( sk2 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,1497]) ).
thf(2359,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ singleton @ singleton @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[2358]) ).
thf(2409,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton @ singleton ) )
| ( B != sk2 ) ),
inference(simp,[status(thm)],[2359]) ).
thf(2419,plain,
! [A: $i] :
( ( sk2 @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton @ singleton ) ),
inference(simp,[status(thm)],[2409]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ set_intersection2 ) ) )
| ~ ( C @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk9 ) ) ) ),
inference(cnfConj,[status(thm)],[78]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk9 ) ) )
| ( C
= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(lifteq,[status(thm)],[80]) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk9 ) ) )
| ( C
= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(simp,[status(thm)],[95]) ).
thf(9105,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( B != sk1 )
| ( A @ ( A @ ( A @ ( B @ sk11 ) ) @ in ) )
| ( B @ ( A @ ( A @ sk9 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2132,138]) ).
thf(9106,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk2 @ ( sk2 @ ( sk2 @ ( A @ sk11 ) ) @ in ) )
| ( A @ ( sk2 @ ( sk2 @ sk9 ) ) ) ),
inference(pattern_uni,[status(thm)],[9105:[bind(A,$thf( sk2 ))]]) ).
thf(10834,plain,
( ( sk2 @ ( sk2 @ ( sk2 @ ( sk1 @ sk11 ) ) @ in ) )
| ( sk1 @ ( sk2 @ ( sk2 @ sk9 ) ) ) ),
inference(simp,[status(thm)],[9106]) ).
thf(9483,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk2 @ singleton ) )
| ( A != sk1 )
| ( A @ ( A @ ( A @ ( B @ sk11 ) ) @ in ) )
| ( B @ ( A @ ( A @ sk9 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2132,137]) ).
thf(9484,plain,
! [A: $i] :
( ( A != sk1 )
| ( A @ ( A @ ( A @ ( sk2 @ singleton @ sk11 ) ) @ in ) )
| ( sk2 @ singleton @ ( A @ ( A @ sk9 ) ) ) ),
inference(pattern_uni,[status(thm)],[9483:[bind(A,$thf( A )),bind(B,$thf( sk2 @ singleton ))]]) ).
thf(10603,plain,
( ( sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ singleton @ sk11 ) ) @ in ) )
| ( sk2 @ singleton @ ( sk1 @ ( sk1 @ sk9 ) ) ) ),
inference(simp,[status(thm)],[9484]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk8 ) ) )
= B )
| ( ( A @ ( B @ ( C @ sk8 ) ) )
= A )
| ( C @ ( B @ ( A @ sk6 ) ) ) ),
inference(cnfConj,[status(thm)],[51]) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ sk6 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk8 ) ) )
= B )
| ( ( A @ ( B @ ( C @ sk8 ) ) )
= A ) ),
inference(lifteq,[status(thm)],[55]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ sk6 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk8 ) ) )
= B )
| ( ( A @ ( B @ ( C @ sk8 ) ) )
= A ) ),
inference(simp,[status(thm)],[72]) ).
thf(664,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk3 @ singleton ) )
| ( A != sk2 )
| ( sk3 = sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,149]) ).
thf(665,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk3 = sk1 )
| ~ ( A @ singleton @ ( sk3 @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[664:[bind(A,$thf( A )),bind(B,$thf( sk3 @ singleton ))]]) ).
thf(1019,plain,
( ( sk3 = sk1 )
| ~ ( sk2 @ singleton @ ( sk3 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[665]) ).
thf(10917,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ ( sk3 @ singleton @ in ) ) )
| ( sk3 = sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,1019]) ).
thf(10918,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ ( sk3 @ singleton @ in ) ) )
| ( sk3 = sk1 ) ),
inference(simp,[status(thm)],[10917]) ).
thf(11089,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk2 @ singleton ) )
| ( A
!= ( sk3 @ singleton ) )
| ( sk3 = sk1 ) ),
inference(simp,[status(thm)],[10918]) ).
thf(11120,plain,
( ( ( sk3 @ singleton @ singleton )
!= ( sk2 @ singleton ) )
| ( sk3 = sk1 ) ),
inference(simp,[status(thm)],[11089]) ).
thf(8900,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ ( sk2 @ in ) ) )
| ( sk12 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,1719]) ).
thf(8901,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ ( sk2 @ in ) ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[8900]) ).
thf(9000,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk13 @ singleton @ singleton ) )
| ( A != sk2 )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[8901]) ).
thf(9021,plain,
( ( ( sk13 @ singleton @ singleton )
!= ( sk2 @ singleton ) )
| ( sk12 != sk1 ) ),
inference(simp,[status(thm)],[9000]) ).
thf(8204,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( sk13 @ unordered_pair ) ) )
| ( B
!= ( sk12 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1265]) ).
thf(8205,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk12 @ singleton ) )
| ~ ( B @ ( sk13 @ unordered_pair ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[8204:[bind(A,$thf( E @ ( sk13 @ unordered_pair ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(8217,plain,
! [A: $i] :
~ ( A @ ( sk13 @ unordered_pair ) @ singleton @ ( sk12 @ singleton @ in ) ),
inference(simp,[status(thm)],[8205]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk5 ) )
= A )
| ( B @ ( A @ ( B @ sk4 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk4 ) @ in ) )
| ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk5 ) )
= A ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk4 ) @ in ) )
| ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk5 ) )
= A ) ),
inference(simp,[status(thm)],[43]) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
| ~ ( C @ ( B @ ( A @ sk6 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) ) ),
inference(cnfConj,[status(thm)],[51]) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk6 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[54]) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk6 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk7 ) ) @ in ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) ) ),
inference(simp,[status(thm)],[70]) ).
thf(1139,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,1041]) ).
thf(1140,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[1139]) ).
thf(1167,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk1 @ singleton ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[1140]) ).
thf(1175,plain,
! [A: $i] :
( ( A @ ( sk2 @ unordered_pair ) )
!= ( sk1 @ singleton ) ),
inference(simp,[status(thm)],[1167]) ).
thf(2177,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( sk2 @ unordered_pair ) ) )
| ( B
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1175]) ).
