%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET665+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 : n011.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 08:30:40 AM UTC 2026
% Result : Theorem 79.32s 20.20s
% Output : Refutation 79.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 35
% Syntax : Number of formulae : 167 ( 29 unt; 0 typ; 7 def)
% Number of atoms : 667 ( 73 equ; 0 cnn)
% Maximal formula atoms : 34 ( 3 avg)
% Number of connectives : 2085 ( 227 ~; 196 |; 70 &;1425 @)
% ( 12 <=>; 155 =>; 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 : 24 ( 21 usr; 6 con; 0-3 aty)
% Number of variables : 337 ( 10 ^; 299 !; 21 ?; 337 :)
% ( 0 !>; 0 ?*; 0 @-; 7 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ilf_type_decl,type,
ilf_type: $i > $i > $o ).
thf(set_type_decl,type,
set_type: $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(identity_relation_of_decl,type,
identity_relation_of: $i > $i ).
thf(cross_product_decl,type,
cross_product: $i > $i > $i ).
thf(subset_type_decl,type,
subset_type: $i > $i ).
thf(binary_relation_type_decl,type,
binary_relation_type: $i ).
thf(relation_type_decl,type,
relation_type: $i > $i > $i ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(relation_like_decl,type,
relation_like: $i > $o ).
thf(power_set_decl,type,
power_set: $i > $i ).
thf(member_type_decl,type,
member_type: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( set_type @ ( A @ ilf_type ) )
=> ( A @ ( A @ cross_product ) @ ( A @ identity_relation_of @ subset ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i] :
@+[B: $i] : ( A @ subset_type @ ( B @ ilf_type ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] : ( binary_relation_type @ ( A @ ilf_type ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [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(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
( ( A
= ( D @ ( C @ ( B @ ( A @ sk5 ) ) @ ordered_pair ) ) )
& ( B @ ( D @ member ) )
& ( C @ ( C @ ( B @ ( A @ sk5 ) ) @ member ) )
& ( set_type @ ( D @ ilf_type ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( set_type @ ( B @ ilf_type ) )
=> ~ ( A @ ( B @ member ) ) ) ) ) ).
thf(9,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',p25) ).
thf(61,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)],[9]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( ( A @ empty )
| ( A @ ( A @ sk7 @ member ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( A @ empty )
| ( set_type @ ( A @ sk7 @ 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)],[61]) ).
thf(65,plain,
! [A: $i] :
( ( A @ empty )
| ( A @ ( A @ sk7 @ member ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[62]) ).
thf(17,axiom,
! [A: $i] : ( set_type @ ( A @ ilf_type ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
thf(102,plain,
! [A: $i] : ( set_type @ ( A @ ilf_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(103,plain,
! [A: $i] : ( set_type @ ( A @ ilf_type ) ),
inference(cnf,[status(esa)],[102]) ).
thf(240,plain,
! [A: $i] :
( ( A @ empty )
| ( A @ ( A @ sk7 @ member ) )
| ~ $true ),
inference(rewrite,[status(thm)],[65,103]) ).
thf(241,plain,
! [A: $i] :
( ( A @ empty )
| ( A @ ( A @ sk7 @ member ) ) ),
inference(simp,[status(thm)],[240]) ).
thf(7,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',p5) ).
thf(42,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)],[7]) ).
thf(43,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 @ sk6 ) ) @ ( A @ ( B @ ( C @ sk5 ) ) @ 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 @ sk6 ) ) @ 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 @ sk5 ) ) @ 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 @ sk6 ) ) @ 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 @ sk5 ) ) @ 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)],[42]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ sk5 ) ) @ member ) )
| ~ ( B @ ( A @ cross_product ) @ ( C @ member ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[43]) ).
thf(276,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ sk5 ) ) @ member ) )
| ~ ( B @ ( A @ cross_product ) @ ( C @ member ) )
| ~ $true
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[44,103]) ).
thf(277,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ sk5 ) ) @ member ) )
| ~ ( B @ ( A @ cross_product ) @ ( C @ member ) ) ),
inference(simp,[status(thm)],[276]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( A @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[62]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ $true
| ~ ( A @ empty )
| ~ $true ),
inference(rewrite,[status(thm)],[63,103]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[153]) ).
thf(278,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ sk5 ) ) @ member ) )
!= ( D @ ( E @ member ) ) )
| ~ $true
| ~ ( D @ empty )
| ~ ( B @ ( A @ cross_product ) @ ( C @ member ) ) ),
inference(paramod_ordered,[status(thm)],[277,154]) ).
