%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET675+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:30:42 AM UTC 2026
% Result : Theorem 51.36s 21.98s
% Output : Refutation 52.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 43
% Syntax : Number of formulae : 173 ( 20 unt; 0 typ; 7 def)
% Number of atoms : 688 ( 147 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 2331 ( 224 ~; 201 |; 48 &;1655 @)
% ( 8 <=>; 195 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 8 con; 0-4 aty)
% Number of variables : 357 ( 4 ^; 332 !; 14 ?; 357 :)
% ( 0 !>; 0 ?*; 0 @-; 7 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ilf_type_decl,type,
ilf_type: $i > $i > $o ).
thf(set_type_decl,type,
set_type: $i ).
thf(relation_type_decl,type,
relation_type: $i > $i > $i ).
thf(image4_decl,type,
image4: $i > $i > $i > $i > $i ).
thf(inverse4_decl,type,
inverse4: $i > $i > $i > $i > $i ).
thf(range_decl,type,
range: $i > $i > $i > $i ).
thf(domain_decl,type,
domain: $i > $i > $i > $i ).
thf(binary_relation_type_decl,type,
binary_relation_type: $i ).
thf(range_of_decl,type,
range_of: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(member_type_decl,type,
member_type: $i > $i ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(cross_product_decl,type,
cross_product: $i > $i > $i ).
thf(subset_type_decl,type,
subset_type: $i > $i ).
thf(power_set_decl,type,
power_set: $i > $i ).
thf(inverse2_decl,type,
inverse2: $i > $i > $i ).
thf(domain_of_decl,type,
domain_of: $i > $i ).
thf(relation_like_decl,type,
relation_like: $i > $o ).
thf(image_decl,type,
image: $i > $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( A @ ( B @ relation_type ) @ ( C @ ilf_type ) )
=> ( ( ( B @ ( C @ ( A @ ( B @ image4 ) ) ) @ ( C @ ( A @ ( B @ inverse4 ) ) ) )
= ( C @ ( A @ ( B @ domain ) ) ) )
& ( ( A @ ( C @ ( A @ ( B @ inverse4 ) ) ) @ ( C @ ( A @ ( B @ image4 ) ) ) )
= ( C @ ( A @ ( B @ range ) ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( sk1 @ ( A @ relation_type ) @ ( B @ ilf_type ) )
=> ( ( ( A @ ( B @ ( sk1 @ ( A @ image4 ) ) ) @ ( B @ ( sk1 @ ( A @ inverse4 ) ) ) )
= ( B @ ( sk1 @ ( A @ domain ) ) ) )
& ( ( sk1 @ ( B @ ( sk1 @ ( A @ inverse4 ) ) ) @ ( B @ ( sk1 @ ( A @ image4 ) ) ) )
= ( B @ ( sk1 @ ( A @ range ) ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( sk1 @ ( sk2 @ relation_type ) @ ( A @ ilf_type ) )
=> ( ( ( sk2 @ ( A @ ( sk1 @ ( sk2 @ image4 ) ) ) @ ( A @ ( sk1 @ ( sk2 @ inverse4 ) ) ) )
= ( A @ ( sk1 @ ( sk2 @ domain ) ) ) )
& ( ( sk1 @ ( A @ ( sk1 @ ( sk2 @ inverse4 ) ) ) @ ( A @ ( sk1 @ ( sk2 @ image4 ) ) ) )
= ( A @ ( sk1 @ ( sk2 @ range ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i] :
@+[B: $i] : ( A @ subset_type @ ( B @ ilf_type ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( set_type @ ( B @ ilf_type ) )
=> ~ ( A @ ( B @ member ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( set_type @ ( C @ ilf_type ) )
=> ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] : ( binary_relation_type @ ( A @ ilf_type ) ) ) ) ).