thf(2178,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( B @ ( sk2 @ unordered_pair ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[2177:[bind(A,$thf( E @ ( sk2 @ unordered_pair ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(2182,plain,
! [A: $i] :
~ ( A @ ( sk2 @ unordered_pair ) @ singleton @ ( sk1 @ singleton @ in ) ),
inference(simp,[status(thm)],[2178]) ).
thf(29191,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( sk2 @ unordered_pair ) @ singleton @ ( sk1 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,2182]) ).
thf(29192,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( sk2 @ unordered_pair ) @ singleton @ ( sk1 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[29191]) ).
thf(29384,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= ( B @ ( sk2 @ unordered_pair ) @ singleton ) )
| ( A
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[29192]) ).
thf(29443,plain,
! [A: $i] :
( ( A @ ( sk2 @ unordered_pair ) @ singleton )
!= ( sk1 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[29384]) ).
thf(8848,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk13 @ singleton ) )
| ( A != sk2 )
| ~ ( sk12 @ singleton @ ( sk1 @ in ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1718]) ).
thf(8849,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( sk12 @ singleton @ ( sk1 @ in ) )
| ~ ( A @ singleton @ ( sk13 @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[8848:[bind(A,$thf( A )),bind(B,$thf( sk13 @ singleton ))]]) ).
thf(8877,plain,
( ~ ( sk12 @ singleton @ ( sk1 @ in ) )
| ~ ( sk2 @ singleton @ ( sk13 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[8849]) ).
thf(7092,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( sk13 @ ( C @ unordered_pair ) ) )
| ( A
!= ( sk12 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1264]) ).
thf(7093,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk12 @ singleton ) )
| ~ ( A @ singleton @ ( sk13 @ ( B @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[7092:[bind(A,$thf( A )),bind(B,$thf( sk13 @ ( D @ unordered_pair ) )),bind(C,$thf( D ))]]) ).
thf(7109,plain,
! [A: $i] :
~ ( sk12 @ singleton @ singleton @ ( sk13 @ ( A @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[7093]) ).
thf(9487,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton ) )
| ( B != sk1 )
| ( A @ ( A @ ( A @ ( B @ sk11 ) ) @ in ) )
| ( B @ ( A @ ( A @ sk9 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2132,137]) ).
thf(9488,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk2 @ singleton @ ( sk2 @ singleton @ ( sk2 @ singleton @ ( A @ sk11 ) ) @ in ) )
| ( A @ ( sk2 @ singleton @ ( sk2 @ singleton @ sk9 ) ) ) ),
inference(pattern_uni,[status(thm)],[9487:[bind(A,$thf( sk2 @ singleton )),bind(B,$thf( B ))]]) ).
thf(10604,plain,
( ( sk2 @ singleton @ ( sk2 @ singleton @ ( sk2 @ singleton @ ( sk1 @ sk11 ) ) @ in ) )
| ( sk1 @ ( sk2 @ singleton @ ( sk2 @ singleton @ sk9 ) ) ) ),
inference(simp,[status(thm)],[9488]) ).
thf(26581,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ singleton @ ( sk2 @ singleton @ ( sk2 @ singleton @ ( sk1 @ sk11 ) ) @ in ) )
!= ( A @ singleton @ ( B @ in ) ) )
| ~ $true
| ( B = A )
| ( sk1 @ ( sk2 @ singleton @ ( sk2 @ singleton @ sk9 ) ) ) ),
inference(paramod_ordered,[status(thm)],[10604,40]) ).
thf(26582,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ singleton @ ( sk2 @ singleton @ ( sk2 @ singleton @ ( sk1 @ sk11 ) ) @ in ) )
!= ( A @ singleton @ ( B @ in ) ) )
| ( B = A )
| ( sk1 @ ( sk2 @ singleton @ ( sk2 @ singleton @ sk9 ) ) ) ),
inference(simp,[status(thm)],[26581]) ).
thf(26583,plain,
( ( ( sk2 @ singleton @ ( sk2 @ singleton @ ( sk1 @ sk11 ) ) )
= sk2 )
| ( sk1 @ ( sk2 @ singleton @ ( sk2 @ singleton @ sk9 ) ) ) ),
inference(pattern_uni,[status(thm)],[26582:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 @ singleton @ ( sk2 @ singleton @ ( sk1 @ sk11 ) ) ))]]) ).
thf(175,plain,
! [A: $i] :
( ( ( A @ ( A @ set_intersection2 ) )
!= ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) ) )
| ( A
!= ( sk1 @ singleton ) ) ),
inference(paramod_ordered,[status(thm)],[105,19]) ).
thf(181,plain,
( ( ( sk1 @ singleton )
!= sk2 )
| ( ( sk3 @ ( sk1 @ unordered_pair ) )
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[175]) ).
thf(31008,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ ( B @ ( sk1 @ unordered_pair ) @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,2639]) ).
thf(31009,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ ( B @ ( sk1 @ unordered_pair ) @ in ) ) ),
inference(simp,[status(thm)],[31008]) ).
thf(31188,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= ( sk2 @ singleton @ singleton ) )
| ( A
!= ( B @ ( sk1 @ unordered_pair ) ) ) ),
inference(simp,[status(thm)],[31009]) ).
thf(31254,plain,
! [A: $i] :
( ( A @ ( sk1 @ unordered_pair ) @ singleton )
!= ( sk2 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[31188]) ).
thf(2291,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk13 @ singleton @ singleton @ ( sk12 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,1421]) ).
thf(2292,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk13 @ singleton @ singleton @ ( sk12 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[2291]) ).
thf(2338,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk13 @ singleton @ singleton ) )
| ( B
!= ( sk12 @ singleton ) ) ),
inference(simp,[status(thm)],[2292]) ).
thf(2346,plain,
! [A: $i] :
( ( sk12 @ singleton @ ( A @ unordered_pair ) )
!= ( sk13 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[2338]) ).
thf(1931,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_intersection2 ) )
!= ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) ) )
| ( C
!= ( sk1 @ singleton ) )
| ( B @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk9 ) ) ) ),
inference(paramod_ordered,[status(thm)],[98,281]) ).
