%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET810+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n003.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 08:30:57 AM UTC 2026
% Result : Theorem 39.77s 13.96s
% Output : Refutation 40.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 24
% Syntax : Number of formulae : 167 ( 58 unt; 0 typ; 4 def)
% Number of atoms : 553 ( 124 equ; 0 cnn)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 1591 ( 183 ~; 97 |; 99 &;1110 @)
% ( 17 <=>; 85 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 7 con; 0-3 aty)
% Number of variables : 367 ( 4 ^; 349 !; 10 ?; 367 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(member_decl,type,
member: $i > $i > $o ).
thf(on_decl,type,
on: $i ).
thf(equal_set_decl,type,
equal_set: $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(least_decl,type,
least: $i > $i > $i > $o ).
thf(apply_decl,type,
apply: $i > $i > $i > $o ).
thf(initial_segment_decl,type,
initial_segment: $i > $i > $i > $i ).
thf(power_set_decl,type,
power_set: $i > $i ).
thf(set_decl,type,
set: $i > $o ).
thf(strict_well_order_decl,type,
strict_well_order: $i > $i > $o ).
thf(member_predicate_decl,type,
member_predicate: $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(product_decl,type,
product: $i > $i ).
thf(strict_order_decl,type,
strict_order: $i > $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(suc_decl,type,
suc: $i > $i ).
thf(union_decl,type,
union: $i > $i > $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(sum_decl,type,
sum: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( on @ ( B @ member ) )
& ( on @ ( A @ member ) ) )
=> ~ ( ( A @ ( B @ member ) )
& ( B @ ( A @ member ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( on @ ( A @ member ) )
& ( on @ ( sk1 @ member ) ) )
=> ~ ( ( sk1 @ ( A @ member ) )
& ( A @ ( sk1 @ member ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ member ) )
=> ( C @ ( B @ member ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) ) ) ) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( member_predicate @ apply ) ) )
<=> ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rel_member) ).
thf(211,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ member ) )
=> ( B @ ( A @ ( member_predicate @ apply ) ) ) )
& ( ( B @ ( A @ ( member_predicate @ apply ) ) )
=> ( B @ ( A @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( on @ ( B @ member ) )
& ( on @ ( A @ member ) ) )
=> ~ ( ( A @ ( B @ member ) )
& ( B @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thV3) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( on @ ( B @ member ) )
& ( on @ ( A @ member ) ) )
=> ~ ( ( A @ ( B @ member ) )
& ( B @ ( A @ member ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(22,plain,
~ ! [A: $i,B: $i] :
( ( ( on @ ( B @ member ) )
& ( on @ ( A @ member ) ) )
=> ~ ( ( A @ ( B @ member ) )
& ( B @ ( A @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(23,plain,
( ( sk1 @ ( sk2 @ member ) )
& ( sk2 @ ( sk1 @ member ) )
& ( on @ ( sk2 @ member ) )
& ( on @ ( sk1 @ member ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(27,plain,
sk1 @ ( sk2 @ member ),
inference(cnfConj,[status(thm)],[23]) ).
thf(13,axiom,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
thf(160,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(161,plain,
~ ? [A: $i] : ( empty_set @ ( A @ member ) ),
inference(miniscope,[status(thm)],[160]) ).
thf(162,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(cnf,[status(esa)],[161]) ).
thf(217,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ member ) )
!= ( empty_set @ ( A @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27,162]) ).
thf(218,plain,
! [A: $i] :
( ( sk1 @ ( sk2 @ member ) )
!= ( empty_set @ ( A @ member ) ) ),
inference(simp,[status(thm)],[217]) ).
thf(225,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[218]) ).
thf(229,plain,
sk1 != empty_set,
inference(simp,[status(thm)],[225]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
<=> ( ( A = C )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
thf(193,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)],[19]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ difference ) @ ( A @ member ) )
<=> ( ~ ( B @ ( A @ member ) )
& ( C @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference) ).
