%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET681+3 : TPTP v9.3.1. Released v2.2.0.
% 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 : 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 08:30:43 AM UTC 2026
% Result : Theorem 8.51s 3.58s
% Output : Refutation 9.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 40
% Syntax : Number of formulae : 155 ( 23 unt; 0 typ; 8 def)
% Number of atoms : 684 ( 89 equ; 0 cnn)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 2226 ( 217 ~; 175 |; 78 &;1544 @)
% ( 12 <=>; 200 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 11 con; 0-3 aty)
% Number of variables : 273 ( 3 ^; 233 !; 29 ?; 273 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% Comments :
%------------------------------------------------------------------------------
thf(empty_decl,type,
empty: $i > $o ).
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(member_type_decl,type,
member_type: $i > $i ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(range_decl,type,
range: $i > $i > $i > $i ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(binary_relation_type_decl,type,
binary_relation_type: $i ).
thf(range_of_decl,type,
range_of: $i > $i ).
thf(domain_of_decl,type,
domain_of: $i > $i ).
thf(subset_type_decl,type,
subset_type: $i > $i ).
thf(cross_product_decl,type,
cross_product: $i > $i > $i ).
thf(domain_decl,type,
domain: $i > $i > $i > $i ).
thf(power_set_decl,type,
power_set: $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(relation_like_decl,type,
relation_like: $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: $i ).
thf(sk5_decl,type,
sk5: $o ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( ( set_type @ ( A @ ilf_type ) )
& ~ ( A @ empty ) )
=> ! [B: $i] :
( ( ( set_type @ ( B @ ilf_type ) )
& ~ ( B @ empty ) )
=> ! [C: $i] :
( ( A @ ( B @ relation_type ) @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( A @ member_type @ ( D @ ilf_type ) )
=> ( ( ? [E: $i] :
( ( C @ ( D @ ( E @ ordered_pair ) @ member ) )
& ( B @ member_type @ ( E @ ilf_type ) ) )
=> ( C @ ( A @ ( B @ range ) ) @ ( D @ member ) ) )
& ( ( C @ ( A @ ( B @ range ) ) @ ( D @ member ) )
=> ? [E: $i] :
( ( C @ ( D @ ( E @ ordered_pair ) @ member ) )
& ( B @ member_type @ ( E @ ilf_type ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( set_type @ ( A @ ilf_type ) )
& ~ ( A @ empty ) )
=> ! [B: $i] :
( ( sk1 @ ( A @ relation_type ) @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( sk1 @ member_type @ ( C @ ilf_type ) )
=> ( ( ? [D: $i] :
( ( B @ ( C @ ( D @ ordered_pair ) @ member ) )
& ( A @ member_type @ ( D @ ilf_type ) ) )
=> ( B @ ( sk1 @ ( A @ range ) ) @ ( C @ member ) ) )
& ( ( B @ ( sk1 @ ( A @ range ) ) @ ( C @ member ) )
=> ? [D: $i] :
( ( B @ ( C @ ( D @ ordered_pair ) @ member ) )
& ( A @ member_type @ ( D @ ilf_type ) ) ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( sk1 @ ( sk2 @ relation_type ) @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( sk1 @ member_type @ ( B @ ilf_type ) )
=> ( ( ? [C: $i] :
( ( A @ ( B @ ( C @ ordered_pair ) @ member ) )
& ( sk2 @ member_type @ ( C @ ilf_type ) ) )
=> ( A @ ( sk1 @ ( sk2 @ range ) ) @ ( B @ member ) ) )
& ( ( A @ ( sk1 @ ( sk2 @ range ) ) @ ( B @ member ) )
=> ? [C: $i] :
( ( A @ ( B @ ( C @ ordered_pair ) @ member ) )
& ( sk2 @ member_type @ ( C @ ilf_type ) ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( sk1 @ member_type @ ( A @ ilf_type ) )
=> ( ( ? [B: $i] :
( ( sk3 @ ( A @ ( B @ ordered_pair ) @ member ) )
& ( sk2 @ member_type @ ( B @ ilf_type ) ) )
=> ( sk3 @ ( sk1 @ ( sk2 @ range ) ) @ ( A @ member ) ) )
& ( ( sk3 @ ( sk1 @ ( sk2 @ range ) ) @ ( A @ member ) )
=> ? [B: $i] :
( ( sk3 @ ( A @ ( B @ ordered_pair ) @ member ) )
& ( sk2 @ member_type @ ( B @ ilf_type ) ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
( ( sk3 @ ( sk4 @ ( A @ ordered_pair ) @ member ) )
& ( sk2 @ member_type @ ( A @ ilf_type ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( A @ ( B @ ( C @ ordered_pair ) @ member ) )
& ( set_type @ ( C @ ilf_type ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i] :
@+[B: $i] : ( A @ subset_type @ ( B @ ilf_type ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] : ( binary_relation_type @ ( A @ ilf_type ) ) ) ) ).
