%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET776+4 : 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 : n006.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 08:30:53 AM UTC 2026
% Result : Theorem 63.50s 14.72s
% Output : Refutation 53.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 25
% Syntax : Number of formulae : 134 ( 46 unt; 0 typ; 8 def)
% Number of atoms : 602 ( 98 equ; 0 cnn)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 1816 ( 148 ~; 98 |; 181 &;1252 @)
% ( 17 <=>; 120 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 10 con; 0-3 aty)
% Number of variables : 334 ( 2 ^; 309 !; 15 ?; 334 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% Comments :
%------------------------------------------------------------------------------
thf(pre_order_decl,type,
pre_order: $i > $i > $o ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(apply_decl,type,
apply: $i > $i > $i > $o ).
thf(equal_set_decl,type,
equal_set: $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(product_decl,type,
product: $i > $i ).
thf(partition_decl,type,
partition: $i > $i > $o ).
thf(union_decl,type,
union: $i > $i > $i ).
thf(sum_decl,type,
sum: $i > $i ).
thf(disjoint_decl,type,
disjoint: $i > $i > $o ).
thf(power_set_decl,type,
power_set: $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(equivalence_decl,type,
equivalence: $i > $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(difference_decl,type,
difference: $i > $i > $i ).
thf(intersection_decl,type,
intersection: $i > $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(equivalence_class_decl,type,
equivalence_class: $i > $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk22_decl,type,
sk22: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( A @ ( E @ member ) )
& ( A @ ( D @ member ) ) )
=> ( ( ( ( D @ ( E @ ( B @ apply ) ) )
& ( E @ ( D @ ( B @ apply ) ) ) )
=> ( E @ ( D @ ( C @ apply ) ) ) )
& ( ( E @ ( D @ ( C @ apply ) ) )
=> ( ( D @ ( E @ ( B @ apply ) ) )
& ( E @ ( D @ ( B @ apply ) ) ) ) ) ) )
& ( A @ ( B @ pre_order ) ) )
=> ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( A @ ( G @ member ) )
& ( A @ ( F @ member ) )
& ( A @ ( E @ member ) )
& ( A @ ( D @ member ) ) )
=> ( ( ( E @ ( D @ ( B @ apply ) ) )
& ( G @ ( E @ ( C @ apply ) ) )
& ( F @ ( D @ ( C @ apply ) ) ) )
=> ( G @ ( F @ ( B @ apply ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ! [C: $i,D: $i] :
( ( ( sk1 @ ( D @ member ) )
& ( sk1 @ ( C @ member ) ) )
=> ( ( ( ( C @ ( D @ ( A @ apply ) ) )
& ( D @ ( C @ ( A @ apply ) ) ) )
=> ( D @ ( C @ ( B @ apply ) ) ) )
& ( ( D @ ( C @ ( B @ apply ) ) )
=> ( ( C @ ( D @ ( A @ apply ) ) )
& ( D @ ( C @ ( A @ apply ) ) ) ) ) ) )
& ( sk1 @ ( A @ pre_order ) ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( sk1 @ ( F @ member ) )
& ( sk1 @ ( E @ member ) )
& ( sk1 @ ( D @ member ) )
& ( sk1 @ ( C @ member ) ) )
=> ( ( ( D @ ( C @ ( A @ apply ) ) )
& ( F @ ( D @ ( B @ apply ) ) )
& ( E @ ( C @ ( B @ apply ) ) ) )
=> ( F @ ( E @ ( A @ apply ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ! [B: $i,C: $i] :
