%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU197+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 : n017.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 08:37:59 AM UTC 2026
% Result : Theorem 189.11s 55.15s
% Output : Refutation 190.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 41
% Syntax : Number of formulae : 322 ( 102 unt; 0 typ; 16 def)
% Number of atoms : 1082 ( 255 equ; 0 cnn)
% Maximal formula atoms : 42 ( 3 avg)
% Number of connectives : 2988 ( 454 ~; 400 |; 81 &;1978 @)
% ( 6 <=>; 69 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 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 : 523 ( 22 ^; 455 !; 30 ?; 523 :)
% ( 0 !>; 0 ?*; 0 @-; 16 @+)
% Comments :
%------------------------------------------------------------------------------
thf(relation_decl,type,
relation: $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(relation_rng_decl,type,
relation_rng: $i > $i ).
thf(relation_rng_restriction_decl,type,
relation_rng_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 ).
thf(sk10_decl,type,
sk10: $i > $i > $i > $o ).
thf(sk11_decl,type,
sk11: $i > $i > $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i > $i > $i ).
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 ).
thf(sk17_decl,type,
sk17: $i > $i > $i ).
thf(sk18_decl,type,
sk18: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( C @ relation )
=> ( ( ( ( C @ relation_rng @ ( A @ in ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( B @ relation_rng_restriction ) @ relation_rng @ ( A @ in ) ) )
& ( ( C @ ( B @ relation_rng_restriction ) @ relation_rng @ ( A @ in ) )
=> ( ( C @ relation_rng @ ( A @ in ) )
& ( B @ ( A @ in ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ relation )
=> ( ( ( ( B @ relation_rng @ ( sk1 @ in ) )
& ( A @ ( sk1 @ in ) ) )
=> ( B @ ( A @ relation_rng_restriction ) @ relation_rng @ ( sk1 @ in ) ) )
& ( ( B @ ( A @ relation_rng_restriction ) @ relation_rng @ ( sk1 @ in ) )
=> ( ( B @ relation_rng @ ( sk1 @ in ) )
& ( A @ ( sk1 @ in ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( A @ relation )
=> ( ( ( ( A @ relation_rng @ ( sk1 @ in ) )
& ( sk2 @ ( sk1 @ in ) ) )
=> ( A @ ( sk2 @ relation_rng_restriction ) @ relation_rng @ ( sk1 @ in ) ) )
& ( ( A @ ( sk2 @ relation_rng_restriction ) @ relation_rng @ ( sk1 @ in ) )
=> ( ( A @ relation_rng @ ( 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] :
( ( A @ relation )
& ~ ( A @ empty ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ! [E: $i] :
( ( A @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( C @ ( E @ in ) ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( A @ ( D @ ( C @ ( B @ ( A @ sk11 ) ) @ ordered_pair ) @ in ) )
=> ( ( B @ ( D @ ( C @ ( B @ ( A @ sk11 ) ) @ ordered_pair ) @ in ) )
& ( C @ ( D @ in ) ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ! [E: $i] :
( ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( C @ ( E @ in ) ) )
=> ( A @ ( E @ ( D @ ordered_pair ) @ in ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( B @ ( D @ ( C @ ( B @ ( A @ sk13 ) ) @ ordered_pair ) @ in ) )
& ( C @ ( D @ in ) ) )
=> ( A @ ( D @ ( C @ ( B @ ( A @ sk13 ) ) @ ordered_pair ) @ in ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] : ( C @ ( A @ ( D @ ordered_pair ) @ in ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ? [D: $i] : ( B @ ( C @ ( D @ ordered_pair ) @ in ) ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ? [D: $i] : ( B @ ( C @ ( D @ ordered_pair ) @ in ) )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( B @ ( B @ ( A @ sk17 ) @ ( C @ ordered_pair ) @ in ) ) ) ) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(88,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( C @ ( B @ relation_rng_restriction ) @ relation_rng @ ( A @ in ) )
<=> ( ( C @ relation_rng @ ( A @ in ) )
& ( B @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_relat_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( C @ ( B @ relation_rng_restriction ) @ relation_rng @ ( A @ in ) )
<=> ( ( C @ relation_rng @ ( A @ in ) )
& ( B @ ( A @ in ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(27,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( ( ( C @ relation_rng @ ( A @ in ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( B @ relation_rng_restriction ) @ relation_rng @ ( A @ in ) ) )
& ( ( C @ ( B @ relation_rng_restriction ) @ relation_rng @ ( A @ in ) )
=> ( ( C @ relation_rng @ ( A @ in ) )
& ( B @ ( A @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28,plain,
( ( ~ ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng @ ( sk1 @ in ) )
| sk4 )
& ( ( sk3 @ relation_rng @ ( sk1 @ in ) )
| sk4 )
& ( ( sk2 @ ( sk1 @ in ) )
| sk4 )
& ( ~ sk4
| ~ ( sk3 @ relation_rng @ ( sk1 @ in ) )
| ~ ( sk2 @ ( sk1 @ in ) ) )
& ( ~ sk4
| ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng @ ( sk1 @ in ) ) )
& ( sk3 @ relation ) ),
inference(cnf,[status(esa)],[27]) ).
thf(31,plain,
( ~ sk4
| ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng @ ( sk1 @ in ) ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(90,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[90]) ).
thf(2484,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ ( A @ in ) ) ),
inference(eqfactor_ordered,[status(thm)],[91]) ).
thf(2485,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[2484:[bind(A,$thf( B ))]]) ).
thf(2490,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(simp,[status(thm)],[2485]) ).
thf(2495,plain,
! [A: $i] :
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng @ ( sk1 @ in ) )
!= ( A @ ( A @ in ) ) )
| ~ $true
| ~ sk4 ),
inference(paramod_ordered,[status(thm)],[31,2490]) ).
thf(2496,plain,
! [A: $i] :
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng @ ( sk1 @ in ) )
!= ( A @ ( A @ in ) ) )
| ~ sk4 ),
inference(simp,[status(thm)],[2495]) ).
thf(2505,plain,
! [A: $i] :
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng )
!= A )
| ( sk1 != A )
| ~ sk4 ),
inference(simp,[status(thm)],[2496]) ).
thf(2512,plain,
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng )
!= sk1 )
| ~ sk4 ),
inference(simp,[status(thm)],[2505]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox2/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(15,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/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(13,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
file('/export/starexec/sandbox2/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(560,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ordered_pair ) @ empty )
!= ( sk8 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,64]) ).
thf(561,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) @ empty )
!= ( sk8 @ empty ) ),
inference(simp,[status(thm)],[560]) ).
thf(572,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) )
!= sk8 ),
inference(simp,[status(thm)],[561]) ).
thf(9,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(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/sandbox2/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(636,plain,
! [A: $i] :
( ( ( sk8 @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[69,59]) ).
thf(637,plain,
! [A: $i] :
( ( ( sk8 @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[636]) ).
thf(638,plain,
sk8 = empty_set,
inference(pattern_uni,[status(thm)],[637:[bind(A,$thf( sk8 ))]]) ).
