%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET640+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 : n015.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 08:30:36 AM UTC 2026
% Result : Theorem 16.72s 4.77s
% Output : Refutation 15.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 32
% Syntax : Number of formulae : 163 ( 28 unt; 0 typ; 12 def)
% Number of atoms : 706 ( 103 equ; 0 cnn)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 2367 ( 292 ~; 255 |; 68 &;1608 @)
% ( 7 <=>; 137 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 7 con; 0-3 aty)
% Number of variables : 386 ( 14 ^; 338 !; 22 ?; 386 :)
% ( 0 !>; 0 ?*; 0 @-; 12 @+)
% 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(subset_decl,type,
subset: $i > $i > $o ).
thf(cross_product_decl,type,
cross_product: $i > $i > $i ).
thf(subset_type_decl,type,
subset_type: $i > $i ).
thf(member_type_decl,type,
member_type: $i > $i ).
thf(power_set_decl,type,
power_set: $i > $i ).
thf(relation_like_decl,type,
relation_like: $i > $o ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(empty_decl,type,
empty: $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: $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i > $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( C @ ( B @ relation_type ) @ ( D @ ilf_type ) )
=> ( ( D @ ( A @ subset ) )
=> ( C @ ( B @ cross_product ) @ ( A @ subset ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ( ( C @ ( sk1 @ subset ) )
=> ( B @ ( A @ cross_product ) @ ( sk1 @ subset ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( A @ ( sk2 @ relation_type ) @ ( B @ ilf_type ) )
=> ( ( B @ ( sk1 @ subset ) )
=> ( A @ ( sk2 @ cross_product ) @ ( sk1 @ subset ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( sk3 @ ( sk2 @ relation_type ) @ ( A @ ilf_type ) )
=> ( ( A @ ( sk1 @ subset ) )
=> ( sk3 @ ( sk2 @ cross_product ) @ ( sk1 @ subset ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i] :
@+[B: $i] : ( A @ subset_type @ ( B @ ilf_type ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( A
= ( D @ ( C @ ordered_pair ) ) )
& ( set_type @ ( D @ ilf_type ) ) )
& ( set_type @ ( C @ ilf_type ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( A
= ( C @ ( B @ ( A @ sk6 ) @ ordered_pair ) ) )
& ( set_type @ ( C @ ilf_type ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i] :
@+[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 ) ) ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
( ? [E: $i] :
( ( A
= ( E @ ( D @ ordered_pair ) ) )
& ( B @ ( E @ member ) )
& ( C @ ( D @ member ) )
& ( set_type @ ( E @ ilf_type ) ) )
& ( set_type @ ( D @ ilf_type ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
( ( A
= ( D @ ( C @ ( B @ ( A @ sk11 ) ) @ ordered_pair ) ) )
& ( B @ ( D @ member ) )
& ( C @ ( C @ ( B @ ( A @ sk11 ) ) @ member ) )
& ( set_type @ ( D @ ilf_type ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i] :
@+[B: $i] : ( A @ member_type @ ( B @ ilf_type ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( set_type @ ( B @ ilf_type ) )
=> ~ ( A @ ( B @ member ) ) ) ) ) ).