thf(279,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ sk5 ) ) @ member ) )
!= ( D @ ( E @ member ) ) )
| ~ ( D @ empty )
| ~ ( B @ ( A @ cross_product ) @ ( C @ member ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(280,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ empty )
| ~ ( B @ ( C @ cross_product ) @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[279:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( H )),bind(E,$thf( H @ ( G @ ( F @ sk5 ) ) ))]]) ).
thf(299,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ empty )
| ~ ( B @ ( C @ cross_product ) @ ( A @ member ) ) ),
inference(simp,[status(thm)],[280]) ).
thf(308,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ member ) )
!= ( C @ ( D @ cross_product ) @ ( B @ member ) ) )
| ~ ( D @ empty )
| ~ $true
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[241,299]) ).
thf(309,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ member ) )
!= ( C @ ( D @ cross_product ) @ ( B @ member ) ) )
| ~ ( D @ empty )
| ( A @ empty ) ),
inference(simp,[status(thm)],[308]) ).
thf(310,plain,
! [B: $i,A: $i] :
( ~ ( A @ empty )
| ( B @ ( A @ cross_product ) @ empty ) ),
inference(pattern_uni,[status(thm)],[309:[bind(A,$thf( G @ ( F @ cross_product ) )),bind(B,$thf( G @ ( F @ cross_product ) @ sk7 )),bind(C,$thf( G )),bind(D,$thf( F ))]]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ~ ( A @ empty )
| ( B @ ( A @ cross_product ) @ empty ) ),
inference(simp,[status(thm)],[310]) ).
thf(14,axiom,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
& ( A @ empty ) )
=> ( A @ relation_like ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).
thf(89,plain,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
& ( A @ empty ) )
=> ( A @ relation_like ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(90,plain,
! [A: $i] :
( ( A @ relation_like )
| ~ ( set_type @ ( A @ ilf_type ) )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[89]) ).
thf(253,plain,
! [A: $i] :
( ( A @ relation_like )
| ~ $true
| ~ ( A @ empty ) ),
inference(rewrite,[status(thm)],[90,103]) ).
thf(254,plain,
! [A: $i] :
( ( A @ relation_like )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[253]) ).
thf(345,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cross_product ) @ empty )
!= ( C @ empty ) )
| ( C @ relation_like )
| ~ $true
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[313,254]) ).
thf(346,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cross_product ) @ empty )
!= ( C @ empty ) )
| ( C @ relation_like )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[345]) ).
thf(347,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cross_product ) @ relation_like )
| ~ ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[346:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ cross_product ) ))]]) ).
thf(352,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cross_product ) @ relation_like )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[347]) ).
thf(27,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( binary_relation_type @ ( A @ identity_relation_of @ ilf_type ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8) ).
thf(142,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( binary_relation_type @ ( A @ identity_relation_of @ ilf_type ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(24,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',p11) ).
thf(125,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)],[24]) ).
thf(143,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ identity_relation_of @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[142]) ).
thf(219,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ identity_relation_of @ ilf_type ) )
| ~ $true ),
inference(rewrite,[status(thm)],[143,103]) ).
thf(220,plain,
! [A: $i] : ( binary_relation_type @ ( A @ identity_relation_of @ ilf_type ) ),
inference(simp,[status(thm)],[219]) ).
thf(4,axiom,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( A @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16) ).
thf(36,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( A @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(37,plain,
! [A: $i] :
( ( A @ ( A @ subset ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[36]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( A @ identity_relation_of @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( B @ ( B @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[220,37]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( A @ identity_relation_of @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( B @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[223]) ).
thf(225,plain,
! [A: $i] : ( A @ identity_relation_of @ ( A @ identity_relation_of @ subset ) ),
inference(pattern_uni,[status(thm)],[224:[bind(A,$thf( C )),bind(B,$thf( C @ identity_relation_of ))]]) ).
thf(226,plain,
! [A: $i] : ( A @ identity_relation_of @ ( A @ identity_relation_of @ subset ) ),
inference(simp,[status(thm)],[225]) ).
thf(1,conjecture,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( A @ ( A @ cross_product ) @ ( A @ identity_relation_of @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_28) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( A @ ( A @ cross_product ) @ ( A @ identity_relation_of @ subset ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(30,plain,
~ ! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( A @ ( A @ cross_product ) @ ( A @ identity_relation_of @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(31,plain,
( ~ ( sk1 @ ( sk1 @ cross_product ) @ ( sk1 @ identity_relation_of @ subset ) )
& ( set_type @ ( sk1 @ ilf_type ) ) ),
inference(cnf,[status(esa)],[30]) ).
thf(33,plain,
~ ( sk1 @ ( sk1 @ cross_product ) @ ( sk1 @ identity_relation_of @ subset ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(227,plain,
! [A: $i] :
( ( ( A @ identity_relation_of @ ( A @ identity_relation_of @ subset ) )
!= ( sk1 @ ( sk1 @ cross_product ) @ ( sk1 @ identity_relation_of @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[226,33]) ).