thf(1159,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) )
!= empty_set ),
inference(rewrite,[status(thm)],[572,53,638]) ).
thf(1160,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)],[37,1159]) ).
thf(1161,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ ( B @ unordered_pair ) @ unordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[1160:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1322,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)],[37,1161]) ).
thf(1323,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ ( B @ unordered_pair ) @ unordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[1322:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(18,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(77,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(32,plain,
( ( sk3 @ relation_rng @ ( sk1 @ in ) )
| sk4 ),
inference(cnfConj,[status(thm)],[28]) ).
thf(29,plain,
( ~ ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng @ ( sk1 @ in ) )
| sk4 ),
inference(cnfConj,[status(thm)],[28]) ).
thf(157,plain,
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng @ ( sk1 @ in ) )
!= ( sk3 @ relation_rng @ ( sk1 @ in ) ) )
| ~ $true
| sk4
| sk4 ),
inference(paramod_ordered,[status(thm)],[32,29]) ).
thf(158,plain,
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng @ ( sk1 @ in ) )
!= ( sk3 @ relation_rng @ ( sk1 @ in ) ) )
| sk4 ),
inference(simp,[status(thm)],[157]) ).
thf(161,plain,
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng )
!= ( sk3 @ relation_rng ) )
| ( sk1 != sk1 )
| sk4 ),
inference(simp,[status(thm)],[158]) ).
thf(163,plain,
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng )
!= ( sk3 @ relation_rng ) )
| sk4 ),
inference(simp,[status(thm)],[161]) ).
thf(209,plain,
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) )
!= sk3 )
| sk4 ),
inference(simp,[status(thm)],[163]) ).
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(1320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( C @ singleton @ ( C @ ( D @ unordered_pair ) @ unordered_pair ) ) )
| ( ( A @ ( B @ unordered_pair ) )
!= empty_set ) ),
inference(paramod_ordered,[status(thm)],[37,1161]) ).
thf(1321,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ singleton @ unordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[1320:[bind(A,$thf( G @ ( E @ unordered_pair ) )),bind(B,$thf( G @ singleton )),bind(C,$thf( G )),bind(D,$thf( E ))]]) ).
thf(1358,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ singleton @ unordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[1321]) ).
thf(3413,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)],[37,1358]) ).
thf(3414,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ singleton @ unordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[3413:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(5,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(42,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(33,plain,
sk3 @ relation,
inference(cnfConj,[status(thm)],[28]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ ( A @ relation_rng_restriction ) @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(92,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ ( A @ relation_rng_restriction ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ relation_rng_restriction ) @ relation )
| ~ ( B @ relation ) ),
inference(cnf,[status(esa)],[92]) ).
thf(2600,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ relation )
!= ( B @ relation ) )
| ( B @ ( A @ relation_rng_restriction ) @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,93]) ).
thf(2601,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ relation )
!= ( B @ relation ) )
| ( B @ ( A @ relation_rng_restriction ) @ relation ) ),
inference(simp,[status(thm)],[2600]) ).
thf(2602,plain,
! [A: $i] : ( sk3 @ ( A @ relation_rng_restriction ) @ relation ),
inference(pattern_uni,[status(thm)],[2601:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(2659,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ relation_rng_restriction ) @ relation )
!= ( C @ relation ) )
| ( C @ ( B @ relation_rng_restriction ) @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2602,93]) ).
thf(2660,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ relation_rng_restriction ) @ relation )
!= ( C @ relation ) )
| ( C @ ( B @ relation_rng_restriction ) @ relation ) ),
inference(simp,[status(thm)],[2659]) ).
thf(2661,plain,
! [B: $i,A: $i] : ( sk3 @ ( B @ relation_rng_restriction ) @ ( A @ relation_rng_restriction ) @ relation ),
inference(pattern_uni,[status(thm)],[2660:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( sk3 @ ( D @ relation_rng_restriction ) ))]]) ).
thf(2670,plain,
! [B: $i,A: $i] : ( sk3 @ ( B @ relation_rng_restriction ) @ ( A @ relation_rng_restriction ) @ relation ),
inference(simp,[status(thm)],[2661]) ).
thf(3245,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( B @ relation_rng_restriction ) @ ( A @ relation_rng_restriction ) @ relation )
!= ( D @ relation ) )
| ( D @ ( C @ relation_rng_restriction ) @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2670,93]) ).
thf(3246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( B @ relation_rng_restriction ) @ ( A @ relation_rng_restriction ) @ relation )
!= ( D @ relation ) )
| ( D @ ( C @ relation_rng_restriction ) @ relation ) ),
inference(simp,[status(thm)],[3245]) ).
thf(3247,plain,
! [C: $i,B: $i,A: $i] : ( sk3 @ ( C @ relation_rng_restriction ) @ ( B @ relation_rng_restriction ) @ ( A @ relation_rng_restriction ) @ relation ),
inference(pattern_uni,[status(thm)],[3246:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( sk3 @ ( G @ relation_rng_restriction ) @ ( E @ relation_rng_restriction ) ))]]) ).
thf(3281,plain,
! [C: $i,B: $i,A: $i] : ( sk3 @ ( C @ relation_rng_restriction ) @ ( B @ relation_rng_restriction ) @ ( A @ relation_rng_restriction ) @ relation ),
inference(simp,[status(thm)],[3247]) ).
thf(6,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/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(34,plain,
( ( sk2 @ ( sk1 @ in ) )
| sk4 ),
inference(cnfConj,[status(thm)],[28]) ).
thf(159,plain,
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng @ ( sk1 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ~ $true
| sk4
| sk4 ),
inference(paramod_ordered,[status(thm)],[34,29]) ).
thf(160,plain,
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng @ ( sk1 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| sk4 ),
inference(simp,[status(thm)],[159]) ).
thf(162,plain,
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng )
!= sk2 )
| ( sk1 != sk1 )
| sk4 ),
inference(simp,[status(thm)],[160]) ).
thf(164,plain,
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng )
!= sk2 )
| sk4 ),
inference(simp,[status(thm)],[162]) ).
thf(8,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(50,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_rng @ relation )
& ( A @ relation_rng @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(81,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_rng @ relation )
& ( A @ relation_rng @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(82,plain,
! [A: $i] :
( ( ( A @ relation_rng @ relation )
| ~ ( A @ empty ) )
& ( ( A @ relation_rng @ empty )
| ~ ( A @ empty ) ) ),
inference(cnf,[status(esa)],[81]) ).
thf(83,plain,
! [A: $i] :
( ( A @ relation_rng @ empty )
| ~ ( A @ empty ) ),
inference(cnfConj,[status(thm)],[82]) ).
thf(1899,plain,
! [A: $i] :
( ( ( empty_set @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,83]) ).
thf(1900,plain,
! [A: $i] :
( ( ( empty_set @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty ) ),
inference(simp,[status(thm)],[1899]) ).
thf(1901,plain,
empty_set @ relation_rng @ empty,
inference(pattern_uni,[status(thm)],[1900:[bind(A,$thf( empty_set ))]]) ).