thf(169,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(170,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ ( A @ member ) )
& ( C @ ( A @ member ) ) )
=> ( B @ ( C @ difference ) @ ( A @ member ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ difference ) @ ( A @ member ) )
=> ( ~ ( B @ ( A @ member ) )
& ( C @ ( A @ member ) ) ) ) ),
inference(miniscope,[status(thm)],[169]) ).
thf(171,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( F @ difference ) @ ( D @ member ) )
| ( E @ ( D @ member ) )
| ~ ( F @ ( D @ member ) ) )
& ( ~ ( B @ ( A @ member ) )
| ~ ( B @ ( C @ difference ) @ ( A @ member ) ) )
& ( ( C @ ( A @ member ) )
| ~ ( B @ ( C @ difference ) @ ( A @ member ) ) ) ),
inference(cnf,[status(esa)],[170]) ).
thf(173,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ member ) )
| ~ ( B @ ( C @ difference ) @ ( A @ member ) ) ),
inference(cnfConj,[status(thm)],[171]) ).
thf(24,plain,
on @ ( sk1 @ member ),
inference(cnfConj,[status(thm)],[23]) ).
thf(26,plain,
sk2 @ ( sk1 @ member ),
inference(cnfConj,[status(thm)],[23]) ).
thf(258,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ member ) )
!= ( B @ ( A @ member ) ) )
| ~ $true
| ~ ( B @ ( C @ difference ) @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[26,173]) ).
thf(259,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ member ) )
!= ( B @ ( A @ member ) ) )
| ~ ( B @ ( C @ difference ) @ ( A @ member ) ) ),
inference(simp,[status(thm)],[258]) ).
thf(260,plain,
! [A: $i] :
~ ( sk2 @ ( A @ difference ) @ ( sk1 @ member ) ),
inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(280,plain,
! [A: $i] :
~ ( sk2 @ ( A @ difference ) @ ( sk1 @ member ) ),
inference(simp,[status(thm)],[260]) ).
thf(301,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ difference ) @ ( sk1 @ member ) )
!= ( on @ ( sk1 @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,280]) ).
thf(302,plain,
! [A: $i] :
( ( sk2 @ ( A @ difference ) @ ( sk1 @ member ) )
!= ( on @ ( sk1 @ member ) ) ),
inference(simp,[status(thm)],[301]) ).
thf(305,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ difference ) )
!= on )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[302]) ).
thf(311,plain,
! [A: $i] :
( ( sk2 @ ( A @ difference ) )
!= on ),
inference(simp,[status(thm)],[305]) ).
thf(194,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)],[193]) ).
thf(195,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)],[194]) ).
thf(197,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[195]) ).
thf(200,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[197]) ).
thf(201,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( A @ member ) ),
inference(simp,[status(thm)],[200]) ).
thf(237,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[201,162]) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ member ) )
!= ( empty_set @ ( C @ member ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(239,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= empty_set )
| ( A != C ) ),
inference(simp,[status(thm)],[238]) ).
thf(240,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[239]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ least ) ) )
<=> ( ! [D: $i] :
( ( B @ ( D @ member ) )
=> ( ( D @ ( C @ ( A @ apply ) ) )
| ( C = D ) ) )
& ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',least) ).
thf(35,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( B @ ( D @ member ) )
=> ( ( D @ ( C @ ( A @ apply ) ) )
| ( C = D ) ) )
& ( B @ ( C @ member ) ) )
=> ( B @ ( A @ ( C @ least ) ) ) )
& ( ( B @ ( A @ ( C @ least ) ) )
=> ( ! [D: $i] :
( ( B @ ( D @ member ) )
=> ( ( D @ ( C @ ( A @ apply ) ) )
| ( C = D ) ) )
& ( B @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equal_set ) )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
thf(28,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(29,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)],[28]) ).
thf(30,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)],[29]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ equal_set ) ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ product @ ( A @ member ) )
<=> ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product) ).
