%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU192+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n014.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 08:37:58 AM UTC 2026
% Result : Theorem 87.84s 18.59s
% Output : Refutation 74.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 41
% Syntax : Number of formulae : 320 ( 82 unt; 0 typ; 16 def)
% Number of atoms : 1202 ( 272 equ; 0 cnn)
% Maximal formula atoms : 42 ( 3 avg)
% Number of connectives : 4078 ( 543 ~; 589 |; 80 &;2791 @)
% ( 6 <=>; 69 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 11 con; 0-3 aty)
% Number of variables : 515 ( 22 ^; 449 !; 28 ?; 515 :)
% ( 0 !>; 0 ?*; 0 @-; 16 @+)
% Comments :
%------------------------------------------------------------------------------
thf(relation_decl,type,
relation: $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(relation_dom_decl,type,
relation_dom: $i > $i ).
thf(relation_dom_restriction_decl,type,
relation_dom_restriction: $i > $i > $i ).
thf(unordered_pair_decl,type,
unordered_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(ordered_pair_decl,type,
ordered_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 > $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i > $i > $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i > $i > $o ).
thf(sk14_decl,type,
sk14: $i > $i > $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i > $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i > $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i > $i > $i ).
thf(sk18_decl,type,
sk18: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( C @ relation )
=> ( ( ( ( C @ relation_dom @ ( A @ in ) )
& ( B @ ( A @ in ) ) )
=> ( B @ ( C @ relation_dom_restriction ) @ relation_dom @ ( A @ in ) ) )
& ( ( B @ ( C @ relation_dom_restriction ) @ relation_dom @ ( A @ in ) )
=> ( ( C @ relation_dom @ ( A @ in ) )
& ( B @ ( A @ in ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ relation )
=> ( ( ( ( B @ relation_dom @ ( sk1 @ in ) )
& ( A @ ( sk1 @ in ) ) )
=> ( A @ ( B @ relation_dom_restriction ) @ relation_dom @ ( sk1 @ in ) ) )
& ( ( A @ ( B @ relation_dom_restriction ) @ relation_dom @ ( sk1 @ in ) )
=> ( ( B @ relation_dom @ ( sk1 @ in ) )
& ( A @ ( sk1 @ in ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( A @ relation )
=> ( ( ( ( A @ relation_dom @ ( sk1 @ in ) )
& ( sk2 @ ( sk1 @ in ) ) )
=> ( sk2 @ ( A @ relation_dom_restriction ) @ relation_dom @ ( sk1 @ in ) ) )
& ( ( sk2 @ ( A @ relation_dom_restriction ) @ relation_dom @ ( sk1 @ in ) )
=> ( ( A @ relation_dom @ ( sk1 @ in ) )
& ( sk2 @ ( sk1 @ in ) ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ element ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
( ( A @ relation )
& ( A @ empty ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] : ( C @ ( D @ ( A @ ordered_pair ) @ in ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ? [D: $i] : ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ? [D: $i] : ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( B @ ( C @ ( B @ ( A @ sk11 ) @ ordered_pair ) @ in ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ! [E: $i] :
( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( A @ ( D @ ( C @ ( B @ ( A @ sk14 ) ) @ ordered_pair ) @ in ) )
=> ( ( C @ ( D @ ( C @ ( B @ ( A @ sk14 ) ) @ ordered_pair ) @ in ) )
& ( B @ ( C @ ( B @ ( A @ sk14 ) ) @ in ) ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ! [E: $i] :
( ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) )
=> ( A @ ( E @ ( D @ ordered_pair ) @ in ) ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( C @ ( D @ ( C @ ( B @ ( A @ sk16 ) ) @ ordered_pair ) @ in ) )
& ( B @ ( C @ ( B @ ( A @ sk16 ) ) @ in ) ) )
=> ( A @ ( D @ ( C @ ( B @ ( A @ sk16 ) ) @ ordered_pair ) @ in ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( @+[A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ relation_dom_restriction ) @ relation_dom @ ( A @ in ) )
<=> ( ( C @ relation_dom @ ( A @ in ) )
& ( B @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ relation_dom_restriction ) @ relation_dom @ ( A @ in ) )
<=> ( ( C @ relation_dom @ ( A @ in ) )
& ( B @ ( A @ in ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(27,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( ( ( C @ relation_dom @ ( A @ in ) )
& ( B @ ( A @ in ) ) )
=> ( B @ ( C @ relation_dom_restriction ) @ relation_dom @ ( A @ in ) ) )
& ( ( B @ ( C @ relation_dom_restriction ) @ relation_dom @ ( A @ in ) )
=> ( ( C @ relation_dom @ ( A @ in ) )
& ( B @ ( A @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28,plain,
( ( ~ ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom @ ( sk1 @ in ) )
| sk4 )
& ( ( sk3 @ relation_dom @ ( sk1 @ in ) )
| sk4 )
& ( ( sk2 @ ( sk1 @ in ) )
| sk4 )
& ( ~ sk4
| ~ ( sk3 @ relation_dom @ ( sk1 @ in ) )
| ~ ( sk2 @ ( sk1 @ in ) ) )
& ( ~ sk4
| ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom @ ( sk1 @ in ) ) )
& ( sk3 @ relation ) ),
inference(cnf,[status(esa)],[27]) ).
thf(34,plain,
( ~ sk4
| ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom @ ( sk1 @ in ) ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(33,plain,
( ~ sk4
| ~ ( sk3 @ relation_dom @ ( sk1 @ in ) )
| ~ ( sk2 @ ( sk1 @ in ) ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(184,plain,
( ~ $true
| ( ( sk3 @ relation_dom @ ( sk1 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ~ sk4
| ~ ( sk2 @ ( sk1 @ in ) ) ),
inference(eqfactor_ordered,[status(thm)],[33]) ).
thf(186,plain,
( ( ( sk3 @ relation_dom )
!= sk2 )
| ( sk1 != sk1 )
| ~ sk4
| ~ ( sk2 @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(189,plain,
( ( ( sk3 @ relation_dom )
!= sk2 )
| ~ sk4
| ~ ( sk2 @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[186]) ).
thf(204,plain,
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom @ ( sk1 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ( ( sk3 @ relation_dom )
!= sk2 )
| ~ sk4
| ~ $true
| ~ sk4 ),
inference(paramod_ordered,[status(thm)],[34,189]) ).
thf(205,plain,
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom @ ( sk1 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ( ( sk3 @ relation_dom )
!= sk2 )
| ~ sk4 ),
inference(simp,[status(thm)],[204]) ).
thf(208,plain,
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom )
!= sk2 )
| ( sk1 != sk1 )
| ( ( sk3 @ relation_dom )
!= sk2 )
| ~ sk4 ),
inference(simp,[status(thm)],[205]) ).
thf(209,plain,
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom )
!= sk2 )
| ( ( sk3 @ relation_dom )
!= sk2 )
| ~ sk4 ),
inference(simp,[status(thm)],[208]) ).
thf(9769,plain,
( ( sk2 != sk2 )
| ( ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom )
!= ( sk3 @ relation_dom ) )
| ( ( sk3 @ relation_dom )
!= sk2 )
| ~ sk4 ),
inference(eqfactor_ordered,[status(thm)],[209]) ).
thf(9771,plain,
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) )
!= sk3 )
| ( ( sk3 @ relation_dom )
!= sk2 )
| ~ sk4 ),
inference(simp,[status(thm)],[9769]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(35,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(5,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(42,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(43,plain,
sk5 @ empty,
inference(cnf,[status(esa)],[42]) ).
thf(13,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(62,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(63,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ ordered_pair ) @ empty ),
inference(miniscope,[status(thm)],[62]) ).
thf(64,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
inference(cnf,[status(esa)],[63]) ).
thf(569,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ordered_pair ) @ empty )
!= ( sk5 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,64]) ).
thf(570,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) @ empty )
!= ( sk5 @ empty ) ),
inference(simp,[status(thm)],[569]) ).