thf(13,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( B @ ( A @ cross_product ) @ ( C @ member ) )
<=> ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ordered_pair ) ) )
& ( B @ ( E @ member ) )
& ( A @ ( D @ member ) )
& ( set_type @ ( E @ ilf_type ) ) )
& ( set_type @ ( D @ ilf_type ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
thf(67,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ordered_pair ) ) )
& ( B @ ( E @ member ) )
& ( A @ ( D @ member ) )
& ( set_type @ ( E @ ilf_type ) ) )
& ( set_type @ ( D @ ilf_type ) ) )
=> ( B @ ( A @ cross_product ) @ ( C @ member ) ) )
& ( ( B @ ( A @ cross_product ) @ ( C @ member ) )
=> ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ordered_pair ) ) )
& ( B @ ( E @ member ) )
& ( A @ ( D @ member ) )
& ( set_type @ ( E @ ilf_type ) ) )
& ( set_type @ ( D @ ilf_type ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(68,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cross_product ) @ ( C @ member ) )
| ( C
!= ( E @ ( D @ ordered_pair ) ) )
| ~ ( B @ ( E @ member ) )
| ~ ( A @ ( D @ member ) )
| ~ ( set_type @ ( E @ ilf_type ) )
| ~ ( set_type @ ( D @ ilf_type ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( C
= ( A @ ( B @ ( C @ sk12 ) ) @ ( A @ ( B @ ( C @ sk11 ) ) @ ordered_pair ) ) )
| ~ ( B @ ( A @ cross_product ) @ ( C @ member ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B @ ( A @ ( B @ ( C @ sk12 ) ) @ member ) )
| ~ ( B @ ( A @ cross_product ) @ ( C @ member ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( A @ ( A @ ( B @ ( C @ sk11 ) ) @ member ) )
| ~ ( B @ ( A @ cross_product ) @ ( C @ member ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( set_type @ ( A @ ( B @ ( C @ sk12 ) ) @ ilf_type ) )
| ~ ( B @ ( A @ cross_product ) @ ( C @ member ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( set_type @ ( A @ ( B @ ( C @ sk11 ) ) @ ilf_type ) )
| ~ ( B @ ( A @ cross_product ) @ ( C @ member ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[67]) ).
thf(74,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ cross_product ) @ ( C @ member ) )
| ( C
!= ( E @ ( D @ ordered_pair ) ) )
| ~ ( B @ ( E @ member ) )
| ~ ( A @ ( D @ member ) )
| ~ ( set_type @ ( E @ ilf_type ) )
| ~ ( set_type @ ( D @ ilf_type ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[68]) ).
thf(75,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ cross_product ) @ ( C @ member ) )
| ~ ( B @ ( E @ member ) )
| ~ ( A @ ( D @ member ) )
| ~ ( set_type @ ( E @ ilf_type ) )
| ~ ( set_type @ ( D @ ilf_type ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) )
| ( C
!= ( E @ ( D @ ordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(76,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ cross_product ) @ ( D @ ( C @ ordered_pair ) @ member ) )
| ~ ( B @ ( D @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( set_type @ ( D @ ilf_type ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( D @ ( C @ ordered_pair ) @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(20,axiom,
! [A: $i] : ( set_type @ ( A @ ilf_type ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
thf(98,plain,
! [A: $i] : ( set_type @ ( A @ ilf_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(99,plain,
! [A: $i] : ( set_type @ ( A @ ilf_type ) ),
inference(cnf,[status(esa)],[98]) ).
thf(129,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ cross_product ) @ ( D @ ( C @ ordered_pair ) @ member ) )
| ~ ( B @ ( D @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[76,99]) ).
thf(130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ cross_product ) @ ( D @ ( C @ ordered_pair ) @ member ) )
| ~ ( B @ ( D @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(17,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',p15) ).
thf(86,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)],[17]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( ( A @ empty )
| ( A @ ( A @ sk14 @ member ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( A @ empty )
| ( set_type @ ( A @ sk14 @ 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)],[86]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( A @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[87]) ).
thf(127,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ $true
| ~ ( A @ empty )
| ~ $true ),
inference(rewrite,[status(thm)],[88,99]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[127]) ).
thf(131,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cross_product ) @ ( D @ ( C @ ordered_pair ) @ member ) )
!= ( E @ ( F @ member ) ) )
| ~ $true
| ~ ( E @ empty )
| ~ ( B @ ( D @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(paramod_ordered,[status(thm)],[130,128]) ).
