%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU203+1 : TPTP v9.3.1. Released v3.3.0.
% 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 08:38:00 AM UTC 2026
% Result : Theorem 108.09s 38.59s
% Output : Refutation 98.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 33
% Syntax : Number of formulae : 202 ( 74 unt; 0 typ; 9 def)
% Number of atoms : 597 ( 131 equ; 0 cnn)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 1390 ( 207 ~; 166 |; 68 &; 899 @)
% ( 6 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 12 con; 0-2 aty)
% Number of variables : 270 ( 1 ^; 221 !; 39 ?; 270 :)
% ( 0 !>; 0 ?*; 0 @-; 9 @+)
% Comments :
%------------------------------------------------------------------------------
thf(relation_decl,type,
relation: $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(relation_image_decl,type,
relation_image: $i > $i > $i ).
thf(relation_dom_decl,type,
relation_dom: $i > $i ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(element_decl,type,
element: $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: $o ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( C @ relation )
=> ( ( ? [D: $i] :
( ( B @ ( D @ in ) )
& ( C @ ( A @ ( D @ ordered_pair ) @ in ) )
& ( C @ relation_dom @ ( D @ in ) ) )
=> ( B @ ( C @ relation_image ) @ ( A @ in ) ) )
& ( ( B @ ( C @ relation_image ) @ ( A @ in ) )
=> ? [D: $i] :
( ( B @ ( D @ in ) )
& ( C @ ( A @ ( D @ ordered_pair ) @ in ) )
& ( C @ relation_dom @ ( D @ in ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ relation )
=> ( ( ? [C: $i] :
( ( A @ ( C @ in ) )
& ( B @ ( sk1 @ ( C @ ordered_pair ) @ in ) )
& ( B @ relation_dom @ ( C @ in ) ) )
=> ( A @ ( B @ relation_image ) @ ( sk1 @ in ) ) )
& ( ( A @ ( B @ relation_image ) @ ( sk1 @ in ) )
=> ? [C: $i] :
( ( A @ ( C @ in ) )
& ( B @ ( sk1 @ ( C @ ordered_pair ) @ in ) )
& ( B @ relation_dom @ ( C @ in ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( A @ relation )
=> ( ( ? [B: $i] :
( ( sk2 @ ( B @ in ) )
& ( A @ ( sk1 @ ( B @ ordered_pair ) @ in ) )
& ( A @ relation_dom @ ( B @ in ) ) )
=> ( sk2 @ ( A @ relation_image ) @ ( sk1 @ in ) ) )
& ( ( sk2 @ ( A @ relation_image ) @ ( sk1 @ in ) )
=> ? [B: $i] :
( ( sk2 @ ( B @ in ) )
& ( A @ ( sk1 @ ( B @ ordered_pair ) @ in ) )
& ( A @ relation_dom @ ( B @ in ) ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
( ( sk2 @ ( A @ in ) )
& ( sk3 @ ( sk1 @ ( A @ ordered_pair ) @ in ) )
& ( sk3 @ relation_dom @ ( A @ in ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ element ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
( ( A @ relation )
& ( A @ empty ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ) ) ) ).
thf(7,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(47,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(54,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(55,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ unordered_pair ) @ empty ),
inference(miniscope,[status(thm)],[54]) ).
thf(56,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
inference(cnf,[status(esa)],[55]) ).
thf(739,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,56]) ).
thf(740,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[739]) ).