thf(1959,plain,
! [A: $i] :
( ( ( empty_set @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1901,83]) ).
thf(1960,plain,
! [A: $i] :
( ( ( empty_set @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ empty ) ),
inference(simp,[status(thm)],[1959]) ).
thf(1961,plain,
empty_set @ relation_rng @ relation_rng @ empty,
inference(pattern_uni,[status(thm)],[1960:[bind(A,$thf( empty_set @ relation_rng ))]]) ).
thf(1947,plain,
! [A: $i] :
( ( ( empty_set @ relation_rng @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[1901,59]) ).
thf(1948,plain,
! [A: $i] :
( ( ( empty_set @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[1947]) ).
thf(1949,plain,
( ( empty_set @ relation_rng )
= empty_set ),
inference(pattern_uni,[status(thm)],[1948:[bind(A,$thf( empty_set @ relation_rng ))]]) ).
thf(2051,plain,
empty_set @ relation_rng @ empty,
inference(rewrite,[status(thm)],[1961,1949]) ).
thf(84,plain,
! [A: $i] :
( ( A @ relation_rng @ relation )
| ~ ( A @ empty ) ),
inference(cnfConj,[status(thm)],[82]) ).
thf(2158,plain,
! [A: $i] :
( ( ( empty_set @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2051,84]) ).
thf(2159,plain,
! [A: $i] :
( ( ( empty_set @ relation_rng @ empty )
!= ( A @ empty ) )
| ( A @ relation_rng @ relation ) ),
inference(simp,[status(thm)],[2158]) ).
thf(2160,plain,
empty_set @ relation_rng @ relation_rng @ relation,
inference(pattern_uni,[status(thm)],[2159:[bind(A,$thf( empty_set @ relation_rng ))]]) ).
thf(2254,plain,
empty_set @ relation_rng @ relation,
inference(rewrite,[status(thm)],[2160,1949]) ).
thf(717,plain,
! [A: $i] :
( ( A != sk2 )
| ( empty_set @ ( sk1 @ in ) )
| sk4
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[59,34]) ).
thf(718,plain,
( ( empty_set @ ( sk1 @ in ) )
| sk4
| ~ ( sk2 @ empty ) ),
inference(pattern_uni,[status(thm)],[717:[bind(A,$thf( sk2 ))]]) ).
thf(1281,plain,
( ( ( sk2 @ empty )
!= ( empty_set @ empty ) )
| ( empty_set @ ( sk1 @ in ) )
| sk4
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,718]) ).
thf(1282,plain,
( ( ( sk2 @ empty )
!= ( empty_set @ empty ) )
| ( empty_set @ ( sk1 @ in ) )
| sk4 ),
inference(simp,[status(thm)],[1281]) ).
thf(1292,plain,
( ( sk2 != empty_set )
| ( empty_set @ ( sk1 @ in ) )
| sk4 ),
inference(simp,[status(thm)],[1282]) ).
thf(20,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(85,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(86,plain,
~ ? [A: $i,B: $i] :
( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(miniscope,[status(thm)],[85]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[86]) ).
thf(2233,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ empty )
!= ( B @ empty ) )
| ~ $true
| ~ ( B @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[50,87]) ).
thf(2234,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ empty )
!= ( B @ empty ) )
| ~ ( B @ ( A @ in ) ) ),
inference(simp,[status(thm)],[2233]) ).
thf(2235,plain,
! [A: $i] :
~ ( empty_set @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[2234:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).
thf(2283,plain,
( ( sk2 != empty_set )
| $false
| sk4 ),
inference(rewrite,[status(thm)],[1292,2235]) ).
thf(2284,plain,
( ( sk2 != empty_set )
| sk4 ),
inference(simp,[status(thm)],[2283]) ).
thf(2236,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ empty )
| ~ $true
| ~ sk4 ),
inference(paramod_ordered,[status(thm)],[31,87]) ).
thf(2237,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ empty )
| ~ sk4 ),
inference(simp,[status(thm)],[2236]) ).
thf(2238,plain,
( ~ ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng @ empty )
| ~ sk4 ),
inference(pattern_uni,[status(thm)],[2237:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng ))]]) ).
thf(2756,plain,
! [A: $i] :
( ( ( A @ relation_rng @ empty )
!= ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng @ empty ) )
| ~ $true
| ~ sk4
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[83,2238]) ).
thf(2757,plain,
! [A: $i] :
( ( ( A @ relation_rng @ empty )
!= ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng @ empty ) )
| ~ sk4
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[2756]) ).
thf(2758,plain,
( ~ sk4
| ~ ( sk3 @ ( sk2 @ relation_rng_restriction ) @ empty ) ),
inference(pattern_uni,[status(thm)],[2757:[bind(A,$thf( sk3 @ ( sk2 @ relation_rng_restriction ) ))]]) ).
thf(3492,plain,
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ empty )
!= ( empty_set @ empty ) )
| ~ sk4
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,2758]) ).
thf(3493,plain,
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ empty )
!= ( empty_set @ empty ) )
| ~ sk4 ),
inference(simp,[status(thm)],[3492]) ).
thf(3505,plain,
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) )
!= empty_set )
| ~ sk4 ),
inference(simp,[status(thm)],[3493]) ).
thf(3535,plain,
( ( sk4 != sk4 )
| ( ( sk3 @ ( sk2 @ relation_rng_restriction ) )
!= empty_set )
| ~ $true
| ( sk2 != empty_set ) ),
inference(paramod_ordered,[status(thm)],[2284,3505]) ).
thf(3536,plain,
( ( sk4 != sk4 )
| ( ( sk3 @ ( sk2 @ relation_rng_restriction ) )
!= empty_set )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[3535]) ).
thf(3537,plain,
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) )
!= empty_set )
| ( sk2 != empty_set ) ),
inference(pattern_uni,[status(thm)],[3536:[]]) ).
thf(12,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/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(89,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ in ) )
| ( B @ empty )
| ~ ( B @ ( A @ element ) ) ),
inference(cnf,[status(esa)],[88]) ).
thf(25,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_rng @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(116,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_rng @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(16,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(71,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(72,plain,
( ( sk9 @ relation )
& ~ ( sk9 @ empty ) ),
inference(cnf,[status(esa)],[71]) ).
thf(74,plain,
sk9 @ relation,
inference(cnfConj,[status(thm)],[72]) ).
thf(2597,plain,
! [B: $i,A: $i] :
( ( ( sk9 @ relation )
!= ( B @ relation ) )
| ( B @ ( A @ relation_rng_restriction ) @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[74,93]) ).
thf(2598,plain,
! [B: $i,A: $i] :
( ( ( sk9 @ relation )
!= ( B @ relation ) )
| ( B @ ( A @ relation_rng_restriction ) @ relation ) ),
inference(simp,[status(thm)],[2597]) ).
thf(2599,plain,
! [A: $i] : ( sk9 @ ( A @ relation_rng_restriction ) @ relation ),
inference(pattern_uni,[status(thm)],[2598:[bind(A,$thf( A )),bind(B,$thf( sk9 ))]]) ).
