%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET634+3 : TPTP v9.3.1. Released v2.2.0.
% 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 : n004.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 08:30:35 AM UTC 2026
% Result : Theorem 122.03s 32.84s
% Output : Refutation 107.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 17
% Syntax : Number of formulae : 214 ( 28 unt; 0 typ; 8 def)
% Number of atoms : 760 ( 226 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 3333 ( 347 ~; 339 |; 47 &;2548 @)
% ( 7 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 503 ( 10 ^; 485 !; 0 ?; 503 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% Comments :
%------------------------------------------------------------------------------
thf(intersection_decl,type,
intersection: $i > $i > $i ).
thf(difference_decl,type,
difference: $i > $i > $i ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $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 ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( C @ ( B @ difference ) @ ( A @ intersection ) )
= ( C @ ( B @ ( A @ intersection ) @ difference ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ difference ) @ ( sk1 @ intersection ) )
= ( B @ ( A @ ( sk1 @ intersection ) @ difference ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
( ( A @ ( sk2 @ difference ) @ ( sk1 @ intersection ) )
!= ( A @ ( sk2 @ ( sk1 @ intersection ) @ difference ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) ) ) ) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ member ) )
<=> ( B @ ( C @ member ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_equal) ).
thf(14,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) )
& ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) )
& ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) )
=> ( A = B ) ),
inference(miniscope,[status(thm)],[14]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( ( A = B )
| ~ ( A @ ( A @ ( B @ sk5 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ member ) ) )
& ( ( A = B )
| ( B @ ( A @ ( B @ sk5 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ member ) ) )
& ( ( A = B )
| ~ ( A @ ( A @ ( B @ sk5 ) @ member ) )
| ( A @ ( A @ ( B @ sk4 ) @ member ) ) )
& ( ( A = B )
| ( B @ ( A @ ( B @ sk5 ) @ member ) )
| ( A @ ( A @ ( B @ sk4 ) @ member ) ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ ( B @ sk5 ) @ member ) )
| ( A @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk5 ) @ member ) )
| ( A @ ( A @ ( B @ sk4 ) @ member ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ difference ) @ ( A @ intersection ) )
= ( C @ ( B @ ( A @ intersection ) @ difference ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_and_intersection) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ difference ) @ ( A @ intersection ) )
= ( C @ ( B @ ( A @ intersection ) @ difference ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ difference ) @ ( A @ intersection ) )
= ( C @ ( B @ ( A @ intersection ) @ difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,plain,
( ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
( ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) )
!= ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) ) )
| ( A
!= ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) ) )
| ( B @ ( A @ ( B @ sk5 ) @ member ) )
| ( A @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[21,13]) ).
thf(133,plain,
! [A: $i] :
( ( A
!= ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) ) )
| ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ ( A @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk5 ) @ member ) )
| ( A @ ( A @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[132:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) ))]]) ).
thf(169,plain,
( ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk5 ) @ member ) )
| ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ difference ) @ ( C @ member ) )
<=> ( ~ ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
thf(32,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) )
=> ( B @ ( A @ difference ) @ ( C @ member ) ) )
& ( ( B @ ( A @ difference ) @ ( C @ member ) )
=> ( ~ ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(33,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) )
=> ( B @ ( A @ difference ) @ ( C @ member ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ difference ) @ ( C @ member ) )
=> ( ~ ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ) ),
inference(miniscope,[status(thm)],[32]) ).
thf(34,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ difference ) @ ( F @ member ) )
| ( E @ ( F @ member ) )
| ~ ( D @ ( F @ member ) ) )
& ( ~ ( B @ ( C @ member ) )
| ~ ( B @ ( A @ difference ) @ ( C @ member ) ) )
& ( ( A @ ( C @ member ) )
| ~ ( B @ ( A @ difference ) @ ( C @ member ) ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ member ) )
| ~ ( B @ ( A @ difference ) @ ( C @ member ) ) ),
inference(cnfConj,[status(thm)],[34]) ).
thf(413,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk5 ) @ member ) )
!= ( B @ ( A @ difference ) @ ( C @ member ) ) )
| ( A @ ( C @ member ) )
| ~ $true
| ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[169,35]) ).
thf(414,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk5 ) @ member ) )
!= ( B @ ( A @ difference ) @ ( C @ member ) ) )
| ( A @ ( C @ member ) )
| ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) ) ),
inference(simp,[status(thm)],[413]) ).
thf(415,plain,
( ( sk2 @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk5 ) @ member ) )
| ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[414:[bind(A,$thf( sk2 @ ( sk1 @ intersection ) )),bind(B,$thf( sk3 )),bind(C,$thf( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk5 ) ))]]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ intersection ) )
= ( A @ ( B @ intersection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(51,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ intersection ) )
= ( A @ ( B @ intersection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ intersection ) )
= ( A @ ( B @ intersection ) ) ),
inference(cnf,[status(esa)],[51]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ intersection ) )
= ( A @ ( B @ intersection ) ) ),
inference(lifteq,[status(thm)],[52]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ intersection ) @ ( C @ member ) )
<=> ( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
thf(25,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) )
=> ( B @ ( A @ intersection ) @ ( C @ member ) ) )
& ( ( B @ ( A @ intersection ) @ ( C @ member ) )
=> ( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(26,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) )
=> ( B @ ( A @ intersection ) @ ( C @ member ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ intersection ) @ ( C @ member ) )
=> ( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ) ),
inference(miniscope,[status(thm)],[25]) ).