( ( ( sk1 @ ( C @ member ) )
& ( sk1 @ ( B @ member ) ) )
=> ( ( ( ( B @ ( C @ ( sk2 @ apply ) ) )
& ( C @ ( B @ ( sk2 @ apply ) ) ) )
=> ( C @ ( B @ ( A @ apply ) ) ) )
& ( ( C @ ( B @ ( A @ apply ) ) )
=> ( ( B @ ( C @ ( sk2 @ apply ) ) )
& ( C @ ( B @ ( sk2 @ apply ) ) ) ) ) ) )
& ( sk1 @ ( sk2 @ pre_order ) ) )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( sk1 @ ( E @ member ) )
& ( sk1 @ ( D @ member ) )
& ( sk1 @ ( C @ member ) )
& ( sk1 @ ( B @ member ) ) )
=> ( ( ( C @ ( B @ ( sk2 @ apply ) ) )
& ( E @ ( C @ ( A @ apply ) ) )
& ( D @ ( B @ ( A @ apply ) ) ) )
=> ( E @ ( D @ ( sk2 @ apply ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( ( sk1 @ ( D @ member ) )
& ( sk1 @ ( C @ member ) )
& ( sk1 @ ( B @ member ) )
& ( sk1 @ ( A @ member ) ) )
=> ( ( ( B @ ( A @ ( sk2 @ apply ) ) )
& ( D @ ( B @ ( sk3 @ apply ) ) )
& ( C @ ( A @ ( sk3 @ apply ) ) ) )
=> ( D @ ( C @ ( sk2 @ apply ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ ( C @ member ) )
& ( sk1 @ ( B @ member ) )
& ( sk1 @ ( A @ member ) )
& ( sk1 @ ( sk4 @ member ) ) )
=> ( ( ( A @ ( sk4 @ ( sk2 @ apply ) ) )
& ( C @ ( A @ ( sk3 @ apply ) ) )
& ( B @ ( sk4 @ ( sk3 @ apply ) ) ) )
=> ( C @ ( B @ ( sk2 @ apply ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ ( B @ member ) )
& ( sk1 @ ( A @ member ) )
& ( sk1 @ ( sk5 @ member ) )
& ( sk1 @ ( sk4 @ member ) ) )
=> ( ( ( sk5 @ ( sk4 @ ( sk2 @ apply ) ) )
& ( B @ ( sk5 @ ( sk3 @ apply ) ) )
& ( A @ ( sk4 @ ( sk3 @ apply ) ) ) )
=> ( B @ ( A @ ( sk2 @ apply ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( ( ( sk1 @ ( A @ member ) )
& ( sk1 @ ( sk6 @ member ) )
& ( sk1 @ ( sk5 @ member ) )
& ( sk1 @ ( sk4 @ member ) ) )
=> ( ( ( sk5 @ ( sk4 @ ( sk2 @ apply ) ) )
& ( A @ ( sk5 @ ( sk3 @ apply ) ) )
& ( sk6 @ ( sk4 @ ( sk3 @ apply ) ) ) )
=> ( A @ ( sk6 @ ( sk2 @ apply ) ) ) ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( A @ ( C @ member ) )
& ( B @ ( C @ member ) ) ) ) ) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ sum @ ( A @ member ) )
<=> ? [C: $i] :
( ( C @ ( A @ member ) )
& ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).
thf(116,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ ( A @ member ) )
& ( B @ ( C @ member ) ) )
=> ( B @ sum @ ( A @ member ) ) )
& ( ( B @ sum @ ( A @ member ) )
=> ? [C: $i] :
( ( C @ ( A @ member ) )
& ( B @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( A @ ( E @ member ) )
& ( A @ ( D @ member ) ) )
=> ( ( E @ ( D @ ( C @ apply ) ) )
<=> ( ( D @ ( E @ ( B @ apply ) ) )
& ( E @ ( D @ ( B @ apply ) ) ) ) ) )
& ( A @ ( B @ pre_order ) ) )
=> ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( A @ ( G @ member ) )
& ( A @ ( F @ member ) )
& ( A @ ( E @ member ) )
& ( A @ ( D @ member ) ) )
=> ( ( ( E @ ( D @ ( B @ apply ) ) )
& ( G @ ( E @ ( C @ apply ) ) )
& ( F @ ( D @ ( C @ apply ) ) ) )
=> ( G @ ( F @ ( B @ apply ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII12) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( A @ ( E @ member ) )
& ( A @ ( D @ member ) ) )
=> ( ( E @ ( D @ ( C @ apply ) ) )
<=> ( ( D @ ( E @ ( B @ apply ) ) )