thf(132,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cross_product ) @ ( D @ ( C @ ordered_pair ) @ member ) )
!= ( E @ ( F @ member ) ) )
| ~ ( E @ empty )
| ~ ( B @ ( D @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ cross_product ) @ empty )
| ~ ( D @ ( B @ member ) )
| ~ ( C @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[132:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( G )),bind(D,$thf( H )),bind(E,$thf( J @ ( I @ cross_product ) )),bind(F,$thf( H @ ( G @ ordered_pair ) ))]]) ).
thf(140,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ cross_product ) @ empty )
| ~ ( D @ ( B @ member ) )
| ~ ( C @ ( A @ member ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( D @ ( B @ member ) )
!= ( C @ ( A @ member ) ) )
| ~ ( D @ ( C @ cross_product ) @ empty )
| ~ ( C @ ( A @ member ) ) ),
inference(eqfactor_ordered,[status(thm)],[140]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ cross_product ) @ empty )
| ~ ( B @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ cross_product ) @ empty )
| ~ ( B @ ( A @ member ) ) ),
inference(simp,[status(thm)],[208]) ).
thf(217,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cross_product ) @ ( D @ ( C @ ordered_pair ) @ member ) )
!= ( F @ ( E @ member ) ) )
| ~ ( F @ ( F @ cross_product ) @ empty )
| ~ $true
| ~ ( B @ ( D @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(paramod_ordered,[status(thm)],[130,209]) ).
thf(218,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cross_product ) @ ( D @ ( C @ ordered_pair ) @ member ) )
!= ( F @ ( E @ member ) ) )
| ~ ( F @ ( F @ cross_product ) @ empty )
| ~ ( B @ ( D @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(simp,[status(thm)],[217]) ).
thf(219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ cross_product ) @ ( D @ ( C @ cross_product ) @ cross_product ) @ empty )
| ~ ( D @ ( B @ member ) )
| ~ ( C @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[218:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( G )),bind(D,$thf( H )),bind(E,$thf( H @ ( G @ ordered_pair ) )),bind(F,$thf( J @ ( I @ cross_product ) ))]]) ).
thf(221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ cross_product ) @ ( D @ ( C @ cross_product ) @ cross_product ) @ empty )
| ~ ( D @ ( B @ member ) )
| ~ ( C @ ( A @ member ) ) ),
inference(simp,[status(thm)],[219]) ).
thf(327,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( D @ ( B @ member ) )
!= ( C @ ( A @ member ) ) )
| ~ ( D @ ( C @ cross_product ) @ ( D @ ( C @ cross_product ) @ cross_product ) @ empty )
| ~ ( C @ ( A @ member ) ) ),
inference(eqfactor_ordered,[status(thm)],[221]) ).
thf(328,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ cross_product ) @ ( B @ ( B @ cross_product ) @ cross_product ) @ empty )
| ~ ( B @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[327:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(333,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ cross_product ) @ ( B @ ( B @ cross_product ) @ cross_product ) @ empty )
| ~ ( B @ ( A @ member ) ) ),
inference(simp,[status(thm)],[328]) ).
thf(3,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( A @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
thf(30,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( A @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(31,plain,
! [A: $i] :
( ( A @ ( A @ subset ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[30]) ).
thf(115,plain,
! [A: $i] :
( ( A @ ( A @ subset ) )
| ~ $true ),
inference(rewrite,[status(thm)],[31,99]) ).
thf(116,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(simp,[status(thm)],[115]) ).
thf(1,conjecture,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( C @ ( B @ relation_type ) @ ( D @ ilf_type ) )
=> ( ( D @ ( A @ subset ) )
=> ( C @ ( B @ cross_product ) @ ( A @ subset ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( C @ ( B @ relation_type ) @ ( D @ ilf_type ) )
=> ( ( D @ ( A @ subset ) )
=> ( C @ ( B @ cross_product ) @ ( A @ subset ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(22,plain,
~ ! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( C @ ( B @ relation_type ) @ ( D @ ilf_type ) )
=> ( ( D @ ( A @ subset ) )
=> ( C @ ( B @ cross_product ) @ ( A @ subset ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(23,plain,
( ~ ( sk3 @ ( sk2 @ cross_product ) @ ( sk1 @ subset ) )
& ( sk4 @ ( sk1 @ subset ) )
& ( sk3 @ ( sk2 @ relation_type ) @ ( sk4 @ ilf_type ) )
& ( set_type @ ( sk3 @ ilf_type ) )
& ( set_type @ ( sk2 @ ilf_type ) )
& ( set_type @ ( sk1 @ ilf_type ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(27,plain,
~ ( sk3 @ ( sk2 @ cross_product ) @ ( sk1 @ subset ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(117,plain,
! [A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( sk3 @ ( sk2 @ cross_product ) @ ( sk1 @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[116,27]) ).