thf(2629,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk9 @ ( A @ relation_rng_restriction ) @ relation )
!= ( C @ relation ) )
| ( C @ ( B @ relation_rng_restriction ) @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2599,93]) ).
thf(2630,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk9 @ ( A @ relation_rng_restriction ) @ relation )
!= ( C @ relation ) )
| ( C @ ( B @ relation_rng_restriction ) @ relation ) ),
inference(simp,[status(thm)],[2629]) ).
thf(2631,plain,
! [B: $i,A: $i] : ( sk9 @ ( B @ relation_rng_restriction ) @ ( A @ relation_rng_restriction ) @ relation ),
inference(pattern_uni,[status(thm)],[2630:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( sk9 @ ( D @ relation_rng_restriction ) ))]]) ).
thf(2641,plain,
! [B: $i,A: $i] : ( sk9 @ ( B @ relation_rng_restriction ) @ ( A @ relation_rng_restriction ) @ relation ),
inference(simp,[status(thm)],[2631]) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/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(539,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ empty )
!= ( sk8 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,56]) ).
thf(540,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ empty )
!= ( sk8 @ empty ) ),
inference(simp,[status(thm)],[539]) ).
thf(555,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
!= sk8 ),
inference(simp,[status(thm)],[540]) ).
thf(818,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
!= empty_set ),
inference(rewrite,[status(thm)],[555,638]) ).
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)],[37,818]) ).
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(2378,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ element ) )
!= ( C @ ( B @ element ) ) )
| ( C @ ( B @ in ) )
| ( C @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[61,89]) ).
thf(2379,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ element ) )
!= ( C @ ( B @ element ) ) )
| ( C @ ( B @ in ) )
| ( C @ empty ) ),
inference(simp,[status(thm)],[2378]) ).
thf(2380,plain,
! [A: $i] :
( ( A @ ( A @ sk7 @ in ) )
| ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[2379:[bind(A,$thf( D )),bind(B,$thf( D @ sk7 )),bind(C,$thf( D ))]]) ).
thf(2387,plain,
! [A: $i] :
( ( A @ ( A @ sk7 @ in ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[2380]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/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(3569,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ in ) )
!= ( C @ ( B @ in ) ) )
| ( C @ ( B @ element ) )
| ~ $true
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[2387,66]) ).
thf(3570,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ in ) )
!= ( C @ ( B @ in ) ) )
| ( C @ ( B @ element ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[3569]) ).
thf(3571,plain,
! [A: $i] :
( ( A @ ( A @ sk7 @ element ) )
| ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[3570:[bind(A,$thf( D )),bind(B,$thf( D @ sk7 )),bind(C,$thf( D ))]]) ).
thf(3600,plain,
! [A: $i] :
( ( A @ ( A @ sk7 @ element ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[3571]) ).
thf(1141,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ relation_rng @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| sk4 ),
inference(paramod_ordered,[status(thm)],[32,66]) ).
thf(1142,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ relation_rng @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| sk4 ),
inference(simp,[status(thm)],[1141]) ).
thf(1143,plain,
( ( sk3 @ relation_rng @ ( sk1 @ element ) )
| sk4 ),
inference(pattern_uni,[status(thm)],[1142:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ relation_rng ))]]) ).
thf(2448,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( A @ ( B @ in ) )
| ~ $true
| sk4 ),
inference(paramod_ordered,[status(thm)],[34,91]) ).
thf(2449,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( A @ ( B @ in ) )
| sk4 ),
inference(simp,[status(thm)],[2448]) ).
thf(2450,plain,
( ~ ( sk1 @ ( sk2 @ in ) )
| sk4 ),
inference(pattern_uni,[status(thm)],[2449:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( C @ relation )
=> ( ( C
= ( B @ ( A @ relation_rng_restriction ) ) )
<=> ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
<=> ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( E @ in ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_1) ).
thf(94,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( C @ relation )
=> ( ( ! [D: $i,E: $i] :
( ( ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( E @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( E @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_rng_restriction ) ) ) )
& ( ( C
= ( B @ ( A @ relation_rng_restriction ) ) )
=> ! [D: $i,E: $i] :
( ( ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( E @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( E @ in ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(95,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( C @ relation )
=> ( ( ( ! [D: $i,E: $i] :
( ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( E @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( E @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_rng_restriction ) ) ) )
& ( ( C
= ( B @ ( A @ relation_rng_restriction ) ) )
=> ( ! [D: $i,E: $i] :
( ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( E @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( E @ in ) ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[94]) ).
thf(96,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C
= ( B @ ( A @ relation_rng_restriction ) ) )
| ~ ( C @ ( A @ ( B @ ( C @ sk14 ) ) @ ( A @ ( B @ ( C @ sk13 ) ) @ ordered_pair ) @ in ) )
| ( C @ ( A @ ( B @ sk10 ) ) )
| ~ ( C @ relation )
| ~ ( B @ relation ) )
& ( ( C
= ( B @ ( A @ relation_rng_restriction ) ) )
| ( B @ ( A @ ( B @ ( C @ sk14 ) ) @ ( A @ ( B @ ( C @ sk13 ) ) @ ordered_pair ) @ in ) )
| ( C @ ( A @ ( B @ sk10 ) ) )
| ~ ( C @ relation )
| ~ ( B @ relation ) )
& ( ( C
= ( B @ ( A @ relation_rng_restriction ) ) )
| ( A @ ( A @ ( B @ ( C @ sk14 ) ) @ in ) )
| ( C @ ( A @ ( B @ sk10 ) ) )
| ~ ( C @ relation )
| ~ ( B @ relation ) )
& ( ( C
= ( B @ ( A @ relation_rng_restriction ) ) )
| ~ ( C @ ( A @ ( B @ sk10 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk12 ) ) @ ( A @ ( B @ ( C @ sk11 ) ) @ ordered_pair ) @ in ) )
| ~ ( A @ ( A @ ( B @ ( C @ sk12 ) ) @ in ) )
| ~ ( C @ relation )
| ~ ( B @ relation ) )
& ( ( C
= ( B @ ( A @ relation_rng_restriction ) ) )
| ~ ( C @ ( A @ ( B @ sk10 ) ) )
| ( C @ ( A @ ( B @ ( C @ sk12 ) ) @ ( A @ ( B @ ( C @ sk11 ) ) @ ordered_pair ) @ in ) )
| ~ ( C @ relation )
| ~ ( B @ relation ) )
& ( ( C @ ( G @ ( F @ ordered_pair ) @ in ) )
| ~ ( B @ ( G @ ( F @ ordered_pair ) @ in ) )
| ~ ( A @ ( G @ in ) )
| ( C
!= ( B @ ( A @ relation_rng_restriction ) ) )
| ~ ( C @ relation )
| ~ ( B @ relation ) )
& ( ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
| ~ ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
| ( C
!= ( B @ ( A @ relation_rng_restriction ) ) )
| ~ ( C @ relation )
| ~ ( B @ relation ) )
& ( ( A @ ( E @ in ) )
| ~ ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
| ( C
!= ( B @ ( A @ relation_rng_restriction ) ) )
| ~ ( C @ relation )
| ~ ( B @ relation ) ) ),
inference(cnf,[status(esa)],[95]) ).