thf(741,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[740]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ relation_image ) @ ( A @ in ) )
<=> ? [D: $i] :
( ( B @ ( D @ in ) )
& ( C @ ( A @ ( D @ ordered_pair ) @ in ) )
& ( C @ relation_dom @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ relation_image ) @ ( A @ in ) )
<=> ? [D: $i] :
( ( B @ ( D @ in ) )
& ( C @ ( A @ ( D @ ordered_pair ) @ in ) )
& ( C @ relation_dom @ ( D @ in ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(26,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( ? [D: $i] :
( ( B @ ( D @ in ) )
& ( C @ ( A @ ( D @ ordered_pair ) @ in ) )
& ( C @ relation_dom @ ( D @ in ) ) )
=> ( B @ ( C @ relation_image ) @ ( A @ in ) ) )
& ( ( B @ ( C @ relation_image ) @ ( A @ in ) )
=> ? [D: $i] :
( ( B @ ( D @ in ) )
& ( C @ ( A @ ( D @ ordered_pair ) @ in ) )
& ( C @ relation_dom @ ( D @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(27,plain,
! [A: $i] :
( ( ~ ( sk2 @ ( sk3 @ relation_image ) @ ( sk1 @ in ) )
| sk4 )
& ( ( sk2 @ ( sk5 @ in ) )
| sk4 )
& ( ( sk3 @ ( sk1 @ ( sk5 @ ordered_pair ) @ in ) )
| sk4 )
& ( ( sk3 @ relation_dom @ ( sk5 @ in ) )
| sk4 )
& ( ~ sk4
| ~ ( sk2 @ ( A @ in ) )
| ~ ( sk3 @ ( sk1 @ ( A @ ordered_pair ) @ in ) )
| ~ ( sk3 @ relation_dom @ ( A @ in ) ) )
& ( ~ sk4
| ( sk2 @ ( sk3 @ relation_image ) @ ( sk1 @ in ) ) )
& ( sk3 @ relation ) ),
inference(cnf,[status(esa)],[26]) ).
thf(31,plain,
( ( sk3 @ relation_dom @ ( sk5 @ in ) )
| sk4 ),
inference(cnfConj,[status(thm)],[27]) ).
thf(32,plain,
( ~ ( sk2 @ ( sk3 @ relation_image ) @ ( sk1 @ in ) )
| sk4 ),
inference(cnfConj,[status(thm)],[27]) ).
thf(192,plain,
( ( ( sk3 @ relation_dom @ ( sk5 @ in ) )
!= ( sk2 @ ( sk3 @ relation_image ) @ ( sk1 @ in ) ) )
| ~ $true
| sk4
| sk4 ),
inference(paramod_ordered,[status(thm)],[31,32]) ).
thf(193,plain,
( ( ( sk3 @ relation_dom @ ( sk5 @ in ) )
!= ( sk2 @ ( sk3 @ relation_image ) @ ( sk1 @ in ) ) )
| sk4 ),
inference(simp,[status(thm)],[192]) ).
thf(196,plain,
( ( ( sk2 @ ( sk3 @ relation_image ) )
!= ( sk3 @ relation_dom ) )
| ( sk5 != sk1 )
| sk4 ),
inference(simp,[status(thm)],[193]) ).
thf(5,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(41,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(59,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ element ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[59]) ).
thf(919,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ relation_dom @ ( sk5 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| sk4 ),
inference(paramod_ordered,[status(thm)],[31,60]) ).
thf(920,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ relation_dom @ ( sk5 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| sk4 ),
inference(simp,[status(thm)],[919]) ).
thf(921,plain,
( ( sk3 @ relation_dom @ ( sk5 @ element ) )
| sk4 ),
inference(pattern_uni,[status(thm)],[920:[bind(A,$thf( sk5 )),bind(B,$thf( sk3 @ relation_dom ))]]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(48,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(83,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(69,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(49,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[48]) ).
thf(50,plain,
! [A: $i] :
( ~ ( A @ empty )
| ( A = empty_set ) ),
inference(lifteq,[status(thm)],[49]) ).
thf(30,plain,
( ( sk2 @ ( sk5 @ in ) )
| sk4 ),
inference(cnfConj,[status(thm)],[27]) ).
thf(537,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk2 @ ( empty_set @ in ) )
| sk4
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[50,30]) ).
thf(538,plain,
( ( sk2 @ ( empty_set @ in ) )
| sk4
| ~ ( sk5 @ empty ) ),
inference(pattern_uni,[status(thm)],[537:[bind(A,$thf( sk5 ))]]) ).
thf(907,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( empty_set @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| sk4
| ~ ( sk5 @ empty ) ),
inference(paramod_ordered,[status(thm)],[538,60]) ).
thf(908,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( empty_set @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| sk4
| ~ ( sk5 @ empty ) ),
inference(simp,[status(thm)],[907]) ).