& ( E @ ( D @ ( B @ apply ) ) ) ) ) )
& ( A @ ( B @ pre_order ) ) )
=> ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( A @ ( G @ member ) )
& ( A @ ( F @ member ) )
& ( A @ ( E @ member ) )
& ( A @ ( D @ member ) ) )
=> ( ( ( E @ ( D @ ( B @ apply ) ) )
& ( G @ ( E @ ( C @ apply ) ) )
& ( F @ ( D @ ( C @ apply ) ) ) )
=> ( G @ ( F @ ( B @ apply ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( A @ ( E @ member ) )
& ( A @ ( D @ member ) ) )
=> ( ( ( ( D @ ( E @ ( B @ apply ) ) )
& ( E @ ( D @ ( B @ apply ) ) ) )
=> ( E @ ( D @ ( C @ apply ) ) ) )
& ( ( E @ ( D @ ( C @ apply ) ) )
=> ( ( D @ ( E @ ( B @ apply ) ) )
& ( E @ ( D @ ( B @ apply ) ) ) ) ) ) )
& ( A @ ( B @ pre_order ) ) )
=> ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( A @ ( G @ member ) )
& ( A @ ( F @ member ) )
& ( A @ ( E @ member ) )
& ( A @ ( D @ member ) ) )
=> ( ( ( E @ ( D @ ( B @ apply ) ) )
& ( G @ ( E @ ( C @ apply ) ) )
& ( F @ ( D @ ( C @ apply ) ) ) )
=> ( G @ ( F @ ( B @ apply ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ~ ( sk7 @ ( sk6 @ ( sk2 @ apply ) ) )
& ( sk5 @ ( sk4 @ ( sk2 @ apply ) ) )
& ( sk7 @ ( sk5 @ ( sk3 @ apply ) ) )
& ( sk6 @ ( sk4 @ ( sk3 @ apply ) ) )
& ( sk1 @ ( sk7 @ member ) )
& ( sk1 @ ( sk6 @ member ) )
& ( sk1 @ ( sk5 @ member ) )
& ( sk1 @ ( sk4 @ member ) )
& ( ( B @ ( A @ ( sk3 @ apply ) ) )
| ~ ( A @ ( B @ ( sk2 @ apply ) ) )
| ~ ( B @ ( A @ ( sk2 @ apply ) ) )
| ~ ( sk1 @ ( B @ member ) )
| ~ ( sk1 @ ( A @ member ) ) )
& ( ( A @ ( B @ ( sk2 @ apply ) ) )
| ~ ( B @ ( A @ ( sk3 @ apply ) ) )
| ~ ( sk1 @ ( B @ member ) )
| ~ ( sk1 @ ( A @ member ) ) )
& ( ( B @ ( A @ ( sk2 @ apply ) ) )
| ~ ( B @ ( A @ ( sk3 @ apply ) ) )
| ~ ( sk1 @ ( B @ member ) )
| ~ ( sk1 @ ( A @ member ) ) )
& ( sk1 @ ( sk2 @ pre_order ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(26,plain,
sk7 @ ( sk5 @ ( sk3 @ apply ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( sk2 @ apply ) ) )
| ~ ( B @ ( A @ ( sk3 @ apply ) ) )
| ~ ( sk1 @ ( B @ member ) )
| ~ ( sk1 @ ( A @ member ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(285,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ ( sk5 @ ( sk3 @ apply ) ) )
!= ( B @ ( A @ ( sk3 @ apply ) ) ) )
| ( B @ ( A @ ( sk2 @ apply ) ) )
| ~ $true
| ~ ( sk1 @ ( B @ member ) )
| ~ ( sk1 @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[26,22]) ).
thf(286,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ ( sk5 @ ( sk3 @ apply ) ) )
!= ( B @ ( A @ ( sk3 @ apply ) ) ) )
| ( B @ ( A @ ( sk2 @ apply ) ) )
| ~ ( sk1 @ ( B @ member ) )
| ~ ( sk1 @ ( A @ member ) ) ),
inference(simp,[status(thm)],[285]) ).
thf(287,plain,
( ( sk7 @ ( sk5 @ ( sk2 @ apply ) ) )
| ~ ( sk1 @ ( sk7 @ member ) )
| ~ ( sk1 @ ( sk5 @ member ) ) ),
inference(pattern_uni,[status(thm)],[286:[bind(A,$thf( sk5 )),bind(B,$thf( sk7 ))]]) ).
thf(24,plain,
sk1 @ ( sk5 @ member ),
inference(cnfConj,[status(thm)],[20]) ).
thf(28,plain,
sk1 @ ( sk7 @ member ),
inference(cnfConj,[status(thm)],[20]) ).
thf(460,plain,
( ( sk7 @ ( sk5 @ ( sk2 @ apply ) ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[287,24,28]) ).