thf(228,plain,
! [A: $i] :
( ( A @ identity_relation_of @ ( A @ identity_relation_of @ subset ) )
!= ( sk1 @ ( sk1 @ cross_product ) @ ( sk1 @ identity_relation_of @ subset ) ) ),
inference(simp,[status(thm)],[227]) ).
thf(229,plain,
! [A: $i] :
( ( ( A @ identity_relation_of )
!= ( sk1 @ ( sk1 @ cross_product ) ) )
| ( ( A @ identity_relation_of )
!= ( sk1 @ identity_relation_of ) ) ),
inference(simp,[status(thm)],[228]) ).
thf(8,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( A @ identity_relation_of @ ( C @ ( B @ ordered_pair ) @ member ) )
<=> ( ( B = C )
& ( A @ ( B @ member ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
thf(53,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( ( ( B = C )
& ( A @ ( B @ member ) ) )
=> ( A @ identity_relation_of @ ( C @ ( B @ ordered_pair ) @ member ) ) )
& ( ( A @ identity_relation_of @ ( C @ ( B @ ordered_pair ) @ member ) )
=> ( ( B = C )
& ( A @ ( B @ member ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(126,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( A @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) )
| ~ ( A @ relation_like )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( set_type @ ( A @ ilf_type ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( A @ relation_like )
| ~ ( binary_relation_type @ ( A @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[125]) ).
thf(127,plain,
! [A: $i] :
( ( A @ relation_like )
| ~ ( binary_relation_type @ ( A @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[126]) ).
thf(255,plain,
! [A: $i] :
( ( A @ relation_like )
| ~ ( binary_relation_type @ ( A @ ilf_type ) )
| ~ $true ),
inference(rewrite,[status(thm)],[127,103]) ).
thf(256,plain,
! [A: $i] :
( ( A @ relation_like )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(simp,[status(thm)],[255]) ).
thf(23,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',p6) ).
thf(123,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)],[23]) ).
thf(16,axiom,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( binary_relation_type @ ( B @ ilf_type ) )
=> ( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( set_type @ ( D @ ilf_type ) )
=> ( ( A @ ( D @ ( C @ ordered_pair ) @ member ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ member ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
thf(95,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( binary_relation_type @ ( B @ ilf_type ) )
=> ( ( ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( set_type @ ( D @ ilf_type ) )
=> ( ( A @ ( D @ ( C @ ordered_pair ) @ member ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ member ) ) ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ! [D: $i] :
( ( set_type @ ( D @ ilf_type ) )
=> ( ( A @ ( D @ ( C @ ordered_pair ) @ member ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ member ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(3,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ? [B: $i] : ( A @ subset_type @ ( B @ ilf_type ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18) ).
thf(34,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ? [B: $i] : ( A @ subset_type @ ( B @ ilf_type ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(35,plain,
! [A: $i] :
( ( A @ subset_type @ ( A @ sk2 @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(176,plain,
! [A: $i] :
( ( A @ subset_type @ ( A @ sk2 @ ilf_type ) )
| ~ $true ),
inference(rewrite,[status(thm)],[35,103]) ).
thf(177,plain,
! [A: $i] : ( A @ subset_type @ ( A @ sk2 @ ilf_type ) ),
inference(simp,[status(thm)],[176]) ).
thf(259,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( A @ identity_relation_of @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( B @ relation_like )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[220,256]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( A @ identity_relation_of @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( B @ relation_like ) ),
inference(simp,[status(thm)],[259]) ).
thf(261,plain,
! [A: $i] : ( A @ identity_relation_of @ relation_like ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( C )),bind(B,$thf( C @ identity_relation_of ))]]) ).
thf(272,plain,
! [A: $i] : ( A @ identity_relation_of @ relation_like ),
inference(simp,[status(thm)],[261]) ).
thf(48,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)],[43]) ).
thf(51,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)],[48]) ).
thf(52,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)],[51]) ).
thf(188,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)],[52,103]) ).
thf(189,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)],[188]) ).