thf(1932,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( A @ sk11 ) ) @ in ) )
| ( A @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk9 ) ) ) ),
inference(pattern_uni,[status(thm)],[1931:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 @ ( sk1 @ unordered_pair ) )),bind(C,$thf( C ))]]) ).
thf(2079,plain,
( ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk1 @ singleton @ sk11 ) ) @ in ) )
| ( sk1 @ singleton @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk9 ) ) ) ),
inference(simp,[status(thm)],[1932]) ).
thf(1706,plain,
! [B: $i,A: $i] :
( ( B != sk12 )
| ( ( sk13 @ singleton )
!= sk2 )
| ( A != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1294]) ).
thf(1707,plain,
! [A: $i] :
( ( ( sk13 @ singleton )
!= sk2 )
| ( A != sk1 )
| ~ ( A @ singleton @ ( sk12 @ in ) ) ),
inference(pattern_uni,[status(thm)],[1706:[bind(A,$thf( A )),bind(B,$thf( sk12 ))]]) ).
thf(1722,plain,
( ( ( sk13 @ singleton )
!= sk2 )
| ~ ( sk1 @ singleton @ ( sk12 @ in ) ) ),
inference(simp,[status(thm)],[1707]) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ ( sk3 @ in ) ) )
| ~ $true
| ( sk3 = sk1 ) ),
inference(paramod_ordered,[status(thm)],[65,18]) ).
thf(227,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ ( sk3 @ in ) ) )
| ( sk3 = sk1 ) ),
inference(simp,[status(thm)],[226]) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= sk2 )
| ( A != sk3 )
| ( sk3 = sk1 ) ),
inference(simp,[status(thm)],[227]) ).
thf(245,plain,
! [A: $i] :
( ( ( A @ ( sk3 @ unordered_pair ) )
!= sk2 )
| ( sk3 = sk1 ) ),
inference(simp,[status(thm)],[242]) ).
thf(949,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) ) )
| ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,19]) ).
thf(950,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[949:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) ))]]) ).
thf(1122,plain,
~ ( sk1 @ singleton @ singleton @ ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) @ in ) ),
inference(simp,[status(thm)],[950]) ).
thf(831,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) ) )
| ( B
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,281]) ).
thf(832,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[831:[bind(A,$thf( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) )),bind(B,$thf( B ))]]) ).
thf(1080,plain,
~ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) @ singleton @ ( sk1 @ singleton @ in ) ),
inference(simp,[status(thm)],[832]) ).
thf(2025,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_intersection2 ) )
!= ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) ) )
| ( C
!= ( sk1 @ singleton ) )
| ( B @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk9 ) ) ) ),
inference(paramod_ordered,[status(thm)],[98,19]) ).
thf(2026,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ ( A @ sk11 ) ) @ in ) )
| ( A @ ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ sk9 ) ) ) ),
inference(pattern_uni,[status(thm)],[2025:[bind(A,$thf( sk3 @ ( sk1 @ unordered_pair ) )),bind(B,$thf( sk2 )),bind(C,$thf( C ))]]) ).
thf(2129,plain,
( ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ ( sk1 @ singleton @ sk11 ) ) @ in ) )
| ( sk1 @ singleton @ ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ sk9 ) ) ) ),
inference(simp,[status(thm)],[2026]) ).
thf(7167,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk12 @ singleton ) )
| ( ( sk13 @ singleton )
!= sk2 )
| ( A != sk2 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,6685]) ).
thf(7168,plain,
! [A: $i] :
( ( ( sk13 @ singleton )
!= sk2 )
| ( A != sk2 )
| ~ ( A @ singleton @ ( sk12 @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[7167:[bind(A,$thf( A )),bind(B,$thf( sk12 @ singleton ))]]) ).
thf(7186,plain,
( ( ( sk13 @ singleton )
!= sk2 )
| ~ ( sk2 @ singleton @ ( sk12 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[7168]) ).
thf(8640,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ ( sk2 @ unordered_pair ) @ singleton ) )
| ( A != sk2 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,8491]) ).
thf(8641,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ~ ( A @ singleton @ ( B @ ( sk2 @ unordered_pair ) @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[8640:[bind(A,$thf( A )),bind(B,$thf( F @ ( sk2 @ unordered_pair ) @ singleton )),bind(C,$thf( F ))]]) ).
thf(8652,plain,
! [A: $i] :
~ ( sk2 @ singleton @ ( A @ ( sk2 @ unordered_pair ) @ singleton @ in ) ),
inference(simp,[status(thm)],[8641]) ).
thf(8267,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( sk12 @ ( C @ unordered_pair ) ) )
| ( B
!= ( sk13 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1302]) ).
thf(8268,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk13 @ singleton ) )
| ~ ( sk12 @ ( B @ unordered_pair ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[8267:[bind(A,$thf( sk12 @ ( D @ unordered_pair ) )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(8280,plain,
! [A: $i] :
~ ( sk12 @ ( A @ unordered_pair ) @ singleton @ ( sk13 @ singleton @ in ) ),
inference(simp,[status(thm)],[8268]) ).
thf(2309,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ ( sk12 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,1421]) ).
thf(2310,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ ( sk12 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[2309]) ).
thf(2342,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk13 @ singleton @ singleton ) )
| ( A
!= ( sk12 @ singleton ) ) ),
inference(simp,[status(thm)],[2310]) ).
thf(2350,plain,
! [A: $i] :
( ( A @ ( sk12 @ singleton @ unordered_pair ) )
!= ( sk13 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[2342]) ).
thf(25972,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ ( sk12 @ singleton @ in ) ) )
| ( ( sk13 @ singleton )
!= sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,7186]) ).
thf(25973,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ ( sk12 @ singleton @ in ) ) )
| ( ( sk13 @ singleton )
!= sk2 ) ),
inference(simp,[status(thm)],[25972]) ).
thf(26170,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk2 @ singleton ) )
| ( A
!= ( sk12 @ singleton ) )
| ( ( sk13 @ singleton )
!= sk2 ) ),
inference(simp,[status(thm)],[25973]) ).