thf(573,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) )
!= sk5 ),
inference(simp,[status(thm)],[570]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(51,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)],[9]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
inference(cnf,[status(esa)],[51]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
inference(lifteq,[status(thm)],[52]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(57,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(58,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[57]) ).
thf(59,plain,
! [A: $i] :
( ~ ( A @ empty )
| ( A = empty_set ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(666,plain,
! [A: $i] :
( ( ( sk5 @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[43,59]) ).
thf(667,plain,
! [A: $i] :
( ( ( sk5 @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[666]) ).
thf(668,plain,
sk5 = empty_set,
inference(pattern_uni,[status(thm)],[667:[bind(A,$thf( sk5 ))]]) ).
thf(1156,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) )
!= empty_set ),
inference(rewrite,[status(thm)],[573,53,668]) ).
thf(1157,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 ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[37,1156]) ).
thf(1158,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ ( B @ unordered_pair ) @ unordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[1157:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ unordered_pair ) )
!= ( C @ singleton @ ( C @ ( D @ unordered_pair ) @ unordered_pair ) ) )
| ( ( B @ ( A @ unordered_pair ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[37,1158]) ).
thf(1762,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ singleton @ unordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[1761:[bind(A,$thf( G @ singleton )),bind(B,$thf( G @ ( E @ unordered_pair ) )),bind(C,$thf( G )),bind(D,$thf( E ))]]) ).
thf(1797,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ singleton @ unordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[1762]) ).
thf(8,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(50,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
file('/export/starexec/sandbox/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(554,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,56]) ).
thf(555,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[554]) ).
thf(556,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[555]) ).
thf(26,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(138,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( C @ relation )
=> ( ( C
= ( B @ ( A @ relation_dom_restriction ) ) )
<=> ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
<=> ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
thf(92,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( C @ relation )
=> ( ( ! [D: $i,E: $i] :
( ( ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_dom_restriction ) ) ) )
& ( ( C
= ( B @ ( A @ relation_dom_restriction ) ) )
=> ! [D: $i,E: $i] :
( ( ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(93,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i,C: $i] :
( ( C @ relation )
=> ( ( ( ! [D: $i,E: $i] :
( ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_dom_restriction ) ) ) )
& ( ( C
= ( B @ ( A @ relation_dom_restriction ) ) )
=> ( ! [D: $i,E: $i] :
( ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[92]) ).
thf(94,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C
= ( B @ ( A @ relation_dom_restriction ) ) )
| ~ ( C @ ( A @ ( B @ ( C @ sk17 ) ) @ ( A @ ( B @ ( C @ sk16 ) ) @ ordered_pair ) @ in ) )
| ( C @ ( A @ ( B @ sk13 ) ) )
| ~ ( C @ relation )
| ~ ( A @ relation ) )
& ( ( C
= ( B @ ( A @ relation_dom_restriction ) ) )
| ( A @ ( A @ ( B @ ( C @ sk17 ) ) @ ( A @ ( B @ ( C @ sk16 ) ) @ ordered_pair ) @ in ) )
| ( C @ ( A @ ( B @ sk13 ) ) )
| ~ ( C @ relation )
| ~ ( A @ relation ) )
& ( ( C
= ( B @ ( A @ relation_dom_restriction ) ) )
| ( B @ ( A @ ( B @ ( C @ sk16 ) ) @ in ) )
| ( C @ ( A @ ( B @ sk13 ) ) )
| ~ ( C @ relation )
| ~ ( A @ relation ) )
& ( ( C
= ( B @ ( A @ relation_dom_restriction ) ) )
| ~ ( C @ ( A @ ( B @ sk13 ) ) )
| ~ ( A @ ( A @ ( B @ ( C @ sk15 ) ) @ ( A @ ( B @ ( C @ sk14 ) ) @ ordered_pair ) @ in ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk14 ) ) @ in ) )
| ~ ( C @ relation )
| ~ ( A @ relation ) )
& ( ( C
= ( B @ ( A @ relation_dom_restriction ) ) )
| ~ ( C @ ( A @ ( B @ sk13 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk15 ) ) @ ( A @ ( B @ ( C @ sk14 ) ) @ ordered_pair ) @ in ) )
| ~ ( C @ relation )
| ~ ( A @ relation ) )
& ( ( C @ ( G @ ( F @ ordered_pair ) @ in ) )
| ~ ( A @ ( G @ ( F @ ordered_pair ) @ in ) )
| ~ ( B @ ( F @ in ) )
| ( C
!= ( B @ ( A @ relation_dom_restriction ) ) )
| ~ ( C @ relation )
| ~ ( A @ relation ) )
& ( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
| ~ ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
| ( C
!= ( B @ ( A @ relation_dom_restriction ) ) )
| ~ ( C @ relation )
| ~ ( A @ relation ) )
& ( ( B @ ( D @ in ) )
| ~ ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
| ( C
!= ( B @ ( A @ relation_dom_restriction ) ) )
| ~ ( C @ relation )
| ~ ( A @ relation ) ) ),
inference(cnf,[status(esa)],[93]) ).
thf(99,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
| ~ ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
| ~ ( B @ ( D @ in ) )
| ( C
!= ( B @ ( A @ relation_dom_restriction ) ) )
| ~ ( C @ relation )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(111,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
| ~ ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
| ~ ( B @ ( D @ in ) )
| ~ ( C @ relation )
| ~ ( A @ relation )
| ( C
!= ( B @ ( A @ relation_dom_restriction ) ) ) ),
inference(lifteq,[status(thm)],[99]) ).
thf(112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ relation_dom_restriction ) @ ( D @ ( C @ ordered_pair ) @ in ) )
| ~ ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
| ~ ( B @ ( C @ in ) )
| ~ ( B @ ( A @ relation_dom_restriction ) @ relation )
| ~ ( A @ relation ) ),
inference(simp,[status(thm)],[111]) ).
thf(15838,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ relation_dom_restriction ) @ ( C @ singleton @ ( D @ ( C @ unordered_pair ) @ unordered_pair ) @ in ) )
| ~ ( A @ ( C @ singleton @ ( D @ ( C @ unordered_pair ) @ unordered_pair ) @ in ) )
| ~ ( B @ ( C @ in ) )
| ~ ( B @ ( A @ relation_dom_restriction ) @ relation )
| ~ ( A @ relation ) ),
inference(rewrite,[status(thm)],[112,53]) ).
thf(682,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( sk3 @ relation_dom )
!= sk2 )
| ~ sk4
| ~ ( sk2 @ ( empty_set @ in ) )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[59,189]) ).
thf(683,plain,
( ( ( sk3 @ relation_dom )
!= sk2 )
| ~ sk4
| ~ ( sk2 @ ( empty_set @ in ) )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[682:[bind(A,$thf( sk1 ))]]) ).
thf(20,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(120,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(121,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(cnf,[status(esa)],[120]) ).
thf(123,plain,
empty_set @ relation,
inference(cnfConj,[status(thm)],[121]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
thf(71,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)],[16]) ).
thf(72,plain,
! [A: $i] :
( ( A @ relation )
=> ( ! [B: $i] :
( ( ! [C: $i] :
( ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) ) ) )
=> ( B
= ( A @ relation_dom ) ) )
& ! [B: $i] :
( ( B
= ( A @ relation_dom ) )
=> ( ! [C: $i] :
( ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ ordered_pair ) @ in ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[71]) ).