thf(27,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ intersection ) @ ( F @ member ) )
| ~ ( E @ ( F @ member ) )
| ~ ( D @ ( F @ member ) ) )
& ( ( B @ ( C @ member ) )
| ~ ( B @ ( A @ intersection ) @ ( C @ member ) ) )
& ( ( A @ ( C @ member ) )
| ~ ( B @ ( A @ intersection ) @ ( C @ member ) ) ) ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ member ) )
| ~ ( B @ ( A @ intersection ) @ ( C @ member ) ) ),
inference(cnfConj,[status(thm)],[27]) ).
thf(91,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection ) )
!= ( D @ ( C @ intersection ) ) )
| ( C @ ( E @ member ) )
| ~ ( A @ ( B @ intersection ) @ ( E @ member ) ) ),
inference(paramod_ordered,[status(thm)],[53,28]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ member ) )
| ~ ( A @ ( B @ intersection ) @ ( C @ member ) ) ),
inference(pattern_uni,[status(thm)],[91:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ member ) )
| ~ ( A @ ( B @ intersection ) @ ( C @ member ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(1397,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk5 ) @ member ) )
!= ( A @ ( B @ intersection ) @ ( C @ member ) ) )
| ( A @ ( C @ member ) )
| ~ $true
| ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[415,95]) ).
thf(1398,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk5 ) @ member ) )
!= ( A @ ( B @ intersection ) @ ( C @ member ) ) )
| ( A @ ( C @ member ) )
| ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) ) ),
inference(simp,[status(thm)],[1397]) ).
thf(1399,plain,
( ( sk2 @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk5 ) @ member ) )
| ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[1398:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 )),bind(C,$thf( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk5 ) ))]]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ member ) )
| ~ ( B @ ( A @ difference ) @ ( C @ member ) ) ),
inference(cnfConj,[status(thm)],[34]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ difference ) @ ( C @ member ) )
!= ( B @ ( C @ member ) ) )
| ~ ( B @ ( C @ member ) ) ),
inference(eqfactor_ordered,[status(thm)],[36]) ).
thf(87,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ difference ) )
!= B )
| ( C != C )
| ~ ( B @ ( C @ member ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ difference ) )
!= B )
| ~ ( B @ ( C @ member ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(2495,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk5 ) @ member ) )
!= ( B @ ( C @ member ) ) )
| ( ( B @ ( A @ difference ) )
!= B )
| ~ $true
| ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[1399,88]) ).
thf(2496,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk5 ) @ member ) )
!= ( B @ ( C @ member ) ) )
| ( ( B @ ( A @ difference ) )
!= B )
| ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) ) ),
inference(simp,[status(thm)],[2495]) ).
thf(2497,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ difference ) )
!= sk2 )
| ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[2496:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk5 ) ))]]) ).
thf(3622,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) )
!= ( B @ ( C @ intersection ) @ ( D @ member ) ) )
| ( B @ ( D @ member ) )
| ~ $true
| ( ( sk2 @ ( A @ difference ) )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[2497,95]) ).
thf(3623,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) )
!= ( B @ ( C @ intersection ) @ ( D @ member ) ) )
| ( B @ ( D @ member ) )
| ( ( sk2 @ ( A @ difference ) )
!= sk2 ) ),
inference(simp,[status(thm)],[3622]) ).
thf(3624,plain,
! [A: $i] :
( ( sk3 @ ( sk2 @ difference ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) )
| ( ( sk2 @ ( A @ difference ) )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[3623:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk2 @ difference ) )),bind(C,$thf( sk1 )),bind(D,$thf( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) ))]]) ).
thf(7673,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ difference ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) )
!= ( C @ ( B @ difference ) @ ( D @ member ) ) )
| ( B @ ( D @ member ) )
| ~ $true
| ( ( sk2 @ ( A @ difference ) )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[3624,35]) ).
thf(7674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ difference ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) )
!= ( C @ ( B @ difference ) @ ( D @ member ) ) )
| ( B @ ( D @ member ) )
| ( ( sk2 @ ( A @ difference ) )
!= sk2 ) ),
inference(simp,[status(thm)],[7673]) ).
thf(7675,plain,
! [A: $i] :
( ( sk2 @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) )
| ( ( sk2 @ ( A @ difference ) )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[7674:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 )),bind(D,$thf( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) ))]]) ).
thf(8570,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) )
!= ( C @ ( D @ member ) ) )
| ( ( C @ ( B @ difference ) )
!= C )
| ~ $true
| ( ( sk2 @ ( A @ difference ) )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[7675,88]) ).
thf(8571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) )
!= ( C @ ( D @ member ) ) )
| ( ( C @ ( B @ difference ) )
!= C )
| ( ( sk2 @ ( A @ difference ) )
!= sk2 ) ),
inference(simp,[status(thm)],[8570]) ).
thf(8572,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( B @ difference ) )
!= sk2 )
| ( ( sk2 @ ( A @ difference ) )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[8571:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 )),bind(D,$thf( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) ))]]) ).