thf(461,plain,
sk7 @ ( sk5 @ ( sk2 @ apply ) ),
inference(simp,[status(thm)],[460]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
<=> ~ ? [C: $i] :
( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint) ).
thf(123,plain,
! [A: $i,B: $i] :
( ( ~ ? [C: $i] :
( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) )
=> ( B @ ( A @ disjoint ) ) )
& ( ( B @ ( A @ disjoint ) )
=> ~ ? [C: $i] :
( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(124,plain,
( ! [A: $i,B: $i] :
( ~ ? [C: $i] :
( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) )
=> ( B @ ( A @ disjoint ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ~ ? [C: $i] :
( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ) ),
inference(miniscope,[status(thm)],[123]) ).
thf(125,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ disjoint ) )
| ( E @ ( D @ ( E @ sk22 ) @ member ) ) )
& ( ( E @ ( D @ disjoint ) )
| ( D @ ( D @ ( E @ sk22 ) @ member ) ) )
& ( ~ ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ disjoint ) ) ) ),
inference(cnf,[status(esa)],[124]) ).
thf(127,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ disjoint ) )
| ( A @ ( A @ ( B @ sk22 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[125]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ disjoint ) )
| ( A @ ( A @ ( B @ sk22 ) @ member ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(32,plain,
sk1 @ ( sk2 @ pre_order ),
inference(cnfConj,[status(thm)],[20]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ member ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(137,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( B @ singleton @ ( A @ member ) ) )
& ( ( B @ singleton @ ( A @ member ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(138,plain,
( ! [A: $i,B: $i] :
( ( A = B )
=> ( B @ singleton @ ( A @ member ) ) )
& ! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ member ) )
=> ( A = B ) ) ),
inference(miniscope,[status(thm)],[137]) ).
thf(139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ singleton @ ( C @ member ) )
| ( C != D ) )
& ( ( A = B )
| ~ ( B @ singleton @ ( A @ member ) ) ) ),
inference(cnf,[status(esa)],[138]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ member ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[139]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ member ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[141]) ).
thf(144,plain,
! [A: $i] : ( A @ singleton @ ( A @ member ) ),
inference(simp,[status(thm)],[143]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ partition ) )
<=> ( ! [C: $i,D: $i] :
( ( ( A @ ( D @ member ) )
& ( A @ ( C @ member ) ) )
=> ( ? [E: $i] :
( ( D @ ( E @ member ) )
& ( C @ ( E @ member ) ) )
=> ( C = D ) ) )
& ! [C: $i] :
( ( B @ ( C @ member ) )
=> ? [D: $i] :
( ( D @ ( C @ member ) )
& ( A @ ( D @ member ) ) ) )
& ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ subset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i,D: $i] :
( ( ( A @ ( D @ member ) )
& ( A @ ( C @ member ) ) )
=> ( ? [E: $i] :
( ( D @ ( E @ member ) )
& ( C @ ( E @ member ) ) )
=> ( C = D ) ) )
& ! [C: $i] :
( ( B @ ( C @ member ) )
=> ? [D: $i] :
( ( D @ ( C @ member ) )
& ( A @ ( D @ member ) ) ) )
& ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ subset ) ) ) )
=> ( B @ ( A @ partition ) ) )
& ( ( B @ ( A @ partition ) )
=> ( ! [C: $i,D: $i] :
( ( ( A @ ( D @ member ) )
& ( A @ ( C @ member ) ) )
=> ( ? [E: $i] :
( ( D @ ( E @ member ) )
& ( C @ ( E @ member ) ) )
=> ( C = D ) ) )
& ! [C: $i] :
( ( B @ ( C @ member ) )
=> ? [D: $i] :
( ( D @ ( C @ member ) )
& ( A @ ( D @ member ) ) ) )
& ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ power_set @ ( A @ member ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).
thf(131,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( B @ power_set @ ( A @ member ) ) )
& ( ( B @ power_set @ ( A @ member ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(14,axiom,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
thf(213,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(214,plain,
~ ? [A: $i] : ( empty_set @ ( A @ member ) ),
inference(miniscope,[status(thm)],[213]) ).
thf(215,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(cnf,[status(esa)],[214]) ).