thf(17,axiom,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( ( A @ domain_of @ ( A @ image ) )
= ( A @ range_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
thf(88,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( ( A @ domain_of @ ( A @ image ) )
= ( A @ range_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(36,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ( ( C @ ( B @ ( A @ domain ) ) )
= ( C @ domain_of ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
thf(153,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ( ( C @ ( B @ ( A @ domain ) ) )
= ( C @ domain_of ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1,conjecture,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( A @ ( B @ relation_type ) @ ( C @ ilf_type ) )
=> ( ( ( B @ ( C @ ( A @ ( B @ image4 ) ) ) @ ( C @ ( A @ ( B @ inverse4 ) ) ) )
= ( C @ ( A @ ( B @ domain ) ) ) )
& ( ( A @ ( C @ ( A @ ( B @ inverse4 ) ) ) @ ( C @ ( A @ ( B @ image4 ) ) ) )
= ( C @ ( A @ ( B @ range ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_39) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( A @ ( B @ relation_type ) @ ( C @ ilf_type ) )
=> ( ( ( B @ ( C @ ( A @ ( B @ image4 ) ) ) @ ( C @ ( A @ ( B @ inverse4 ) ) ) )
= ( C @ ( A @ ( B @ domain ) ) ) )
& ( ( A @ ( C @ ( A @ ( B @ inverse4 ) ) ) @ ( C @ ( A @ ( B @ image4 ) ) ) )
= ( C @ ( A @ ( B @ range ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(38,plain,
~ ! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( A @ ( B @ relation_type ) @ ( C @ ilf_type ) )
=> ( ( ( B @ ( C @ ( A @ ( B @ image4 ) ) ) @ ( C @ ( A @ ( B @ inverse4 ) ) ) )
= ( C @ ( A @ ( B @ domain ) ) ) )
& ( ( A @ ( C @ ( A @ ( B @ inverse4 ) ) ) @ ( C @ ( A @ ( B @ image4 ) ) ) )
= ( C @ ( A @ ( B @ range ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(39,plain,
( ( ( ( sk2 @ ( sk3 @ ( sk1 @ ( sk2 @ image4 ) ) ) @ ( sk3 @ ( sk1 @ ( sk2 @ inverse4 ) ) ) )
!= ( sk3 @ ( sk1 @ ( sk2 @ domain ) ) ) )
| ( ( sk1 @ ( sk3 @ ( sk1 @ ( sk2 @ inverse4 ) ) ) @ ( sk3 @ ( sk1 @ ( sk2 @ image4 ) ) ) )
!= ( sk3 @ ( sk1 @ ( sk2 @ range ) ) ) ) )
& ( sk1 @ ( sk2 @ relation_type ) @ ( sk3 @ ilf_type ) )
& ( set_type @ ( sk2 @ ilf_type ) )
& ( set_type @ ( sk1 @ ilf_type ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(42,plain,
sk1 @ ( sk2 @ relation_type ) @ ( sk3 @ ilf_type ),
inference(cnfConj,[status(thm)],[39]) ).
thf(28,axiom,
! [A: $i] : ( set_type @ ( A @ ilf_type ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p35) ).
thf(124,plain,
! [A: $i] : ( set_type @ ( A @ ilf_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(125,plain,
! [A: $i] : ( set_type @ ( A @ ilf_type ) ),
inference(cnf,[status(esa)],[124]) ).
thf(14,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( B @ power_set @ ( A @ member ) )
<=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18) ).
thf(76,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) )
=> ( B @ power_set @ ( A @ member ) ) )
& ( ( B @ power_set @ ( A @ member ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(24,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( set_type @ ( B @ ( A @ ordered_pair ) @ ilf_type ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
thf(112,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( set_type @ ( B @ ( A @ ordered_pair ) @ ilf_type ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(26,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( A @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17) ).
thf(116,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( A @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(117,plain,
! [A: $i] :
( ( A @ ( A @ subset ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[116]) ).
thf(204,plain,
! [A: $i] :
( ( A @ ( A @ subset ) )
| ~ $true ),
inference(rewrite,[status(thm)],[117,125]) ).
thf(205,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(simp,[status(thm)],[204]) ).
thf(18,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p16) ).
thf(91,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk7 ) @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk7 ) @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B @ ( A @ subset ) )
| ( set_type @ ( A @ ( B @ sk7 ) @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( B @ ( A @ subset ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[91]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( B @ ( A @ subset ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[92]) ).
thf(192,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ $true
| ~ ( B @ ( A @ subset ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[93,125]) ).
thf(193,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[192]) ).
thf(13,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( ( A @ empty )
<=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ~ ( A @ ( B @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25) ).
thf(71,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( ( ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ~ ( A @ ( B @ member ) ) )
=> ( A @ empty ) )
& ( ( A @ empty )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ~ ( A @ ( B @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( ( A @ empty )
| ( A @ ( A @ sk5 @ member ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( A @ empty )
| ( set_type @ ( A @ sk5 @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ~ ( A @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( A @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[71]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( A @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[72]) ).
thf(190,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ $true
| ~ ( A @ empty )
| ~ $true ),
inference(rewrite,[status(thm)],[73,125]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[190]) ).
thf(197,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ member ) )
!= ( D @ ( E @ member ) ) )
| ~ $true
| ~ ( D @ empty )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[193,191]) ).