thf(9132,plain,
! [B: $i,A: $i] :
( ( sk2 != sk2 )
| ( ( sk2 @ ( B @ difference ) )
!= ( sk2 @ ( A @ difference ) ) )
| ( ( sk2 @ ( A @ difference ) )
!= sk2 ) ),
inference(eqfactor_ordered,[status(thm)],[8572]) ).
thf(9133,plain,
! [A: $i] :
( ( sk2 @ ( A @ difference ) )
!= sk2 ),
inference(pattern_uni,[status(thm)],[9132:[bind(A,$thf( B ))]]) ).
thf(9165,plain,
! [A: $i] :
( ( sk2 @ ( A @ difference ) )
!= sk2 ),
inference(simp,[status(thm)],[9133]) ).
thf(9195,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( sk2 @ ( C @ difference ) ) )
| ( A != sk2 )
| ( B @ ( A @ ( B @ sk5 ) @ member ) )
| ( A @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[21,9165]) ).
thf(9196,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( sk2 @ ( B @ difference ) @ ( A @ ( sk2 @ ( B @ difference ) @ sk5 ) @ member ) )
| ( A @ ( A @ ( sk2 @ ( B @ difference ) @ sk4 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[9195:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( D @ difference ) )),bind(C,$thf( D ))]]) ).
thf(9221,plain,
! [A: $i] :
( ( sk2 @ ( A @ difference ) @ ( sk2 @ ( sk2 @ ( A @ difference ) @ sk5 ) @ member ) )
| ( sk2 @ ( sk2 @ ( sk2 @ ( A @ difference ) @ sk4 ) @ member ) ) ),
inference(simp,[status(thm)],[9196]) ).
thf(11005,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ difference ) @ ( sk2 @ ( sk2 @ ( A @ difference ) @ sk5 ) @ member ) )
!= ( C @ ( B @ difference ) @ ( D @ member ) ) )
| ( B @ ( D @ member ) )
| ~ $true
| ( sk2 @ ( sk2 @ ( sk2 @ ( A @ difference ) @ sk4 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[9221,35]) ).
thf(11006,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ difference ) @ ( sk2 @ ( sk2 @ ( A @ difference ) @ sk5 ) @ member ) )
!= ( C @ ( B @ difference ) @ ( D @ member ) ) )
| ( B @ ( D @ member ) )
| ( sk2 @ ( sk2 @ ( sk2 @ ( A @ difference ) @ sk4 ) @ member ) ) ),
inference(simp,[status(thm)],[11005]) ).
thf(11007,plain,
! [A: $i] :
( ( A @ ( sk2 @ ( sk2 @ ( A @ difference ) @ sk5 ) @ member ) )
| ( sk2 @ ( sk2 @ ( sk2 @ ( A @ difference ) @ sk4 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[11006:[bind(A,$thf( G )),bind(B,$thf( G )),bind(C,$thf( sk2 )),bind(D,$thf( sk2 @ ( sk2 @ ( G @ difference ) @ sk5 ) ))]]) ).
thf(11140,plain,
! [A: $i] :
( ( A @ ( sk2 @ ( sk2 @ ( A @ difference ) @ sk5 ) @ member ) )
| ( sk2 @ ( sk2 @ ( sk2 @ ( A @ difference ) @ sk4 ) @ member ) ) ),
inference(simp,[status(thm)],[11007]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( A @ ( B @ sk5 ) @ member ) )
| ( A @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk5 ) @ member ) )
| ( A @ ( A @ ( B @ sk4 ) @ member ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(12999,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk2 @ ( A @ difference ) @ sk5 ) @ member ) )
!= ( B @ ( B @ ( C @ sk5 ) @ member ) ) )
| ~ $true
| ( B @ ( B @ ( C @ sk4 ) @ member ) )
| ( B = C )
| ( sk2 @ ( sk2 @ ( sk2 @ ( A @ difference ) @ sk4 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[11140,22]) ).
thf(13000,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk2 @ ( A @ difference ) @ sk5 ) @ member ) )
!= ( B @ ( B @ ( C @ sk5 ) @ member ) ) )
| ( B @ ( B @ ( C @ sk4 ) @ member ) )
| ( B = C )
| ( sk2 @ ( sk2 @ ( sk2 @ ( A @ difference ) @ sk4 ) @ member ) ) ),
inference(simp,[status(thm)],[12999]) ).
thf(13001,plain,
( ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) )
| ( ( sk2 @ ( sk2 @ difference ) )
= sk2 )
| ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[13000:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 )),bind(C,$thf( sk2 @ ( sk2 @ difference ) ))]]) ).
thf(13200,plain,
( ( ( sk2 @ ( sk2 @ difference ) )
= sk2 )
| ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) ) ),
inference(simp,[status(thm)],[13001]) ).
thf(13240,plain,
sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ),
inference(simplifyReflect,[status(thm)],[13200,9165]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ difference ) @ ( C @ member ) )
| ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(cnfConj,[status(thm)],[34]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ difference ) @ ( C @ member ) )
| ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(simp,[status(thm)],[37]) ).