thf(73,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( A @ relation_dom ) )
| ~ ( F @ ( A @ ( F @ sk11 ) @ in ) )
| ~ ( A @ ( G @ ( A @ ( F @ sk10 ) @ ordered_pair ) @ in ) )
| ~ ( A @ relation ) )
& ( ( F
= ( A @ relation_dom ) )
| ( A @ ( A @ ( F @ sk12 ) @ ( A @ ( F @ sk11 ) @ ordered_pair ) @ in ) )
| ~ ( A @ ( G @ ( A @ ( F @ sk10 ) @ ordered_pair ) @ in ) )
| ~ ( A @ relation ) )
& ( ( F
= ( A @ relation_dom ) )
| ~ ( F @ ( A @ ( F @ sk11 ) @ in ) )
| ( F @ ( A @ ( F @ sk10 ) @ in ) )
| ~ ( A @ relation ) )
& ( ( F
= ( A @ relation_dom ) )
| ( A @ ( A @ ( F @ sk12 ) @ ( A @ ( F @ sk11 ) @ ordered_pair ) @ in ) )
| ( F @ ( A @ ( F @ sk10 ) @ in ) )
| ~ ( A @ relation ) )
& ( ( B @ ( D @ in ) )
| ~ ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
| ( B
!= ( A @ relation_dom ) )
| ~ ( A @ relation ) )
& ( ( A @ ( A @ ( B @ ( C @ sk9 ) ) @ ( C @ ordered_pair ) @ in ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ relation_dom ) )
| ~ ( A @ relation ) ) ),
inference(cnf,[status(esa)],[72]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ relation_dom ) )
| ( A @ ( A @ ( B @ sk12 ) @ ( A @ ( B @ sk11 ) @ ordered_pair ) @ in ) )
| ( B @ ( A @ ( B @ sk10 ) @ in ) )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[73]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk12 ) @ ( A @ ( B @ sk11 ) @ ordered_pair ) @ in ) )
| ( B @ ( A @ ( B @ sk10 ) @ in ) )
| ~ ( A @ relation )
| ( B
= ( A @ relation_dom ) ) ),
inference(lifteq,[status(thm)],[79]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk12 ) @ ( A @ ( B @ sk11 ) @ ordered_pair ) @ in ) )
| ( B @ ( A @ ( B @ sk10 ) @ in ) )
| ~ ( A @ relation )
| ( B
= ( A @ relation_dom ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(835,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk11 ) @ singleton @ ( A @ ( B @ sk12 ) @ ( A @ ( B @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ( B @ ( A @ ( B @ sk10 ) @ in ) )
| ~ ( A @ relation )
| ( B
= ( A @ relation_dom ) ) ),
inference(rewrite,[status(thm)],[91,53]) ).
thf(992,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ relation )
!= ( A @ relation ) )
| ( A @ ( A @ ( B @ sk11 ) @ singleton @ ( A @ ( B @ sk12 ) @ ( A @ ( B @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ( B @ ( A @ ( B @ sk10 ) @ in ) )
| ~ $true
| ( B
= ( A @ relation_dom ) ) ),
inference(paramod_ordered,[status(thm)],[123,835]) ).
thf(993,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ relation )
!= ( A @ relation ) )
| ( A @ ( A @ ( B @ sk11 ) @ singleton @ ( A @ ( B @ sk12 ) @ ( A @ ( B @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ( B @ ( A @ ( B @ sk10 ) @ in ) )
| ( B
= ( A @ relation_dom ) ) ),
inference(simp,[status(thm)],[992]) ).
thf(994,plain,
! [A: $i] :
( ( empty_set @ ( empty_set @ ( A @ sk11 ) @ singleton @ ( empty_set @ ( A @ sk12 ) @ ( empty_set @ ( A @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ( A @ ( empty_set @ ( A @ sk10 ) @ in ) )
| ( A
= ( empty_set @ relation_dom ) ) ),
inference(pattern_uni,[status(thm)],[993:[bind(A,$thf( empty_set ))]]) ).
thf(1068,plain,
! [A: $i] :
( ( empty_set @ ( empty_set @ ( A @ sk11 ) @ singleton @ ( empty_set @ ( A @ sk12 ) @ ( empty_set @ ( A @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ( A @ ( empty_set @ ( A @ sk10 ) @ in ) )
| ( A
= ( empty_set @ relation_dom ) ) ),
inference(simp,[status(thm)],[994]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ sk9 ) ) @ ( C @ ordered_pair ) @ in ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ relation_dom ) )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[73]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ sk9 ) ) @ ( C @ ordered_pair ) @ in ) )
| ~ ( B @ ( C @ in ) )
| ~ ( A @ relation )
| ( B
!= ( A @ relation_dom ) ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ relation_dom @ ( B @ sk9 ) ) @ ( B @ ordered_pair ) @ in ) )
| ~ ( A @ relation_dom @ ( B @ in ) )
| ~ ( A @ relation ) ),
inference(simp,[status(thm)],[82]) ).
thf(2381,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ singleton @ ( A @ ( A @ relation_dom @ ( B @ sk9 ) ) @ ( B @ unordered_pair ) @ unordered_pair ) @ in ) )
| ~ ( A @ relation_dom @ ( B @ in ) )
| ~ ( A @ relation ) ),
inference(rewrite,[status(thm)],[83,53]) ).
thf(77,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ~ ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
| ( B
!= ( A @ relation_dom ) )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[73]) ).
thf(84,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ~ ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
| ~ ( A @ relation )
| ( B
!= ( A @ relation_dom ) ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ relation_dom @ ( B @ in ) )
| ~ ( A @ ( C @ ( B @ ordered_pair ) @ in ) )
| ~ ( A @ relation ) ),
inference(simp,[status(thm)],[84]) ).
thf(3377,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ relation_dom @ ( B @ in ) )
| ~ ( A @ ( B @ singleton @ ( C @ ( B @ unordered_pair ) @ unordered_pair ) @ in ) )
| ~ ( A @ relation ) ),
inference(rewrite,[status(thm)],[85,53]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(65,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ element ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[65]) ).
thf(1140,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ~ sk4 ),
inference(paramod_ordered,[status(thm)],[34,66]) ).
thf(1141,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ sk4 ),
inference(simp,[status(thm)],[1140]) ).
thf(1142,plain,
( ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom @ ( sk1 @ element ) )
| ~ sk4 ),
inference(pattern_uni,[status(thm)],[1141:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom ))]]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(134,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(135,plain,
! [A: $i] :
( ( ( A @ relation_dom @ relation )
| ~ ( A @ empty ) )
& ( ( A @ relation_dom @ empty )
| ~ ( A @ empty ) ) ),
inference(cnf,[status(esa)],[134]) ).
thf(136,plain,
! [A: $i] :
( ( A @ relation_dom @ empty )
| ~ ( A @ empty ) ),
inference(cnfConj,[status(thm)],[135]) ).
thf(19108,plain,
! [A: $i] :
( ( ( empty_set @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,136]) ).
thf(19109,plain,
! [A: $i] :
( ( ( empty_set @ empty )
!= ( A @ empty ) )
| ( A @ relation_dom @ empty ) ),
inference(simp,[status(thm)],[19108]) ).
thf(19110,plain,
empty_set @ relation_dom @ empty,
inference(pattern_uni,[status(thm)],[19109:[bind(A,$thf( empty_set ))]]) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(38,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(39,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ( B @ empty )
& ( A != B ) )
& ( A @ empty ) ),
inference(miniscope,[status(thm)],[38]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ( A = B )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[39]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( A @ empty )
| ( A = B ) ),
inference(lifteq,[status(thm)],[40]) ).
thf(301,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk3 @ relation_dom ) )
| ( B != sk2 )
| ~ sk4
| ~ ( sk2 @ ( sk1 @ in ) )
| ~ ( B @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[41,189]) ).
thf(302,plain,
! [A: $i] :
( ( A != sk2 )
| ~ sk4
| ~ ( sk2 @ ( sk1 @ in ) )
| ~ ( A @ empty )
| ~ ( sk3 @ relation_dom @ empty ) ),
inference(pattern_uni,[status(thm)],[301:[bind(A,$thf( sk3 @ relation_dom )),bind(B,$thf( B ))]]) ).
thf(472,plain,
( ~ sk4
| ~ ( sk2 @ ( sk1 @ in ) )
| ~ ( sk2 @ empty )
| ~ ( sk3 @ relation_dom @ empty ) ),
inference(simp,[status(thm)],[302]) ).
thf(6,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(44,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(45,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[44]) ).
thf(46,plain,
~ ( sk6 @ empty ),
inference(cnf,[status(esa)],[45]) ).
thf(19192,plain,
( ( ( empty_set @ relation_dom @ empty )
!= ( sk6 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19110,46]) ).