thf(140,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ singleton @ ( A @ member ) ) ),
inference(cnfConj,[status(thm)],[139]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ~ ( B @ singleton @ ( A @ member ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[140]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ equivalence ) )
<=> ( ! [C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ member ) )
& ( A @ ( D @ member ) )
& ( A @ ( C @ member ) ) )
=> ( ( ( E @ ( D @ ( B @ apply ) ) )
& ( D @ ( C @ ( B @ apply ) ) ) )
=> ( E @ ( C @ ( B @ apply ) ) ) ) )
& ! [C: $i,D: $i] :
( ( ( A @ ( D @ member ) )
& ( A @ ( C @ member ) ) )
=> ( ( D @ ( C @ ( B @ apply ) ) )
=> ( C @ ( D @ ( B @ apply ) ) ) ) )
& ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( C @ ( C @ ( B @ apply ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence) ).
thf(153,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ member ) )
& ( A @ ( D @ member ) )
& ( A @ ( C @ member ) ) )
=> ( ( ( E @ ( D @ ( B @ apply ) ) )
& ( D @ ( C @ ( B @ apply ) ) ) )
=> ( E @ ( C @ ( B @ apply ) ) ) ) )
& ! [C: $i,D: $i] :
( ( ( A @ ( D @ member ) )
& ( A @ ( C @ member ) ) )
=> ( ( D @ ( C @ ( B @ apply ) ) )
=> ( C @ ( D @ ( B @ apply ) ) ) ) )
& ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( C @ ( C @ ( B @ apply ) ) ) ) )
=> ( A @ ( B @ equivalence ) ) )
& ( ( A @ ( B @ equivalence ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ member ) )
& ( A @ ( D @ member ) )
& ( A @ ( C @ member ) ) )
=> ( ( ( E @ ( D @ ( B @ apply ) ) )
& ( D @ ( C @ ( B @ apply ) ) ) )
=> ( E @ ( C @ ( B @ apply ) ) ) ) )
& ! [C: $i,D: $i] :
( ( ( A @ ( D @ member ) )
& ( A @ ( C @ member ) ) )
=> ( ( D @ ( C @ ( B @ apply ) ) )
=> ( C @ ( D @ ( B @ apply ) ) ) ) )
& ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( C @ ( C @ ( B @ apply ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equal_set ) )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( A @ equal_set ) ) )
& ( ( B @ ( A @ equal_set ) )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(34,plain,
( ! [A: $i,B: $i] :
( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( A @ equal_set ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ equal_set ) )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(miniscope,[status(thm)],[33]) ).
thf(35,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ equal_set ) )
| ~ ( C @ ( D @ subset ) )
| ~ ( D @ ( C @ subset ) ) )
& ( ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ equal_set ) ) )
& ( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ equal_set ) ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ equal_set ) ) ),
inference(cnfConj,[status(thm)],[35]) ).
thf(25,plain,
~ ( sk7 @ ( sk6 @ ( sk2 @ apply ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ pre_order ) )
<=> ( ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ member ) )
& ( B @ ( D @ member ) )
& ( B @ ( C @ member ) ) )
=> ( ( ( E @ ( D @ ( A @ apply ) ) )
& ( D @ ( C @ ( A @ apply ) ) ) )
=> ( E @ ( C @ ( A @ apply ) ) ) ) )
& ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( C @ ( A @ apply ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pre_order) ).
thf(78,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ member ) )
& ( B @ ( D @ member ) )
& ( B @ ( C @ member ) ) )
=> ( ( ( E @ ( D @ ( A @ apply ) ) )
& ( D @ ( C @ ( A @ apply ) ) ) )
=> ( E @ ( C @ ( A @ apply ) ) ) ) )
& ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( C @ ( A @ apply ) ) ) ) )
=> ( B @ ( A @ pre_order ) ) )
& ( ( B @ ( A @ pre_order ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ member ) )
& ( B @ ( D @ member ) )
& ( B @ ( C @ member ) ) )
=> ( ( ( E @ ( D @ ( A @ apply ) ) )
& ( D @ ( C @ ( A @ apply ) ) ) )
=> ( E @ ( C @ ( A @ apply ) ) ) ) )
& ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( C @ ( A @ apply ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( sk2 @ apply ) ) )
| ~ ( B @ ( A @ ( sk3 @ apply ) ) )
| ~ ( sk1 @ ( B @ member ) )
| ~ ( sk1 @ ( A @ member ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ difference ) @ ( A @ member ) )
<=> ( ~ ( B @ ( A @ member ) )
& ( C @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).