thf(13391,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) )
!= ( A @ ( C @ member ) ) )
| ( B @ ( A @ difference ) @ ( C @ member ) )
| ( B @ ( C @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13240,38]) ).
thf(13392,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) )
!= ( A @ ( C @ member ) ) )
| ( B @ ( A @ difference ) @ ( C @ member ) )
| ( B @ ( C @ member ) ) ),
inference(simp,[status(thm)],[13391]) ).
thf(13393,plain,
! [A: $i] :
( ( A @ ( sk2 @ difference ) @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) )
| ( A @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[13392:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) ))]]) ).
thf(13488,plain,
! [A: $i] :
( ( A @ ( sk2 @ difference ) @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) )
| ( A @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) ) ),
inference(simp,[status(thm)],[13393]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
thf(75,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(76,plain,
( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) )
=> ( B @ ( A @ subset ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ),
inference(miniscope,[status(thm)],[75]) ).
thf(77,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ subset ) )
| ~ ( E @ ( D @ ( E @ sk8 ) @ member ) ) )
& ( ( E @ ( D @ subset ) )
| ( D @ ( D @ ( E @ sk8 ) @ member ) ) )
& ( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ) ),
inference(cnf,[status(esa)],[76]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk8 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[77]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk8 ) @ member ) ) ),
inference(simp,[status(thm)],[80]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
thf(39,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(40,plain,
( ! [A: $i,B: $i] :
( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( A = B ) )
& ! [A: $i,B: $i] :
( ( A = B )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(miniscope,[status(thm)],[39]) ).
thf(41,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C = D )
| ~ ( C @ ( D @ subset ) )
| ~ ( D @ ( C @ subset ) ) )
& ( ( A @ ( B @ subset ) )
| ( A != B ) )
& ( ( B @ ( A @ subset ) )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[40]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[41]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[44]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) )
| ( A = B ) ),
inference(simp,[status(thm)],[49]) ).
thf(9207,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( sk2 @ ( C @ difference ) ) )
| ( B != sk2 )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[50,9165]) ).
thf(9208,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ~ ( sk2 @ ( B @ difference ) @ ( A @ subset ) )
| ~ ( A @ ( sk2 @ ( B @ difference ) @ subset ) ) ),
inference(pattern_uni,[status(thm)],[9207:[bind(A,$thf( sk2 @ ( D @ difference ) )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(9228,plain,
! [A: $i] :
( ~ ( sk2 @ ( A @ difference ) @ ( sk2 @ subset ) )
| ~ ( sk2 @ ( sk2 @ ( A @ difference ) @ subset ) ) ),
inference(simp,[status(thm)],[9208]) ).
thf(9511,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( sk2 @ ( C @ difference ) @ subset ) ) )
| ~ ( sk2 @ ( C @ difference ) @ ( sk2 @ subset ) )
| ~ $true
| ~ ( B @ ( A @ ( B @ sk8 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[82,9228]) ).
thf(9512,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( sk2 @ ( C @ difference ) @ subset ) ) )
| ~ ( sk2 @ ( C @ difference ) @ ( sk2 @ subset ) )
| ~ ( B @ ( A @ ( B @ sk8 ) @ member ) ) ),
inference(simp,[status(thm)],[9511]) ).
thf(9513,plain,
! [A: $i] :
( ~ ( sk2 @ ( A @ difference ) @ ( sk2 @ subset ) )
| ~ ( sk2 @ ( sk2 @ ( A @ difference ) @ ( sk2 @ sk8 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[9512:[bind(A,$thf( sk2 @ ( D @ difference ) )),bind(B,$thf( sk2 )),bind(C,$thf( D ))]]) ).
thf(9636,plain,
! [A: $i] :
( ~ ( sk2 @ ( A @ difference ) @ ( sk2 @ subset ) )
| ~ ( sk2 @ ( sk2 @ ( A @ difference ) @ ( sk2 @ sk8 ) @ member ) ) ),
inference(simp,[status(thm)],[9513]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk8 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[77]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk8 ) @ member ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(205,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk8 ) @ member ) )
!= ( D @ ( E @ member ) ) )
| ( ( D @ ( C @ difference ) )
!= D )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[81,88]) ).
thf(206,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk8 ) @ member ) )
!= ( D @ ( E @ member ) ) )
| ( ( D @ ( C @ difference ) )
!= D )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(207,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ difference ) )
!= C )
| ( B @ ( C @ subset ) ) ),
inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( G @ ( F @ sk8 ) ))]]) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ difference ) )
!= C )
| ( B @ ( C @ subset ) ) ),
inference(simp,[status(thm)],[207]) ).
thf(294,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) ) )
| ( B
!= ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) ) )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[50,13]) ).
thf(295,plain,
! [A: $i] :
( ( A
!= ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ ( A @ subset ) )
| ~ ( A @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ subset ) ) ),
inference(pattern_uni,[status(thm)],[294:[bind(A,$thf( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) )),bind(B,$thf( B ))]]) ).
thf(392,plain,
( ~ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ subset ) )
| ~ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ subset ) ) ),
inference(simp,[status(thm)],[295]) ).
thf(1160,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ subset ) )
!= ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ subset ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ subset ) )
| ~ $true
| ( ( C @ ( A @ difference ) )
!= C ) ),
inference(paramod_ordered,[status(thm)],[234,392]) ).