thf(19193,plain,
( ( empty_set @ relation_dom @ empty )
!= ( sk6 @ empty ) ),
inference(simp,[status(thm)],[19192]) ).
thf(19318,plain,
( ( empty_set @ relation_dom )
!= sk6 ),
inference(simp,[status(thm)],[19193]) ).
thf(3596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ unordered_pair ) )
!= ( D @ ( C @ unordered_pair ) ) )
| ( ( B @ ( A @ unordered_pair ) @ ( D @ singleton @ unordered_pair ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[37,1797]) ).
thf(3597,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ singleton @ unordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[3596:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(102,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ relation_dom_restriction ) ) )
| ~ ( C @ ( A @ ( B @ ( C @ sk17 ) ) @ ( A @ ( B @ ( C @ sk16 ) ) @ ordered_pair ) @ in ) )
| ( C @ ( A @ ( B @ sk13 ) ) )
| ~ ( C @ relation )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( C @ sk17 ) ) @ ( A @ ( B @ ( C @ sk16 ) ) @ ordered_pair ) @ in ) )
| ( C @ ( A @ ( B @ sk13 ) ) )
| ~ ( C @ relation )
| ~ ( A @ relation )
| ( C
= ( B @ ( A @ relation_dom_restriction ) ) ) ),
inference(lifteq,[status(thm)],[102]) ).
thf(7311,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( C @ sk16 ) ) @ singleton @ ( A @ ( B @ ( C @ sk17 ) ) @ ( A @ ( B @ ( C @ sk16 ) ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ( C @ ( A @ ( B @ sk13 ) ) )
| ~ ( C @ relation )
| ~ ( A @ relation )
| ( C
= ( B @ ( A @ relation_dom_restriction ) ) ) ),
inference(rewrite,[status(thm)],[105,53]) ).
thf(15,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(67,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(68,plain,
( ( sk8 @ relation )
& ( sk8 @ empty ) ),
inference(cnf,[status(esa)],[67]) ).
thf(69,plain,
sk8 @ empty,
inference(cnfConj,[status(thm)],[68]) ).
thf(30,plain,
( ( sk3 @ relation_dom @ ( sk1 @ in ) )
| sk4 ),
inference(cnfConj,[status(thm)],[28]) ).
thf(29,plain,
( ~ ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom @ ( sk1 @ in ) )
| sk4 ),
inference(cnfConj,[status(thm)],[28]) ).
thf(160,plain,
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom @ ( sk1 @ in ) )
!= ( sk3 @ relation_dom @ ( sk1 @ in ) ) )
| ~ $true
| sk4
| sk4 ),
inference(paramod_ordered,[status(thm)],[30,29]) ).
thf(161,plain,
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom @ ( sk1 @ in ) )
!= ( sk3 @ relation_dom @ ( sk1 @ in ) ) )
| sk4 ),
inference(simp,[status(thm)],[160]) ).
thf(163,plain,
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom )
!= ( sk3 @ relation_dom ) )
| ( sk1 != sk1 )
| sk4 ),
inference(simp,[status(thm)],[161]) ).
thf(165,plain,
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom )
!= ( sk3 @ relation_dom ) )
| sk4 ),
inference(simp,[status(thm)],[163]) ).
thf(210,plain,
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) )
!= sk3 )
| sk4 ),
inference(simp,[status(thm)],[165]) ).
thf(285,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ ( sk3 @ relation_dom_restriction ) ) )
| ( B != sk3 )
| sk4
| ~ ( B @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[41,210]) ).
thf(286,plain,
! [A: $i] :
( ( A != sk3 )
| sk4
| ~ ( A @ empty )
| ~ ( sk2 @ ( sk3 @ relation_dom_restriction ) @ empty ) ),
inference(pattern_uni,[status(thm)],[285:[bind(A,$thf( sk2 @ ( sk3 @ relation_dom_restriction ) )),bind(B,$thf( B ))]]) ).
thf(466,plain,
( sk4
| ~ ( sk3 @ empty )
| ~ ( sk2 @ ( sk3 @ relation_dom_restriction ) @ empty ) ),
inference(simp,[status(thm)],[286]) ).
thf(589,plain,
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) @ empty )
!= ( sk8 @ empty ) )
| sk4
| ~ ( sk3 @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,466]) ).
thf(590,plain,
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) @ empty )
!= ( sk8 @ empty ) )
| sk4
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[589]) ).
thf(622,plain,
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) )
!= sk8 )
| ~ ( sk3 @ empty )
| sk4 ),
inference(simp,[status(thm)],[590]) ).
thf(637,plain,
! [A: $i] :
( ( ( sk8 @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[69,59]) ).
thf(638,plain,
! [A: $i] :
( ( ( sk8 @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[637]) ).
thf(639,plain,
sk8 = empty_set,
inference(pattern_uni,[status(thm)],[638:[bind(A,$thf( sk8 ))]]) ).
thf(7241,plain,
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) )
!= empty_set )
| ~ ( sk3 @ empty )
| sk4 ),
inference(rewrite,[status(thm)],[622,639]) ).
thf(1759,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( C @ ( D @ unordered_pair ) ) )
| ( ( C @ singleton @ ( A @ ( B @ unordered_pair ) @ unordered_pair ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[37,1158]) ).
thf(1760,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ ( B @ unordered_pair ) @ unordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[1759:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(1149,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ relation_dom @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| sk4 ),
inference(paramod_ordered,[status(thm)],[30,66]) ).
thf(1150,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ relation_dom @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| sk4 ),
inference(simp,[status(thm)],[1149]) ).
thf(1151,plain,
( ( sk3 @ relation_dom @ ( sk1 @ element ) )
| sk4 ),
inference(pattern_uni,[status(thm)],[1150:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ relation_dom ))]]) ).
thf(2886,plain,
! [A: $i] :
( ( A
!= ( sk3 @ relation_dom ) )
| ( empty_set @ relation_dom @ ( sk1 @ element ) )
| sk4
| ( empty_set @ ( empty_set @ ( A @ sk11 ) @ singleton @ ( empty_set @ ( A @ sk12 ) @ ( empty_set @ ( A @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ( A @ ( empty_set @ ( A @ sk10 ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[1068,1151]) ).
thf(2887,plain,
( ( empty_set @ relation_dom @ ( sk1 @ element ) )
| sk4
| ( empty_set @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ( sk3 @ relation_dom @ ( empty_set @ ( sk3 @ relation_dom @ sk10 ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[2886:[bind(A,$thf( sk3 @ relation_dom ))]]) ).
thf(3996,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ relation_dom @ ( empty_set @ ( sk3 @ relation_dom @ sk10 ) @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ( empty_set @ relation_dom @ ( sk1 @ element ) )
| sk4
| ( empty_set @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[2887,66]) ).
thf(3997,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ relation_dom @ ( empty_set @ ( sk3 @ relation_dom @ sk10 ) @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ( empty_set @ relation_dom @ ( sk1 @ element ) )
| sk4
| ( empty_set @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) ) ),
inference(simp,[status(thm)],[3996]) ).
thf(3998,plain,
( ( sk3 @ relation_dom @ ( empty_set @ ( sk3 @ relation_dom @ sk10 ) @ element ) )
| ( empty_set @ relation_dom @ ( sk1 @ element ) )
| sk4
| ( empty_set @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[3997:[bind(A,$thf( empty_set @ ( sk3 @ relation_dom @ sk10 ) )),bind(B,$thf( sk3 @ relation_dom ))]]) ).
thf(32,plain,
( ( sk2 @ ( sk1 @ in ) )
| sk4 ),
inference(cnfConj,[status(thm)],[28]) ).
thf(158,plain,
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom @ ( sk1 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ~ $true
| sk4
| sk4 ),
inference(paramod_ordered,[status(thm)],[32,29]) ).
thf(159,plain,
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom @ ( sk1 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| sk4 ),
inference(simp,[status(thm)],[158]) ).
thf(162,plain,
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom )
!= sk2 )
| ( sk1 != sk1 )
| sk4 ),
inference(simp,[status(thm)],[159]) ).