thf(216,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( B @ ( A @ member ) )
& ( C @ ( A @ member ) ) )
=> ( B @ ( C @ difference ) @ ( A @ member ) ) )
& ( ( B @ ( C @ difference ) @ ( A @ member ) )
=> ( ~ ( B @ ( A @ member ) )
& ( C @ ( A @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
<=> ( ( A = C )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
thf(230,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A = C )
| ( A = B ) )
=> ( C @ ( B @ unordered_pair ) @ ( A @ member ) ) )
& ( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
=> ( ( A = C )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(231,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( A = C )
| ( A = B ) )
=> ( C @ ( B @ unordered_pair ) @ ( A @ member ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
=> ( ( A = C )
| ( A = B ) ) ) ),
inference(miniscope,[status(thm)],[230]) ).
thf(232,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ unordered_pair ) @ ( D @ member ) )
| ( D != F ) )
& ( ( F @ ( E @ unordered_pair ) @ ( D @ member ) )
| ( D != E ) )
& ( ( A = C )
| ( A = B )
| ~ ( C @ ( B @ unordered_pair ) @ ( A @ member ) ) ) ),
inference(cnf,[status(esa)],[231]) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[232]) ).
thf(237,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[234]) ).
thf(238,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( A @ member ) ),
inference(simp,[status(thm)],[237]) ).
thf(462,plain,
( ( ( sk7 @ ( sk6 @ ( sk2 @ apply ) ) )
!= ( sk7 @ ( sk5 @ ( sk2 @ apply ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[461,25]) ).
thf(463,plain,
( ( sk7 @ ( sk6 @ ( sk2 @ apply ) ) )
!= ( sk7 @ ( sk5 @ ( sk2 @ apply ) ) ) ),
inference(simp,[status(thm)],[462]) ).
thf(472,plain,
( ( sk7 != sk7 )
| ( sk6 != sk5 )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[463]) ).
thf(474,plain,
sk6 != sk5,
inference(simp,[status(thm)],[472]) ).
thf(777,plain,
! [B: $i,A: $i] :
( ( B != sk6 )
| ( A != sk5 )
| ~ ( B @ singleton @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[142,474]) ).
thf(778,plain,
! [A: $i] :
( ( A != sk5 )
| ~ ( sk6 @ singleton @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[777:[bind(A,$thf( A )),bind(B,$thf( sk6 ))]]) ).
thf(792,plain,
~ ( sk6 @ singleton @ ( sk5 @ member ) ),
inference(simp,[status(thm)],[778]) ).
thf(992,plain,
( ( ( sk6 @ singleton @ ( sk5 @ member ) )
!= ( sk1 @ ( sk5 @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,792]) ).
thf(993,plain,
( ( sk6 @ singleton @ ( sk5 @ member ) )
!= ( sk1 @ ( sk5 @ member ) ) ),
inference(simp,[status(thm)],[992]) ).
thf(1012,plain,
( ( ( sk6 @ singleton )
!= sk1 )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[993]) ).
thf(1021,plain,
( ( sk6 @ singleton )
!= sk1 ),
inference(simp,[status(thm)],[1012]) ).
thf(248,plain,
! [A: $i] :
( ( ( sk1 @ ( sk7 @ member ) )
!= ( empty_set @ ( A @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,215]) ).
thf(249,plain,
! [A: $i] :
( ( sk1 @ ( sk7 @ member ) )
!= ( empty_set @ ( A @ member ) ) ),
inference(simp,[status(thm)],[248]) ).
thf(256,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( sk7 != A ) ),
inference(simp,[status(thm)],[249]) ).
thf(260,plain,
sk1 != empty_set,
inference(simp,[status(thm)],[256]) ).
thf(21,plain,
sk6 @ ( sk4 @ ( sk3 @ apply ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(264,plain,
( ( ( sk6 @ ( sk4 @ ( sk3 @ apply ) ) )
!= ( sk7 @ ( sk6 @ ( sk2 @ apply ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,25]) ).
thf(265,plain,
( ( sk6 @ ( sk4 @ ( sk3 @ apply ) ) )
!= ( sk7 @ ( sk6 @ ( sk2 @ apply ) ) ) ),
inference(simp,[status(thm)],[264]) ).