thf(13,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( ( set_type @ ( A @ power_set @ ilf_type ) )
& ~ ( A @ power_set @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).
thf(88,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)],[13]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
& ~ ( A @ empty ) )
=> ! [B: $i] :
( ( ( set_type @ ( B @ ilf_type ) )
& ~ ( B @ empty ) )
=> ! [C: $i] :
( ( A @ ( B @ relation_type ) @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( A @ member_type @ ( D @ ilf_type ) )
=> ( ( C @ ( A @ ( B @ range ) ) @ ( D @ member ) )
<=> ? [E: $i] :
( ( C @ ( D @ ( E @ ordered_pair ) @ member ) )
& ( B @ member_type @ ( E @ ilf_type ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_48) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
& ~ ( A @ empty ) )
=> ! [B: $i] :
( ( ( set_type @ ( B @ ilf_type ) )
& ~ ( B @ empty ) )
=> ! [C: $i] :
( ( A @ ( B @ relation_type ) @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( A @ member_type @ ( D @ ilf_type ) )
=> ( ( C @ ( A @ ( B @ range ) ) @ ( D @ member ) )
<=> ? [E: $i] :
( ( C @ ( D @ ( E @ ordered_pair ) @ member ) )
& ( B @ member_type @ ( E @ ilf_type ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(34,plain,
~ ! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
& ~ ( A @ empty ) )
=> ! [B: $i] :
( ( ( set_type @ ( B @ ilf_type ) )
& ~ ( B @ empty ) )
=> ! [C: $i] :
( ( A @ ( B @ relation_type ) @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( A @ member_type @ ( D @ ilf_type ) )
=> ( ( ? [E: $i] :
( ( C @ ( D @ ( E @ ordered_pair ) @ member ) )
& ( B @ member_type @ ( E @ ilf_type ) ) )
=> ( C @ ( A @ ( B @ range ) ) @ ( D @ member ) ) )
& ( ( C @ ( A @ ( B @ range ) ) @ ( D @ member ) )
=> ? [E: $i] :
( ( C @ ( D @ ( E @ ordered_pair ) @ member ) )
& ( B @ member_type @ ( E @ ilf_type ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(35,plain,
! [A: $i] :
( ( ~ ( sk3 @ ( sk1 @ ( sk2 @ range ) ) @ ( sk4 @ member ) )
| sk5 )
& ( ( sk3 @ ( sk4 @ ( sk6 @ ordered_pair ) @ member ) )
| sk5 )
& ( ( sk2 @ member_type @ ( sk6 @ ilf_type ) )
| sk5 )
& ( ~ sk5
| ~ ( sk3 @ ( sk4 @ ( A @ ordered_pair ) @ member ) )
| ~ ( sk2 @ member_type @ ( A @ ilf_type ) ) )
& ( ~ sk5
| ( sk3 @ ( sk1 @ ( sk2 @ range ) ) @ ( sk4 @ member ) ) )
& ( sk1 @ member_type @ ( sk4 @ ilf_type ) )
& ( sk1 @ ( sk2 @ relation_type ) @ ( sk3 @ ilf_type ) )
& ( set_type @ ( sk2 @ ilf_type ) )
& ~ ( sk2 @ empty )
& ( set_type @ ( sk1 @ ilf_type ) )
& ~ ( sk1 @ empty ) ),
inference(cnf,[status(esa)],[34]) ).
thf(41,plain,
sk1 @ ( sk2 @ relation_type ) @ ( sk3 @ ilf_type ),
inference(cnfConj,[status(thm)],[35]) ).