thf(26200,plain,
( ( ( sk12 @ singleton @ singleton )
!= ( sk2 @ singleton ) )
| ( ( sk13 @ singleton )
!= sk2 ) ),
inference(simp,[status(thm)],[26170]) ).
thf(1315,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton ) )
| ( B
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1173]) ).
thf(1316,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( sk2 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[1315:[bind(A,$thf( sk2 @ singleton )),bind(B,$thf( B ))]]) ).
thf(1320,plain,
~ ( sk2 @ singleton @ singleton @ ( sk1 @ singleton @ in ) ),
inference(simp,[status(thm)],[1316]) ).
thf(1726,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ singleton @ singleton @ ( sk1 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,1320]) ).
thf(1727,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ singleton @ singleton @ ( sk1 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1726]) ).
thf(1768,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton ) )
| ( B
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[1727]) ).
thf(1775,plain,
! [A: $i] :
( ( sk1 @ singleton @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1768]) ).
thf(1663,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk2 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,1319]) ).
thf(1664,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk2 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1663]) ).
thf(1686,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk1 @ singleton @ singleton ) )
| ( A
!= ( sk2 @ singleton ) ) ),
inference(simp,[status(thm)],[1664]) ).
thf(1694,plain,
! [A: $i] :
( ( A @ ( sk2 @ singleton @ unordered_pair ) )
!= ( sk1 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1686]) ).
thf(2376,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ singleton @ ( sk2 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,1497]) ).
thf(2377,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[2376]) ).
thf(2408,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton @ singleton ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[2377]) ).
thf(2418,plain,
! [A: $i] :
( ( A @ ( sk2 @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton @ singleton ) ),
inference(simp,[status(thm)],[2408]) ).
thf(13378,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,3186]) ).
thf(13379,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ singleton @ singleton @ ( sk2 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[13378]) ).
thf(13557,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk2 @ singleton @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk2 @ singleton ) ) ),
inference(simp,[status(thm)],[13379]) ).
thf(13593,plain,
( ( sk2 @ singleton @ singleton @ singleton @ singleton )
!= ( sk2 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[13557]) ).
thf(815,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( sk2 @ unordered_pair ) ) )
| ( B != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,244]) ).
thf(816,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ~ ( B @ ( sk2 @ unordered_pair ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[815:[bind(A,$thf( E @ ( sk2 @ unordered_pair ) )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(1076,plain,
! [A: $i] :
~ ( A @ ( sk2 @ unordered_pair ) @ singleton @ ( sk1 @ in ) ),
inference(simp,[status(thm)],[816]) ).
thf(28316,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk2 @ ( B @ unordered_pair ) @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,2157]) ).
thf(28317,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk2 @ ( B @ unordered_pair ) @ in ) ) ),
inference(simp,[status(thm)],[28316]) ).
thf(28494,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton @ singleton ) )
| ( A
!= ( sk2 @ ( B @ unordered_pair ) ) ) ),
inference(simp,[status(thm)],[28317]) ).
thf(28561,plain,
! [A: $i] :
( ( sk2 @ ( A @ unordered_pair ) @ singleton )
!= ( sk1 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[28494]) ).
thf(3129,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk13 @ singleton @ singleton ) )
| ( A
!= ( sk12 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,2278]) ).
thf(3130,plain,
! [A: $i] :
( ( A
!= ( sk12 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( sk13 @ singleton @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[3129:[bind(A,$thf( A )),bind(B,$thf( sk13 @ singleton @ singleton ))]]) ).
thf(3146,plain,
~ ( sk12 @ singleton @ singleton @ singleton @ ( sk13 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[3130]) ).
thf(7179,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk13 @ singleton ) )
| ( B != sk2 )
| ( ( sk12 @ singleton )
!= sk2 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,6685]) ).
thf(7180,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( sk12 @ singleton )
!= sk2 )
| ~ ( sk13 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[7179:[bind(A,$thf( sk13 @ singleton )),bind(B,$thf( B ))]]) ).
thf(7190,plain,
( ( ( sk12 @ singleton )
!= sk2 )
| ~ ( sk13 @ singleton @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[7180]) ).
thf(16269,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk1 @ sk9 ) ) )
!= ( C @ ( B @ ( A @ sk9 ) ) ) )
| ~ $true
| ( C @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) )
| ( C
= ( B @ ( A @ set_intersection2 ) ) )
| ( sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ sk11 ) ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[10832,92]) ).
thf(16270,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk1 @ sk9 ) ) )
!= ( C @ ( B @ ( A @ sk9 ) ) ) )
| ( C @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) )
| ( C
= ( B @ ( A @ set_intersection2 ) ) )
| ( sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ sk11 ) ) @ in ) ) ),
inference(simp,[status(thm)],[16269]) ).
thf(16271,plain,
( ( sk2 @ ( sk1 @ ( sk1 @ ( sk2 @ sk10 ) ) @ in ) )
| ( ( sk1 @ ( sk1 @ set_intersection2 ) )
= sk2 )
| ( sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ sk11 ) ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[16270:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 ))]]) ).
thf(38528,plain,
( ( sk2 @ ( sk1 @ ( sk1 @ ( sk2 @ sk10 ) ) @ in ) )
| ( sk2 = sk1 )
| ( sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ sk11 ) ) @ in ) ) ),
inference(rewrite,[status(thm)],[16271,105]) ).
thf(38529,plain,
( ( sk2 @ ( sk1 @ ( sk1 @ ( sk2 @ sk10 ) ) @ in ) )
| ( sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ sk11 ) ) @ in ) ) ),
inference(simplifyReflect,[status(thm)],[38528,138]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk5 ) )
= A )
| ( ( A @ ( B @ sk4 ) )
!= A ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk5 ) )
= A )
| ( ( A @ ( B @ sk4 ) )
!= A ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ singleton ) )
| ( ( A @ ( B @ sk5 ) )
= A )
| ( ( A @ ( B @ sk4 ) )
!= A ) ),
inference(simp,[status(thm)],[47]) ).
thf(52,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)],[51]) ).
thf(62,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)],[52]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ unordered_pair ) @ ( C @ in ) )
| ( C = B )
| ( C = A ) ),
inference(simp,[status(thm)],[62]) ).