thf(98,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
| ~ ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
| ~ ( A @ ( E @ in ) )
| ( C
!= ( B @ ( A @ relation_rng_restriction ) ) )
| ~ ( C @ relation )
| ~ ( B @ relation ) ),
inference(cnfConj,[status(thm)],[96]) ).
thf(108,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
| ~ ( B @ ( E @ ( D @ ordered_pair ) @ in ) )
| ~ ( A @ ( E @ in ) )
| ~ ( C @ relation )
| ~ ( B @ relation )
| ( C
!= ( B @ ( A @ relation_rng_restriction ) ) ) ),
inference(lifteq,[status(thm)],[98]) ).
thf(109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ relation_rng_restriction ) @ ( D @ ( C @ ordered_pair ) @ in ) )
| ~ ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
| ~ ( A @ ( D @ in ) )
| ~ ( B @ ( A @ relation_rng_restriction ) @ relation )
| ~ ( B @ relation ) ),
inference(simp,[status(thm)],[108]) ).
thf(5369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ relation_rng_restriction ) @ ( C @ singleton @ ( D @ ( C @ unordered_pair ) @ unordered_pair ) @ in ) )
| ~ ( B @ ( C @ singleton @ ( D @ ( C @ unordered_pair ) @ unordered_pair ) @ in ) )
| ~ ( A @ ( D @ in ) )
| ~ ( B @ ( A @ relation_rng_restriction ) @ relation )
| ~ ( B @ relation ) ),
inference(rewrite,[status(thm)],[109,53]) ).
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(73,plain,
~ ( sk9 @ empty ),
inference(cnfConj,[status(thm)],[72]) ).
thf(101,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ relation_rng_restriction ) ) )
| ( A @ ( A @ ( B @ ( C @ sk14 ) ) @ in ) )
| ( C @ ( A @ ( B @ sk10 ) ) )
| ~ ( C @ relation )
| ~ ( B @ relation ) ),
inference(cnfConj,[status(thm)],[96]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ sk14 ) ) @ in ) )
| ( C @ ( A @ ( B @ sk10 ) ) )
| ~ ( C @ relation )
| ~ ( B @ relation )
| ( C
= ( B @ ( A @ relation_rng_restriction ) ) ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(1144,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| sk4 ),
inference(paramod_ordered,[status(thm)],[34,66]) ).
thf(1145,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| sk4 ),
inference(simp,[status(thm)],[1144]) ).
thf(1146,plain,
( ( sk2 @ ( sk1 @ element ) )
| sk4 ),
inference(pattern_uni,[status(thm)],[1145:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(145,plain,
( ( ( sk9 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,73]) ).
thf(146,plain,
( ( sk9 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[145]) ).
thf(149,plain,
sk9 != empty_set,
inference(simp,[status(thm)],[146]) ).
thf(2224,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ relation_rng @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ empty )
| ~ $true
| sk4 ),
inference(paramod_ordered,[status(thm)],[32,87]) ).
thf(2225,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ relation_rng @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ empty )
| sk4 ),
inference(simp,[status(thm)],[2224]) ).
thf(2226,plain,
( ~ ( sk3 @ relation_rng @ empty )
| sk4 ),
inference(pattern_uni,[status(thm)],[2225:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ relation_rng ))]]) ).
thf(2833,plain,
! [A: $i] :
( ( ( A @ relation_rng @ empty )
!= ( sk3 @ relation_rng @ empty ) )
| ~ $true
| sk4
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[83,2226]) ).
thf(2834,plain,
! [A: $i] :
( ( ( A @ relation_rng @ empty )
!= ( sk3 @ relation_rng @ empty ) )
| sk4
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[2833]) ).
thf(2835,plain,
( sk4
| ~ ( sk3 @ empty ) ),
inference(pattern_uni,[status(thm)],[2834:[bind(A,$thf( sk3 ))]]) ).
thf(2852,plain,
( ( ( sk3 @ empty )
!= ( empty_set @ empty ) )
| sk4
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,2835]) ).
thf(2853,plain,
( ( ( sk3 @ empty )
!= ( empty_set @ empty ) )
| sk4 ),
inference(simp,[status(thm)],[2852]) ).
thf(2859,plain,
( ( sk3 != empty_set )
| sk4 ),
inference(simp,[status(thm)],[2853]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B
= ( A @ relation_rng ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] : ( A @ ( C @ ( D @ ordered_pair ) @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
thf(118,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] : ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] : ( A @ ( C @ ( D @ ordered_pair ) @ in ) ) ) )
=> ( B
= ( A @ relation_rng ) ) )
& ( ( B
= ( A @ relation_rng ) )
=> ! [C: $i] :
( ( ? [D: $i] : ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] : ( A @ ( C @ ( D @ ordered_pair ) @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(142,plain,
( ( ( sk6 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,46]) ).
thf(143,plain,
( ( sk6 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[142]) ).
thf(144,plain,
sk6 != empty_set,
inference(simp,[status(thm)],[143]) ).
thf(7,axiom,
! [A: $i] :
~ ( A @ singleton @ empty ),
file('/export/starexec/sandbox2/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(2295,plain,
! [A: $i] :
( ( ( sk3 @ relation_rng @ ( sk1 @ in ) )
!= ( empty_set @ ( A @ in ) ) )
| ~ $true
| sk4 ),
inference(paramod_ordered,[status(thm)],[32,2235]) ).
thf(2296,plain,
! [A: $i] :
( ( ( sk3 @ relation_rng @ ( sk1 @ in ) )
!= ( empty_set @ ( A @ in ) ) )
| sk4 ),
inference(simp,[status(thm)],[2295]) ).
thf(2312,plain,
! [A: $i] :
( ( ( sk3 @ relation_rng )
!= empty_set )
| ( sk1 != A )
| sk4 ),
inference(simp,[status(thm)],[2296]) ).
thf(2319,plain,
( ( ( sk3 @ relation_rng )
!= empty_set )
| sk4 ),
inference(simp,[status(thm)],[2312]) ).
thf(2227,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ empty )
| ~ $true
| sk4 ),
inference(paramod_ordered,[status(thm)],[34,87]) ).
thf(2228,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ empty )
| sk4 ),
inference(simp,[status(thm)],[2227]) ).
thf(2229,plain,
( ~ ( sk2 @ empty )
| sk4 ),
inference(pattern_uni,[status(thm)],[2228:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(75,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(76,plain,
! [A: $i] :
( ( A @ relation )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[75]) ).
thf(78,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(cnf,[status(esa)],[77]) ).
thf(80,plain,
empty_set @ relation,
inference(cnfConj,[status(thm)],[78]) ).