thf(266,plain,
( ( sk7 != sk6 )
| ( sk6 != sk4 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[265]) ).
thf(27,plain,
sk1 @ ( sk4 @ member ),
inference(cnfConj,[status(thm)],[20]) ).
thf(31,plain,
sk5 @ ( sk4 @ ( sk2 @ apply ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(271,plain,
( ( ( sk7 @ ( sk6 @ ( sk2 @ apply ) ) )
!= ( sk5 @ ( sk4 @ ( sk2 @ apply ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31,25]) ).
thf(272,plain,
( ( sk7 @ ( sk6 @ ( sk2 @ apply ) ) )
!= ( sk5 @ ( sk4 @ ( sk2 @ apply ) ) ) ),
inference(simp,[status(thm)],[271]) ).
thf(273,plain,
( ( sk7 != sk5 )
| ( sk6 != sk4 )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[272]) ).
thf(274,plain,
( ( sk7 != sk5 )
| ( sk6 != sk4 ) ),
inference(simp,[status(thm)],[273]) ).
thf(235,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
| ( A != C ) ),
inference(cnfConj,[status(thm)],[232]) ).
thf(239,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
| ( A != C ) ),
inference(lifteq,[status(thm)],[235]) ).
thf(240,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( B @ member ) ),
inference(simp,[status(thm)],[239]) ).
thf(30,plain,
sk1 @ ( sk6 @ member ),
inference(cnfConj,[status(thm)],[20]) ).
thf(775,plain,
! [B: $i,A: $i] :
( ( A != sk6 )
| ( B != sk5 )
| ~ ( B @ singleton @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[142,474]) ).
thf(776,plain,
! [A: $i] :
( ( A != sk5 )
| ~ ( A @ singleton @ ( sk6 @ member ) ) ),
inference(pattern_uni,[status(thm)],[775:[bind(A,$thf( sk6 ))]]) ).
thf(791,plain,
~ ( sk5 @ singleton @ ( sk6 @ member ) ),
inference(simp,[status(thm)],[776]) ).
thf(903,plain,
( ( ( sk5 @ singleton @ ( sk6 @ member ) )
!= ( sk1 @ ( sk6 @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[30,791]) ).
thf(904,plain,
( ( sk5 @ singleton @ ( sk6 @ member ) )
!= ( sk1 @ ( sk6 @ member ) ) ),
inference(simp,[status(thm)],[903]) ).
thf(909,plain,
( ( ( sk5 @ singleton )
!= sk1 )
| ( sk6 != sk6 ) ),
inference(simp,[status(thm)],[904]) ).
thf(915,plain,
( ( sk5 @ singleton )
!= sk1 ),
inference(simp,[status(thm)],[909]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ union ) @ ( A @ member ) )
<=> ( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
thf(108,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) ) )
=> ( C @ ( B @ union ) @ ( A @ member ) ) )
& ( ( C @ ( B @ union ) @ ( A @ member ) )
=> ( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ disjoint ) )
| ( B @ ( A @ ( B @ sk22 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[125]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ disjoint ) )
| ( B @ ( A @ ( B @ sk22 ) @ member ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(275,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ member ) )
!= ( empty_set @ ( B @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[144,215]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ member ) )
!= ( empty_set @ ( B @ member ) ) ),
inference(simp,[status(thm)],[275]) ).
thf(277,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= empty_set )
| ( A != B ) ),
inference(simp,[status(thm)],[276]) ).
thf(278,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(simp,[status(thm)],[277]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ intersection ) @ ( A @ member ) )
<=> ( ( C @ ( A @ member ) )
& ( B @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
thf(223,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ member ) )
& ( B @ ( A @ member ) ) )
=> ( C @ ( B @ intersection ) @ ( A @ member ) ) )
& ( ( C @ ( B @ intersection ) @ ( A @ member ) )
=> ( ( C @ ( A @ member ) )
& ( B @ ( A @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ equivalence_class ) ) @ ( D @ member ) )
<=> ( ( D @ ( C @ ( A @ apply ) ) )
& ( B @ ( D @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_class) ).