thf(15,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( ( A @ empty )
<=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ~ ( A @ ( B @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
thf(98,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)],[15]) ).
thf(10,axiom,
? [A: $i] : ( binary_relation_type @ ( A @ ilf_type ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18) ).
thf(66,plain,
? [A: $i] : ( binary_relation_type @ ( A @ ilf_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(67,plain,
binary_relation_type @ ( sk10 @ ilf_type ),
inference(cnf,[status(esa)],[66]) ).
thf(3,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( binary_relation_type @ ( B @ ilf_type ) )
=> ( ( B @ range_of @ ( A @ member ) )
<=> ? [C: $i] :
( ( B @ ( A @ ( C @ ordered_pair ) @ member ) )
& ( set_type @ ( C @ ilf_type ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
thf(47,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( binary_relation_type @ ( B @ ilf_type ) )
=> ( ( ? [C: $i] :
( ( B @ ( A @ ( C @ ordered_pair ) @ member ) )
& ( set_type @ ( C @ ilf_type ) ) )
=> ( B @ range_of @ ( A @ member ) ) )
& ( ( B @ range_of @ ( A @ member ) )
=> ? [C: $i] :
( ( B @ ( A @ ( C @ ordered_pair ) @ member ) )
& ( set_type @ ( C @ ilf_type ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ range_of @ ( A @ member ) )
| ~ ( B @ ( A @ ( C @ ordered_pair ) @ member ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( binary_relation_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B @ ( A @ ( A @ ( B @ sk7 ) @ ordered_pair ) @ member ) )
| ~ ( B @ range_of @ ( A @ member ) )
| ~ ( binary_relation_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( set_type @ ( A @ ( B @ sk7 ) @ ilf_type ) )
| ~ ( B @ range_of @ ( A @ member ) )
| ~ ( binary_relation_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ ( B @ sk7 ) @ ordered_pair ) @ member ) )
| ~ ( B @ range_of @ ( A @ member ) )
| ~ ( binary_relation_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[48]) ).
thf(28,axiom,
! [A: $i] : ( set_type @ ( A @ ilf_type ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).
thf(148,plain,
! [A: $i] : ( set_type @ ( A @ ilf_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(149,plain,
! [A: $i] : ( set_type @ ( A @ ilf_type ) ),
inference(cnf,[status(esa)],[148]) ).
thf(269,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ ( B @ sk7 ) @ ordered_pair ) @ member ) )
| ~ ( B @ range_of @ ( A @ member ) )
| ~ ( binary_relation_type @ ( B @ ilf_type ) )
| ~ $true ),
inference(rewrite,[status(thm)],[50,149]) ).
thf(270,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ ( B @ sk7 ) @ ordered_pair ) @ member ) )
| ~ ( B @ range_of @ ( A @ member ) )
| ~ ( binary_relation_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[269]) ).
thf(297,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( B @ ( A @ ( A @ ( B @ sk7 ) @ ordered_pair ) @ member ) )
| ~ ( B @ range_of @ ( A @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[67,270]) ).
thf(298,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( B @ ( A @ ( A @ ( B @ sk7 ) @ ordered_pair ) @ member ) )
| ~ ( B @ range_of @ ( A @ member ) ) ),
inference(simp,[status(thm)],[297]) ).
thf(299,plain,
! [A: $i] :
( ( sk10 @ ( A @ ( A @ ( sk10 @ sk7 ) @ ordered_pair ) @ member ) )
| ~ ( sk10 @ range_of @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[298:[bind(A,$thf( A )),bind(B,$thf( sk10 ))]]) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',p5) ).
thf(150,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)],[29]) ).
thf(43,plain,
( ~ ( sk3 @ ( sk1 @ ( sk2 @ range ) ) @ ( sk4 @ member ) )
| sk5 ),
inference(cnfConj,[status(thm)],[35]) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',p30) ).
thf(56,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)],[5]) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',p19) ).
thf(142,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)],[26]) ).
thf(42,plain,
( ( sk2 @ member_type @ ( sk6 @ ilf_type ) )
| sk5 ),
inference(cnfConj,[status(thm)],[35]) ).
thf(37,plain,
~ ( sk2 @ empty ),
inference(cnfConj,[status(thm)],[35]) ).