thf(6666,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk12 @ singleton ) )
| ( B != sk2 )
| ~ ( sk13 @ singleton @ ( sk1 @ in ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1568]) ).
thf(6667,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( sk13 @ singleton @ ( sk1 @ in ) )
| ~ ( sk12 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[6666:[bind(A,$thf( sk12 @ singleton )),bind(B,$thf( B ))]]) ).
thf(6683,plain,
( ~ ( sk13 @ singleton @ ( sk1 @ in ) )
| ~ ( sk12 @ singleton @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[6667]) ).
thf(1553,plain,
! [B: $i,A: $i] :
( ( B != sk13 )
| ( ( sk12 @ singleton )
!= sk2 )
| ( A != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1257]) ).
thf(1554,plain,
! [A: $i] :
( ( ( sk12 @ singleton )
!= sk2 )
| ( A != sk1 )
| ~ ( A @ singleton @ ( sk13 @ in ) ) ),
inference(pattern_uni,[status(thm)],[1553:[bind(A,$thf( A )),bind(B,$thf( sk13 ))]]) ).
thf(1566,plain,
( ( ( sk12 @ singleton )
!= sk2 )
| ~ ( sk1 @ singleton @ ( sk13 @ in ) ) ),
inference(simp,[status(thm)],[1554]) ).
thf(3197,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk13 @ in ) ) )
| ( ( sk12 @ singleton )
!= sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,1566]) ).
thf(3198,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk13 @ in ) ) )
| ( ( sk12 @ singleton )
!= sk2 ) ),
inference(simp,[status(thm)],[3197]) ).
thf(3246,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton ) )
| ( A != sk13 )
| ( ( sk12 @ singleton )
!= sk2 ) ),
inference(simp,[status(thm)],[3198]) ).
thf(3260,plain,
( ( ( sk13 @ singleton )
!= ( sk1 @ singleton ) )
| ( ( sk12 @ singleton )
!= sk2 ) ),
inference(simp,[status(thm)],[3246]) ).
thf(9675,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk3 @ singleton ) )
| ( A != sk2 )
| ( sk3 = sk1 )
| ( A @ ( A @ ( A @ ( B @ sk11 ) ) @ in ) )
| ( B @ ( A @ ( A @ sk9 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2132,149]) ).
thf(9676,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk3 = sk1 )
| ( A @ ( A @ ( A @ ( sk3 @ singleton @ sk11 ) ) @ in ) )
| ( sk3 @ singleton @ ( A @ ( A @ sk9 ) ) ) ),
inference(pattern_uni,[status(thm)],[9675:[bind(A,$thf( A )),bind(B,$thf( sk3 @ singleton ))]]) ).
thf(10667,plain,
( ( sk3 = sk1 )
| ( sk2 @ ( sk2 @ ( sk2 @ ( sk3 @ singleton @ sk11 ) ) @ in ) )
| ( sk3 @ singleton @ ( sk2 @ ( sk2 @ sk9 ) ) ) ),
inference(simp,[status(thm)],[9676]) ).
thf(1340,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,1069]) ).
thf(1341,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1340]) ).
thf(1360,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk1 @ singleton ) )
| ( A
!= ( sk2 @ singleton ) ) ),
inference(simp,[status(thm)],[1341]) ).
thf(1368,plain,
! [A: $i] :
( ( A @ ( sk2 @ singleton @ unordered_pair ) )
!= ( sk1 @ singleton ) ),
inference(simp,[status(thm)],[1360]) ).
thf(3101,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton @ singleton ) )
| ( B
!= ( sk1 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1695]) ).
thf(3102,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton @ singleton ) )
| ~ ( sk2 @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[3101:[bind(A,$thf( sk2 @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(3112,plain,
~ ( sk2 @ singleton @ singleton @ singleton @ ( sk1 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[3102]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
| ~ ( C @ ( B @ ( A @ sk6 ) ) )
| ( ( A @ ( B @ ( C @ sk7 ) ) )
!= A ) ),
inference(cnfConj,[status(thm)],[51]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk6 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk7 ) ) )
!= A ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk6 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk7 ) ) )
!= A ) ),
inference(simp,[status(thm)],[66]) ).
thf(173,plain,
! [A: $i] :
( ( ( A @ ( A @ set_intersection2 ) )
!= ( sk2 @ ( sk1 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) ) )
| ( sk3 != sk1 )
| ( A
!= ( sk1 @ singleton ) ) ),
inference(paramod_ordered,[status(thm)],[105,169]) ).
thf(177,plain,
( ( ( sk1 @ singleton )
!= sk2 )
| ( ( sk1 @ ( sk1 @ unordered_pair ) )
!= ( sk1 @ singleton ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[173]) ).
thf(1516,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ ( sk2 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,1229]) ).
thf(1517,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[1516]) ).
thf(1536,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[1517]) ).
thf(1538,plain,
! [A: $i] :
( ( A @ ( sk2 @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1536]) ).
thf(9495,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk2 @ singleton ) )
| ( A != sk2 )
| ( A @ ( A @ ( A @ ( B @ sk11 ) ) @ in ) )
| ( B @ ( A @ ( A @ sk9 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2132,1210]) ).
thf(9496,plain,
! [A: $i] :
( ( A != sk2 )
| ( A @ ( A @ ( A @ ( sk2 @ singleton @ sk11 ) ) @ in ) )
| ( sk2 @ singleton @ ( A @ ( A @ sk9 ) ) ) ),
inference(pattern_uni,[status(thm)],[9495:[bind(A,$thf( A )),bind(B,$thf( sk2 @ singleton ))]]) ).
thf(10608,plain,
( ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ singleton @ sk11 ) ) @ in ) )
| ( sk2 @ singleton @ ( sk2 @ ( sk2 @ sk9 ) ) ) ),
inference(simp,[status(thm)],[9496]) ).
thf(317,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( C @ ( C @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,122]) ).
thf(318,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( C @ ( C @ in ) ) ),
inference(simp,[status(thm)],[317]) ).
thf(329,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= C )
| ( B != C ) ),
inference(simp,[status(thm)],[318]) ).
thf(336,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
!= B ),
inference(simp,[status(thm)],[329]) ).