thf(79,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)],[9]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( A @ suc @ ( B @ member ) )
<=> ( A @ singleton @ ( A @ union ) @ ( B @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor) ).
thf(163,plain,
! [A: $i,B: $i] :
( ( ( A @ singleton @ ( A @ union ) @ ( B @ member ) )
=> ( A @ suc @ ( B @ member ) ) )
& ( ( A @ suc @ ( B @ member ) )
=> ( A @ singleton @ ( A @ union ) @ ( B @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(263,plain,
! [C: $i,B: $i,A: $i] :
( ( ( on @ ( sk1 @ member ) )
!= ( B @ ( A @ member ) ) )
| ~ $true
| ~ ( B @ ( C @ difference ) @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[24,173]) ).
thf(264,plain,
! [C: $i,B: $i,A: $i] :
( ( ( on @ ( sk1 @ member ) )
!= ( B @ ( A @ member ) ) )
| ~ ( B @ ( C @ difference ) @ ( A @ member ) ) ),
inference(simp,[status(thm)],[263]) ).
thf(265,plain,
! [A: $i] :
~ ( on @ ( A @ difference ) @ ( sk1 @ member ) ),
inference(pattern_uni,[status(thm)],[264:[bind(A,$thf( sk1 )),bind(B,$thf( on ))]]) ).
thf(281,plain,
! [A: $i] :
~ ( on @ ( A @ difference ) @ ( sk1 @ member ) ),
inference(simp,[status(thm)],[265]) ).
thf(337,plain,
! [A: $i] :
( ( ( on @ ( A @ difference ) @ ( sk1 @ member ) )
!= ( on @ ( sk1 @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,281]) ).
thf(338,plain,
! [A: $i] :
( ( on @ ( A @ difference ) @ ( sk1 @ member ) )
!= ( on @ ( sk1 @ member ) ) ),
inference(simp,[status(thm)],[337]) ).
thf(349,plain,
! [A: $i] :
( ( ( on @ ( A @ difference ) )
!= on )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[338]) ).
thf(354,plain,
! [A: $i] :
( ( on @ ( A @ difference ) )
!= on ),
inference(simp,[status(thm)],[349]) ).
thf(253,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ member ) )
!= ( B @ ( A @ member ) ) )
| ~ $true
| ~ ( B @ ( C @ difference ) @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[27,173]) ).
thf(254,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ member ) )
!= ( B @ ( A @ member ) ) )
| ~ ( B @ ( C @ difference ) @ ( A @ member ) ) ),
inference(simp,[status(thm)],[253]) ).
thf(255,plain,
! [A: $i] :
~ ( sk1 @ ( A @ difference ) @ ( sk2 @ member ) ),
inference(pattern_uni,[status(thm)],[254:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(292,plain,
! [A: $i] :
~ ( sk1 @ ( A @ difference ) @ ( sk2 @ member ) ),
inference(simp,[status(thm)],[255]) ).
thf(393,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ difference ) @ ( sk2 @ member ) )
!= ( sk1 @ ( sk2 @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27,292]) ).
thf(394,plain,
! [A: $i] :
( ( sk1 @ ( A @ difference ) @ ( sk2 @ member ) )
!= ( sk1 @ ( sk2 @ member ) ) ),
inference(simp,[status(thm)],[393]) ).
thf(401,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ difference ) )
!= sk1 )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[394]) ).
thf(404,plain,
! [A: $i] :
( ( sk1 @ ( A @ difference ) )
!= sk1 ),
inference(simp,[status(thm)],[401]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ union ) @ ( A @ member ) )
<=> ( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
thf(185,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)],[18]) ).
thf(25,plain,
on @ ( sk2 @ member ),
inference(cnfConj,[status(thm)],[23]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
thf(152,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(8,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ member ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(71,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)],[8]) ).
thf(72,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)],[71]) ).
thf(73,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)],[72]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ member ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[73]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ member ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[75]) ).