thf(118,plain,
! [A: $i] :
( ( A @ ( A @ subset ) )
!= ( sk3 @ ( sk2 @ cross_product ) @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(119,plain,
! [A: $i] :
( ( A
!= ( sk3 @ ( sk2 @ cross_product ) ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[118]) ).
thf(120,plain,
( ( sk3 @ ( sk2 @ cross_product ) )
!= sk1 ),
inference(simp,[status(thm)],[119]) ).
thf(8,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',p16) ).
thf(42,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)],[8]) ).
thf(14,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',p14) ).
thf(78,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)],[14]) ).
thf(16,axiom,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
& ( A @ empty ) )
=> ( A @ relation_like ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17) ).
thf(84,plain,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
& ( A @ empty ) )
=> ( A @ relation_like ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(9,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',p5) ).
thf(53,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)],[9]) ).
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',p9) ).
thf(38,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(39,plain,
! [A: $i] :
( ( A @ subset_type @ ( A @ sk5 @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(123,plain,
! [A: $i] :
( ( A @ subset_type @ ( A @ sk5 @ ilf_type ) )
| ~ $true ),
inference(rewrite,[status(thm)],[39,99]) ).
thf(124,plain,
! [A: $i] : ( A @ subset_type @ ( A @ sk5 @ ilf_type ) ),
inference(simp,[status(thm)],[123]) ).
thf(4,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',p8) ).
thf(32,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)],[4]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type @ ( B @ ilf_type ) )
| ~ ( A @ power_set @ member_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( A @ power_set @ member_type @ ( B @ ilf_type ) )
| ~ ( A @ subset_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( A @ power_set @ member_type @ ( B @ ilf_type ) )
| ~ ( A @ subset_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[33]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( A @ power_set @ member_type @ ( B @ ilf_type ) )
| ~ ( A @ subset_type @ ( B @ ilf_type ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[34,99]) ).
thf(162,plain,
! [B: $i,A: $i] :
( ( A @ power_set @ member_type @ ( B @ ilf_type ) )
| ~ ( A @ subset_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[161]) ).
thf(169,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk5 @ ilf_type ) )
!= ( B @ subset_type @ ( C @ ilf_type ) ) )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[124,162]) ).
thf(170,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk5 @ ilf_type ) )
!= ( B @ subset_type @ ( C @ ilf_type ) ) )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[169]) ).
thf(171,plain,
! [A: $i] : ( A @ power_set @ member_type @ ( A @ sk5 @ ilf_type ) ),
inference(pattern_uni,[status(thm)],[170:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk5 ))]]) ).
thf(175,plain,
! [A: $i] : ( A @ power_set @ member_type @ ( A @ sk5 @ ilf_type ) ),
inference(simp,[status(thm)],[171]) ).
thf(167,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( B @ subset_type @ ( C @ ilf_type ) ) )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[99,162]) ).
thf(168,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( B @ subset_type @ ( C @ ilf_type ) ) )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[167]) ).
thf(174,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ subset_type )
!= set_type )
| ( A != C )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[168]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type )
!= set_type )
| ( A @ power_set @ member_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[174]) ).
thf(21,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',p11) ).
thf(100,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)],[21]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',p6) ).