thf(1161,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ subset ) )
!= ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ subset ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ subset ) )
| ( ( C @ ( A @ difference ) )
!= C ) ),
inference(simp,[status(thm)],[1160]) ).
thf(1162,plain,
! [A: $i] :
( ~ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ subset ) )
| ( ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ ( A @ difference ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) ) ) ),
inference(pattern_uni,[status(thm)],[1161:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) )),bind(C,$thf( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) ))]]) ).
thf(4306,plain,
! [A: $i] :
( ~ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ subset ) )
| ( ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) )
!= sk3 )
| ( A
!= ( sk2 @ ( sk1 @ intersection ) ) ) ),
inference(simp,[status(thm)],[1162]) ).
thf(4770,plain,
( ~ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ subset ) )
| ( ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) )
!= sk3 ) ),
inference(simp,[status(thm)],[4306]) ).
thf(5057,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ subset ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ subset ) ) )
| ~ $true
| ( ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) )
!= sk3 )
| ( ( C @ ( A @ difference ) )
!= C ) ),
inference(paramod_ordered,[status(thm)],[234,4770]) ).
thf(5058,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ subset ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ subset ) ) )
| ( ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) )
!= sk3 )
| ( ( C @ ( A @ difference ) )
!= C ) ),
inference(simp,[status(thm)],[5057]) ).
thf(5059,plain,
! [A: $i] :
( ( ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) )
!= sk3 )
| ( ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( A @ difference ) )
!= ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) ) ) ),
inference(pattern_uni,[status(thm)],[5058:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) )),bind(C,$thf( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) ))]]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( B @ ( A @ intersection ) @ ( C @ member ) ) ),
inference(cnfConj,[status(thm)],[27]) ).
thf(97,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection ) )
!= ( D @ ( C @ intersection ) ) )
| ( D @ ( E @ member ) )
| ~ ( A @ ( B @ intersection ) @ ( E @ member ) ) ),
inference(paramod_ordered,[status(thm)],[53,29]) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( B @ intersection ) @ ( C @ member ) ) ),
inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(101,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( B @ intersection ) @ ( C @ member ) ) ),
inference(simp,[status(thm)],[98]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( A @ ( B @ sk5 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk5 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ member ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(5054,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ subset ) ) )
| ~ $true
| ( ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) )
!= sk3 )
| ~ ( B @ ( A @ ( B @ sk8 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[82,4770]) ).
thf(5055,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ subset ) ) )
| ( ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) )
!= sk3 )
| ~ ( B @ ( A @ ( B @ sk8 ) @ member ) ) ),
inference(simp,[status(thm)],[5054]) ).
thf(5056,plain,
( ( ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) )
!= sk3 )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk8 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[5055:[bind(A,$thf( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) )),bind(B,$thf( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) ))]]) ).
thf(13326,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ sk8 ) @ member ) )
!= ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) ) )
| ( B @ ( A @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13240,82]) ).
thf(13327,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ sk8 ) @ member ) )
!= ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[13326]) ).
thf(13469,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( ( A @ ( B @ sk8 ) )
!= ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[13327]) ).
thf(13511,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ sk8 ) )
!= ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) ) )
| ( sk2 @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[13469]) ).
thf(9209,plain,
! [C: $i,B: $i,A: $i] :
( ( A != sk2 )
| ( ( B @ ( C @ difference ) )
!= sk2 )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[50,9165]) ).
thf(9210,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ difference ) )
!= sk2 )
| ~ ( sk2 @ ( A @ subset ) )
| ~ ( A @ ( sk2 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[9209:[bind(A,$thf( sk2 ))]]) ).
thf(9230,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ difference ) )
!= sk2 )
| ~ ( sk2 @ ( A @ subset ) )
| ~ ( A @ ( sk2 @ subset ) ) ),
inference(simp,[status(thm)],[9210]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[41]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[42]) ).
thf(46,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(simp,[status(thm)],[45]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[77]) ).
thf(306,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( ( sk3 @ ( sk2 @ ( A @ intersection ) @ difference ) )
!= ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) ) )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[50,13]) ).
thf(307,plain,
! [A: $i] :
( ( ( sk3 @ ( sk2 @ ( A @ intersection ) @ difference ) )
!= ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) ) )
| ~ ( A @ ( sk1 @ subset ) )
| ~ ( sk1 @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[306:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(13422,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) )
!= ( B @ ( A @ difference ) @ ( C @ member ) ) )
| ( A @ ( C @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13240,35]) ).
thf(13423,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) )
!= ( B @ ( A @ difference ) @ ( C @ member ) ) )
| ( A @ ( C @ member ) ) ),
inference(simp,[status(thm)],[13422]) ).
thf(13460,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ difference ) )
!= sk2 )
| ( ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) )
!= C )
| ( A @ ( C @ member ) ) ),
inference(simp,[status(thm)],[13423]) ).
thf(13503,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ difference ) )
!= sk2 )
| ( A @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) ) ),
inference(simp,[status(thm)],[13460]) ).
thf(18029,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) )
!= ( D @ ( E @ member ) ) )
| ( ( D @ ( C @ difference ) )
!= D )
| ~ $true
| ( ( B @ ( A @ difference ) )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[13503,88]) ).