thf(78,plain,
! [A: $i] : ( A @ singleton @ ( A @ member ) ),
inference(simp,[status(thm)],[77]) ).
thf(7,axiom,
! [A: $i] :
( ( on @ ( A @ member ) )
<=> ( ! [B: $i] :
( ( A @ ( B @ member ) )
=> ( A @ ( B @ subset ) ) )
& ( A @ ( member_predicate @ strict_well_order ) )
& ( A @ set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_number) ).
thf(61,plain,
! [A: $i] :
( ( ( ! [B: $i] :
( ( A @ ( B @ member ) )
=> ( A @ ( B @ subset ) ) )
& ( A @ ( member_predicate @ strict_well_order ) )
& ( A @ set ) )
=> ( on @ ( A @ member ) ) )
& ( ( on @ ( A @ member ) )
=> ( ! [B: $i] :
( ( A @ ( B @ member ) )
=> ( A @ ( B @ subset ) ) )
& ( A @ ( member_predicate @ strict_well_order ) )
& ( A @ set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(299,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ difference ) @ ( sk1 @ member ) )
!= ( sk2 @ ( sk1 @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26,280]) ).
thf(300,plain,
! [A: $i] :
( ( sk2 @ ( A @ difference ) @ ( sk1 @ member ) )
!= ( sk2 @ ( sk1 @ member ) ) ),
inference(simp,[status(thm)],[299]) ).
thf(307,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ difference ) )
!= sk2 )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[300]) ).
thf(312,plain,
! [A: $i] :
( ( sk2 @ ( A @ difference ) )
!= sk2 ),
inference(simp,[status(thm)],[307]) ).
thf(268,plain,
! [C: $i,B: $i,A: $i] :
( ( ( on @ ( sk2 @ member ) )
!= ( B @ ( A @ member ) ) )
| ~ $true
| ~ ( B @ ( C @ difference ) @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[25,173]) ).
thf(269,plain,
! [C: $i,B: $i,A: $i] :
( ( ( on @ ( sk2 @ member ) )
!= ( B @ ( A @ member ) ) )
| ~ ( B @ ( C @ difference ) @ ( A @ member ) ) ),
inference(simp,[status(thm)],[268]) ).
thf(270,plain,
! [A: $i] :
~ ( on @ ( A @ difference ) @ ( sk2 @ member ) ),
inference(pattern_uni,[status(thm)],[269:[bind(A,$thf( sk2 )),bind(B,$thf( on ))]]) ).
thf(282,plain,
! [A: $i] :
~ ( on @ ( A @ difference ) @ ( sk2 @ member ) ),
inference(simp,[status(thm)],[270]) ).
thf(367,plain,
! [A: $i] :
( ( ( on @ ( A @ difference ) @ ( sk2 @ member ) )
!= ( sk1 @ ( sk2 @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27,282]) ).
thf(368,plain,
! [A: $i] :
( ( on @ ( A @ difference ) @ ( sk2 @ member ) )
!= ( sk1 @ ( sk2 @ member ) ) ),
inference(simp,[status(thm)],[367]) ).
thf(375,plain,
! [A: $i] :
( ( ( on @ ( A @ difference ) )
!= sk1 )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[368]) ).
thf(381,plain,
! [A: $i] :
( ( on @ ( A @ difference ) )
!= sk1 ),
inference(simp,[status(thm)],[375]) ).
thf(80,plain,
( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( A @ member ) ) )
=> ( B @ product @ ( A @ member ) ) )
& ! [A: $i,B: $i] :
( ( B @ product @ ( A @ member ) )
=> ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( A @ member ) ) ) ) ),
inference(miniscope,[status(thm)],[79]) ).