thf(2603,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ relation )
!= ( B @ relation ) )
| ( B @ ( A @ relation_rng_restriction ) @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[80,93]) ).
thf(2604,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ relation )
!= ( B @ relation ) )
| ( B @ ( A @ relation_rng_restriction ) @ relation ) ),
inference(simp,[status(thm)],[2603]) ).
thf(2605,plain,
! [A: $i] : ( empty_set @ ( A @ relation_rng_restriction ) @ relation ),
inference(pattern_uni,[status(thm)],[2604:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).
thf(2785,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk9 @ ( B @ relation_rng_restriction ) @ ( A @ relation_rng_restriction ) @ relation )
!= ( D @ relation ) )
| ( D @ ( C @ relation_rng_restriction ) @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2641,93]) ).
thf(2786,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk9 @ ( B @ relation_rng_restriction ) @ ( A @ relation_rng_restriction ) @ relation )
!= ( D @ relation ) )
| ( D @ ( C @ relation_rng_restriction ) @ relation ) ),
inference(simp,[status(thm)],[2785]) ).
thf(2787,plain,
! [C: $i,B: $i,A: $i] : ( sk9 @ ( C @ relation_rng_restriction ) @ ( B @ relation_rng_restriction ) @ ( A @ relation_rng_restriction ) @ relation ),
inference(pattern_uni,[status(thm)],[2786:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( sk9 @ ( G @ relation_rng_restriction ) @ ( E @ relation_rng_restriction ) ))]]) ).
thf(2797,plain,
! [C: $i,B: $i,A: $i] : ( sk9 @ ( C @ relation_rng_restriction ) @ ( B @ relation_rng_restriction ) @ ( A @ relation_rng_restriction ) @ relation ),
inference(simp,[status(thm)],[2787]) ).
thf(2491,plain,
! [A: $i] :
( ( ( sk3 @ relation_rng @ ( sk1 @ in ) )
!= ( A @ ( A @ in ) ) )
| ~ $true
| sk4 ),
inference(paramod_ordered,[status(thm)],[32,2490]) ).
thf(2492,plain,
! [A: $i] :
( ( ( sk3 @ relation_rng @ ( sk1 @ in ) )
!= ( A @ ( A @ in ) ) )
| sk4 ),
inference(simp,[status(thm)],[2491]) ).
thf(2506,plain,
! [A: $i] :
( ( ( sk3 @ relation_rng )
!= A )
| ( sk1 != A )
| sk4 ),
inference(simp,[status(thm)],[2492]) ).
thf(2513,plain,
( ( ( sk3 @ relation_rng )
!= sk1 )
| sk4 ),
inference(simp,[status(thm)],[2506]) ).
thf(102,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ relation_rng_restriction ) ) )
| ( B @ ( A @ ( B @ ( C @ sk14 ) ) @ ( A @ ( B @ ( C @ sk13 ) ) @ ordered_pair ) @ in ) )
| ( C @ ( A @ ( B @ sk10 ) ) )
| ~ ( C @ relation )
| ~ ( B @ relation ) ),
inference(cnfConj,[status(thm)],[96]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( C @ sk14 ) ) @ ( A @ ( B @ ( C @ sk13 ) ) @ ordered_pair ) @ in ) )
| ( C @ ( A @ ( B @ sk10 ) ) )
| ~ ( C @ relation )
| ~ ( B @ relation )
| ( C
= ( B @ ( A @ relation_rng_restriction ) ) ) ),
inference(lifteq,[status(thm)],[102]) ).
thf(3659,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( C @ sk13 ) ) @ singleton @ ( A @ ( B @ ( C @ sk14 ) ) @ ( A @ ( B @ ( C @ sk13 ) ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ( C @ ( A @ ( B @ sk10 ) ) )
| ~ ( C @ relation )
| ~ ( B @ relation )
| ( C
= ( B @ ( A @ relation_rng_restriction ) ) ) ),
inference(rewrite,[status(thm)],[106,53]) ).
thf(195,plain,
! [A: $i] :
( ( ( A @ singleton @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,49]) ).
thf(196,plain,
! [A: $i] :
( ( A @ singleton @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[195]) ).
thf(199,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(simp,[status(thm)],[196]) ).
thf(2691,plain,
! [C: $i,B: $i,A: $i] :
( ( ( empty_set @ ( A @ relation_rng_restriction ) @ relation )
!= ( C @ relation ) )
| ( C @ ( B @ relation_rng_restriction ) @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2605,93]) ).
thf(2692,plain,
! [C: $i,B: $i,A: $i] :
( ( ( empty_set @ ( A @ relation_rng_restriction ) @ relation )
!= ( C @ relation ) )
| ( C @ ( B @ relation_rng_restriction ) @ relation ) ),
inference(simp,[status(thm)],[2691]) ).
thf(2693,plain,
! [B: $i,A: $i] : ( empty_set @ ( B @ relation_rng_restriction ) @ ( A @ relation_rng_restriction ) @ relation ),
inference(pattern_uni,[status(thm)],[2692:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( empty_set @ ( D @ relation_rng_restriction ) ))]]) ).
thf(2701,plain,
! [B: $i,A: $i] : ( empty_set @ ( B @ relation_rng_restriction ) @ ( A @ relation_rng_restriction ) @ relation ),
inference(simp,[status(thm)],[2693]) ).
thf(3309,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( empty_set @ ( B @ relation_rng_restriction ) @ ( A @ relation_rng_restriction ) @ relation )
!= ( D @ relation ) )
| ( D @ ( C @ relation_rng_restriction ) @ relation )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2701,93]) ).
thf(3310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( empty_set @ ( B @ relation_rng_restriction ) @ ( A @ relation_rng_restriction ) @ relation )
!= ( D @ relation ) )
| ( D @ ( C @ relation_rng_restriction ) @ relation ) ),
inference(simp,[status(thm)],[3309]) ).
thf(3311,plain,
! [C: $i,B: $i,A: $i] : ( empty_set @ ( C @ relation_rng_restriction ) @ ( B @ relation_rng_restriction ) @ ( A @ relation_rng_restriction ) @ relation ),
inference(pattern_uni,[status(thm)],[3310:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( empty_set @ ( G @ relation_rng_restriction ) @ ( E @ relation_rng_restriction ) ))]]) ).
thf(3344,plain,
! [C: $i,B: $i,A: $i] : ( empty_set @ ( C @ relation_rng_restriction ) @ ( B @ relation_rng_restriction ) @ ( A @ relation_rng_restriction ) @ relation ),
inference(simp,[status(thm)],[3311]) ).
thf(97,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ relation_rng_restriction ) ) )
| ~ ( C @ ( A @ ( B @ ( C @ sk14 ) ) @ ( A @ ( B @ ( C @ sk13 ) ) @ ordered_pair ) @ in ) )
| ( C @ ( A @ ( B @ sk10 ) ) )
| ~ ( C @ relation )
| ~ ( B @ relation ) ),
inference(cnfConj,[status(thm)],[96]) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( C @ sk14 ) ) @ ( A @ ( B @ ( C @ sk13 ) ) @ ordered_pair ) @ in ) )
| ( C @ ( A @ ( B @ sk10 ) ) )
| ~ ( C @ relation )
| ~ ( B @ relation )
| ( C
= ( B @ ( A @ relation_rng_restriction ) ) ) ),
inference(lifteq,[status(thm)],[97]) ).