thf(2243,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,1420]) ).
thf(2244,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk12 @ singleton @ singleton @ ( sk13 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[2243]) ).
thf(2273,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk12 @ singleton @ singleton ) )
| ( A
!= ( sk13 @ singleton ) ) ),
inference(simp,[status(thm)],[2244]) ).
thf(2279,plain,
! [A: $i] :
( ( A @ ( sk13 @ singleton @ unordered_pair ) )
!= ( sk12 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[2273]) ).
thf(3242,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk12 @ singleton ) )
| ( B != sk2 )
| ~ ( sk1 @ singleton @ ( sk13 @ in ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1566]) ).
thf(3243,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( sk1 @ singleton @ ( sk13 @ in ) )
| ~ ( sk12 @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[3242:[bind(A,$thf( sk12 @ singleton )),bind(B,$thf( B ))]]) ).
thf(3256,plain,
( ~ ( sk1 @ singleton @ ( sk13 @ in ) )
| ~ ( sk12 @ singleton @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[3243]) ).
thf(11830,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ singleton @ ( sk12 @ singleton @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,3141]) ).
thf(11831,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk13 @ singleton @ singleton @ singleton @ ( sk12 @ singleton @ singleton @ in ) ) ),
inference(simp,[status(thm)],[11830]) ).
thf(12002,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk13 @ singleton @ singleton @ singleton ) )
| ( A
!= ( sk12 @ singleton @ singleton ) ) ),
inference(simp,[status(thm)],[11831]) ).
thf(12039,plain,
( ( sk13 @ singleton @ singleton @ singleton )
!= ( sk12 @ singleton @ singleton @ singleton ) ),
inference(simp,[status(thm)],[12002]) ).
thf(6947,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton @ singleton @ singleton ) )
| ( B
!= ( sk1 @ singleton @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,6148]) ).
thf(6948,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton @ singleton ) )
| ~ ( sk2 @ singleton @ singleton @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[6947:[bind(A,$thf( sk2 @ singleton @ singleton @ singleton )),bind(B,$thf( B ))]]) ).
thf(6965,plain,
~ ( sk2 @ singleton @ singleton @ singleton @ singleton @ ( sk1 @ singleton @ singleton @ in ) ),
inference(simp,[status(thm)],[6948]) ).
thf(32915,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ singleton @ ( sk2 @ singleton @ ( sk2 @ singleton @ ( sk2 @ sk11 ) ) @ in ) )
!= ( A @ singleton @ ( B @ in ) ) )
| ~ $true
| ( B = A )
| ( sk2 @ ( sk2 @ singleton @ ( sk2 @ singleton @ sk9 ) ) ) ),
inference(paramod_ordered,[status(thm)],[10609,40]) ).
thf(32916,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ singleton @ ( sk2 @ singleton @ ( sk2 @ singleton @ ( sk2 @ sk11 ) ) @ in ) )
!= ( A @ singleton @ ( B @ in ) ) )
| ( B = A )
| ( sk2 @ ( sk2 @ singleton @ ( sk2 @ singleton @ sk9 ) ) ) ),
inference(simp,[status(thm)],[32915]) ).
thf(32917,plain,
( ( ( sk2 @ singleton @ ( sk2 @ singleton @ ( sk2 @ sk11 ) ) )
= sk2 )
| ( sk2 @ ( sk2 @ singleton @ ( sk2 @ singleton @ sk9 ) ) ) ),
inference(pattern_uni,[status(thm)],[32916:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 @ singleton @ ( sk2 @ singleton @ ( sk2 @ sk11 ) ) ))]]) ).
thf(959,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) ) )
| ( B
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,19]) ).
thf(960,plain,
! [A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[959:[bind(A,$thf( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )),bind(B,$thf( B ))]]) ).
thf(1126,plain,
~ ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) @ singleton @ ( sk1 @ singleton @ in ) ),
inference(simp,[status(thm)],[960]) ).
thf(2173,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ ( sk2 @ unordered_pair ) ) )
| ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1175]) ).
thf(2174,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ ( sk2 @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[2173:[bind(A,$thf( A )),bind(B,$thf( E @ ( sk2 @ unordered_pair ) )),bind(C,$thf( E ))]]) ).
thf(2187,plain,
! [A: $i] :
~ ( sk1 @ singleton @ singleton @ ( A @ ( sk2 @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[2174]) ).
thf(152,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( B @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,122]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( B @ ( B @ in ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[153]) ).
thf(158,plain,
! [A: $i] :
( ( A @ singleton )
!= A ),
inference(simp,[status(thm)],[156]) ).
thf(3232,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk12 @ singleton ) )
| ( A != sk2 )
| ~ ( sk1 @ singleton @ ( sk13 @ in ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1566]) ).
thf(3233,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( sk1 @ singleton @ ( sk13 @ in ) )
| ~ ( A @ singleton @ ( sk12 @ singleton @ in ) ) ),
inference(pattern_uni,[status(thm)],[3232:[bind(A,$thf( A )),bind(B,$thf( sk12 @ singleton ))]]) ).
thf(3252,plain,
( ~ ( sk1 @ singleton @ ( sk13 @ in ) )
| ~ ( sk2 @ singleton @ ( sk12 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[3233]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
| ~ ( C @ ( B @ ( A @ sk6 ) ) )
| ( ( A @ ( B @ ( C @ sk7 ) ) )
!= B ) ),
inference(cnfConj,[status(thm)],[51]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk6 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk7 ) ) )
!= B ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk6 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk7 ) ) )
!= B ) ),
inference(simp,[status(thm)],[74]) ).
thf(23301,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,1122]) ).
thf(23302,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) @ in ) ) ),
inference(simp,[status(thm)],[23301]) ).
thf(23590,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton @ singleton ) )
| ( A
!= ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) ) ) ),
inference(simp,[status(thm)],[23302]) ).
thf(23605,plain,
( ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) @ singleton )
!= ( sk1 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[23590]) ).
thf(230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( D @ ( C @ in ) ) )
| ~ ( C @ ( D @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,21]) ).