thf(909,plain,
( ( sk2 @ ( empty_set @ element ) )
| sk4
| ~ ( sk5 @ empty ) ),
inference(pattern_uni,[status(thm)],[908:[bind(A,$thf( empty_set )),bind(B,$thf( sk2 ))]]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(85,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(86,plain,
! [A: $i] :
( ( ( A @ relation_dom @ relation )
| ~ ( A @ empty ) )
& ( ( A @ relation_dom @ empty )
| ~ ( A @ empty ) ) ),
inference(cnf,[status(esa)],[85]) ).
thf(88,plain,
! [A: $i] :
( ( A @ relation_dom @ relation )
| ~ ( A @ empty ) ),
inference(cnfConj,[status(thm)],[86]) ).
thf(14,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(65,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(66,plain,
( ( sk10 @ relation )
& ~ ( sk10 @ empty ) ),
inference(cnf,[status(esa)],[65]) ).
thf(67,plain,
~ ( sk10 @ empty ),
inference(cnfConj,[status(thm)],[66]) ).
thf(150,plain,
( ( ( sk10 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,67]) ).
thf(151,plain,
( ( sk10 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[150]) ).
thf(153,plain,
sk10 != empty_set,
inference(simp,[status(thm)],[151]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(80,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
inference(cnf,[status(esa)],[80]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) )
= ( B @ ( A @ ordered_pair ) ) ),
inference(lifteq,[status(thm)],[81]) ).
thf(777,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) )
!= ( D @ ( C @ unordered_pair ) ) )
| ( ( B @ ( A @ ordered_pair ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[82,741]) ).
thf(778,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[777:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F @ ( G @ unordered_pair ) )),bind(D,$thf( G @ singleton ))]]) ).
thf(817,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[778]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(51,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(cnf,[status(esa)],[51]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(lifteq,[status(thm)],[52]) ).
thf(797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( D @ ( C @ unordered_pair ) ) )
| ( ( C @ singleton @ ( A @ ( B @ unordered_pair ) @ unordered_pair ) )
= ( D @ ( C @ ordered_pair ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,82]) ).
thf(798,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ ( B @ unordered_pair ) @ unordered_pair ) )
= ( B @ ( A @ ordered_pair ) ) ),
inference(pattern_uni,[status(thm)],[797:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1059,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ ( B @ unordered_pair ) @ unordered_pair ) )
!= ( D @ ( C @ unordered_pair ) ) )
| ( ( B @ ( A @ ordered_pair ) )
= ( C @ ( D @ unordered_pair ) ) ) ),
inference(paramod_ordered,[status(thm)],[798,53]) ).
thf(1060,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ singleton @ unordered_pair ) )
= ( A @ ( B @ ordered_pair ) ) ),
inference(pattern_uni,[status(thm)],[1059:[bind(A,$thf( G )),bind(B,$thf( E )),bind(C,$thf( G @ ( E @ unordered_pair ) )),bind(D,$thf( G @ singleton ))]]) ).
thf(1087,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ singleton @ unordered_pair ) )
= ( A @ ( B @ ordered_pair ) ) ),
inference(simp,[status(thm)],[1060]) ).
thf(6,axiom,
! [A: $i] :
~ ( A @ singleton @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(44,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(45,plain,
~ ? [A: $i] : ( A @ singleton @ empty ),
inference(miniscope,[status(thm)],[44]) ).
thf(46,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(cnf,[status(esa)],[45]) ).
thf(11,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(57,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(78,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(29,plain,
( ( sk3 @ ( sk1 @ ( sk5 @ ordered_pair ) @ in ) )
| sk4 ),
inference(cnfConj,[status(thm)],[27]) ).
thf(25,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(139,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(140,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ ordered_pair ) @ empty ),
inference(miniscope,[status(thm)],[139]) ).
thf(141,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
inference(cnf,[status(esa)],[140]) ).
thf(754,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ordered_pair ) @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,141]) ).
thf(755,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[754]) ).
thf(756,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[755]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[83]) ).
thf(765,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( D @ ( C @ unordered_pair ) ) )
| ( ( A @ ( B @ unordered_pair ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[53,741]) ).
thf(766,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[765:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(42,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[41]) ).
thf(43,plain,
~ ( sk7 @ empty ),
inference(cnf,[status(esa)],[42]) ).
thf(145,plain,
( ( ( sk7 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,43]) ).
thf(146,plain,
( ( sk7 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[145]) ).