thf(4,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( binary_relation_type @ ( C @ ilf_type ) )
=> ( ( C @ ( B @ ( A @ ordered_pair ) @ member ) )
=> ( ( C @ range_of @ ( B @ member ) )
& ( C @ domain_of @ ( A @ member ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
thf(52,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( binary_relation_type @ ( C @ ilf_type ) )
=> ( ( C @ ( B @ ( A @ ordered_pair ) @ member ) )
=> ( ( C @ range_of @ ( B @ member ) )
& ( C @ domain_of @ ( A @ member ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(45,plain,
( ( sk3 @ ( sk4 @ ( sk6 @ ordered_pair ) @ member ) )
| sk5 ),
inference(cnfConj,[status(thm)],[35]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ range_of @ ( A @ member ) )
| ~ ( B @ ( A @ ( C @ ordered_pair ) @ member ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( binary_relation_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[48]) ).
thf(442,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ range_of @ ( A @ member ) )
| ~ ( B @ ( A @ ( C @ ordered_pair ) @ member ) )
| ~ $true
| ~ ( binary_relation_type @ ( B @ ilf_type ) )
| ~ $true ),
inference(rewrite,[status(thm)],[51,149]) ).
thf(443,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ range_of @ ( A @ member ) )
| ~ ( B @ ( A @ ( C @ ordered_pair ) @ member ) )
| ~ ( binary_relation_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[442]) ).
thf(458,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk4 @ ( sk6 @ ordered_pair ) @ member ) )
!= ( B @ ( A @ ( C @ ordered_pair ) @ member ) ) )
| ( B @ range_of @ ( A @ member ) )
| ~ $true
| ~ ( binary_relation_type @ ( B @ ilf_type ) )
| sk5 ),
inference(paramod_ordered,[status(thm)],[45,443]) ).
thf(459,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk4 @ ( sk6 @ ordered_pair ) @ member ) )
!= ( B @ ( A @ ( C @ ordered_pair ) @ member ) ) )
| ( B @ range_of @ ( A @ member ) )
| ~ ( binary_relation_type @ ( B @ ilf_type ) )
| sk5 ),
inference(simp,[status(thm)],[458]) ).
thf(460,plain,
( ( sk3 @ range_of @ ( sk4 @ member ) )
| ~ ( binary_relation_type @ ( sk3 @ ilf_type ) )
| sk5 ),
inference(pattern_uni,[status(thm)],[459:[bind(A,$thf( sk4 )),bind(B,$thf( sk3 )),bind(C,$thf( sk6 ))]]) ).
thf(46,plain,
~ ( sk1 @ empty ),
inference(cnfConj,[status(thm)],[35]) ).
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 ) )
=> ( ( C @ ( B @ ( A @ range ) ) )
= ( C @ range_of ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p29) ).
thf(152,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)],[30]) ).
thf(36,plain,
sk1 @ member_type @ ( sk4 @ ilf_type ),
inference(cnfConj,[status(thm)],[35]) ).
thf(38,plain,
! [A: $i] :
( ~ sk5
| ~ ( sk3 @ ( sk4 @ ( A @ ordered_pair ) @ member ) )
| ~ ( sk2 @ member_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[35]) ).
thf(189,plain,
! [A: $i] :
( ( ( sk1 @ member_type @ ( sk4 @ ilf_type ) )
!= ( sk2 @ member_type @ ( A @ ilf_type ) ) )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( A @ ordered_pair ) @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36,38]) ).
thf(190,plain,
! [A: $i] :
( ( ( sk1 @ member_type @ ( sk4 @ ilf_type ) )
!= ( sk2 @ member_type @ ( A @ ilf_type ) ) )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( A @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[189]) ).
thf(195,plain,
! [A: $i] :
( ( ( sk2 @ member_type )
!= ( sk1 @ member_type ) )
| ( sk4 != A )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( A @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[190]) ).
thf(199,plain,
( ( ( sk2 @ member_type )
!= ( sk1 @ member_type ) )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( sk4 @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[195]) ).
thf(261,plain,
( ( sk2 != sk1 )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( sk4 @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[199]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( sk2 @ member_type @ ( B @ ilf_type ) ) )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( B @ ordered_pair ) @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[149,38]) ).