thf(198,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ member ) )
!= ( D @ ( E @ member ) ) )
| ~ ( D @ empty )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[197]) ).
thf(199,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[198:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(255,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ member ) )
!= ( D @ ( F @ member ) ) )
| ~ ( E @ empty )
| ~ $true
| ~ ( E @ ( D @ subset ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[193,199]) ).
thf(256,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ member ) )
!= ( D @ ( F @ member ) ) )
| ~ ( E @ empty )
| ~ ( E @ ( D @ subset ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[255]) ).
thf(257,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ empty )
| ~ ( D @ ( B @ subset ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( E )),bind(F,$thf( C ))]]) ).
thf(264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ empty )
| ~ ( D @ ( B @ subset ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(273,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( E @ ( C @ subset ) ) )
| ~ ( E @ empty )
| ~ $true
| ~ ( B @ ( D @ member ) )
| ~ ( C @ ( B @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[205,264]) ).
thf(274,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( E @ ( C @ subset ) ) )
| ~ ( E @ empty )
| ~ ( B @ ( D @ member ) )
| ~ ( C @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[273]) ).
thf(275,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ empty )
| ~ ( B @ ( C @ member ) )
| ~ ( A @ ( B @ subset ) ) ),
inference(pattern_uni,[status(thm)],[274:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).
thf(282,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ empty )
| ~ ( B @ ( C @ member ) )
| ~ ( A @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[275]) ).
thf(4,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( ( set_type @ ( B @ ilf_type ) )
& ~ ( B @ empty ) )
=> ( ( B @ member_type @ ( A @ ilf_type ) )
<=> ( B @ ( A @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).
thf(47,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( ( set_type @ ( B @ ilf_type ) )
& ~ ( B @ empty ) )
=> ( ( ( B @ ( A @ member ) )
=> ( B @ member_type @ ( A @ ilf_type ) ) )
& ( ( B @ member_type @ ( A @ ilf_type ) )
=> ( B @ ( A @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( ( B @ member_type @ ( A @ ilf_type ) )
| ~ ( B @ ( A @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ( B @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B @ ( A @ member ) )
| ~ ( B @ member_type @ ( A @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ( B @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( B @ member_type @ ( A @ ilf_type ) )
| ~ ( B @ ( A @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ( B @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[48]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( B @ member_type @ ( A @ ilf_type ) )
| ~ ( B @ ( A @ member ) )
| ~ $true
| ( B @ empty )
| ~ $true ),
inference(rewrite,[status(thm)],[50,125]) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( B @ member_type @ ( A @ ilf_type ) )
| ~ ( B @ ( A @ member ) )
| ( B @ empty ) ),
inference(simp,[status(thm)],[313]) ).
thf(8,axiom,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( ( A @ range_of @ ( A @ inverse2 ) )
= ( A @ domain_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
thf(59,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( ( A @ range_of @ ( A @ inverse2 ) )
= ( A @ domain_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(60,plain,
! [A: $i] :
( ( ( A @ range_of @ ( A @ inverse2 ) )
= ( A @ domain_of ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[59]) ).
thf(61,plain,
! [A: $i] :
( ~ ( binary_relation_type @ ( A @ ilf_type ) )
| ( ( A @ range_of @ ( A @ inverse2 ) )
= ( A @ domain_of ) ) ),
inference(lifteq,[status(thm)],[60]) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ~ $true
| ( ( B @ range_of @ ( B @ inverse2 ) )
= ( B @ domain_of ) ) ),
inference(paramod_ordered,[status(thm)],[125,61]) ).
thf(243,plain,
! [B: $i,A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( ( B @ range_of @ ( B @ inverse2 ) )
= ( B @ domain_of ) ) ),
inference(simp,[status(thm)],[242]) ).
thf(250,plain,
! [B: $i,A: $i] :
( ( binary_relation_type != set_type )
| ( A != B )
| ( ( B @ range_of @ ( B @ inverse2 ) )
= ( B @ domain_of ) ) ),
inference(simp,[status(thm)],[243]) ).
thf(253,plain,
! [A: $i] :
( ( binary_relation_type != set_type )
| ( ( A @ range_of @ ( A @ inverse2 ) )
= ( A @ domain_of ) ) ),
inference(simp,[status(thm)],[250]) ).
thf(23,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( ( binary_relation_type @ ( A @ ilf_type ) )
<=> ( ( set_type @ ( A @ ilf_type ) )
& ( A @ relation_like ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12) ).