thf(147,plain,
sk7 != empty_set,
inference(simp,[status(thm)],[146]) ).
thf(13,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(61,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ relation_image ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( D @ ( E @ ordered_pair ) @ in ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
thf(89,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( D @ ( E @ ordered_pair ) @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( D @ ( E @ ordered_pair ) @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_image ) ) ) )
& ( ( C
= ( B @ ( A @ relation_image ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( D @ ( E @ ordered_pair ) @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ( B @ ( E @ in ) )
& ( A @ ( D @ ( E @ ordered_pair ) @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B
= ( A @ relation_dom ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
thf(116,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) ) ) )
=> ( B
= ( A @ relation_dom ) ) )
& ( ( B
= ( A @ relation_dom ) )
=> ! [C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(16,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(71,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(72,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(cnf,[status(esa)],[71]) ).
thf(74,plain,
empty_set @ relation,
inference(cnfConj,[status(thm)],[72]) ).
thf(539,plain,
! [A: $i] :
( ( A != sk2 )
| ( empty_set @ ( sk5 @ in ) )
| sk4
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[50,30]) ).
thf(540,plain,
( ( empty_set @ ( sk5 @ in ) )
| sk4
| ~ ( sk2 @ empty ) ),
inference(pattern_uni,[status(thm)],[539:[bind(A,$thf( sk2 ))]]) ).
thf(859,plain,
( ( ( sk2 @ empty )
!= ( empty_set @ empty ) )
| ( empty_set @ ( sk5 @ in ) )
| sk4
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,540]) ).
thf(860,plain,
( ( ( sk2 @ empty )
!= ( empty_set @ empty ) )
| ( empty_set @ ( sk5 @ in ) )
| sk4 ),
inference(simp,[status(thm)],[859]) ).
thf(861,plain,
( ( sk2 != empty_set )
| ( empty_set @ ( sk5 @ in ) )
| sk4 ),
inference(simp,[status(thm)],[860]) ).
thf(17,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(75,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(76,plain,
~ ? [A: $i,B: $i] :
( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(miniscope,[status(thm)],[75]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[76]) ).
thf(1217,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ empty )
!= ( B @ empty ) )
| ~ $true
| ~ ( B @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[47,77]) ).
thf(1218,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ empty )
!= ( B @ empty ) )
| ~ ( B @ ( A @ in ) ) ),
inference(simp,[status(thm)],[1217]) ).
thf(1219,plain,
! [A: $i] :
~ ( empty_set @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[1218:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).
thf(1222,plain,
( ( sk2 != empty_set )
| $false
| sk4 ),
inference(rewrite,[status(thm)],[861,1219]) ).
thf(1223,plain,
( ( sk2 != empty_set )
| sk4 ),
inference(simp,[status(thm)],[1222]) ).
thf(70,plain,
! [A: $i] :
( ( A @ relation )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[69]) ).
thf(24,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(137,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(33,plain,
( ~ sk4
| ( sk2 @ ( sk3 @ relation_image ) @ ( sk1 @ in ) ) ),
inference(cnfConj,[status(thm)],[27]) ).
thf(28,plain,
! [A: $i] :
( ~ sk4
| ~ ( sk2 @ ( A @ in ) )
| ~ ( sk3 @ ( sk1 @ ( A @ ordered_pair ) @ in ) )
| ~ ( sk3 @ relation_dom @ ( A @ in ) ) ),
inference(cnfConj,[status(thm)],[27]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(35,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(36,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ( B @ empty )
& ( A != B ) )
& ( A @ empty ) ),
inference(miniscope,[status(thm)],[35]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ( A = B )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[36]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( A @ empty )
| ( A = B ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(1208,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ relation_image ) @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ empty )
| ~ $true
| ~ sk4 ),
inference(paramod_ordered,[status(thm)],[33,77]) ).
thf(1209,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ relation_image ) @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ empty )
| ~ sk4 ),
inference(simp,[status(thm)],[1208]) ).
thf(1210,plain,
( ~ ( sk2 @ ( sk3 @ relation_image ) @ empty )
| ~ sk4 ),
inference(pattern_uni,[status(thm)],[1209:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 @ ( sk3 @ relation_image ) ))]]) ).