thf(81,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ product @ ( D @ member ) )
| ~ ( D @ ( E @ sk5 ) @ ( D @ member ) ) )
& ( ( E @ product @ ( D @ member ) )
| ( E @ ( D @ ( E @ sk5 ) @ member ) ) )
& ( ( C @ ( A @ member ) )
| ~ ( B @ ( C @ member ) )
| ~ ( B @ product @ ( A @ member ) ) ) ),
inference(cnf,[status(esa)],[80]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( B @ product @ ( A @ member ) )
| ( B @ ( A @ ( B @ sk5 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( B @ product @ ( A @ member ) )
| ( B @ ( A @ ( B @ sk5 ) @ member ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(331,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ member ) )
!= ( on @ ( B @ difference ) @ ( sk1 @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,281]) ).
thf(332,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ member ) )
!= ( on @ ( B @ difference ) @ ( sk1 @ member ) ) ),
inference(simp,[status(thm)],[331]) ).
thf(351,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= ( on @ ( B @ difference ) ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[332]) ).
thf(356,plain,
! [A: $i] :
( ( on @ ( A @ difference ) )
!= ( sk1 @ singleton ) ),
inference(simp,[status(thm)],[351]) ).
thf(153,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)],[152]) ).
thf(154,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ subset ) )
| ~ ( E @ ( D @ ( E @ sk14 ) @ member ) ) )
& ( ( E @ ( D @ subset ) )
| ( D @ ( D @ ( E @ sk14 ) @ member ) ) )
& ( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ) ),
inference(cnf,[status(esa)],[153]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk14 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[154]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk14 ) @ member ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(423,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk14 ) @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[158,162]) ).
thf(424,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk14 ) @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[423]) ).
thf(425,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(pattern_uni,[status(thm)],[424:[bind(A,$thf( empty_set )),bind(B,$thf( D )),bind(C,$thf( empty_set @ ( D @ sk14 ) ))]]) ).
thf(430,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(simp,[status(thm)],[425]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ equal_set ) ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equal_set ) )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equal_set ) )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ intersection ) @ ( A @ member ) )
<=> ( ( C @ ( A @ member ) )
& ( B @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
thf(176,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(20,axiom,
! [A: $i,B: $i] :
( ( B @ sum @ ( A @ member ) )
<=> ? [C: $i] :
( ( C @ ( A @ member ) )
& ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum) ).
thf(204,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)],[20]) ).
thf(357,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ member ) )
!= ( on @ ( B @ difference ) @ ( sk2 @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,282]) ).
thf(358,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ member ) )
!= ( on @ ( B @ difference ) @ ( sk2 @ member ) ) ),
inference(simp,[status(thm)],[357]) ).
thf(376,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= ( on @ ( B @ difference ) ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[358]) ).
thf(382,plain,
! [A: $i] :
( ( on @ ( A @ difference ) )
!= ( sk2 @ singleton ) ),
inference(simp,[status(thm)],[376]) ).
thf(293,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ member ) )
!= ( sk2 @ ( B @ difference ) @ ( sk1 @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,280]) ).
thf(294,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ member ) )
!= ( sk2 @ ( B @ difference ) @ ( sk1 @ member ) ) ),
inference(simp,[status(thm)],[293]) ).
thf(308,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= ( sk2 @ ( B @ difference ) ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[294]) ).
thf(313,plain,
! [A: $i] :
( ( sk2 @ ( A @ difference ) )
!= ( sk1 @ singleton ) ),
inference(simp,[status(thm)],[308]) ).
thf(233,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ member ) )
!= ( empty_set @ ( B @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,162]) ).
thf(234,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ member ) )
!= ( empty_set @ ( B @ member ) ) ),
inference(simp,[status(thm)],[233]) ).
thf(235,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= empty_set )
| ( A != B ) ),
inference(simp,[status(thm)],[234]) ).
thf(236,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(simp,[status(thm)],[235]) ).
thf(383,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ member ) )
!= ( sk1 @ ( B @ difference ) @ ( sk2 @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,292]) ).