thf(214,plain,
! [B: $i,A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( sk2 @ member_type @ ( B @ ilf_type ) ) )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( B @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[213]) ).
thf(215,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ member_type )
!= set_type )
| ( A != B )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( B @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[214]) ).
thf(216,plain,
! [A: $i] :
( ( ( sk2 @ member_type )
!= set_type )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( A @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[215]) ).
thf(89,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)],[88]) ).
thf(90,plain,
! [A: $i] :
( ~ ( A @ power_set @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[89]) ).
thf(210,plain,
! [A: $i] :
( ~ ( A @ power_set @ empty )
| ~ $true ),
inference(rewrite,[status(thm)],[90,149]) ).
thf(211,plain,
! [A: $i] :
~ ( A @ power_set @ empty ),
inference(simp,[status(thm)],[210]) ).
thf(20,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16) ).
thf(121,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(7,axiom,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( set_type @ ( A @ domain_of @ ilf_type ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11) ).
thf(60,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( set_type @ ( A @ domain_of @ ilf_type ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(33,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/sandbox2/benchmark/theBenchmark.p',p24) ).
thf(160,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)],[33]) ).
thf(12,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( A = B )
<=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( A @ ( C @ member ) )
<=> ( B @ ( C @ member ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21) ).
thf(70,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) )
& ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) )
& ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
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/sandbox2/benchmark/theBenchmark.p',p22) ).
thf(92,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(39,plain,
set_type @ ( sk2 @ ilf_type ),
inference(cnfConj,[status(thm)],[35]) ).
thf(185,plain,
! [A: $i] :
( ( ( set_type @ ( sk2 @ ilf_type ) )
!= ( sk2 @ member_type @ ( A @ ilf_type ) ) )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( A @ ordered_pair ) @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,38]) ).
thf(186,plain,
! [A: $i] :
( ( ( set_type @ ( sk2 @ ilf_type ) )
!= ( sk2 @ member_type @ ( A @ ilf_type ) ) )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( A @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[185]) ).
thf(193,plain,
! [A: $i] :
( ( ( sk2 @ member_type )
!= set_type )
| ( sk2 != A )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( A @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[186]) ).
thf(197,plain,
( ( ( sk2 @ member_type )
!= set_type )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( sk2 @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[193]) ).
thf(21,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( set_type @ ( D @ ilf_type ) )
=> ! [E: $i] :
( ( B @ ( A @ relation_type ) @ ( E @ ilf_type ) )
=> ( ( E @ ( D @ ( C @ ordered_pair ) @ member ) )
=> ( ( B @ ( D @ member ) )
& ( A @ ( C @ member ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
thf(124,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( set_type @ ( D @ ilf_type ) )
=> ! [E: $i] :
( ( B @ ( A @ relation_type ) @ ( E @ ilf_type ) )
=> ( ( E @ ( D @ ( C @ ordered_pair ) @ member ) )
=> ( ( B @ ( D @ member ) )
& ( A @ ( C @ member ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(524,plain,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( binary_relation_type @ ( sk3 @ ilf_type ) ) )
| ( sk3 @ range_of @ ( sk4 @ member ) )
| ~ $true
| sk5 ),
inference(paramod_ordered,[status(thm)],[149,460]) ).
thf(525,plain,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( binary_relation_type @ ( sk3 @ ilf_type ) ) )
| ( sk3 @ range_of @ ( sk4 @ member ) )
| sk5 ),
inference(simp,[status(thm)],[524]) ).
thf(542,plain,
! [A: $i] :
( ( binary_relation_type != set_type )
| ( A != sk3 )
| ( sk3 @ range_of @ ( sk4 @ member ) )
| sk5 ),
inference(simp,[status(thm)],[525]) ).
thf(554,plain,
( ( binary_relation_type != set_type )
| ( sk3 @ range_of @ ( sk4 @ member ) )
| sk5 ),
inference(simp,[status(thm)],[542]) ).
thf(23,axiom,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( set_type @ ( A @ range_of @ ilf_type ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).
thf(134,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( set_type @ ( A @ range_of @ ilf_type ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',p17) ).
thf(128,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)],[22]) ).