thf(164,plain,
( ( ( sk2 @ ( sk3 @ relation_dom_restriction ) @ relation_dom )
!= sk2 )
| sk4 ),
inference(simp,[status(thm)],[162]) ).
thf(3999,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ( empty_set @ relation_dom @ ( sk1 @ element ) )
| sk4
| ( sk3 @ relation_dom @ ( empty_set @ ( sk3 @ relation_dom @ sk10 ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[2887,66]) ).
thf(4000,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ( empty_set @ relation_dom @ ( sk1 @ element ) )
| sk4
| ( sk3 @ relation_dom @ ( empty_set @ ( sk3 @ relation_dom @ sk10 ) @ in ) ) ),
inference(simp,[status(thm)],[3999]) ).
thf(4001,plain,
( ( empty_set @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ element ) )
| ( empty_set @ relation_dom @ ( sk1 @ element ) )
| sk4
| ( sk3 @ relation_dom @ ( empty_set @ ( sk3 @ relation_dom @ sk10 ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[4000:[bind(A,$thf( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ unordered_pair ) )),bind(B,$thf( empty_set ))]]) ).
thf(730,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk2 @ ( empty_set @ in ) )
| sk4
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[59,32]) ).
thf(731,plain,
( ( sk2 @ ( empty_set @ in ) )
| sk4
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[730:[bind(A,$thf( sk1 ))]]) ).
thf(1134,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( empty_set @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| sk4
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[731,66]) ).
thf(1135,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( empty_set @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| sk4
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[1134]) ).
thf(1136,plain,
( ( sk2 @ ( empty_set @ element ) )
| sk4
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[1135:[bind(A,$thf( empty_set )),bind(B,$thf( sk2 ))]]) ).
thf(686,plain,
! [A: $i] :
( ( A
!= ( sk3 @ relation_dom ) )
| ( sk2 != empty_set )
| ~ sk4
| ~ ( sk2 @ ( sk1 @ in ) )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[59,189]) ).
thf(687,plain,
( ( sk2 != empty_set )
| ~ sk4
| ~ ( sk2 @ ( sk1 @ in ) )
| ~ ( sk3 @ relation_dom @ empty ) ),
inference(pattern_uni,[status(thm)],[686:[bind(A,$thf( sk3 @ relation_dom ))]]) ).
thf(12,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(60,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(61,plain,
! [A: $i] : ( A @ ( A @ sk7 @ element ) ),
inference(cnf,[status(esa)],[60]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ relation_dom ) )
| ~ ( B @ ( A @ ( B @ sk11 ) @ in ) )
| ( B @ ( A @ ( B @ sk10 ) @ in ) )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[73]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk11 ) @ in ) )
| ( B @ ( A @ ( B @ sk10 ) @ in ) )
| ~ ( A @ relation )
| ( B
= ( A @ relation_dom ) ) ),
inference(lifteq,[status(thm)],[75]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk11 ) @ in ) )
| ( B @ ( A @ ( B @ sk10 ) @ in ) )
| ~ ( A @ relation )
| ( B
= ( A @ relation_dom ) ) ),
inference(simp,[status(thm)],[88]) ).
thf(18,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(114,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(115,plain,
( ( sk18 @ relation )
& ~ ( sk18 @ empty ) ),
inference(cnf,[status(esa)],[114]) ).
thf(116,plain,
~ ( sk18 @ empty ),
inference(cnfConj,[status(thm)],[115]) ).
thf(117,plain,
sk18 @ relation,
inference(cnfConj,[status(thm)],[115]) ).
thf(777,plain,
! [A: $i] :
( ( A
!= ( sk3 @ relation_dom ) )
| ( empty_set @ ( sk1 @ in ) )
| sk4
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[59,30]) ).
thf(778,plain,
( ( empty_set @ ( sk1 @ in ) )
| sk4
| ~ ( sk3 @ relation_dom @ empty ) ),
inference(pattern_uni,[status(thm)],[777:[bind(A,$thf( sk3 @ relation_dom ))]]) ).
thf(819,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)],[37,556]) ).
thf(820,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[819:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1124,plain,
( ( ( sk1 @ empty )
!= ( empty_set @ empty ) )
| ( sk2 @ ( empty_set @ in ) )
| sk4
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,731]) ).
thf(1125,plain,
( ( ( sk1 @ empty )
!= ( empty_set @ empty ) )
| ( sk2 @ ( empty_set @ in ) )
| sk4 ),
inference(simp,[status(thm)],[1124]) ).
thf(1130,plain,
( ( sk1 != empty_set )
| ( sk2 @ ( empty_set @ in ) )
| sk4 ),
inference(simp,[status(thm)],[1125]) ).
thf(2330,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( empty_set @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ( sk1 != empty_set )
| sk4 ),
inference(paramod_ordered,[status(thm)],[1130,66]) ).
thf(2331,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( empty_set @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ( sk1 != empty_set )
| sk4 ),
inference(simp,[status(thm)],[2330]) ).
thf(2332,plain,
( ( sk2 @ ( empty_set @ element ) )
| ( sk1 != empty_set )
| sk4 ),
inference(pattern_uni,[status(thm)],[2331:[bind(A,$thf( empty_set )),bind(B,$thf( sk2 ))]]) ).
thf(3666,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ unordered_pair ) ) )
| ( empty_set @ relation_dom @ ( sk1 @ element ) )
| sk4
| ( empty_set @ ( A @ ( B @ unordered_pair ) @ in ) )
| ( sk3 @ relation_dom @ ( empty_set @ ( sk3 @ relation_dom @ sk10 ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[37,2887]) ).
thf(3667,plain,
( ( empty_set @ relation_dom @ ( sk1 @ element ) )
| sk4
| ( empty_set @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ unordered_pair ) @ in ) )
| ( sk3 @ relation_dom @ ( empty_set @ ( sk3 @ relation_dom @ sk10 ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[3666:[bind(A,$thf( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) )),bind(B,$thf( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton ))]]) ).
thf(857,plain,
! [B: $i,A: $i] :
( ( ( sk18 @ relation )
!= ( A @ relation ) )
| ( A @ ( A @ ( B @ sk11 ) @ singleton @ ( A @ ( B @ sk12 ) @ ( A @ ( B @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ( B @ ( A @ ( B @ sk10 ) @ in ) )
| ~ $true
| ( B
= ( A @ relation_dom ) ) ),
inference(paramod_ordered,[status(thm)],[117,835]) ).
thf(858,plain,
! [B: $i,A: $i] :
( ( ( sk18 @ relation )
!= ( A @ relation ) )
| ( A @ ( A @ ( B @ sk11 ) @ singleton @ ( A @ ( B @ sk12 ) @ ( A @ ( B @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ( B @ ( A @ ( B @ sk10 ) @ in ) )
| ( B
= ( A @ relation_dom ) ) ),
inference(simp,[status(thm)],[857]) ).
thf(859,plain,
! [A: $i] :
( ( sk18 @ ( sk18 @ ( A @ sk11 ) @ singleton @ ( sk18 @ ( A @ sk12 ) @ ( sk18 @ ( A @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ( A @ ( sk18 @ ( A @ sk10 ) @ in ) )
| ( A
= ( sk18 @ relation_dom ) ) ),
inference(pattern_uni,[status(thm)],[858:[bind(A,$thf( sk18 ))]]) ).
thf(1064,plain,
! [A: $i] :
( ( sk18 @ ( sk18 @ ( A @ sk11 ) @ singleton @ ( sk18 @ ( A @ sk12 ) @ ( sk18 @ ( A @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ( A @ ( sk18 @ ( A @ sk10 ) @ in ) )
| ( A
= ( sk18 @ relation_dom ) ) ),
inference(simp,[status(thm)],[859]) ).
thf(19203,plain,
( ( ( empty_set @ relation_dom @ empty )
!= ( sk18 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19110,116]) ).
thf(19204,plain,
( ( empty_set @ relation_dom @ empty )
!= ( sk18 @ empty ) ),
inference(simp,[status(thm)],[19203]) ).