thf(106,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( ( ( ( set_type @ ( A @ ilf_type ) )
& ( A @ relation_like ) )
=> ( binary_relation_type @ ( A @ ilf_type ) ) )
& ( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( ( set_type @ ( A @ ilf_type ) )
& ( A @ relation_like ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(32,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( set_type @ ( D @ ilf_type ) )
=> ( ( D @ ( C @ ( B @ ( A @ image4 ) ) ) )
= ( D @ ( C @ image ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p31) ).
thf(132,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( set_type @ ( D @ ilf_type ) )
=> ( ( D @ ( C @ ( B @ ( A @ image4 ) ) ) )
= ( D @ ( C @ image ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(31,axiom,
? [A: $i] : ( binary_relation_type @ ( A @ ilf_type ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).
thf(130,plain,
? [A: $i] : ( binary_relation_type @ ( A @ ilf_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(131,plain,
binary_relation_type @ ( sk10 @ ilf_type ),
inference(cnf,[status(esa)],[130]) ).
thf(246,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ~ $true
| ( ( A @ range_of @ ( A @ inverse2 ) )
= ( A @ domain_of ) ) ),
inference(paramod_ordered,[status(thm)],[131,61]) ).
thf(247,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( ( A @ range_of @ ( A @ inverse2 ) )
= ( A @ domain_of ) ) ),
inference(simp,[status(thm)],[246]) ).
thf(248,plain,
( ( sk10 @ range_of @ ( sk10 @ inverse2 ) )
= ( sk10 @ domain_of ) ),
inference(pattern_uni,[status(thm)],[247:[bind(A,$thf( sk10 ))]]) ).
thf(21,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ? [C: $i] : ( A @ ( B @ relation_type ) @ ( C @ ilf_type ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5) ).
thf(102,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ? [C: $i] : ( A @ ( B @ relation_type ) @ ( C @ ilf_type ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(89,plain,
! [A: $i] :
( ( ( A @ domain_of @ ( A @ image ) )
= ( A @ range_of ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[88]) ).
thf(90,plain,
! [A: $i] :
( ~ ( binary_relation_type @ ( A @ ilf_type ) )
| ( ( A @ domain_of @ ( A @ image ) )
= ( A @ range_of ) ) ),
inference(lifteq,[status(thm)],[89]) ).
thf(337,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ relation_type ) @ ( sk3 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ~ $true
| ( ( A @ domain_of @ ( A @ image ) )
= ( A @ range_of ) ) ),
inference(paramod_ordered,[status(thm)],[42,90]) ).
thf(338,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ relation_type ) @ ( sk3 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( ( A @ domain_of @ ( A @ image ) )
= ( A @ range_of ) ) ),
inference(simp,[status(thm)],[337]) ).
thf(346,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ relation_type ) )
!= binary_relation_type )
| ( sk3 != A )
| ( ( A @ domain_of @ ( A @ image ) )
= ( A @ range_of ) ) ),
inference(simp,[status(thm)],[338]) ).
thf(349,plain,
( ( ( sk1 @ ( sk2 @ relation_type ) )
!= binary_relation_type )
| ( ( sk3 @ domain_of @ ( sk3 @ image ) )
= ( sk3 @ range_of ) ) ),
inference(simp,[status(thm)],[346]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( B @ member_type @ ( A @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ( B @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[48]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( B @ member_type @ ( A @ ilf_type ) )
| ~ $true
| ( B @ empty )
| ~ $true ),
inference(rewrite,[status(thm)],[49,125]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( B @ member_type @ ( A @ ilf_type ) )
| ( B @ empty ) ),
inference(simp,[status(thm)],[209]) ).
thf(211,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ relation_type ) @ ( sk3 @ ilf_type ) )
!= ( B @ member_type @ ( A @ ilf_type ) ) )
| ( B @ ( A @ member ) )
| ~ $true
| ( B @ empty ) ),
inference(paramod_ordered,[status(thm)],[42,210]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ relation_type ) @ ( sk3 @ ilf_type ) )
!= ( B @ member_type @ ( A @ ilf_type ) ) )
| ( B @ ( A @ member ) )
| ( B @ empty ) ),
inference(simp,[status(thm)],[211]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ relation_type ) )
!= ( B @ member_type ) )
| ( sk3 != A )
| ( B @ ( A @ member ) )
| ( B @ empty ) ),
inference(simp,[status(thm)],[212]) ).
thf(229,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ relation_type ) )
!= ( A @ member_type ) )
| ( A @ ( sk3 @ member ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[223]) ).