thf(384,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ member ) )
!= ( sk1 @ ( B @ difference ) @ ( sk2 @ member ) ) ),
inference(simp,[status(thm)],[383]) ).
thf(397,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ ( B @ difference ) ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[384]) ).
thf(406,plain,
! [A: $i] :
( ( sk1 @ ( A @ difference ) )
!= ( sk2 @ singleton ) ),
inference(simp,[status(thm)],[397]) ).
thf(219,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ member ) )
!= ( empty_set @ ( A @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26,162]) ).
thf(220,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ member ) )
!= ( empty_set @ ( A @ member ) ) ),
inference(simp,[status(thm)],[219]) ).
thf(226,plain,
! [A: $i] :
( ( sk2 != empty_set )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[220]) ).
thf(230,plain,
sk2 != empty_set,
inference(simp,[status(thm)],[226]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ strict_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,D: $i] :
( ( ( B @ ( D @ member ) )
& ( B @ ( C @ member ) ) )
=> ~ ( ( C @ ( D @ ( A @ apply ) ) )
& ( D @ ( C @ ( A @ apply ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strict_order) ).
thf(98,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,D: $i] :
( ( ( B @ ( D @ member ) )
& ( B @ ( C @ member ) ) )
=> ~ ( ( C @ ( D @ ( A @ apply ) ) )
& ( D @ ( C @ ( A @ apply ) ) ) ) ) )
=> ( B @ ( A @ strict_order ) ) )
& ( ( B @ ( A @ strict_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,D: $i] :
( ( ( B @ ( D @ member ) )
& ( B @ ( C @ member ) ) )
=> ~ ( ( C @ ( D @ ( A @ apply ) ) )
& ( D @ ( C @ ( A @ apply ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(335,plain,
! [A: $i] :
( ( ( on @ ( A @ difference ) @ ( sk1 @ member ) )
!= ( sk2 @ ( sk1 @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26,281]) ).
thf(336,plain,
! [A: $i] :
( ( on @ ( A @ difference ) @ ( sk1 @ member ) )
!= ( sk2 @ ( sk1 @ member ) ) ),
inference(simp,[status(thm)],[335]) ).
thf(350,plain,
! [A: $i] :
( ( ( on @ ( A @ difference ) )
!= sk2 )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[336]) ).
thf(355,plain,
! [A: $i] :
( ( on @ ( A @ difference ) )
!= sk2 ),
inference(simp,[status(thm)],[350]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ initial_segment ) ) @ ( D @ member ) )
<=> ( ( A @ ( D @ ( B @ apply ) ) )
& ( C @ ( D @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_segment) ).
thf(48,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( D @ ( B @ apply ) ) )
& ( C @ ( D @ member ) ) )
=> ( C @ ( B @ ( A @ initial_segment ) ) @ ( D @ member ) ) )
& ( ( C @ ( B @ ( A @ initial_segment ) ) @ ( D @ member ) )
=> ( ( A @ ( D @ ( B @ apply ) ) )
& ( C @ ( D @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(221,plain,
! [A: $i] :
( ( ( on @ ( sk1 @ member ) )
!= ( empty_set @ ( A @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,162]) ).
thf(222,plain,
! [A: $i] :
( ( on @ ( sk1 @ member ) )
!= ( empty_set @ ( A @ member ) ) ),
inference(simp,[status(thm)],[221]) ).
thf(227,plain,
! [A: $i] :
( ( empty_set != on )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[222]) ).
thf(231,plain,
empty_set != on,
inference(simp,[status(thm)],[227]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ strict_well_order ) )
<=> ( ! [C: $i] :
( ( ? [D: $i] : ( C @ ( D @ member ) )
& ( B @ ( C @ subset ) ) )
=> ? [D: $i] : ( C @ ( A @ ( D @ least ) ) ) )
& ( B @ ( A @ strict_order ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strict_well_order) ).