thf(61,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)],[12]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( A @ subset_type @ ( B @ ilf_type ) )
| ~ ( A @ power_set @ member_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[33]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ( A @ subset_type @ ( B @ ilf_type ) )
| ~ ( A @ power_set @ member_type @ ( B @ ilf_type ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[35,99]) ).
thf(259,plain,
! [B: $i,A: $i] :
( ( A @ subset_type @ ( B @ ilf_type ) )
| ~ ( A @ power_set @ member_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[258]) ).
thf(268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( B @ ilf_type ) )
!= ( C @ power_set @ member_type @ ( D @ ilf_type ) ) )
| ( C @ subset_type @ ( D @ ilf_type ) )
| ~ $true
| ( ( A @ subset_type )
!= set_type ) ),
inference(paramod_ordered,[status(thm)],[178,259]) ).
thf(269,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( B @ ilf_type ) )
!= ( C @ power_set @ member_type @ ( D @ ilf_type ) ) )
| ( C @ subset_type @ ( D @ ilf_type ) )
| ( ( A @ subset_type )
!= set_type ) ),
inference(simp,[status(thm)],[268]) ).
thf(270,plain,
! [B: $i,A: $i] :
( ( A @ subset_type @ ( B @ ilf_type ) )
| ( ( A @ subset_type )
!= set_type ) ),
inference(pattern_uni,[status(thm)],[269:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ relation_like )
| ( ( A @ sk8 )
!= ( D @ ( C @ ordered_pair ) ) )
| ~ ( set_type @ ( D @ ilf_type ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( A @ relation_like )
| ( A @ ( A @ sk8 @ member ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( A @ relation_like )
| ( set_type @ ( A @ sk8 @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B
= ( A @ ( B @ sk7 ) @ ( A @ ( B @ sk6 ) @ ordered_pair ) ) )
| ~ ( A @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( A @ relation_like )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( set_type @ ( A @ ( B @ sk7 ) @ ilf_type ) )
| ~ ( A @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( A @ relation_like )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( set_type @ ( A @ ( B @ sk6 ) @ ilf_type ) )
| ~ ( A @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( A @ relation_like )
| ~ ( set_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[42]) ).
thf(47,plain,
! [A: $i] :
( ( A @ relation_like )
| ( A @ ( A @ sk8 @ member ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[43]) ).
thf(147,plain,
! [A: $i] :
( ( A @ relation_like )
| ( A @ ( A @ sk8 @ member ) )
| ~ $true ),
inference(rewrite,[status(thm)],[47,99]) ).
thf(148,plain,
! [A: $i] :
( ( A @ relation_like )
| ( A @ ( A @ sk8 @ member ) ) ),
inference(simp,[status(thm)],[147]) ).
thf(214,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk8 @ member ) )
!= ( C @ ( B @ member ) ) )
| ~ ( C @ ( C @ cross_product ) @ empty )
| ~ $true
| ( A @ relation_like ) ),
inference(paramod_ordered,[status(thm)],[148,209]) ).
thf(215,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk8 @ member ) )
!= ( C @ ( B @ member ) ) )
| ~ ( C @ ( C @ cross_product ) @ empty )
| ( A @ relation_like ) ),
inference(simp,[status(thm)],[214]) ).
thf(216,plain,
! [A: $i] :
( ~ ( A @ ( A @ cross_product ) @ empty )
| ( A @ relation_like ) ),
inference(pattern_uni,[status(thm)],[215:[bind(A,$thf( D )),bind(B,$thf( D @ sk8 )),bind(C,$thf( D ))]]) ).
thf(220,plain,
! [A: $i] :
( ~ ( A @ ( A @ cross_product ) @ empty )
| ( A @ relation_like ) ),
inference(simp,[status(thm)],[216]) ).
thf(79,plain,
! [A: $i] :
( ( A @ member_type @ ( A @ sk13 @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) )
| ( A @ empty ) ),
inference(cnf,[status(esa)],[78]) ).