thf(240,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ relation_type ) @ ( sk3 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ~ $true
| ( ( A @ range_of @ ( A @ inverse2 ) )
= ( A @ domain_of ) ) ),
inference(paramod_ordered,[status(thm)],[42,61]) ).
thf(241,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ relation_type ) @ ( sk3 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( ( A @ range_of @ ( A @ inverse2 ) )
= ( A @ domain_of ) ) ),
inference(simp,[status(thm)],[240]) ).
thf(249,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ relation_type ) )
!= binary_relation_type )
| ( sk3 != A )
| ( ( A @ range_of @ ( A @ inverse2 ) )
= ( A @ domain_of ) ) ),
inference(simp,[status(thm)],[241]) ).
thf(252,plain,
( ( ( sk1 @ ( sk2 @ relation_type ) )
!= binary_relation_type )
| ( ( sk3 @ range_of @ ( sk3 @ inverse2 ) )
= ( sk3 @ domain_of ) ) ),
inference(simp,[status(thm)],[249]) ).
thf(19,axiom,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( set_type @ ( B @ ( A @ inverse2 ) @ ilf_type ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
thf(97,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( set_type @ ( B @ ( A @ inverse2 ) @ ilf_type ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(37,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( A = B )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
thf(156,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(6,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ? [B: $i] : ( A @ subset_type @ ( B @ ilf_type ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).
thf(53,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ? [B: $i] : ( A @ subset_type @ ( B @ ilf_type ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(294,plain,
( ( ( sk10 @ range_of @ ( sk10 @ inverse2 ) )
!= ( sk3 @ range_of @ ( sk3 @ inverse2 ) ) )
| ( ( sk10 @ domain_of )
= ( sk3 @ domain_of ) )
| ( ( sk1 @ ( sk2 @ relation_type ) )
!= binary_relation_type ) ),
inference(paramod_ordered,[status(thm)],[252,248]) ).
thf(296,plain,
( ( ( sk10 @ range_of )
!= ( sk3 @ range_of ) )
| ( sk10 != sk3 )
| ( ( sk1 @ ( sk2 @ relation_type ) )
!= binary_relation_type )
| ( ( sk10 @ domain_of )
= ( sk3 @ domain_of ) ) ),
inference(simp,[status(thm)],[294]) ).
thf(419,plain,
( ( sk10 != sk3 )
| ( sk10 != sk3 )
| ( ( sk1 @ ( sk2 @ relation_type ) )
!= binary_relation_type )
| ( ( sk10 @ domain_of )
= ( sk3 @ domain_of ) ) ),
inference(simp,[status(thm)],[296]) ).
thf(420,plain,
( ( sk10 != sk3 )
| ( ( sk1 @ ( sk2 @ relation_type ) )
!= binary_relation_type )
| ( ( sk10 @ domain_of )
= ( sk3 @ domain_of ) ) ),
inference(simp,[status(thm)],[419]) ).
thf(30,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( set_type @ ( D @ ilf_type ) )
=> ( A @ subset_type @ ( D @ ( C @ ( B @ ( A @ inverse4 ) ) ) @ ilf_type ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p34) ).
thf(128,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( set_type @ ( D @ ilf_type ) )
=> ( A @ subset_type @ ( D @ ( C @ ( B @ ( A @ inverse4 ) ) ) @ ilf_type ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(3,axiom,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( set_type @ ( A @ range_of @ ilf_type ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
thf(45,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( set_type @ ( A @ range_of @ ilf_type ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( set_type @ ( D @ ilf_type ) )
=> ( B @ subset_type @ ( D @ ( C @ ( B @ ( A @ image4 ) ) ) @ ilf_type ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p32) ).
thf(64,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( set_type @ ( D @ ilf_type ) )
=> ( B @ subset_type @ ( D @ ( C @ ( B @ ( A @ image4 ) ) ) @ ilf_type ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(43,plain,
( ( ( sk2 @ ( sk3 @ ( sk1 @ ( sk2 @ image4 ) ) ) @ ( sk3 @ ( sk1 @ ( sk2 @ inverse4 ) ) ) )
!= ( sk3 @ ( sk1 @ ( sk2 @ domain ) ) ) )
| ( ( sk1 @ ( sk3 @ ( sk1 @ ( sk2 @ inverse4 ) ) ) @ ( sk3 @ ( sk1 @ ( sk2 @ image4 ) ) ) )
!= ( sk3 @ ( sk1 @ ( sk2 @ range ) ) ) ) ),
inference(cnfConj,[status(thm)],[39]) ).