thf(1205,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ ( sk5 @ ordered_pair ) @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ empty )
| ~ $true
| sk4 ),
inference(paramod_ordered,[status(thm)],[29,77]) ).
thf(1206,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ ( sk5 @ ordered_pair ) @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ empty )
| sk4 ),
inference(simp,[status(thm)],[1205]) ).
thf(1207,plain,
( ~ ( sk3 @ empty )
| sk4 ),
inference(pattern_uni,[status(thm)],[1206:[bind(A,$thf( sk1 @ ( sk5 @ ordered_pair ) )),bind(B,$thf( sk3 ))]]) ).
thf(904,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk5 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| sk4 ),
inference(paramod_ordered,[status(thm)],[30,60]) ).
thf(905,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk5 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| sk4 ),
inference(simp,[status(thm)],[904]) ).
thf(906,plain,
( ( sk2 @ ( sk5 @ element ) )
| sk4 ),
inference(pattern_uni,[status(thm)],[905:[bind(A,$thf( sk5 )),bind(B,$thf( sk2 ))]]) ).
thf(1228,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ ( sk5 @ ordered_pair ) @ in ) )
!= ( empty_set @ ( A @ in ) ) )
| ~ $true
| sk4 ),
inference(paramod_ordered,[status(thm)],[29,1219]) ).
thf(1229,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ ( sk5 @ ordered_pair ) @ in ) )
!= ( empty_set @ ( A @ in ) ) )
| sk4 ),
inference(simp,[status(thm)],[1228]) ).
thf(1249,plain,
! [A: $i] :
( ( sk3 != empty_set )
| ( ( sk1 @ ( sk5 @ ordered_pair ) )
!= A )
| sk4 ),
inference(simp,[status(thm)],[1229]) ).
thf(1251,plain,
( ( sk3 != empty_set )
| sk4 ),
inference(simp,[status(thm)],[1249]) ).
thf(34,plain,
sk3 @ relation,
inference(cnfConj,[status(thm)],[27]) ).
thf(1522,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ ( A @ in ) ) ),
inference(eqfactor_ordered,[status(thm)],[84]) ).
thf(1523,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[1522:[bind(A,$thf( B ))]]) ).
thf(1524,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(simp,[status(thm)],[1523]) ).
thf(4,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(39,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(910,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ ( sk5 @ ordered_pair ) @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| sk4 ),
inference(paramod_ordered,[status(thm)],[29,60]) ).
thf(911,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ ( sk5 @ ordered_pair ) @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| sk4 ),
inference(simp,[status(thm)],[910]) ).
thf(912,plain,
( ( sk3 @ ( sk1 @ ( sk5 @ ordered_pair ) @ element ) )
| sk4 ),
inference(pattern_uni,[status(thm)],[911:[bind(A,$thf( sk1 @ ( sk5 @ ordered_pair ) )),bind(B,$thf( sk3 ))]]) ).
thf(1196,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk5 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ empty )
| ~ $true
| sk4 ),
inference(paramod_ordered,[status(thm)],[30,77]) ).
thf(1197,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk5 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ empty )
| sk4 ),
inference(simp,[status(thm)],[1196]) ).
thf(1198,plain,
( ~ ( sk2 @ empty )
| sk4 ),
inference(pattern_uni,[status(thm)],[1197:[bind(A,$thf( sk5 )),bind(B,$thf( sk2 ))]]) ).
thf(720,plain,
( ( ( sk5 @ empty )
!= ( empty_set @ empty ) )
| ( sk2 @ ( empty_set @ in ) )
| sk4
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,538]) ).
thf(721,plain,
( ( ( sk5 @ empty )
!= ( empty_set @ empty ) )
| ( sk2 @ ( empty_set @ in ) )
| sk4 ),
inference(simp,[status(thm)],[720]) ).
thf(722,plain,
( ( sk5 != empty_set )
| ( sk2 @ ( empty_set @ in ) )
| sk4 ),
inference(simp,[status(thm)],[721]) ).
thf(188,plain,
( ( ( sk2 @ ( sk5 @ in ) )
!= ( sk2 @ ( sk3 @ relation_image ) @ ( sk1 @ in ) ) )
| ~ $true
| sk4
| sk4 ),
inference(paramod_ordered,[status(thm)],[30,32]) ).