thf(19302,plain,
( ( empty_set @ relation_dom )
!= sk18 ),
inference(simp,[status(thm)],[19204]) ).
thf(95,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
| ~ ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
| ( C
!= ( B @ ( A @ relation_dom_restriction ) ) )
| ~ ( C @ relation )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(109,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
| ~ ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
| ~ ( C @ relation )
| ~ ( A @ relation )
| ( C
!= ( B @ ( A @ relation_dom_restriction ) ) ) ),
inference(lifteq,[status(thm)],[95]) ).
thf(110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
| ~ ( B @ ( A @ relation_dom_restriction ) @ ( D @ ( C @ ordered_pair ) @ in ) )
| ~ ( B @ ( A @ relation_dom_restriction ) @ relation )
| ~ ( A @ relation ) ),
inference(simp,[status(thm)],[109]) ).
thf(14120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ singleton @ ( D @ ( C @ unordered_pair ) @ unordered_pair ) @ in ) )
| ~ ( B @ ( A @ relation_dom_restriction ) @ ( C @ singleton @ ( D @ ( C @ unordered_pair ) @ unordered_pair ) @ in ) )
| ~ ( B @ ( A @ relation_dom_restriction ) @ relation )
| ~ ( A @ relation ) ),
inference(rewrite,[status(thm)],[110,53]) ).
thf(21,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(124,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(732,plain,
! [A: $i] :
( ( A != sk2 )
| ( empty_set @ ( sk1 @ in ) )
| sk4
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[59,32]) ).
thf(733,plain,
( ( empty_set @ ( sk1 @ in ) )
| sk4
| ~ ( sk2 @ empty ) ),
inference(pattern_uni,[status(thm)],[732:[bind(A,$thf( sk2 ))]]) ).
thf(1286,plain,
( ( ( sk2 @ empty )
!= ( empty_set @ empty ) )
| ( empty_set @ ( sk1 @ in ) )
| sk4
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,733]) ).
thf(1287,plain,
( ( ( sk2 @ empty )
!= ( empty_set @ empty ) )
| ( empty_set @ ( sk1 @ in ) )
| sk4 ),
inference(simp,[status(thm)],[1286]) ).
thf(1292,plain,
( ( sk2 != empty_set )
| ( empty_set @ ( sk1 @ in ) )
| sk4 ),
inference(simp,[status(thm)],[1287]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ relation_dom ) )
| ( A @ ( A @ ( B @ sk12 ) @ ( A @ ( B @ sk11 ) @ ordered_pair ) @ in ) )
| ~ ( A @ ( C @ ( A @ ( B @ sk10 ) @ ordered_pair ) @ in ) )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[73]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk12 ) @ ( A @ ( B @ sk11 ) @ ordered_pair ) @ in ) )
| ~ ( A @ ( C @ ( A @ ( B @ sk10 ) @ ordered_pair ) @ in ) )
| ~ ( A @ relation )
| ( B
= ( A @ relation_dom ) ) ),
inference(lifteq,[status(thm)],[78]) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk12 ) @ ( A @ ( B @ sk11 ) @ ordered_pair ) @ in ) )
| ~ ( A @ ( C @ ( A @ ( B @ sk10 ) @ ordered_pair ) @ in ) )
| ~ ( A @ relation )
| ( B
= ( A @ relation_dom ) ) ),
inference(simp,[status(thm)],[80]) ).
thf(1297,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk11 ) @ singleton @ ( A @ ( B @ sk12 ) @ ( A @ ( B @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ~ ( A @ ( A @ ( B @ sk10 ) @ singleton @ ( C @ ( A @ ( B @ sk10 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ~ ( A @ relation )
| ( B
= ( A @ relation_dom ) ) ),
inference(rewrite,[status(thm)],[81,53]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(129,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(748,plain,
! [A: $i] :
( ( A != sk3 )
| sk4
| ~ ( sk3 @ empty )
| ~ ( sk2 @ ( empty_set @ relation_dom_restriction ) @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[59,466]) ).
thf(749,plain,
( sk4
| ~ ( sk3 @ empty )
| ~ ( sk2 @ ( empty_set @ relation_dom_restriction ) @ empty )
| ~ ( sk3 @ empty ) ),
inference(pattern_uni,[status(thm)],[748:[bind(A,$thf( sk3 ))]]) ).
thf(792,plain,
( sk4
| ~ ( sk2 @ ( empty_set @ relation_dom_restriction ) @ empty )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[749]) ).
thf(673,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( empty_set @ ( sk3 @ relation_dom_restriction ) )
!= sk3 )
| sk4
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[59,210]) ).
thf(674,plain,
( ( ( empty_set @ ( sk3 @ relation_dom_restriction ) )
!= sk3 )
| sk4
| ~ ( sk2 @ empty ) ),
inference(pattern_uni,[status(thm)],[673:[bind(A,$thf( sk2 ))]]) ).
thf(688,plain,
! [A: $i] :
( ( A != sk3 )
| ( ( empty_set @ relation_dom )
!= sk2 )
| ~ sk4
| ~ ( sk2 @ ( sk1 @ in ) )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[59,189]) ).
thf(689,plain,
( ( ( empty_set @ relation_dom )
!= sk2 )
| ~ sk4
| ~ ( sk2 @ ( sk1 @ in ) )
| ~ ( sk3 @ empty ) ),
inference(pattern_uni,[status(thm)],[688:[bind(A,$thf( sk3 ))]]) ).
thf(97,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ relation_dom_restriction ) ) )
| ( A @ ( A @ ( B @ ( C @ sk17 ) ) @ ( A @ ( B @ ( C @ sk16 ) ) @ ordered_pair ) @ in ) )
| ( C @ ( A @ ( B @ sk13 ) ) )
| ~ ( C @ relation )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ sk17 ) ) @ ( A @ ( B @ ( C @ sk16 ) ) @ ordered_pair ) @ in ) )
| ( C @ ( A @ ( B @ sk13 ) ) )
| ~ ( C @ relation )
| ~ ( A @ relation )
| ( C
= ( B @ ( A @ relation_dom_restriction ) ) ) ),
inference(lifteq,[status(thm)],[97]) ).
thf(8762,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ sk16 ) ) @ singleton @ ( A @ ( B @ ( C @ sk17 ) ) @ ( A @ ( B @ ( C @ sk16 ) ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ( C @ ( A @ ( B @ sk13 ) ) )
| ~ ( C @ relation )
| ~ ( A @ relation )
| ( C
= ( B @ ( A @ relation_dom_restriction ) ) ) ),
inference(rewrite,[status(thm)],[106,53]) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ relation_dom_restriction ) ) )
| ~ ( C @ ( A @ ( B @ sk13 ) ) )
| ~ ( A @ ( A @ ( B @ ( C @ sk15 ) ) @ ( A @ ( B @ ( C @ sk14 ) ) @ ordered_pair ) @ in ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk14 ) ) @ in ) )
| ~ ( C @ relation )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(108,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ sk13 ) ) )
| ~ ( A @ ( A @ ( B @ ( C @ sk15 ) ) @ ( A @ ( B @ ( C @ sk14 ) ) @ ordered_pair ) @ in ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk14 ) ) @ in ) )
| ~ ( C @ relation )
| ~ ( A @ relation )
| ( C
= ( B @ ( A @ relation_dom_restriction ) ) ) ),
inference(lifteq,[status(thm)],[98]) ).
thf(12259,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ sk13 ) ) )
| ~ ( A @ ( A @ ( B @ ( C @ sk14 ) ) @ singleton @ ( A @ ( B @ ( C @ sk15 ) ) @ ( A @ ( B @ ( C @ sk14 ) ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk14 ) ) @ in ) )
| ~ ( C @ relation )
| ~ ( A @ relation )
| ( C
= ( B @ ( A @ relation_dom_restriction ) ) ) ),
inference(rewrite,[status(thm)],[108,53]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(118,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(7,axiom,
! [A: $i] :
~ ( A @ singleton @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(47,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(48,plain,
~ ? [A: $i] : ( A @ singleton @ empty ),
inference(miniscope,[status(thm)],[47]) ).