thf(241,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( C @ ( A @ apply ) ) )
& ( B @ ( D @ member ) ) )
=> ( A @ ( B @ ( C @ equivalence_class ) ) @ ( D @ member ) ) )
& ( ( A @ ( B @ ( C @ equivalence_class ) ) @ ( D @ member ) )
=> ( ( D @ ( C @ ( A @ apply ) ) )
& ( B @ ( D @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(440,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk22 ) @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ~ $true
| ( B @ ( A @ disjoint ) ) ),
inference(paramod_ordered,[status(thm)],[129,215]) ).
thf(441,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk22 ) @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ( B @ ( A @ disjoint ) ) ),
inference(simp,[status(thm)],[440]) ).
thf(442,plain,
! [A: $i] : ( A @ ( empty_set @ disjoint ) ),
inference(pattern_uni,[status(thm)],[441:[bind(A,$thf( empty_set )),bind(B,$thf( D )),bind(C,$thf( empty_set @ ( D @ sk22 ) ))]]) ).
thf(458,plain,
! [A: $i] : ( A @ ( empty_set @ disjoint ) ),
inference(simp,[status(thm)],[442]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
thf(145,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)],[12]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ product @ ( A @ member ) )
<=> ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product) ).
thf(40,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( A @ member ) ) )
=> ( B @ product @ ( A @ member ) ) )
& ( ( B @ product @ ( A @ member ) )
=> ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( A @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( sk3 @ apply ) ) )
| ~ ( A @ ( B @ ( sk2 @ apply ) ) )
| ~ ( B @ ( A @ ( sk2 @ apply ) ) )
| ~ ( sk1 @ ( B @ member ) )
| ~ ( sk1 @ ( A @ member ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ equal_set ) ) ),
inference(cnfConj,[status(thm)],[35]) ).
thf(418,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[240,215]) ).
thf(419,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ member ) )
!= ( empty_set @ ( C @ member ) ) ),
inference(simp,[status(thm)],[418]) ).
thf(431,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= empty_set )
| ( B != C ) ),
inference(simp,[status(thm)],[419]) ).
thf(437,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[431]) ).
thf(398,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[238,215]) ).
thf(399,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ member ) )
!= ( empty_set @ ( C @ member ) ) ),
inference(simp,[status(thm)],[398]) ).
thf(410,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= empty_set )
| ( A != C ) ),
inference(simp,[status(thm)],[399]) ).
thf(415,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[410]) ).
thf(16055,plain,
$false,
inference(e,[status(thm)],[116,461,129,32,144,48,131,215,142,153,24,37,25,78,29,216,238,1021,260,28,33,21,137,792,266,22,27,274,230,213,240,915,108,130,278,223,241,123,458,145,791,31,40,26,23,36,30,19,437,474,415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET776+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.09 % 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
% 0.15/0.47 % Computer : n006.cluster.edu
% 0.15/0.47 % Model : x86_64 x86_64
% 0.15/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.47 % Memory : 8046.5625MB
% 0.15/0.47 % OS : Linux 6.8.0-71-generic
% 0.15/0.48 % CPULimit : 300
% 0.15/0.48 % WCLimit : 300
% 0.15/0.48 % DateTime : Sat Sep 26 08:14:25 UTC 2026
% 0.15/0.48 % CPUTime :
% 0.15/0.48 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
% 1.14/1.26 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.79/1.51 % [INFO] Parsing done (243ms).
% 1.79/1.53 % [INFO] Running in sequential loop mode.
% 2.63/2.14 % [INFO] eprover registered as external prover.
% 2.63/2.15 % [INFO] Scanning for conjecture ...
% 3.15/2.31 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 3.31/2.41 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 3.31/2.49 % [INFO] Problem is first-order (TPTP FOF).
% 3.54/2.50 % [INFO] Type checking passed.
% 3.54/2.51 % [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 ...
% 63.50/14.71 % External prover 'e' found a proof!
% 63.50/14.71 % [INFO] Killing All external provers ...
% 63.50/14.71 % Time passed: 14035ms (effective reasoning time: 13171ms)
% 63.50/14.71 % 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)>
% 63.50/14.72 % Axioms used in derivation (16): power_set, unordered_pair, pre_order, intersection, empty_set, subset, equal_set, singleton, disjoint, difference, sum, product, equivalence, union, partition, equivalence_class
% 63.50/14.72 % No. of inferences in proof: 126
% 63.50/14.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 14035 ms resp. 13171 ms w/o parsing
% 53.74/14.91 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 53.74/14.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------