thf(231,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( D @ ( C @ in ) ) )
| ~ ( C @ ( D @ in ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(232,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ unordered_pair ) @ in ) ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ unordered_pair ) ))]]) ).
thf(246,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[232]) ).
thf(1744,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ ( sk1 @ singleton @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,1320]) ).
thf(1745,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ ( sk1 @ singleton @ in ) ) ),
inference(simp,[status(thm)],[1744]) ).
thf(1767,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton ) )
| ( A
!= ( sk1 @ singleton ) ) ),
inference(simp,[status(thm)],[1745]) ).
thf(1774,plain,
! [A: $i] :
( ( A @ ( sk1 @ singleton @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1767]) ).
thf(1502,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ singleton @ singleton @ ( sk2 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,1229]) ).
thf(1503,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ singleton @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[1502]) ).
thf(1535,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton ) )
| ( B != sk2 ) ),
inference(simp,[status(thm)],[1503]) ).
thf(1546,plain,
! [A: $i] :
( ( sk2 @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1535]) ).
thf(8550,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( sk2 @ ( C @ unordered_pair ) @ singleton ) )
| ( B != sk2 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,7431]) ).
thf(8551,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ~ ( sk2 @ ( B @ unordered_pair ) @ singleton @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[8550:[bind(A,$thf( sk2 @ ( E @ unordered_pair ) @ singleton )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(8574,plain,
! [A: $i] :
~ ( sk2 @ ( A @ unordered_pair ) @ singleton @ singleton @ ( sk2 @ in ) ),
inference(simp,[status(thm)],[8551]) ).
thf(272,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_intersection2 ) )
!= ( sk2 @ ( sk1 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) ) )
| ( ( A @ ( B @ set_intersection2 ) )
!= ( sk1 @ singleton ) )
| ~ ( sk2 @ ( sk3 @ in ) ) ),
inference(paramod_ordered,[status(thm)],[27,144]) ).
thf(273,plain,
( ( ( sk1 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) )
!= ( sk1 @ singleton ) )
| ~ ( sk2 @ ( sk3 @ in ) ) ),
inference(pattern_uni,[status(thm)],[272:[bind(A,$thf( sk1 @ ( sk1 @ unordered_pair ) )),bind(B,$thf( sk2 ))]]) ).
thf(22594,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,1078]) ).
thf(22595,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ singleton @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) @ in ) ) ),
inference(simp,[status(thm)],[22594]) ).
thf(22865,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton @ singleton ) )
| ( A
!= ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) ) ) ),
inference(simp,[status(thm)],[22595]) ).
thf(22901,plain,
( ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) @ singleton )
!= ( sk1 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[22865]) ).
thf(6542,plain,
! [B: $i,A: $i] :
( ( A != sk13 )
| ( B != sk1 )
| ~ ( sk2 @ singleton @ ( sk12 @ singleton @ in ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1567]) ).
thf(6543,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( sk2 @ singleton @ ( sk12 @ singleton @ in ) )
| ~ ( sk13 @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[6542:[bind(A,$thf( sk13 ))]]) ).
thf(6558,plain,
( ~ ( sk2 @ singleton @ ( sk12 @ singleton @ in ) )
| ~ ( sk13 @ singleton @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[6543]) ).
thf(8263,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( sk12 @ ( C @ unordered_pair ) ) )
| ( A
!= ( sk13 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1302]) ).
thf(8264,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk13 @ singleton ) )
| ~ ( A @ singleton @ ( sk12 @ ( B @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[8263:[bind(A,$thf( A )),bind(B,$thf( sk12 @ ( D @ unordered_pair ) )),bind(C,$thf( D ))]]) ).
thf(8277,plain,
! [A: $i] :
~ ( sk13 @ singleton @ singleton @ ( sk12 @ ( A @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[8264]) ).
thf(2654,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( sk1 @ ( C @ unordered_pair ) ) )
| ( A
!= ( sk2 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1213]) ).
thf(2655,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ singleton ) )
| ~ ( A @ singleton @ ( sk1 @ ( B @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[2654:[bind(A,$thf( A )),bind(B,$thf( sk1 @ ( D @ unordered_pair ) )),bind(C,$thf( D ))]]) ).
thf(2668,plain,
! [A: $i] :
~ ( sk2 @ singleton @ singleton @ ( sk1 @ ( A @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[2655]) ).
thf(81,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ in ) )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(cnfConj,[status(thm)],[78]) ).
thf(93,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ in ) )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(lifteq,[status(thm)],[81]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ~ ( B @ ( A @ set_intersection2 ) @ ( C @ in ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(9839,plain,
! [B: $i,A: $i] :
( ( B != sk13 )
| ( A != sk12 )
| ( A @ ( A @ ( A @ ( B @ sk11 ) ) @ in ) )
| ( B @ ( A @ ( A @ sk9 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2132,113]) ).
thf(9840,plain,
! [A: $i] :
( ( A != sk12 )
| ( A @ ( A @ ( A @ ( sk13 @ sk11 ) ) @ in ) )
| ( sk13 @ ( A @ ( A @ sk9 ) ) ) ),
inference(pattern_uni,[status(thm)],[9839:[bind(A,$thf( A )),bind(B,$thf( sk13 ))]]) ).
thf(10718,plain,
( ( sk12 @ ( sk12 @ ( sk12 @ ( sk13 @ sk11 ) ) @ in ) )
| ( sk13 @ ( sk12 @ ( sk12 @ sk9 ) ) ) ),
inference(simp,[status(thm)],[9840]) ).
thf(2152,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( sk2 @ ( C @ unordered_pair ) ) )
| ( B
!= ( sk1 @ singleton ) )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[40,1174]) ).
thf(2153,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk1 @ singleton ) )
| ~ ( sk2 @ ( B @ unordered_pair ) @ singleton @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[2152:[bind(A,$thf( sk2 @ ( D @ unordered_pair ) )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(2159,plain,
! [A: $i] :
~ ( sk2 @ ( A @ unordered_pair ) @ singleton @ ( sk1 @ singleton @ in ) ),
inference(simp,[status(thm)],[2153]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ set_intersection2 ) ) )
| ~ ( C @ ( B @ ( A @ sk9 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) )
| ~ ( A @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) ) ),
inference(cnfConj,[status(thm)],[78]) ).