thf(17,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( set_type @ ( D @ ilf_type ) )
=> ! [E: $i] :
( ( set_type @ ( E @ ilf_type ) )
=> ( ( E
= ( D @ ( C @ ordered_pair ) ) )
<=> ( E
= ( C @ singleton @ ( D @ ( C @ unordered_pair ) @ unordered_pair ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
thf(105,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( set_type @ ( D @ ilf_type ) )
=> ! [E: $i] :
( ( set_type @ ( E @ ilf_type ) )
=> ( ( ( E
= ( C @ singleton @ ( D @ ( C @ unordered_pair ) @ unordered_pair ) ) )
=> ( E
= ( D @ ( C @ ordered_pair ) ) ) )
& ( ( E
= ( D @ ( C @ ordered_pair ) ) )
=> ( E
= ( C @ singleton @ ( D @ ( C @ unordered_pair ) @ unordered_pair ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,axiom,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
& ~ ( A @ empty ) )
=> ? [B: $i] : ( A @ member_type @ ( B @ ilf_type ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9) ).
thf(64,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)],[9]) ).
thf(356,plain,
! [A: $i] :
( ( ( sk3 @ ( sk4 @ ( sk6 @ ordered_pair ) @ member ) )
!= ( sk10 @ range_of @ ( A @ member ) ) )
| ( sk10 @ ( A @ ( A @ ( sk10 @ sk7 ) @ ordered_pair ) @ member ) )
| ~ $true
| sk5 ),
inference(paramod_ordered,[status(thm)],[45,299]) ).
thf(357,plain,
! [A: $i] :
( ( ( sk3 @ ( sk4 @ ( sk6 @ ordered_pair ) @ member ) )
!= ( sk10 @ range_of @ ( A @ member ) ) )
| ( sk10 @ ( A @ ( A @ ( sk10 @ sk7 ) @ ordered_pair ) @ member ) )
| sk5 ),
inference(simp,[status(thm)],[356]) ).
thf(364,plain,
! [A: $i] :
( ( ( sk10 @ range_of )
!= sk3 )
| ( ( sk4 @ ( sk6 @ ordered_pair ) )
!= A )
| ( sk10 @ ( A @ ( A @ ( sk10 @ sk7 ) @ ordered_pair ) @ member ) )
| sk5 ),
inference(simp,[status(thm)],[357]) ).
thf(375,plain,
( ( ( sk10 @ range_of )
!= sk3 )
| ( sk10 @ ( sk4 @ ( sk6 @ ordered_pair ) @ ( sk4 @ ( sk6 @ ordered_pair ) @ ( sk10 @ sk7 ) @ ordered_pair ) @ member ) )
| sk5 ),
inference(simp,[status(thm)],[364]) ).
thf(468,plain,
! [C: $i,B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( B @ range_of @ ( A @ member ) )
| ~ ( B @ ( A @ ( C @ ordered_pair ) @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[67,443]) ).
thf(469,plain,
! [C: $i,B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( B @ range_of @ ( A @ member ) )
| ~ ( B @ ( A @ ( C @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[468]) ).
thf(470,plain,
! [B: $i,A: $i] :
( ( sk10 @ range_of @ ( A @ member ) )
| ~ ( sk10 @ ( A @ ( B @ ordered_pair ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[469:[bind(A,$thf( A )),bind(B,$thf( sk10 ))]]) ).
thf(477,plain,
! [B: $i,A: $i] :
( ( sk10 @ range_of @ ( A @ member ) )
| ~ ( sk10 @ ( A @ ( B @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[470]) ).
thf(532,plain,
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( binary_relation_type @ ( sk3 @ ilf_type ) ) )
| ( sk3 @ range_of @ ( sk4 @ member ) )
| ~ $true
| sk5 ),
inference(paramod_ordered,[status(thm)],[67,460]) ).
thf(533,plain,
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( binary_relation_type @ ( sk3 @ ilf_type ) ) )
| ( sk3 @ range_of @ ( sk4 @ member ) )
| sk5 ),
inference(simp,[status(thm)],[532]) ).
thf(538,plain,
( ( binary_relation_type != binary_relation_type )
| ( sk10 != sk3 )
| ( sk3 @ range_of @ ( sk4 @ member ) )
| sk5 ),
inference(simp,[status(thm)],[533]) ).