thf(44,plain,
( ( ( sk2 @ ( sk3 @ ( sk1 @ ( sk2 @ image4 ) ) ) @ ( sk3 @ ( sk1 @ ( sk2 @ inverse4 ) ) ) )
!= ( sk3 @ ( sk1 @ ( sk2 @ domain ) ) ) )
| ( ( sk1 @ ( sk3 @ ( sk1 @ ( sk2 @ inverse4 ) ) ) @ ( sk3 @ ( sk1 @ ( sk2 @ image4 ) ) ) )
!= ( sk3 @ ( sk1 @ ( sk2 @ range ) ) ) ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(270,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ~ ( E @ empty )
| ~ ( E @ ( C @ subset ) )
| ~ ( B @ ( D @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,264]) ).
thf(271,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ~ ( E @ empty )
| ~ ( E @ ( C @ subset ) )
| ~ ( B @ ( D @ member ) ) ),
inference(simp,[status(thm)],[270]) ).
thf(272,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ empty )
| ~ ( C @ ( A @ subset ) )
| ~ ( A @ ( B @ member ) ) ),
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(281,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ empty )
| ~ ( C @ ( A @ subset ) )
| ~ ( A @ ( B @ member ) ) ),
inference(simp,[status(thm)],[272]) ).
thf(27,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ( ( ( B @ ( C @ ( B @ ( A @ inverse4 ) ) ) )
= ( C @ ( B @ ( A @ domain ) ) ) )
& ( ( A @ ( C @ ( B @ ( A @ image4 ) ) ) )
= ( C @ ( B @ ( A @ range ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
thf(118,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ( ( ( B @ ( C @ ( B @ ( A @ inverse4 ) ) ) )
= ( C @ ( B @ ( A @ domain ) ) ) )
& ( ( A @ ( C @ ( B @ ( A @ image4 ) ) ) )
= ( C @ ( B @ ( A @ range ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(7,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( ( set_type @ ( A @ power_set @ ilf_type ) )
& ~ ( A @ power_set @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
thf(55,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( ( set_type @ ( A @ power_set @ ilf_type ) )
& ~ ( A @ power_set @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(56,plain,
! [A: $i] :
( ( ( set_type @ ( A @ power_set @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ~ ( A @ power_set @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(57,plain,
! [A: $i] :
( ~ ( A @ power_set @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(180,plain,
! [A: $i] :
( ~ ( A @ power_set @ empty )
| ~ $true ),
inference(rewrite,[status(thm)],[57,125]) ).
thf(181,plain,
! [A: $i] :
~ ( A @ power_set @ empty ),
inference(simp,[status(thm)],[180]) ).
thf(339,plain,
! [B: $i,A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ~ $true
| ( ( B @ domain_of @ ( B @ image ) )
= ( B @ range_of ) ) ),
inference(paramod_ordered,[status(thm)],[125,90]) ).
thf(340,plain,
! [B: $i,A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( ( B @ domain_of @ ( B @ image ) )
= ( B @ range_of ) ) ),
inference(simp,[status(thm)],[339]) ).
thf(347,plain,
! [B: $i,A: $i] :
( ( binary_relation_type != set_type )
| ( A != B )
| ( ( B @ domain_of @ ( B @ image ) )
= ( B @ range_of ) ) ),
inference(simp,[status(thm)],[340]) ).
thf(350,plain,
! [A: $i] :
( ( binary_relation_type != set_type )
| ( ( A @ domain_of @ ( A @ image ) )
= ( A @ range_of ) ) ),
inference(simp,[status(thm)],[347]) ).
thf(16,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) )
=> ( C @ relation_like ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23) ).
thf(86,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) )
=> ( C @ relation_like ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(343,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ~ $true
| ( ( A @ domain_of @ ( A @ image ) )
= ( A @ range_of ) ) ),
inference(paramod_ordered,[status(thm)],[131,90]) ).
thf(344,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( ( A @ domain_of @ ( A @ image ) )
= ( A @ range_of ) ) ),
inference(simp,[status(thm)],[343]) ).
thf(345,plain,
( ( sk10 @ domain_of @ ( sk10 @ image ) )
= ( sk10 @ range_of ) ),
inference(pattern_uni,[status(thm)],[344:[bind(A,$thf( sk10 ))]]) ).