thf(348,plain,
! [A: $i] :
( ( A @ member_type @ ( A @ sk13 @ ilf_type ) )
| ~ $true
| ( A @ empty ) ),
inference(rewrite,[status(thm)],[79,99]) ).
thf(349,plain,
! [A: $i] :
( ( A @ member_type @ ( A @ sk13 @ ilf_type ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[348]) ).
thf(28,plain,
sk3 @ ( sk2 @ relation_type ) @ ( sk4 @ ilf_type ),
inference(cnfConj,[status(thm)],[23]) ).
thf(163,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ relation_type ) @ ( sk4 @ ilf_type ) )
!= ( A @ subset_type @ ( B @ ilf_type ) ) )
| ( A @ power_set @ member_type @ ( B @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,162]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ relation_type ) @ ( sk4 @ ilf_type ) )
!= ( A @ subset_type @ ( B @ ilf_type ) ) )
| ( A @ power_set @ member_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[163]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ relation_type ) )
!= ( A @ subset_type ) )
| ( sk4 != B )
| ( A @ power_set @ member_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[164]) ).
thf(176,plain,
! [A: $i] :
( ( ( sk3 @ ( sk2 @ relation_type ) )
!= ( A @ subset_type ) )
| ( A @ power_set @ member_type @ ( sk4 @ ilf_type ) ) ),
inference(simp,[status(thm)],[172]) ).
thf(273,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( sk4 @ ilf_type ) )
!= ( B @ power_set @ member_type @ ( C @ ilf_type ) ) )
| ( B @ subset_type @ ( C @ ilf_type ) )
| ~ $true
| ( ( sk3 @ ( sk2 @ relation_type ) )
!= ( A @ subset_type ) ) ),
inference(paramod_ordered,[status(thm)],[176,259]) ).
thf(274,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( sk4 @ ilf_type ) )
!= ( B @ power_set @ member_type @ ( C @ ilf_type ) ) )
| ( B @ subset_type @ ( C @ ilf_type ) )
| ( ( sk3 @ ( sk2 @ relation_type ) )
!= ( A @ subset_type ) ) ),
inference(simp,[status(thm)],[273]) ).
thf(275,plain,
! [A: $i] :
( ( A @ subset_type @ ( sk4 @ ilf_type ) )
| ( ( sk3 @ ( sk2 @ relation_type ) )
!= ( A @ subset_type ) ) ),
inference(pattern_uni,[status(thm)],[274:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk4 ))]]) ).
thf(26,plain,
sk4 @ ( sk1 @ subset ),
inference(cnfConj,[status(thm)],[23]) ).
thf(106,plain,
( ( ( sk3 @ ( sk2 @ cross_product ) @ ( sk1 @ subset ) )
!= ( sk4 @ ( sk1 @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26,27]) ).
thf(107,plain,
( ( sk3 @ ( sk2 @ cross_product ) @ ( sk1 @ subset ) )
!= ( sk4 @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(108,plain,
( ( ( sk3 @ ( sk2 @ cross_product ) )
!= sk4 )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[107]) ).
thf(109,plain,
( ( sk3 @ ( sk2 @ cross_product ) )
!= sk4 ),
inference(simp,[status(thm)],[108]) ).
thf(19,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',p3) ).
thf(96,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)],[19]) ).
thf(11,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
thf(59,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
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',p4) ).
thf(91,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(90,plain,
! [A: $i] :
( ( A @ empty )
| ( A @ ( A @ sk14 @ member ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[87]) ).
thf(222,plain,
! [A: $i] :
( ( A @ empty )
| ( A @ ( A @ sk14 @ member ) )
| ~ $true ),
inference(rewrite,[status(thm)],[90,99]) ).
thf(223,plain,
! [A: $i] :
( ( A @ empty )
| ( A @ ( A @ sk14 @ member ) ) ),
inference(simp,[status(thm)],[222]) ).
thf(15,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',p12) ).
thf(80,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)],[15]) ).