thf(49,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(cnf,[status(esa)],[48]) ).
thf(671,plain,
! [A: $i] :
( ( A != sk3 )
| ( ( sk2 @ ( empty_set @ relation_dom_restriction ) )
!= sk3 )
| sk4
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[59,210]) ).
thf(672,plain,
( ( ( sk2 @ ( empty_set @ relation_dom_restriction ) )
!= sk3 )
| sk4
| ~ ( sk3 @ empty ) ),
inference(pattern_uni,[status(thm)],[671:[bind(A,$thf( sk3 ))]]) ).
thf(1137,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| sk4 ),
inference(paramod_ordered,[status(thm)],[32,66]) ).
thf(1138,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| sk4 ),
inference(simp,[status(thm)],[1137]) ).
thf(1139,plain,
( ( sk2 @ ( sk1 @ element ) )
| sk4 ),
inference(pattern_uni,[status(thm)],[1138:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(1161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ unordered_pair ) )
!= ( D @ ( C @ unordered_pair ) ) )
| ( ( C @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[37,1156]) ).
thf(1162,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[1161:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(684,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( sk3 @ relation_dom )
!= sk2 )
| ~ sk4
| ~ ( empty_set @ ( sk1 @ in ) )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[59,189]) ).
thf(685,plain,
( ( ( sk3 @ relation_dom )
!= sk2 )
| ~ sk4
| ~ ( empty_set @ ( sk1 @ in ) )
| ~ ( sk2 @ empty ) ),
inference(pattern_uni,[status(thm)],[684:[bind(A,$thf( sk2 ))]]) ).
thf(779,plain,
! [A: $i] :
( ( A != sk3 )
| ( empty_set @ relation_dom @ ( sk1 @ in ) )
| sk4
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[59,30]) ).
thf(780,plain,
( ( empty_set @ relation_dom @ ( sk1 @ in ) )
| sk4
| ~ ( sk3 @ empty ) ),
inference(pattern_uni,[status(thm)],[779:[bind(A,$thf( sk3 ))]]) ).
thf(1159,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 ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[37,1156]) ).
thf(1160,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) @ ( B @ singleton @ unordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[1159:[bind(A,$thf( F @ ( G @ unordered_pair ) )),bind(B,$thf( G @ singleton )),bind(C,$thf( G )),bind(D,$thf( F ))]]) ).
thf(1193,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) @ ( B @ singleton @ unordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[1160]) ).
thf(2664,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( C @ ( D @ unordered_pair ) ) )
| ( ( A @ ( B @ unordered_pair ) @ ( D @ singleton @ unordered_pair ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[37,1193]) ).
thf(2665,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) @ ( A @ singleton @ unordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[2664:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(3160,plain,
! [A: $i] :
( ( A
!= ( sk3 @ relation_dom ) )
| ( empty_set @ relation_dom @ ( sk1 @ in ) )
| sk4
| ( empty_set @ ( empty_set @ ( A @ sk11 ) @ singleton @ ( empty_set @ ( A @ sk12 ) @ ( empty_set @ ( A @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ( A @ ( empty_set @ ( A @ sk10 ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[1068,30]) ).
thf(3161,plain,
( ( empty_set @ relation_dom @ ( sk1 @ in ) )
| sk4
| ( empty_set @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ( sk3 @ relation_dom @ ( empty_set @ ( sk3 @ relation_dom @ sk10 ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[3160:[bind(A,$thf( sk3 @ relation_dom ))]]) ).
thf(143,plain,
( ( ( sk6 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,46]) ).
thf(144,plain,
( ( sk6 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[143]) ).
thf(145,plain,
sk6 != empty_set,
inference(simp,[status(thm)],[144]) ).
thf(775,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk3 @ relation_dom @ ( empty_set @ in ) )
| sk4
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[59,30]) ).
thf(776,plain,
( ( sk3 @ relation_dom @ ( empty_set @ in ) )
| sk4
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[775:[bind(A,$thf( sk1 ))]]) ).
thf(11524,plain,
( ( ( sk3 @ relation_dom @ empty )
!= ( empty_set @ empty ) )
| ~ sk4
| ~ ( sk2 @ ( sk1 @ in ) )
| ~ ( sk2 @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,472]) ).
thf(11525,plain,
( ( ( sk3 @ relation_dom @ empty )
!= ( empty_set @ empty ) )
| ~ sk4
| ~ ( sk2 @ ( sk1 @ in ) )
| ~ ( sk2 @ empty ) ),
inference(simp,[status(thm)],[11524]) ).
thf(11575,plain,
( ( ( sk3 @ relation_dom )
!= empty_set )
| ~ sk4
| ~ ( sk2 @ ( sk1 @ in ) )
| ~ ( sk2 @ empty ) ),
inference(simp,[status(thm)],[11525]) ).
thf(101,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ in ) )
| ~ ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
| ( C
!= ( B @ ( A @ relation_dom_restriction ) ) )
| ~ ( C @ relation )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(103,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ in ) )
| ~ ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
| ~ ( C @ relation )
| ~ ( A @ relation )
| ( C
!= ( B @ ( A @ relation_dom_restriction ) ) ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ~ ( B @ ( A @ relation_dom_restriction ) @ ( D @ ( C @ ordered_pair ) @ in ) )
| ~ ( B @ ( A @ relation_dom_restriction ) @ relation )
| ~ ( A @ relation ) ),
inference(simp,[status(thm)],[103]) ).
thf(6912,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ~ ( B @ ( A @ relation_dom_restriction ) @ ( C @ singleton @ ( D @ ( C @ unordered_pair ) @ unordered_pair ) @ in ) )
| ~ ( B @ ( A @ relation_dom_restriction ) @ relation )
| ~ ( A @ relation ) ),
inference(rewrite,[status(thm)],[104,53]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(127,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(4981,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ unordered_pair ) ) )
| ( empty_set @ relation_dom @ ( sk1 @ in ) )
| sk4
| ( empty_set @ ( A @ ( B @ unordered_pair ) @ in ) )
| ( sk3 @ relation_dom @ ( empty_set @ ( sk3 @ relation_dom @ sk10 ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[37,3161]) ).
thf(4982,plain,
( ( empty_set @ relation_dom @ ( sk1 @ in ) )
| sk4
| ( empty_set @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ unordered_pair ) @ in ) )
| ( sk3 @ relation_dom @ ( empty_set @ ( sk3 @ relation_dom @ sk10 ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[4981:[bind(A,$thf( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) )),bind(B,$thf( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton ))]]) ).
thf(31,plain,
sk3 @ relation,
inference(cnfConj,[status(thm)],[28]) ).
thf(5275,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ relation_dom @ ( empty_set @ ( sk3 @ relation_dom @ sk10 ) @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ( empty_set @ relation_dom @ ( sk1 @ in ) )
| sk4
| ( empty_set @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[3161,66]) ).
thf(5276,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ relation_dom @ ( empty_set @ ( sk3 @ relation_dom @ sk10 ) @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ( empty_set @ relation_dom @ ( sk1 @ in ) )
| sk4
| ( empty_set @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) ) ),
inference(simp,[status(thm)],[5275]) ).
thf(5277,plain,
( ( sk3 @ relation_dom @ ( empty_set @ ( sk3 @ relation_dom @ sk10 ) @ element ) )
| ( empty_set @ relation_dom @ ( sk1 @ in ) )
| sk4
| ( empty_set @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[5276:[bind(A,$thf( empty_set @ ( sk3 @ relation_dom @ sk10 ) )),bind(B,$thf( sk3 @ relation_dom ))]]) ).
thf(1219,plain,
! [A: $i] :
( ( A != sk2 )
| ( empty_set @ ( sk1 @ element ) )
| sk4
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[59,1139]) ).
thf(1220,plain,
( ( empty_set @ ( sk1 @ element ) )
| sk4
| ~ ( sk2 @ empty ) ),
inference(pattern_uni,[status(thm)],[1219:[bind(A,$thf( sk2 ))]]) ).