thf(34,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( ( A @ relation_like )
<=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( A @ ( B @ member ) )
=> ? [C: $i] :
( ? [D: $i] :
( ( B
= ( D @ ( C @ ordered_pair ) ) )
& ( set_type @ ( D @ ilf_type ) ) )
& ( set_type @ ( C @ ilf_type ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
thf(140,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( ( ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( A @ ( B @ member ) )
=> ? [C: $i] :
( ? [D: $i] :
( ( B
= ( D @ ( C @ ordered_pair ) ) )
& ( set_type @ ( D @ ilf_type ) ) )
& ( set_type @ ( C @ ilf_type ) ) ) ) )
=> ( A @ relation_like ) )
& ( ( A @ relation_like )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( A @ ( B @ member ) )
=> ? [C: $i] :
( ? [D: $i] :
( ( B
= ( D @ ( C @ ordered_pair ) ) )
& ( set_type @ ( D @ ilf_type ) ) )
& ( set_type @ ( C @ ilf_type ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(11,axiom,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( set_type @ ( A @ domain_of @ ilf_type ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8) ).
thf(66,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( set_type @ ( A @ domain_of @ ilf_type ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(33,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) ) )
& ! [C: $i] :
( ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) )
=> ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
thf(135,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) ) )
& ! [C: $i] :
( ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) )
=> ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(218,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( B @ member_type @ ( A @ ilf_type ) ) )
| ( B @ ( A @ member ) )
| ~ $true
| ( B @ empty ) ),
inference(paramod_ordered,[status(thm)],[131,210]) ).
thf(219,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( B @ member_type @ ( A @ ilf_type ) ) )
| ( B @ ( A @ member ) )
| ( B @ empty ) ),
inference(simp,[status(thm)],[218]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( ( B @ member_type )
!= binary_relation_type )
| ( sk10 != A )
| ( B @ ( A @ member ) )
| ( B @ empty ) ),
inference(simp,[status(thm)],[219]) ).
thf(226,plain,
! [A: $i] :
( ( ( A @ member_type )
!= binary_relation_type )
| ( A @ ( sk10 @ member ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[224]) ).
thf(20,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ( ( C @ ( B @ ( A @ range ) ) )
= ( C @ range_of ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p29) ).
thf(99,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ( ( C @ ( B @ ( A @ range ) ) )
= ( C @ range_of ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(22,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ( B @ subset_type @ ( C @ ( B @ ( A @ range ) ) @ ilf_type ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p30) ).
thf(104,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ( B @ subset_type @ ( C @ ( B @ ( A @ range ) ) @ ilf_type ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(54,plain,
! [A: $i] :
( ( A @ subset_type @ ( A @ sk4 @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(234,plain,
! [A: $i] :
( ( A @ subset_type @ ( A @ sk4 @ ilf_type ) )
| ~ $true ),
inference(rewrite,[status(thm)],[54,125]) ).
thf(235,plain,
! [A: $i] : ( A @ subset_type @ ( A @ sk4 @ ilf_type ) ),
inference(simp,[status(thm)],[234]) ).
thf(341,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk4 @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ~ $true
| ( ( B @ domain_of @ ( B @ image ) )
= ( B @ range_of ) ) ),
inference(paramod_ordered,[status(thm)],[235,90]) ).
thf(342,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk4 @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( ( B @ domain_of @ ( B @ image ) )
= ( B @ range_of ) ) ),
inference(simp,[status(thm)],[341]) ).
thf(348,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type )
!= binary_relation_type )
| ( ( A @ sk4 )
!= B )
| ( ( B @ domain_of @ ( B @ image ) )
= ( B @ range_of ) ) ),
inference(simp,[status(thm)],[342]) ).
thf(351,plain,
! [A: $i] :
( ( ( A @ subset_type )
!= binary_relation_type )
| ( ( A @ sk4 @ domain_of @ ( A @ sk4 @ image ) )
= ( A @ sk4 @ range_of ) ) ),
inference(simp,[status(thm)],[348]) ).
thf(25,axiom,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( set_type @ ( B @ ( A @ image ) @ ilf_type ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11) ).
thf(114,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( set_type @ ( B @ ( A @ image ) @ ilf_type ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(15,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( A @ subset_type @ ( B @ ilf_type ) )
<=> ( A @ power_set @ member_type @ ( B @ ilf_type ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14) ).
thf(82,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( ( A @ power_set @ member_type @ ( B @ ilf_type ) )
=> ( A @ subset_type @ ( B @ ilf_type ) ) )
& ( ( A @ subset_type @ ( B @ ilf_type ) )
=> ( A @ power_set @ member_type @ ( B @ ilf_type ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(35,axiom,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
& ( A @ empty ) )
=> ( A @ relation_like ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
thf(151,plain,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
& ( A @ empty ) )
=> ( A @ relation_like ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(5,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( set_type @ ( B @ ( A @ cross_product ) @ ilf_type ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9) ).