thf(18030,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) )
!= ( D @ ( E @ member ) ) )
| ( ( D @ ( C @ difference ) )
!= D )
| ( ( B @ ( A @ difference ) )
!= sk2 ) ),
inference(simp,[status(thm)],[18029]) ).
thf(18031,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ difference ) )
!= A )
| ( ( B @ ( A @ difference ) )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[18030:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) ))]]) ).
thf(18572,plain,
! [C: $i,B: $i,A: $i] :
( ( A != sk2 )
| ( ( A @ ( C @ difference ) )
!= ( B @ ( A @ difference ) ) )
| ( ( B @ ( A @ difference ) )
!= sk2 ) ),
inference(eqfactor_ordered,[status(thm)],[18031]) ).
thf(18573,plain,
( ( sk2 @ ( sk2 @ difference ) )
!= sk2 ),
inference(pattern_uni,[status(thm)],[18572:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 )),bind(C,$thf( sk2 ))]]) ).
thf(18688,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk2 @ ( sk2 @ difference ) ) )
| ( A != sk2 )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[50,18573]) ).
thf(18689,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( A @ ( sk2 @ ( sk2 @ difference ) @ subset ) )
| ~ ( sk2 @ ( sk2 @ difference ) @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[18688:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk2 @ difference ) ))]]) ).
thf(18718,plain,
( ~ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ subset ) )
| ~ ( sk2 @ ( sk2 @ difference ) @ ( sk2 @ subset ) ) ),
inference(simp,[status(thm)],[18689]) ).
thf(13456,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) )
!= ( B @ ( C @ member ) ) )
| ~ $true
| ~ ( B @ ( A @ difference ) @ ( C @ member ) ) ),
inference(paramod_ordered,[status(thm)],[13240,36]) ).
thf(13457,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) )
!= ( B @ ( C @ member ) ) )
| ~ ( B @ ( A @ difference ) @ ( C @ member ) ) ),
inference(simp,[status(thm)],[13456]) ).
thf(13458,plain,
! [A: $i] :
~ ( sk2 @ ( A @ difference ) @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) ),
inference(pattern_uni,[status(thm)],[13457:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) ))]]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk2 @ ( sk1 @ intersection ) ) )
| ( ( sk3 @ ( A @ difference ) )
!= ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) ) )
| ( B @ ( A @ ( B @ sk5 ) @ member ) )
| ( A @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[21,13]) ).
thf(129,plain,
! [A: $i] :
( ( ( sk3 @ ( A @ difference ) )
!= ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) ) )
| ( sk2 @ ( sk1 @ intersection ) @ ( A @ ( sk2 @ ( sk1 @ intersection ) @ sk5 ) @ member ) )
| ( A @ ( A @ ( sk2 @ ( sk1 @ intersection ) @ sk4 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ intersection ) ))]]) ).
thf(19036,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( sk2 @ difference ) @ ( sk2 @ subset ) ) )
| ~ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ subset ) )
| ~ $true
| ~ ( B @ ( A @ ( B @ sk8 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[82,18718]) ).
thf(19037,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( sk2 @ difference ) @ ( sk2 @ subset ) ) )
| ~ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ subset ) )
| ~ ( B @ ( A @ ( B @ sk8 ) @ member ) ) ),
inference(simp,[status(thm)],[19036]) ).
thf(19038,plain,
( ~ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ subset ) )
| ~ ( sk2 @ ( sk2 @ difference ) @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk8 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[19037:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 @ ( sk2 @ difference ) ))]]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ! [C: $i] :
( ( A @ ( C @ member ) )
<=> ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) )
& ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: $i] :
( ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) )
& ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(55,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) )
& ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) )
=> ( A = B ) )
& ! [A: $i,B: $i] :
( ( A = B )
=> ( ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) )
& ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ) ),
inference(miniscope,[status(thm)],[54]) ).
thf(56,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E = F )
| ~ ( E @ ( E @ ( F @ sk7 ) @ member ) )
| ~ ( F @ ( E @ ( F @ sk6 ) @ member ) ) )
& ( ( E = F )
| ( F @ ( E @ ( F @ sk7 ) @ member ) )
| ~ ( F @ ( E @ ( F @ sk6 ) @ member ) ) )
& ( ( E = F )
| ~ ( E @ ( E @ ( F @ sk7 ) @ member ) )
| ( E @ ( E @ ( F @ sk6 ) @ member ) ) )
& ( ( E = F )
| ( F @ ( E @ ( F @ sk7 ) @ member ) )
| ( E @ ( E @ ( F @ sk6 ) @ member ) ) )
& ( ( A @ ( D @ member ) )
| ~ ( B @ ( D @ member ) )
| ( A != B ) )
& ( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ ( B @ sk7 ) @ member ) )
| ( A @ ( A @ ( B @ sk6 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk7 ) @ member ) )
| ( A @ ( A @ ( B @ sk6 ) @ member ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk7 ) @ member ) )
| ( A @ ( A @ ( B @ sk6 ) @ member ) )
| ( A = B ) ),
inference(simp,[status(thm)],[63]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ difference ) @ ( C @ member ) )
!= ( B @ ( C @ member ) ) )
| ~ ( B @ ( C @ member ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(302,plain,
! [B: $i,A: $i] :
( ( B != sk3 )
| ( ( A @ ( sk2 @ ( sk1 @ intersection ) @ difference ) )
!= ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) ) )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[50,13]) ).