thf(119,plain,
! [A: $i] :
( ( A @ relation )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[118]) ).
thf(148,plain,
( ( ( sk18 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,116]) ).
thf(149,plain,
( ( sk18 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[148]) ).
thf(151,plain,
sk18 != empty_set,
inference(simp,[status(thm)],[149]) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ relation_dom_restriction ) ) )
| ~ ( C @ ( A @ ( B @ sk13 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk15 ) ) @ ( A @ ( B @ ( C @ sk14 ) ) @ ordered_pair ) @ in ) )
| ~ ( C @ relation )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(113,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ sk13 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk15 ) ) @ ( A @ ( B @ ( C @ sk14 ) ) @ ordered_pair ) @ in ) )
| ~ ( C @ relation )
| ~ ( A @ relation )
| ( C
= ( B @ ( A @ relation_dom_restriction ) ) ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(17693,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ sk13 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk14 ) ) @ singleton @ ( A @ ( B @ ( C @ sk15 ) ) @ ( A @ ( B @ ( C @ sk14 ) ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ~ ( C @ relation )
| ~ ( A @ relation )
| ( C
= ( B @ ( A @ relation_dom_restriction ) ) ) ),
inference(rewrite,[status(thm)],[113,53]) ).
thf(3368,plain,
( ( ( sk2 @ empty )
!= ( empty_set @ empty ) )
| ( empty_set @ ( sk1 @ element ) )
| sk4
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,1220]) ).
thf(3369,plain,
( ( ( sk2 @ empty )
!= ( empty_set @ empty ) )
| ( empty_set @ ( sk1 @ element ) )
| sk4 ),
inference(simp,[status(thm)],[3368]) ).
thf(3373,plain,
( ( sk2 != empty_set )
| ( empty_set @ ( sk1 @ element ) )
| sk4 ),
inference(simp,[status(thm)],[3369]) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ relation_dom_restriction ) ) )
| ( B @ ( A @ ( B @ ( C @ sk16 ) ) @ in ) )
| ( C @ ( A @ ( B @ sk13 ) ) )
| ~ ( C @ relation )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( C @ sk16 ) ) @ in ) )
| ( C @ ( A @ ( B @ sk13 ) ) )
| ~ ( C @ relation )
| ~ ( A @ relation )
| ( C
= ( B @ ( A @ relation_dom_restriction ) ) ) ),
inference(lifteq,[status(thm)],[96]) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ relation_dom ) )
| ~ ( B @ ( A @ ( B @ sk11 ) @ in ) )
| ~ ( A @ ( C @ ( A @ ( B @ sk10 ) @ ordered_pair ) @ in ) )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[73]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk11 ) @ in ) )
| ~ ( A @ ( C @ ( A @ ( B @ sk10 ) @ ordered_pair ) @ in ) )
| ~ ( A @ relation )
| ( B
= ( A @ relation_dom ) ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(87,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk11 ) @ in ) )
| ~ ( A @ ( C @ ( A @ ( B @ sk10 ) @ ordered_pair ) @ in ) )
| ~ ( A @ relation )
| ( B
= ( A @ relation_dom ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(4193,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ sk11 ) @ in ) )
| ~ ( A @ ( A @ ( B @ sk10 ) @ singleton @ ( C @ ( A @ ( B @ sk10 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ~ ( A @ relation )
| ( B
= ( A @ relation_dom ) ) ),
inference(rewrite,[status(thm)],[87,53]) ).
thf(619,plain,
( ( ( sk3 @ empty )
!= ( empty_set @ empty ) )
| sk4
| ~ $true
| ~ ( sk2 @ ( sk3 @ relation_dom_restriction ) @ empty ) ),
inference(paramod_ordered,[status(thm)],[50,466]) ).
thf(620,plain,
( ( ( sk3 @ empty )
!= ( empty_set @ empty ) )
| sk4
| ~ ( sk2 @ ( sk3 @ relation_dom_restriction ) @ empty ) ),
inference(simp,[status(thm)],[619]) ).
thf(624,plain,
( ( sk3 != empty_set )
| ~ ( sk2 @ ( sk3 @ relation_dom_restriction ) @ empty )
| sk4 ),
inference(simp,[status(thm)],[620]) ).
thf(5278,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| ( empty_set @ relation_dom @ ( sk1 @ in ) )
| sk4
| ( sk3 @ relation_dom @ ( empty_set @ ( sk3 @ relation_dom @ sk10 ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[3161,66]) ).
thf(5279,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ( empty_set @ relation_dom @ ( sk1 @ in ) )
| sk4
| ( sk3 @ relation_dom @ ( empty_set @ ( sk3 @ relation_dom @ sk10 ) @ in ) ) ),
inference(simp,[status(thm)],[5278]) ).
thf(5280,plain,
( ( empty_set @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ unordered_pair ) @ element ) )
| ( empty_set @ relation_dom @ ( sk1 @ in ) )
| sk4
| ( sk3 @ relation_dom @ ( empty_set @ ( sk3 @ relation_dom @ sk10 ) @ in ) ) ),
inference(pattern_uni,[status(thm)],[5279:[bind(A,$thf( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ singleton @ ( empty_set @ ( sk3 @ relation_dom @ sk12 ) @ ( empty_set @ ( sk3 @ relation_dom @ sk11 ) @ unordered_pair ) @ unordered_pair ) )),bind(B,$thf( empty_set ))]]) ).
thf(196,plain,
! [A: $i] :
( ( ( A @ singleton @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,49]) ).
thf(197,plain,
! [A: $i] :
( ( A @ singleton @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[196]) ).
thf(200,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(simp,[status(thm)],[197]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( B @ ( A @ relation_dom_restriction ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(131,plain,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( B @ ( A @ relation_dom_restriction ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(25427,plain,
$false,
inference(e,[status(thm)],[9771,1797,556,138,15838,1158,683,1068,2381,3377,120,1142,56,19110,472,42,19318,37,3597,7311,7241,1760,3998,189,46,57,29,164,4001,1136,1151,687,61,89,116,60,117,778,38,820,165,33,92,65,2332,3667,1064,19302,53,14120,124,1292,1297,129,41,134,792,674,689,733,32,34,8762,44,12259,27,59,118,54,49,466,672,71,1139,1162,66,668,685,780,35,2665,3161,209,123,145,776,11575,1156,50,67,6912,127,4982,1130,31,5277,1220,114,731,119,1193,151,835,30,51,17693,3373,210,107,136,4193,624,5280,200,62,131,47,2887,639]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU192+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % 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
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 08:47:01 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 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
% 0.92/0.95 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.36/1.16 % [INFO] Parsing done (199ms).
% 1.36/1.17 % [INFO] Running in sequential loop mode.
% 2.07/1.58 % [INFO] eprover registered as external prover.
% 2.07/1.59 % [INFO] Scanning for conjecture ...
% 2.28/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 30 axioms. Running axiom selection ...
% 2.45/1.76 % [INFO] Axiom selection finished. Selected 24 axioms (removed 6 axioms).
% 2.67/1.80 % [INFO] Problem is first-order (TPTP FOF).
% 2.67/1.81 % [INFO] Type checking passed.
% 2.67/1.82 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 87.84/18.58 % External prover 'e' found a proof!
% 87.84/18.58 % [INFO] Killing All external provers ...
% 87.84/18.58 % Time passed: 18063ms (effective reasoning time: 17406ms)
% 87.84/18.58 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 87.84/18.59 % Axioms used in derivation (24): fc1_zfmisc_1, cc1_relat_1, t6_boole, fc3_subset_1, t7_boole, d11_relat_1, fc5_relat_1, dt_k7_relat_1, rc2_relat_1, rc1_relat_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, d5_tarski, fc4_relat_1, t1_subset, d4_relat_1, fc2_subset_1, existence_m1_subset_1, commutativity_k2_tarski, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1
% 87.84/18.59 % No. of inferences in proof: 304
% 87.84/18.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 18063 ms resp. 17406 ms w/o parsing
% 74.01/18.77 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 74.01/18.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------