thf(51,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( set_type @ ( B @ ( A @ cross_product ) @ ilf_type ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(29,axiom,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
& ~ ( A @ empty ) )
=> ? [B: $i] : ( A @ member_type @ ( B @ ilf_type ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
thf(126,plain,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
& ~ ( A @ empty ) )
=> ? [B: $i] : ( A @ member_type @ ( B @ ilf_type ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(12,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( set_type @ ( D @ ilf_type ) )
=> ( ( D @ ( C @ ( B @ ( A @ inverse4 ) ) ) )
= ( D @ ( C @ inverse2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p33) ).
thf(68,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( set_type @ ( D @ ilf_type ) )
=> ( ( D @ ( C @ ( B @ ( A @ inverse4 ) ) ) )
= ( D @ ( C @ inverse2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ( A @ subset_type @ ( C @ ( B @ ( A @ domain ) ) @ ilf_type ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p28) ).
thf(62,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ( A @ subset_type @ ( C @ ( B @ ( A @ domain ) ) @ ilf_type ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk4 @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ~ $true
| ( ( B @ range_of @ ( B @ inverse2 ) )
= ( B @ domain_of ) ) ),
inference(paramod_ordered,[status(thm)],[235,61]) ).
thf(245,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk4 @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( ( B @ range_of @ ( B @ inverse2 ) )
= ( B @ domain_of ) ) ),
inference(simp,[status(thm)],[244]) ).
thf(251,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type )
!= binary_relation_type )
| ( ( A @ sk4 )
!= B )
| ( ( B @ range_of @ ( B @ inverse2 ) )
= ( B @ domain_of ) ) ),
inference(simp,[status(thm)],[245]) ).
thf(254,plain,
! [A: $i] :
( ( ( A @ subset_type )
!= binary_relation_type )
| ( ( A @ sk4 @ range_of @ ( A @ sk4 @ inverse2 ) )
= ( A @ sk4 @ domain_of ) ) ),
inference(simp,[status(thm)],[251]) ).
thf(12055,plain,
$false,
inference(e,[status(thm)],[88,153,42,125,76,112,282,199,314,253,106,61,132,116,248,102,349,38,229,252,97,156,53,420,124,193,128,205,264,45,64,191,44,281,59,118,71,181,350,86,345,140,91,66,130,135,226,99,104,351,55,114,235,82,151,51,210,126,68,62,131,47,90,254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET675+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.12 % 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
% 0.21/10.50 % Computer : n020.cluster.edu
% 0.21/10.50 % Model : x86_64 x86_64
% 0.21/10.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/10.50 % Memory : 8046.5625MB
% 0.21/10.50 % OS : Linux 6.8.0-71-generic
% 0.21/10.51 % CPULimit : 300
% 0.21/10.51 % WCLimit : 300
% 0.21/10.51 % DateTime : Sat Sep 26 08:05:31 UTC 2026
% 0.21/10.51 % CPUTime :
% 0.21/10.51 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
% 0.96/11.10 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.43/11.33 % [INFO] Parsing done (231ms).
% 1.43/11.35 % [INFO] Running in sequential loop mode.
% 2.08/11.76 % [INFO] eprover registered as external prover.
% 2.08/11.76 % [INFO] Scanning for conjecture ...
% 2.31/11.89 % [INFO] Found a conjecture (or negated_conjecture) and 35 axioms. Running axiom selection ...
% 2.51/11.98 % [INFO] Axiom selection finished. Selected 35 axioms (removed 0 axioms).
% 2.83/12.05 % [INFO] Problem is first-order (TPTP FOF).
% 2.83/12.07 % [INFO] Type checking passed.
% 2.83/12.08 % [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 ...
% 51.36/21.97 % External prover 'e' found a proof!
% 51.36/21.97 % [INFO] Killing All external provers ...
% 51.36/21.97 % Time passed: 11318ms (effective reasoning time: 10618ms)
% 51.36/21.97 % 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)>
% 51.36/21.97 % Axioms used in derivation (35): p27, p12, p34, p18, p26, p22, p11, p2, p17, p9, p24, p16, p20, p10, p19, p4, p7, p5, p23, p32, p21, p29, p15, p3, p33, p25, p14, p28, p1, p31, p30, p13, p6, p8, p35
% 51.36/21.97 % No. of inferences in proof: 166
% 51.36/21.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 11318 ms resp. 10618 ms w/o parsing
% 52.89/22.10 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 52.89/22.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------