thf(303,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ intersection ) @ difference ) )
!= ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) ) )
| ~ ( A @ ( sk3 @ subset ) )
| ~ ( sk3 @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[302:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(1469,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk5 ) @ member ) )
!= ( B @ ( A @ intersection ) @ ( C @ member ) ) )
| ( A @ ( C @ member ) )
| ~ $true
| ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[415,28]) ).
thf(1470,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk5 ) @ member ) )
!= ( B @ ( A @ intersection ) @ ( C @ member ) ) )
| ( A @ ( C @ member ) )
| ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) ) ),
inference(simp,[status(thm)],[1469]) ).
thf(1471,plain,
( ( sk1 @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk5 ) @ member ) )
| ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk4 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[1470:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ difference ) @ sk5 ) ))]]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( A @ ( B @ sk7 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk6 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk7 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk6 ) @ member ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[61]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk7 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk6 ) @ member ) )
| ( A = B ) ),
inference(simp,[status(thm)],[65]) ).
thf(19116,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( sk2 @ difference ) @ ( sk2 @ subset ) ) )
| ~ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ subset ) )
| ~ $true
| ( A @ ( A @ ( B @ sk8 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[81,18718]) ).
thf(19117,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( sk2 @ difference ) @ ( sk2 @ subset ) ) )
| ~ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ subset ) )
| ( A @ ( A @ ( B @ sk8 ) @ member ) ) ),
inference(simp,[status(thm)],[19116]) ).
thf(19118,plain,
( ~ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ subset ) )
| ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk8 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[19117:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 @ ( sk2 @ difference ) ))]]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ intersection ) @ ( C @ member ) )
| ~ ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(cnfConj,[status(thm)],[27]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ intersection ) @ ( C @ member ) )
| ~ ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ ( B @ sk7 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk6 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk7 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk6 ) @ member ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk7 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk6 ) @ member ) )
| ( A = B ) ),
inference(simp,[status(thm)],[71]) ).
thf(9191,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( sk2 @ ( C @ difference ) ) )
| ( B != sk2 )
| ( B @ ( A @ ( B @ sk5 ) @ member ) )
| ( A @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[21,9165]) ).
thf(9192,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( A @ ( sk2 @ ( B @ difference ) @ ( A @ sk5 ) @ member ) )
| ( sk2 @ ( B @ difference ) @ ( sk2 @ ( B @ difference ) @ ( A @ sk4 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[9191:[bind(A,$thf( sk2 @ ( D @ difference ) )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(9219,plain,
! [A: $i] :
( ( sk2 @ ( sk2 @ ( A @ difference ) @ ( sk2 @ sk5 ) @ member ) )
| ( sk2 @ ( A @ difference ) @ ( sk2 @ ( A @ difference ) @ ( sk2 @ sk4 ) @ member ) ) ),
inference(simp,[status(thm)],[9192]) ).
thf(9578,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( C @ difference ) @ ( sk2 @ subset ) ) )
| ~ $true
| ~ ( sk2 @ ( sk2 @ ( C @ difference ) @ subset ) )
| ( A @ ( A @ ( B @ sk8 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[81,9228]) ).
thf(9579,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( C @ difference ) @ ( sk2 @ subset ) ) )
| ~ ( sk2 @ ( sk2 @ ( C @ difference ) @ subset ) )
| ( A @ ( A @ ( B @ sk8 ) @ member ) ) ),
inference(simp,[status(thm)],[9578]) ).
thf(9580,plain,
! [A: $i] :
( ~ ( sk2 @ ( sk2 @ ( A @ difference ) @ subset ) )
| ( sk2 @ ( sk2 @ ( sk2 @ ( A @ difference ) @ sk8 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[9579:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 @ ( D @ difference ) )),bind(C,$thf( D ))]]) ).
thf(9665,plain,
! [A: $i] :
( ~ ( sk2 @ ( sk2 @ ( A @ difference ) @ subset ) )
| ( sk2 @ ( sk2 @ ( sk2 @ ( A @ difference ) @ sk8 ) @ member ) ) ),
inference(simp,[status(thm)],[9580]) ).
thf(18610,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ ( sk2 @ difference ) ) )
| ( B != sk2 )
| ( B @ ( A @ ( B @ sk7 ) @ member ) )
| ( A @ ( A @ ( B @ sk6 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[64,18573]) ).
thf(18611,plain,
! [A: $i] :
( ( A != sk2 )
| ( A @ ( sk2 @ ( sk2 @ difference ) @ ( A @ sk7 ) @ member ) )
| ( sk2 @ ( sk2 @ difference ) @ ( sk2 @ ( sk2 @ difference ) @ ( A @ sk6 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[18610:[bind(A,$thf( sk2 @ ( sk2 @ difference ) )),bind(B,$thf( B ))]]) ).