thf(179,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( A @ sk5 @ ilf_type ) )
!= ( B @ subset_type @ ( C @ ilf_type ) ) )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[175,162]) ).
thf(180,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( A @ sk5 @ ilf_type ) )
!= ( B @ subset_type @ ( C @ ilf_type ) ) )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[179]) ).
thf(181,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type )
!= ( B @ subset_type ) )
| ( ( A @ sk5 )
!= C )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[180]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ( ( A @ power_set @ member_type )
!= ( B @ subset_type ) )
| ( B @ power_set @ member_type @ ( A @ sk5 @ ilf_type ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(183,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( sk4 @ ilf_type ) )
!= ( B @ subset_type @ ( C @ ilf_type ) ) )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) )
| ~ $true
| ( ( sk3 @ ( sk2 @ relation_type ) )
!= ( A @ subset_type ) ) ),
inference(paramod_ordered,[status(thm)],[176,162]) ).
thf(184,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( sk4 @ ilf_type ) )
!= ( B @ subset_type @ ( C @ ilf_type ) ) )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) )
| ( ( sk3 @ ( sk2 @ relation_type ) )
!= ( A @ subset_type ) ) ),
inference(simp,[status(thm)],[183]) ).
thf(185,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type )
!= ( B @ subset_type ) )
| ( sk4 != C )
| ( ( sk3 @ ( sk2 @ relation_type ) )
!= ( A @ subset_type ) )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( ( A @ power_set @ member_type )
!= ( B @ subset_type ) )
| ( ( sk3 @ ( sk2 @ relation_type ) )
!= ( A @ subset_type ) )
| ( B @ power_set @ member_type @ ( sk4 @ ilf_type ) ) ),
inference(simp,[status(thm)],[185]) ).
thf(247,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ power_set @ member_type @ ( sk4 @ ilf_type ) )
!= ( C @ subset_type @ ( D @ ilf_type ) ) )
| ( C @ power_set @ member_type @ ( D @ ilf_type ) )
| ~ $true
| ( ( A @ power_set @ member_type )
!= ( B @ subset_type ) )
| ( ( sk3 @ ( sk2 @ relation_type ) )
!= ( A @ subset_type ) ) ),
inference(paramod_ordered,[status(thm)],[186,162]) ).
thf(248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ power_set @ member_type @ ( sk4 @ ilf_type ) )
!= ( C @ subset_type @ ( D @ ilf_type ) ) )
| ( C @ power_set @ member_type @ ( D @ ilf_type ) )
| ( ( A @ power_set @ member_type )
!= ( B @ subset_type ) )
| ( ( sk3 @ ( sk2 @ relation_type ) )
!= ( A @ subset_type ) ) ),
inference(simp,[status(thm)],[247]) ).
thf(249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ power_set @ member_type )
!= ( C @ subset_type ) )
| ( sk4 != D )
| ( ( A @ power_set @ member_type )
!= ( B @ subset_type ) )
| ( ( sk3 @ ( sk2 @ relation_type ) )
!= ( A @ subset_type ) )
| ( C @ power_set @ member_type @ ( D @ ilf_type ) ) ),
inference(simp,[status(thm)],[248]) ).
thf(250,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ power_set @ member_type )
!= ( C @ subset_type ) )
| ( ( A @ power_set @ member_type )
!= ( B @ subset_type ) )
| ( ( sk3 @ ( sk2 @ relation_type ) )
!= ( A @ subset_type ) )
| ( C @ power_set @ member_type @ ( sk4 @ ilf_type ) ) ),
inference(simp,[status(thm)],[249]) ).
thf(7,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',p7) ).
thf(40,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)],[7]) ).
thf(10,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',p13) ).
thf(55,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)],[10]) ).
thf(81,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)],[80]) ).
thf(82,plain,
! [A: $i] :
( ~ ( A @ power_set @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(113,plain,
! [A: $i] :
( ~ ( A @ power_set @ empty )
| ~ $true ),
inference(rewrite,[status(thm)],[82,99]) ).