thf(4436,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( C @ sk13 ) ) @ singleton @ ( A @ ( B @ ( C @ sk14 ) ) @ ( A @ ( B @ ( C @ sk13 ) ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ( C @ ( A @ ( B @ sk10 ) ) )
| ~ ( C @ relation )
| ~ ( B @ relation )
| ( C
= ( B @ ( A @ relation_rng_restriction ) ) ) ),
inference(rewrite,[status(thm)],[107,53]) ).
thf(2299,plain,
! [A: $i] :
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng @ ( sk1 @ in ) )
!= ( empty_set @ ( A @ in ) ) )
| ~ $true
| ~ sk4 ),
inference(paramod_ordered,[status(thm)],[31,2235]) ).
thf(2300,plain,
! [A: $i] :
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng @ ( sk1 @ in ) )
!= ( empty_set @ ( A @ in ) ) )
| ~ sk4 ),
inference(simp,[status(thm)],[2299]) ).
thf(2313,plain,
! [A: $i] :
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng )
!= empty_set )
| ( sk1 != A )
| ~ sk4 ),
inference(simp,[status(thm)],[2300]) ).
thf(2320,plain,
( ( ( sk3 @ ( sk2 @ relation_rng_restriction ) @ relation_rng )
!= empty_set )
| ~ sk4 ),
inference(simp,[status(thm)],[2313]) ).
thf(715,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk2 @ ( empty_set @ in ) )
| sk4
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[59,34]) ).
thf(716,plain,
( ( sk2 @ ( empty_set @ in ) )
| sk4
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[715:[bind(A,$thf( sk1 ))]]) ).
thf(1138,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( empty_set @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| ~ $true
| sk4
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[716,66]) ).
thf(1139,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( empty_set @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ element ) )
| sk4
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[1138]) ).
thf(1140,plain,
( ( sk2 @ ( empty_set @ element ) )
| sk4
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[1139:[bind(A,$thf( empty_set )),bind(B,$thf( sk2 ))]]) ).
thf(103,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ relation_rng_restriction ) ) )
| ~ ( C @ ( A @ ( B @ sk10 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk12 ) ) @ ( A @ ( B @ ( C @ sk11 ) ) @ ordered_pair ) @ in ) )
| ~ ( A @ ( A @ ( B @ ( C @ sk12 ) ) @ in ) )
| ~ ( C @ relation )
| ~ ( B @ relation ) ),
inference(cnfConj,[status(thm)],[96]) ).
thf(110,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ sk10 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk12 ) ) @ ( A @ ( B @ ( C @ sk11 ) ) @ ordered_pair ) @ in ) )
| ~ ( A @ ( A @ ( B @ ( C @ sk12 ) ) @ in ) )
| ~ ( C @ relation )
| ~ ( B @ relation )
| ( C
= ( B @ ( A @ relation_rng_restriction ) ) ) ),
inference(lifteq,[status(thm)],[103]) ).
thf(6086,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ sk10 ) ) )
| ~ ( B @ ( A @ ( B @ ( C @ sk11 ) ) @ singleton @ ( A @ ( B @ ( C @ sk12 ) ) @ ( A @ ( B @ ( C @ sk11 ) ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ~ ( A @ ( A @ ( B @ ( C @ sk12 ) ) @ in ) )
| ~ ( C @ relation )
| ~ ( B @ relation )
| ( C
= ( B @ ( A @ relation_rng_restriction ) ) ) ),
inference(rewrite,[status(thm)],[110,53]) ).
thf(43,plain,
sk5 @ empty,
inference(cnf,[status(esa)],[42]) ).
thf(669,plain,
! [A: $i] :
( ( ( sk5 @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[43,59]) ).
thf(670,plain,
! [A: $i] :
( ( ( sk5 @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[669]) ).
thf(671,plain,
sk5 = empty_set,
inference(pattern_uni,[status(thm)],[670:[bind(A,$thf( sk5 ))]]) ).
thf(1122,plain,
( ( ( sk1 @ empty )
!= ( empty_set @ empty ) )
| ( sk2 @ ( empty_set @ in ) )
| sk4
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,716]) ).
thf(1123,plain,
( ( ( sk1 @ empty )
!= ( empty_set @ empty ) )
| ( sk2 @ ( empty_set @ in ) )
| sk4 ),
inference(simp,[status(thm)],[1122]) ).
thf(1133,plain,
( ( sk1 != empty_set )
| ( sk2 @ ( empty_set @ in ) )
| sk4 ),
inference(simp,[status(thm)],[1123]) ).
thf(2493,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ in ) )
!= ( A @ ( A @ in ) ) )
| ~ $true
| sk4 ),
inference(paramod_ordered,[status(thm)],[34,2490]) ).
thf(2494,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ in ) )
!= ( A @ ( A @ in ) ) )
| sk4 ),
inference(simp,[status(thm)],[2493]) ).
thf(2510,plain,
! [A: $i] :
( ( sk2 != A )
| ( sk1 != A )
| sk4 ),
inference(simp,[status(thm)],[2494]) ).
thf(2517,plain,
( ( sk2 != sk1 )
| sk4 ),
inference(simp,[status(thm)],[2510]) ).
thf(119,plain,
! [A: $i] :
( ( A @ relation )
=> ( ! [B: $i] :
( ( ! [C: $i] :
( ? [D: $i] : ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ? [D: $i] : ( A @ ( C @ ( D @ ordered_pair ) @ in ) ) ) )
=> ( B
= ( A @ relation_rng ) ) )
& ! [B: $i] :
( ( B
= ( A @ relation_rng ) )
=> ( ! [C: $i] :
( ? [D: $i] : ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ? [D: $i] : ( A @ ( C @ ( D @ ordered_pair ) @ in ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[118]) ).