thf(18727,plain,
( ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ ( sk2 @ sk7 ) @ member ) )
| ( sk2 @ ( sk2 @ difference ) @ ( sk2 @ ( sk2 @ difference ) @ ( sk2 @ sk6 ) @ member ) ) ),
inference(simp,[status(thm)],[18611]) ).
thf(19039,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ subset ) ) )
| ~ $true
| ~ ( sk2 @ ( sk2 @ difference ) @ ( sk2 @ subset ) )
| ~ ( B @ ( A @ ( B @ sk8 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[82,18718]) ).
thf(19040,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ subset ) ) )
| ~ ( sk2 @ ( sk2 @ difference ) @ ( sk2 @ subset ) )
| ~ ( B @ ( A @ ( B @ sk8 ) @ member ) ) ),
inference(simp,[status(thm)],[19039]) ).
thf(19041,plain,
( ~ ( sk2 @ ( sk2 @ difference ) @ ( sk2 @ subset ) )
| ~ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ ( sk2 @ sk8 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[19040:[bind(A,$thf( sk2 @ ( sk2 @ difference ) )),bind(B,$thf( sk2 ))]]) ).
thf(18096,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) )
!= ( sk2 @ ( C @ difference ) @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) ) )
| ~ $true
| ( ( B @ ( A @ difference ) )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[13503,13458]) ).
thf(18097,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) )
!= ( sk2 @ ( C @ difference ) @ ( sk2 @ ( sk2 @ ( sk2 @ difference ) @ sk4 ) @ member ) ) )
| ( ( B @ ( A @ difference ) )
!= sk2 ) ),
inference(simp,[status(thm)],[18096]) ).
thf(18098,plain,
! [B: $i,A: $i] :
( ( A @ ( sk2 @ ( B @ difference ) @ difference ) )
!= sk2 ),
inference(pattern_uni,[status(thm)],[18097:[bind(A,$thf( sk2 @ ( D @ difference ) )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(18305,plain,
! [B: $i,A: $i] :
( ( A @ ( sk2 @ ( B @ difference ) @ difference ) )
!= sk2 ),
inference(simp,[status(thm)],[18098]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ ( B @ sk5 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk5 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ member ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( A @ ( B @ sk7 ) @ member ) )
| ( A @ ( A @ ( B @ sk6 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk7 ) @ member ) )
| ( A @ ( A @ ( B @ sk6 ) @ member ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[60]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk7 ) @ member ) )
| ( A @ ( A @ ( B @ sk6 ) @ member ) )
| ( A = B ) ),
inference(simp,[status(thm)],[67]) ).
thf(10,axiom,
! [A: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(83,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(308,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( ( sk3 @ ( A @ ( sk1 @ intersection ) @ difference ) )
!= ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) ) )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[50,13]) ).
thf(309,plain,
! [A: $i] :
( ( ( sk3 @ ( A @ ( sk1 @ intersection ) @ difference ) )
!= ( sk3 @ ( sk2 @ difference ) @ ( sk1 @ intersection ) ) )
| ~ ( A @ ( sk2 @ subset ) )
| ~ ( sk2 @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[308:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(89562,plain,
$false,
inference(e,[status(thm)],[13488,9636,5059,22,415,101,234,88,24,5056,25,14,13511,9230,46,78,29,307,9221,18031,392,21,28,38,18718,53,169,13458,13,129,19038,32,64,13503,86,18573,54,13240,81,39,303,1471,1162,66,9228,9165,35,19118,95,50,31,11,72,4770,9219,9665,18727,19041,18305,23,75,82,36,11140,51,68,1399,83,309]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET634+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % 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
% 0.13/0.49 % Computer : n004.cluster.edu
% 0.13/0.49 % Model : x86_64 x86_64
% 0.13/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.49 % Memory : 8046.5625MB
% 0.13/0.49 % OS : Linux 6.8.0-71-generic
% 0.13/0.49 % CPULimit : 300
% 0.13/0.49 % WCLimit : 300
% 0.13/0.49 % DateTime : Sat Sep 26 08:02:07 UTC 2026
% 0.13/0.50 % CPUTime :
% 0.13/0.50 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
% 0.93/1.08 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/1.28 % [INFO] Parsing done (193ms).
% 1.23/1.29 % [INFO] Running in sequential loop mode.
% 1.87/1.69 % [INFO] eprover registered as external prover.
% 2.08/1.70 % [INFO] Scanning for conjecture ...
% 2.08/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.27/1.83 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.27/1.86 % [INFO] Problem is first-order (TPTP FOF).
% 2.27/1.86 % [INFO] Type checking passed.
% 2.27/1.87 % [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 ...
% 122.03/32.83 % External prover 'e' found a proof!
% 122.03/32.83 % [INFO] Killing All external provers ...
% 122.03/32.84 % Time passed: 32197ms (effective reasoning time: 31536ms)
% 122.03/32.84 % 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)>
% 122.03/32.84 % Axioms used in derivation (8): reflexivity_of_subset, equal_member_defn, member_equal, equal_defn, subset_defn, intersection_defn, commutativity_of_intersection, difference_defn
% 122.03/32.84 % No. of inferences in proof: 206
% 122.03/32.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 32197 ms resp. 31536 ms w/o parsing
% 107.67/32.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 107.67/32.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------