thf(189,plain,
( ( ( sk2 @ ( sk5 @ in ) )
!= ( sk2 @ ( sk3 @ relation_image ) @ ( sk1 @ in ) ) )
| sk4 ),
inference(simp,[status(thm)],[188]) ).
thf(194,plain,
( ( ( sk2 @ ( sk3 @ relation_image ) )
!= sk2 )
| ( sk5 != sk1 )
| sk4 ),
inference(simp,[status(thm)],[189]) ).
thf(1525,plain,
! [A: $i] :
( ( ( sk2 @ ( sk5 @ in ) )
!= ( A @ ( A @ in ) ) )
| ~ $true
| sk4 ),
inference(paramod_ordered,[status(thm)],[30,1524]) ).
thf(1526,plain,
! [A: $i] :
( ( ( sk2 @ ( sk5 @ in ) )
!= ( A @ ( A @ in ) ) )
| sk4 ),
inference(simp,[status(thm)],[1525]) ).
thf(1537,plain,
! [A: $i] :
( ( sk2 != A )
| ( sk5 != A )
| sk4 ),
inference(simp,[status(thm)],[1526]) ).
thf(1543,plain,
( ( sk5 != sk2 )
| sk4 ),
inference(simp,[status(thm)],[1537]) ).
thf(87,plain,
! [A: $i] :
( ( A @ relation_dom @ empty )
| ~ ( A @ empty ) ),
inference(cnfConj,[status(thm)],[86]) ).
thf(1615,plain,
! [A: $i] :
( ( ( empty_set @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,87]) ).
thf(1616,plain,
! [A: $i] :
( ( ( empty_set @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty ) ),
inference(simp,[status(thm)],[1615]) ).
thf(1617,plain,
empty_set @ relation_dom @ empty,
inference(pattern_uni,[status(thm)],[1616:[bind(A,$thf( empty_set ))]]) ).
thf(1668,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[1617,50]) ).
thf(1669,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[1668]) ).
thf(1670,plain,
( ( empty_set @ relation_dom )
= empty_set ),
inference(pattern_uni,[status(thm)],[1669:[bind(A,$thf( empty_set @ relation_dom ))]]) ).
thf(40,plain,
sk6 @ empty,
inference(cnf,[status(esa)],[39]) ).
thf(610,plain,
! [A: $i] :
( ( ( sk6 @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[40,50]) ).
thf(611,plain,
! [A: $i] :
( ( ( sk6 @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[610]) ).
thf(612,plain,
sk6 = empty_set,
inference(pattern_uni,[status(thm)],[611:[bind(A,$thf( sk6 ))]]) ).
thf(448,plain,
! [A: $i] :
( ( ( A @ singleton @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,46]) ).
thf(449,plain,
! [A: $i] :
( ( A @ singleton @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[448]) ).
thf(450,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(simp,[status(thm)],[449]) ).
thf(1214,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ relation_dom @ ( sk5 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ empty )
| ~ $true
| sk4 ),
inference(paramod_ordered,[status(thm)],[31,77]) ).
thf(1215,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ relation_dom @ ( sk5 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ empty )
| sk4 ),
inference(simp,[status(thm)],[1214]) ).
thf(1216,plain,
( ~ ( sk3 @ relation_dom @ empty )
| sk4 ),
inference(pattern_uni,[status(thm)],[1215:[bind(A,$thf( sk5 )),bind(B,$thf( sk3 @ relation_dom ))]]) ).
thf(799,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( C @ singleton @ ( D @ ( C @ unordered_pair ) @ unordered_pair ) ) )
| ( ( A @ ( B @ unordered_pair ) )
= ( D @ ( C @ ordered_pair ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,82]) ).
thf(800,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) @ ( B @ singleton @ unordered_pair ) )
= ( A @ ( B @ ordered_pair ) ) ),
inference(pattern_uni,[status(thm)],[799:[bind(A,$thf( F @ ( G @ unordered_pair ) )),bind(B,$thf( G @ singleton )),bind(C,$thf( G )),bind(D,$thf( F ))]]) ).
thf(813,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) @ ( B @ singleton @ unordered_pair ) )
= ( A @ ( B @ ordered_pair ) ) ),
inference(simp,[status(thm)],[800]) ).