thf(120,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( A @ relation_rng ) )
| ~ ( F @ ( A @ ( F @ sk17 ) @ in ) )
| ~ ( A @ ( A @ ( F @ sk16 ) @ ( G @ ordered_pair ) @ in ) )
| ~ ( A @ relation ) )
& ( ( F
= ( A @ relation_rng ) )
| ( A @ ( A @ ( F @ sk17 ) @ ( A @ ( F @ sk18 ) @ ordered_pair ) @ in ) )
| ~ ( A @ ( A @ ( F @ sk16 ) @ ( G @ ordered_pair ) @ in ) )
| ~ ( A @ relation ) )
& ( ( F
= ( A @ relation_rng ) )
| ~ ( F @ ( A @ ( F @ sk17 ) @ in ) )
| ( F @ ( A @ ( F @ sk16 ) @ in ) )
| ~ ( A @ relation ) )
& ( ( F
= ( A @ relation_rng ) )
| ( A @ ( A @ ( F @ sk17 ) @ ( A @ ( F @ sk18 ) @ ordered_pair ) @ in ) )
| ( F @ ( A @ ( F @ sk16 ) @ in ) )
| ~ ( A @ relation ) )
& ( ( B @ ( D @ in ) )
| ~ ( A @ ( D @ ( E @ ordered_pair ) @ in ) )
| ( B
!= ( A @ relation_rng ) )
| ~ ( A @ relation ) )
& ( ( A @ ( C @ ( A @ ( B @ ( C @ sk15 ) ) @ ordered_pair ) @ in ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ relation_rng ) )
| ~ ( A @ relation ) ) ),
inference(cnf,[status(esa)],[119]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ relation_rng ) )
| ( A @ ( A @ ( B @ sk17 ) @ ( A @ ( B @ sk18 ) @ ordered_pair ) @ in ) )
| ( B @ ( A @ ( B @ sk16 ) @ in ) )
| ~ ( A @ relation ) ),
inference(cnfConj,[status(thm)],[120]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk17 ) @ ( A @ ( B @ sk18 ) @ ordered_pair ) @ in ) )
| ( B @ ( A @ ( B @ sk16 ) @ in ) )
| ~ ( A @ relation )
| ( B
= ( A @ relation_rng ) ) ),
inference(lifteq,[status(thm)],[122]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk17 ) @ ( A @ ( B @ sk18 ) @ ordered_pair ) @ in ) )
| ( B @ ( A @ ( B @ sk16 ) @ in ) )
| ~ ( A @ relation )
| ( B
= ( A @ relation_rng ) ) ),
inference(simp,[status(thm)],[137]) ).
thf(835,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk18 ) @ singleton @ ( A @ ( B @ sk17 ) @ ( A @ ( B @ sk18 ) @ unordered_pair ) @ unordered_pair ) @ in ) )
| ( B @ ( A @ ( B @ sk16 ) @ in ) )
| ~ ( A @ relation )
| ( B
= ( A @ relation_rng ) ) ),
inference(rewrite,[status(thm)],[138,53]) ).
thf(30,plain,
( ~ sk4
| ~ ( sk3 @ relation_rng @ ( sk1 @ in ) )
| ~ ( sk2 @ ( sk1 @ in ) ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(1162,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)],[37,1159]) ).
thf(1163,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) @ ( B @ singleton @ unordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[1162:[bind(A,$thf( F @ ( G @ unordered_pair ) )),bind(B,$thf( G @ singleton )),bind(C,$thf( G )),bind(D,$thf( F ))]]) ).
thf(1197,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) @ ( B @ singleton @ unordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[1163]) ).
thf(2521,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)],[37,1197]) ).
thf(2522,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) @ ( A @ singleton @ unordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[2521:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(183,plain,
( ~ $true
| ( ( sk3 @ relation_rng @ ( sk1 @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ~ sk4
| ~ ( sk2 @ ( sk1 @ in ) ) ),
inference(eqfactor_ordered,[status(thm)],[30]) ).
thf(187,plain,
( ( ( sk3 @ relation_rng )
!= sk2 )
| ( sk1 != sk1 )
| ~ sk4
| ~ ( sk2 @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[183]) ).
thf(190,plain,
( ( ( sk3 @ relation_rng )
!= sk2 )
| ~ sk4
| ~ ( sk2 @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[187]) ).
thf(3494,plain,
( ( sk4 != sk4 )
| ~ $true
| ~ ( sk3 @ ( sk2 @ relation_rng_restriction ) @ empty )
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[2517,2758]) ).
thf(3495,plain,
( ( sk4 != sk4 )
| ~ ( sk3 @ ( sk2 @ relation_rng_restriction ) @ empty )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[3494]) ).
thf(3496,plain,
( ~ ( sk3 @ ( sk2 @ relation_rng_restriction ) @ empty )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[3495:[]]) ).
thf(1164,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)],[37,1159]) ).
thf(1165,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[1164:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(3487,plain,
( ( sk4 != sk4 )
| ~ $true
| ~ ( sk3 @ ( sk2 @ relation_rng_restriction ) @ empty )
| ( sk2 != empty_set ) ),
inference(paramod_ordered,[status(thm)],[2284,2758]) ).
thf(3488,plain,
( ( sk4 != sk4 )
| ~ ( sk3 @ ( sk2 @ relation_rng_restriction ) @ empty )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[3487]) ).
thf(3489,plain,
( ~ ( sk3 @ ( sk2 @ relation_rng_restriction ) @ empty )
| ( sk2 != empty_set ) ),
inference(pattern_uni,[status(thm)],[3488:[]]) ).
thf(22637,plain,
$false,
inference(e,[status(thm)],[88,2512,1323,77,209,56,3414,42,3281,37,638,46,93,57,29,164,2254,84,3537,61,3505,89,116,74,60,85,2641,38,820,33,92,2758,3600,1159,65,2670,1143,53,2450,2387,5369,41,73,105,2235,1146,2602,149,32,34,2859,44,27,59,118,71,54,144,49,2319,2229,81,2284,76,2605,91,66,2835,2051,2797,80,35,2513,3659,50,67,199,3344,31,2701,2599,1358,4436,2320,1140,6086,87,1949,671,2490,2226,75,716,1161,1133,2517,835,30,51,818,2522,190,3496,1197,1165,94,3489,47,163,62,90,83,2238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU197+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n017.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 08:44:03 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.34/1.23 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.90/1.53 % [INFO] Parsing done (295ms).
% 1.90/1.55 % [INFO] Running in sequential loop mode.
% 2.91/2.14 % [INFO] eprover registered as external prover.
% 2.91/2.15 % [INFO] Scanning for conjecture ...
% 3.38/2.30 % [INFO] Found a conjecture (or negated_conjecture) and 30 axioms. Running axiom selection ...
% 3.57/2.40 % [INFO] Axiom selection finished. Selected 24 axioms (removed 6 axioms).
% 3.57/2.46 % [INFO] Problem is first-order (TPTP FOF).
% 3.57/2.47 % [INFO] Type checking passed.
% 3.57/2.48 % [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 ...
% 189.11/55.14 % External prover 'e' found a proof!
% 189.11/55.14 % [INFO] Killing All external provers ...
% 189.11/55.15 % Time passed: 54551ms (effective reasoning time: 53586ms)
% 189.11/55.15 % 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)>
% 189.11/55.15 % Axioms used in derivation (24): fc1_zfmisc_1, d5_relat_1, cc1_relat_1, t6_boole, fc3_subset_1, fc2_subset_1, t7_boole, rc1_relat_1, fc6_relat_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, d5_tarski, fc4_relat_1, d12_relat_1, t1_subset, existence_m1_subset_1, commutativity_k2_tarski, dt_k8_relat_1, rc2_relat_1, t8_boole, rc1_xboole_0, t2_subset, fc8_relat_1
% 189.11/55.15 % No. of inferences in proof: 306
% 189.11/55.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 54551 ms resp. 53586 ms w/o parsing
% 190.24/55.37 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 190.24/55.38 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------