thf(89,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk9 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) )
| ~ ( A @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) )
| ( C
= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(lifteq,[status(thm)],[85]) ).
thf(90,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ sk9 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) )
| ~ ( A @ ( A @ ( B @ ( C @ sk10 ) ) @ in ) )
| ( C
= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(4582,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk1 @ singleton @ sk11 ) ) @ in ) )
!= ( B @ ( A @ unordered_pair ) @ ( C @ in ) ) )
| ~ $true
| ( C = B )
| ( C = A )
| ( sk1 @ singleton @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk9 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2079,63]) ).
thf(4583,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk1 @ singleton @ sk11 ) ) @ in ) )
!= ( B @ ( A @ unordered_pair ) @ ( C @ in ) ) )
| ( C = B )
| ( C = A )
| ( sk1 @ singleton @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk9 ) ) ) ),
inference(simp,[status(thm)],[4582]) ).
thf(4584,plain,
( ( ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk1 @ singleton @ sk11 ) ) )
= sk3 )
| ( ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk1 @ singleton @ sk11 ) ) )
= sk1 )
| ( sk1 @ singleton @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk9 ) ) ) ),
inference(pattern_uni,[status(thm)],[4583:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 )),bind(C,$thf( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk1 @ singleton @ sk11 ) ) ))]]) ).
thf(1439,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[65,1070]) ).
thf(1440,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ singleton @ singleton @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[1439]) ).
thf(1460,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[1440]) ).
thf(1468,plain,
! [A: $i] :
( ( A @ ( sk1 @ unordered_pair ) )
!= ( sk2 @ singleton @ singleton ) ),
inference(simp,[status(thm)],[1460]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ set_intersection2 ) ) )
| ( A @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk9 ) ) ) ),
inference(cnfConj,[status(thm)],[78]) ).
thf(99,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk9 ) ) )
| ( C
= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(lifteq,[status(thm)],[79]) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ sk11 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk9 ) ) )
| ( C
= ( B @ ( A @ set_intersection2 ) ) ) ),
inference(simp,[status(thm)],[99]) ).
thf(12943,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ ( B @ ( sk2 @ unordered_pair ) @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,1074]) ).
thf(12944,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ ( B @ ( sk2 @ unordered_pair ) @ in ) ) ),
inference(simp,[status(thm)],[12943]) ).
thf(13053,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton ) )
| ( A
!= ( B @ ( sk2 @ unordered_pair ) ) ) ),
inference(simp,[status(thm)],[12944]) ).
thf(13107,plain,
! [A: $i] :
( ( A @ ( sk2 @ unordered_pair ) @ singleton )
!= ( sk1 @ singleton ) ),
inference(simp,[status(thm)],[13053]) ).
thf(49060,plain,
$false,
inference(e,[status(thm)],[69,138,88,10609,1718,523,8883,1569,202,1041,1173,217,10832,1497,1078,8342,7188,25311,7431,1001,6268,42,24,1366,1265,25,2339,110,1264,10719,2274,8214,20,1319,8571,1568,25929,46,1609,7112,261,1465,1302,179,253,1136,106,6964,1020,2281,2639,1104,1696,6685,61,116,243,1074,248,8655,39639,3186,27813,6560,2641,102,334,1723,1042,11587,2132,8491,7301,1174,28,38,21,137,92,10756,65,2663,1210,2157,8339,1719,169,6148,1567,3141,6428,2419,7059,96,10834,1539,1266,10603,129,73,1695,11120,105,244,1103,9021,3111,149,8217,22,44,281,27,71,12,29443,144,8877,7109,49,26583,181,31254,2346,2079,113,2415,76,1722,245,1175,98,1122,2182,1080,2129,103,7186,2278,8652,108,8280,2350,1213,26200,1775,1694,2418,13593,1076,28561,1420,3146,7190,10604,38529,1467,48,63,6683,1566,3260,10667,1368,18,1070,3112,67,1637,177,1538,10608,336,1257,2279,3256,12039,1421,6965,32917,1126,2187,40,158,3252,75,23605,1294,1212,1614,7187,246,999,1774,168,1229,1546,1303,19,8574,273,22901,107,6558,8277,2668,94,10718,2159,1019,15,90,1320,122,1367,4584,1468,1069,100,13107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET919+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
% 0.22/0.49 % Computer : n015.cluster.edu
% 0.22/0.49 % Model : x86_64 x86_64
% 0.22/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.49 % Memory : 8046.5625MB
% 0.22/0.49 % OS : Linux 6.8.0-71-generic
% 0.22/0.49 % CPULimit : 300
% 0.22/0.49 % WCLimit : 300
% 0.22/0.49 % DateTime : Sat Sep 26 08:28:58 UTC 2026
% 0.22/0.49 % CPUTime :
% 0.22/0.49 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
% 1.28/1.29 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.83/1.57 % [INFO] Parsing done (268ms).
% 1.83/1.59 % [INFO] Running in sequential loop mode.
% 2.56/2.04 % [INFO] eprover registered as external prover.
% 2.87/2.05 % [INFO] Scanning for conjecture ...
% 3.16/2.20 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 3.16/2.26 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 3.16/2.29 % [INFO] Problem is first-order (TPTP FOF).
% 3.35/2.30 % [INFO] Type checking passed.
% 3.35/2.31 % [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 ...
% 87.49/19.18 % External prover 'e' found a proof!
% 87.49/19.18 % [INFO] Killing All external provers ...
% 87.49/19.18 % Time passed: 18480ms (effective reasoning time: 17587ms)
% 87.49/19.18 % 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)>
% 87.49/19.19 % Axioms used in derivation (9): d1_tarski, idempotence_k3_xboole_0, commutativity_k3_xboole_0, d2_tarski, commutativity_k2_tarski, rc1_xboole_0, rc2_xboole_0, d3_xboole_0, antisymmetry_r2_hidden
% 87.49/19.19 % No. of inferences in proof: 713
% 87.49/19.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 18480 ms resp. 17587 ms w/o parsing
% 74.04/19.42 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 74.04/19.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------