thf(114,plain,
! [A: $i] :
~ ( A @ power_set @ empty ),
inference(simp,[status(thm)],[113]) ).
thf(5,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',p18) ).
thf(36,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)],[5]) ).
thf(239,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk14 @ member ) )
!= ( C @ ( B @ member ) ) )
| ~ ( C @ ( C @ cross_product ) @ empty )
| ~ $true
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[223,209]) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk14 @ member ) )
!= ( C @ ( B @ member ) ) )
| ~ ( C @ ( C @ cross_product ) @ empty )
| ( A @ empty ) ),
inference(simp,[status(thm)],[239]) ).
thf(241,plain,
! [A: $i] :
( ~ ( A @ ( A @ cross_product ) @ empty )
| ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[240:[bind(A,$thf( D )),bind(B,$thf( D @ sk14 )),bind(C,$thf( D ))]]) ).
thf(242,plain,
! [A: $i] :
( ~ ( A @ ( A @ cross_product ) @ empty )
| ( A @ empty ) ),
inference(simp,[status(thm)],[241]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ relation_type ) @ ( sk4 @ ilf_type ) )
!= ( A @ power_set @ member_type @ ( B @ ilf_type ) ) )
| ( A @ subset_type @ ( B @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,259]) ).
thf(261,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ relation_type ) @ ( sk4 @ ilf_type ) )
!= ( A @ power_set @ member_type @ ( B @ ilf_type ) ) )
| ( A @ subset_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[260]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ relation_type ) )
!= ( A @ power_set @ member_type ) )
| ( sk4 != B )
| ( A @ subset_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[261]) ).
thf(294,plain,
! [A: $i] :
( ( ( sk3 @ ( sk2 @ relation_type ) )
!= ( A @ power_set @ member_type ) )
| ( A @ subset_type @ ( sk4 @ ilf_type ) ) ),
inference(simp,[status(thm)],[287]) ).
thf(85,plain,
! [A: $i] :
( ( A @ relation_like )
| ~ ( set_type @ ( A @ ilf_type ) )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[84]) ).
thf(125,plain,
! [A: $i] :
( ( A @ relation_like )
| ~ $true
| ~ ( A @ empty ) ),
inference(rewrite,[status(thm)],[85,99]) ).
thf(126,plain,
! [A: $i] :
( ( A @ relation_like )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[125]) ).
thf(3084,plain,
$false,
inference(e,[status(thm)],[333,120,42,78,84,53,128,86,98,175,178,100,61,221,116,270,220,349,275,28,38,109,124,96,32,148,176,22,59,259,27,140,91,130,223,80,162,209,67,182,250,99,40,26,186,55,114,36,30,242,294,126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET640+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n015.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 08:05:29 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.88/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.41/1.22 % [INFO] Parsing done (216ms).
% 1.41/1.24 % [INFO] Running in sequential loop mode.
% 2.11/1.65 % [INFO] eprover registered as external prover.
% 2.11/1.66 % [INFO] Scanning for conjecture ...
% 2.33/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ...
% 2.55/1.85 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 2.78/1.91 % [INFO] Problem is first-order (TPTP FOF).
% 2.78/1.92 % [INFO] Type checking passed.
% 2.78/1.93 % [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 ...
% 16.72/4.77 % External prover 'e' found a proof!
% 16.72/4.77 % [INFO] Killing All external provers ...
% 16.72/4.77 % Time passed: 4217ms (effective reasoning time: 3527ms)
% 16.72/4.77 % 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)>
% 16.72/4.77 % Axioms used in derivation (19): p16, p12, p18, p15, p3, p11, p2, p14, p17, p9, p1, p13, p10, p19, p4, p7, p5, p6, p8
% 16.72/4.77 % No. of inferences in proof: 151
% 16.72/4.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4217 ms resp. 3527 ms w/o parsing
% 15.29/4.85 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.29/4.85 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------