thf(58,plain,
! [A: $i] : ( A @ ( A @ sk8 @ element ) ),
inference(cnf,[status(esa)],[57]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ in ) )
| ( B @ empty )
| ~ ( B @ ( A @ element ) ) ),
inference(cnf,[status(esa)],[78]) ).
thf(62,plain,
( ( sk9 @ relation )
& ( sk9 @ empty ) ),
inference(cnf,[status(esa)],[61]) ).
thf(63,plain,
sk9 @ empty,
inference(cnfConj,[status(thm)],[62]) ).
thf(530,plain,
! [A: $i] :
( ( ( sk9 @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[63,50]) ).
thf(531,plain,
! [A: $i] :
( ( ( sk9 @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[530]) ).
thf(532,plain,
sk9 = empty_set,
inference(pattern_uni,[status(thm)],[531:[bind(A,$thf( sk9 ))]]) ).
thf(1681,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1617,87]) ).
thf(1682,plain,
! [A: $i] :
( ( ( empty_set @ relation_dom @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty ) ),
inference(simp,[status(thm)],[1681]) ).
thf(1683,plain,
empty_set @ relation_dom @ relation_dom @ empty,
inference(pattern_uni,[status(thm)],[1682:[bind(A,$thf( empty_set @ relation_dom ))]]) ).
thf(1742,plain,
empty_set @ relation_dom @ empty,
inference(rewrite,[status(thm)],[1683,1670]) ).
thf(68,plain,
sk10 @ relation,
inference(cnfConj,[status(thm)],[66]) ).
thf(50258,plain,
$false,
inference(e,[status(thm)],[741,196,41,921,48,83,69,909,88,56,538,153,817,1087,46,57,78,29,756,84,766,147,61,89,116,74,60,85,798,1223,70,137,33,28,38,65,1210,53,141,77,1207,906,1251,1219,32,34,44,59,71,54,1524,39,912,1198,80,35,722,194,50,67,31,1543,1670,612,43,450,87,1216,813,26,139,75,58,82,30,51,79,532,1742,47,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU203+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % 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
% 0.13/10.62 % Computer : n006.cluster.edu
% 0.13/10.62 % Model : x86_64 x86_64
% 0.13/10.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.62 % Memory : 8046.5625MB
% 0.13/10.62 % OS : Linux 6.8.0-71-generic
% 0.13/10.62 % CPULimit : 300
% 0.13/10.62 % WCLimit : 300
% 0.13/10.62 % DateTime : Sat Sep 26 08:48:50 UTC 2026
% 0.13/10.63 % CPUTime :
% 0.13/10.63 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
% 0.94/11.22 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/11.42 % [INFO] Parsing done (199ms).
% 1.27/11.43 % [INFO] Running in sequential loop mode.
% 1.90/11.83 % [INFO] eprover registered as external prover.
% 1.90/11.84 % [INFO] Scanning for conjecture ...
% 2.09/11.95 % [INFO] Found a conjecture (or negated_conjecture) and 30 axioms. Running axiom selection ...
% 2.09/12.02 % [INFO] Axiom selection finished. Selected 23 axioms (removed 7 axioms).
% 2.31/12.06 % [INFO] Problem is first-order (TPTP FOF).
% 2.31/12.07 % [INFO] Type checking passed.
% 2.31/12.07 % [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 ...
% 108.09/38.58 % External prover 'e' found a proof!
% 108.09/38.58 % [INFO] Killing All external provers ...
% 108.09/38.59 % Time passed: 27814ms (effective reasoning time: 27149ms)
% 108.09/38.59 % 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)>
% 108.09/38.59 % Axioms used in derivation (23): fc1_zfmisc_1, cc1_relat_1, fc3_subset_1, t7_boole, fc5_relat_1, rc2_relat_1, rc1_relat_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, d5_tarski, fc4_relat_1, t1_subset, d13_relat_1, t6_boole, d4_relat_1, fc2_subset_1, existence_m1_subset_1, commutativity_k2_tarski, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1
% 108.09/38.59 % No. of inferences in proof: 193
% 108.09/38.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 27814 ms resp. 27149 ms w/o parsing
% 98.96/38.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 98.96/38.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------