thf(87,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i] :
( ( ? [D: $i] : ( C @ ( D @ member ) )
& ( B @ ( C @ subset ) ) )
=> ? [D: $i] : ( C @ ( A @ ( D @ least ) ) ) )
& ( B @ ( A @ strict_order ) ) )
=> ( B @ ( A @ strict_well_order ) ) )
& ( ( B @ ( A @ strict_well_order ) )
=> ( ! [C: $i] :
( ( ? [D: $i] : ( C @ ( D @ member ) )
& ( B @ ( C @ subset ) ) )
=> ? [D: $i] : ( C @ ( A @ ( D @ least ) ) ) )
& ( B @ ( A @ strict_order ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(198,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
| ( A != C ) ),
inference(cnfConj,[status(thm)],[195]) ).
thf(202,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
| ( A != C ) ),
inference(lifteq,[status(thm)],[198]) ).
thf(203,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( B @ member ) ),
inference(simp,[status(thm)],[202]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ power_set @ ( A @ member ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_set) ).
thf(55,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)],[6]) ).
thf(389,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ difference ) @ ( sk2 @ member ) )
!= ( on @ ( sk2 @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,292]) ).
thf(390,plain,
! [A: $i] :
( ( sk1 @ ( A @ difference ) @ ( sk2 @ member ) )
!= ( on @ ( sk2 @ member ) ) ),
inference(simp,[status(thm)],[389]) ).
thf(403,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ difference ) )
!= on )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[390]) ).
thf(405,plain,
! [A: $i] :
( ( sk1 @ ( A @ difference ) )
!= on ),
inference(simp,[status(thm)],[403]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ set )
=> ! [B: $i] :
( ( A @ ( B @ member ) )
=> ( B @ set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_member) ).
thf(183,plain,
! [A: $i] :
( ( A @ set )
=> ! [B: $i] :
( ( A @ ( B @ member ) )
=> ( B @ set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(10195,plain,
$false,
inference(e,[status(thm)],[211,229,193,173,311,240,35,31,79,163,354,404,185,24,25,152,78,280,61,312,292,381,85,201,28,160,356,169,430,32,34,176,22,27,281,204,71,382,313,236,406,230,98,162,355,48,282,231,87,203,26,158,55,405,183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET810+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/5.60 % Computer : n003.cluster.edu
% 0.13/5.60 % Model : x86_64 x86_64
% 0.13/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.60 % Memory : 8046.5625MB
% 0.13/5.60 % OS : Linux 6.8.0-71-generic
% 0.13/5.60 % CPULimit : 300
% 0.13/5.60 % WCLimit : 300
% 0.13/5.60 % DateTime : Sat Sep 26 08:19:30 UTC 2026
% 0.13/5.60 % CPUTime :
% 0.13/5.60 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.93/6.19 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/6.41 % [INFO] Parsing done (213ms).
% 1.23/6.42 % [INFO] Running in sequential loop mode.
% 2.19/6.81 % [INFO] eprover registered as external prover.
% 2.19/6.82 % [INFO] Scanning for conjecture ...
% 2.37/6.92 % [INFO] Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ...
% 2.37/6.99 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 2.65/7.04 % [INFO] Problem is first-order (TPTP FOF).
% 2.65/7.05 % [INFO] Type checking passed.
% 2.65/7.05 % [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 ...
% 39.77/13.95 % External prover 'e' found a proof!
% 39.77/13.95 % [INFO] Killing All external provers ...
% 39.77/13.96 % Time passed: 8211ms (effective reasoning time: 7530ms)
% 39.77/13.96 % 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)>
% 39.77/13.96 % Axioms used in derivation (19): power_set, unordered_pair, rel_member, union, strict_well_order, intersection, set_member, initial_segment, least, subset, equal_set, singleton, ordinal_number, difference, strict_order, sum, product, successor, empty_set
% 39.77/13.96 % No. of inferences in proof: 163
% 39.77/13.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 8211 ms resp. 7530 ms w/o parsing
% 40.56/14.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 40.56/14.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------