thf(552,plain,
( ( sk10 != sk3 )
| ( sk3 @ range_of @ ( sk4 @ member ) )
| sk5 ),
inference(simp,[status(thm)],[538]) ).
thf(16,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( set_type @ ( A @ singleton @ ilf_type ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
thf(103,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( set_type @ ( A @ singleton @ ilf_type ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',p7) ).
thf(140,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)],[25]) ).
thf(31,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/sandbox2/benchmark/theBenchmark.p',p27) ).
thf(155,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)],[31]) ).
thf(187,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( sk2 @ member_type @ ( A @ ilf_type ) ) )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( A @ ordered_pair ) @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[67,38]) ).
thf(188,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( sk2 @ member_type @ ( A @ ilf_type ) ) )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( A @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[187]) ).
thf(194,plain,
! [A: $i] :
( ( ( sk2 @ member_type )
!= binary_relation_type )
| ( sk10 != A )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( A @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[188]) ).
thf(198,plain,
( ( ( sk2 @ member_type )
!= binary_relation_type )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( sk10 @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[194]) ).
thf(6,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ? [B: $i] : ( A @ subset_type @ ( B @ ilf_type ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).
thf(58,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(59,plain,
! [A: $i] :
( ( A @ subset_type @ ( A @ sk8 @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(329,plain,
! [A: $i] :
( ( A @ subset_type @ ( A @ sk8 @ ilf_type ) )
| ~ $true ),
inference(rewrite,[status(thm)],[59,149]) ).
thf(330,plain,
! [A: $i] : ( A @ subset_type @ ( A @ sk8 @ ilf_type ) ),
inference(simp,[status(thm)],[329]) ).
thf(40,plain,
( ~ sk5
| ( sk3 @ ( sk1 @ ( sk2 @ range ) ) @ ( sk4 @ member ) ) ),
inference(cnfConj,[status(thm)],[35]) ).
thf(32,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/sandbox2/benchmark/theBenchmark.p',p26) ).
thf(158,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)],[32]) ).
thf(18,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/sandbox2/benchmark/theBenchmark.p',p6) ).
thf(114,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)],[18]) ).
thf(233,plain,
( ( ( sk3 @ ( sk4 @ ( sk6 @ ordered_pair ) @ member ) )
!= ( sk3 @ ( sk1 @ ( sk2 @ range ) ) @ ( sk4 @ member ) ) )
| ~ $true
| sk5
| sk5 ),
inference(paramod_ordered,[status(thm)],[45,43]) ).
thf(234,plain,
( ( ( sk3 @ ( sk4 @ ( sk6 @ ordered_pair ) @ member ) )
!= ( sk3 @ ( sk1 @ ( sk2 @ range ) ) @ ( sk4 @ member ) ) )
| sk5 ),
inference(simp,[status(thm)],[233]) ).
thf(235,plain,
( ( ( sk3 @ ( sk1 @ ( sk2 @ range ) ) )
!= sk3 )
| ( ( sk4 @ ( sk6 @ ordered_pair ) )
!= sk4 )
| sk5 ),
inference(simp,[status(thm)],[234]) ).
thf(201,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ relation_type ) @ ( sk3 @ ilf_type ) )
!= ( sk2 @ member_type @ ( A @ ilf_type ) ) )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( A @ ordered_pair ) @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41,38]) ).
thf(202,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ relation_type ) @ ( sk3 @ ilf_type ) )
!= ( sk2 @ member_type @ ( A @ ilf_type ) ) )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( A @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[201]) ).
thf(205,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ relation_type ) )
!= ( sk2 @ member_type ) )
| ( sk3 != A )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( A @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[202]) ).
thf(207,plain,
( ( ( sk1 @ ( sk2 @ relation_type ) )
!= ( sk2 @ member_type ) )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( sk3 @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(19,axiom,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
& ( A @ empty ) )
=> ( A @ relation_like ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25) ).
thf(119,plain,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
& ( A @ empty ) )
=> ( A @ relation_like ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(27,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( set_type @ ( B @ ( A @ unordered_pair ) @ ilf_type ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
thf(146,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( set_type @ ( B @ ( A @ unordered_pair ) @ ilf_type ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',p8) ).
thf(136,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)],[24]) ).
thf(262,plain,
( ( ( sk3 @ ( sk1 @ ( sk2 @ range ) ) @ ( sk4 @ member ) )
!= ( sk3 @ ( sk4 @ ( sk4 @ ordered_pair ) @ member ) ) )
| ( ( sk2 @ member_type )
!= ( sk1 @ member_type ) )
| ~ sk5
| ~ $true
| ~ sk5 ),
inference(paramod_ordered,[status(thm)],[40,199]) ).
thf(263,plain,
( ( ( sk3 @ ( sk1 @ ( sk2 @ range ) ) @ ( sk4 @ member ) )
!= ( sk3 @ ( sk4 @ ( sk4 @ ordered_pair ) @ member ) ) )
| ( ( sk2 @ member_type )
!= ( sk1 @ member_type ) )
| ~ sk5 ),
inference(simp,[status(thm)],[262]) ).
thf(268,plain,
( ( ( sk3 @ ( sk1 @ ( sk2 @ range ) ) )
!= sk3 )
| ( ( sk4 @ ( sk4 @ ordered_pair ) )
!= sk4 )
| ( sk2 != sk1 )
| ~ sk5 ),
inference(simp,[status(thm)],[263]) ).
thf(44,plain,
set_type @ ( sk1 @ ilf_type ),
inference(cnfConj,[status(thm)],[35]) ).
thf(191,plain,
! [A: $i] :
( ( ( set_type @ ( sk1 @ ilf_type ) )
!= ( sk2 @ member_type @ ( A @ ilf_type ) ) )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( A @ ordered_pair ) @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44,38]) ).
thf(192,plain,
! [A: $i] :
( ( ( set_type @ ( sk1 @ ilf_type ) )
!= ( sk2 @ member_type @ ( A @ ilf_type ) ) )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( A @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[191]) ).
thf(196,plain,
! [A: $i] :
( ( ( sk2 @ member_type )
!= set_type )
| ( sk1 != A )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( A @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[192]) ).
thf(200,plain,
( ( ( sk2 @ member_type )
!= set_type )
| ~ sk5
| ~ ( sk3 @ ( sk4 @ ( sk1 @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[196]) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',p28) ).
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 ) )
=> ( A @ subset_type @ ( C @ ( B @ ( A @ domain ) ) @ ilf_type ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',p13) ).
thf(62,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)],[8]) ).
thf(819,plain,
$false,
inference(e,[status(thm)],[88,41,98,299,150,43,56,142,42,37,52,460,46,152,261,216,443,211,121,60,270,38,160,70,92,197,124,554,134,128,105,34,148,45,64,149,375,477,552,103,140,66,155,198,330,67,199,40,158,114,235,207,119,58,36,146,136,268,47,200,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET681+3 : TPTP v9.3.1. Released v2.2.0.
% 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 : n020.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 08:06:05 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
% 0.84/0.95 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/1.17 % [INFO] Parsing done (214ms).
% 1.23/1.18 % [INFO] Running in sequential loop mode.
% 1.91/1.57 % [INFO] eprover registered as external prover.
% 1.91/1.58 % [INFO] Scanning for conjecture ...
% 2.11/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 31 axioms. Running axiom selection ...
% 2.27/1.78 % [INFO] Axiom selection finished. Selected 31 axioms (removed 0 axioms).
% 2.48/1.84 % [INFO] Problem is first-order (TPTP FOF).
% 2.48/1.86 % [INFO] Type checking passed.
% 2.48/1.86 % [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 ...
% 8.51/3.58 % External prover 'e' found a proof!
% 8.51/3.58 % [INFO] Killing All external provers ...
% 8.51/3.58 % Time passed: 3053ms (effective reasoning time: 2391ms)
% 8.51/3.58 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 8.51/3.58 % Axioms used in derivation (31): p27, p12, p18, p26, p3, p22, p11, p2, p17, p9, p24, p16, p20, p10, p19, p4, p7, p5, p23, p21, p29, p15, p25, p14, p28, p1, p31, p30, p13, p6, p8
% 8.51/3.58 % No. of inferences in proof: 147
% 8.51/3.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3053 ms resp. 2391 ms w/o parsing
% 9.66/3.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.66/3.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------