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',p22) ).
thf(91,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(92,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)],[91]) ).
thf(93,plain,
! [A: $i] :
( ~ ( A @ power_set @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[92]) ).
thf(151,plain,
! [A: $i] :
( ~ ( A @ power_set @ empty )
| ~ $true ),
inference(rewrite,[status(thm)],[93,103]) ).
thf(152,plain,
! [A: $i] :
~ ( A @ power_set @ empty ),
inference(simp,[status(thm)],[151]) ).
thf(13,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',p19) ).
thf(78,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)],[13]) ).
thf(6,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',p14) ).
thf(40,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)],[6]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ relation_type ) @ ( A @ ( B @ sk4 ) @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[40]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ relation_type ) @ ( A @ ( B @ sk4 ) @ ilf_type ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[41,103]) ).
thf(211,plain,
! [B: $i,A: $i] : ( A @ ( B @ relation_type ) @ ( A @ ( B @ sk4 ) @ ilf_type ) ),
inference(simp,[status(thm)],[210]) ).
thf(19,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( A @ identity_relation_of @ ( C @ ( B @ ordered_pair ) @ member ) )
<=> ( ( B = C )
& ( A @ ( B @ member ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
thf(106,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( ( ( B = C )
& ( A @ ( B @ member ) ) )
=> ( A @ identity_relation_of @ ( C @ ( B @ ordered_pair ) @ member ) ) )
& ( ( A @ identity_relation_of @ ( C @ ( B @ ordered_pair ) @ member ) )
=> ( ( B = C )
& ( A @ ( B @ member ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(22,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( A @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
thf(121,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( A @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(21,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',p13) ).
thf(116,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)],[21]) ).
thf(12,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',p23) ).
thf(74,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)],[12]) ).
thf(5,axiom,
? [A: $i] : ( binary_relation_type @ ( A @ ilf_type ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
thf(38,plain,
? [A: $i] : ( binary_relation_type @ ( A @ ilf_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(293,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ member ) )
!= ( C @ ( B @ cross_product ) @ ( D @ member ) ) )
| ( B @ ( B @ ( C @ ( D @ sk5 ) ) @ member ) )
| ~ $true
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[241,277]) ).
thf(294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ member ) )
!= ( C @ ( B @ cross_product ) @ ( D @ member ) ) )
| ( B @ ( B @ ( C @ ( D @ sk5 ) ) @ member ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[293]) ).
thf(295,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ ( A @ cross_product ) @ sk7 @ sk5 ) ) @ member ) )
| ( B @ ( A @ cross_product ) @ empty ) ),
inference(pattern_uni,[status(thm)],[294:[bind(A,$thf( G @ ( F @ cross_product ) )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( G @ ( F @ cross_product ) @ sk7 ))]]) ).
thf(298,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( B @ ( A @ cross_product ) @ sk7 @ sk5 ) ) @ member ) )
| ( B @ ( A @ cross_product ) @ empty ) ),
inference(simp,[status(thm)],[295]) ).
thf(28,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',p10) ).
thf(144,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)],[28]) ).
thf(39,plain,
binary_relation_type @ ( sk3 @ ilf_type ),
inference(cnf,[status(esa)],[38]) ).
thf(159,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk3 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( A @ ( A @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,37]) ).
thf(160,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk3 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( A @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[159]) ).
thf(161,plain,
sk3 @ ( sk3 @ subset ),
inference(pattern_uni,[status(thm)],[160:[bind(A,$thf( sk3 ))]]) ).
thf(185,plain,
( ( ( sk1 @ ( sk1 @ cross_product ) @ ( sk1 @ identity_relation_of @ subset ) )
!= ( sk3 @ ( sk3 @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[161,33]) ).
thf(186,plain,
( ( sk1 @ ( sk1 @ cross_product ) @ ( sk1 @ identity_relation_of @ subset ) )
!= ( sk3 @ ( sk3 @ subset ) ) ),
inference(simp,[status(thm)],[185]) ).
thf(187,plain,
( ( ( sk1 @ ( sk1 @ cross_product ) )
!= sk3 )
| ( ( sk1 @ identity_relation_of )
!= sk3 ) ),
inference(simp,[status(thm)],[186]) ).
thf(262,plain,
! [B: $i,A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( B @ relation_like )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,256]) ).
thf(263,plain,
! [B: $i,A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( B @ relation_like ) ),
inference(simp,[status(thm)],[262]) ).
thf(270,plain,
! [B: $i,A: $i] :
( ( binary_relation_type != set_type )
| ( A != B )
| ( B @ relation_like ) ),
inference(simp,[status(thm)],[263]) ).
thf(274,plain,
! [A: $i] :
( ( binary_relation_type != set_type )
| ( A @ relation_like ) ),
inference(simp,[status(thm)],[270]) ).
thf(10,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',p20) ).
thf(66,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)],[10]) ).
thf(162,plain,
! [B: $i,A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( B @ ( B @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,37]) ).
thf(163,plain,
! [B: $i,A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( B @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[162]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( binary_relation_type != set_type )
| ( A != B )
| ( B @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[163]) ).
thf(167,plain,
! [A: $i] :
( ( binary_relation_type != set_type )
| ( A @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(122,plain,
! [A: $i] :
( ( A @ ( A @ subset ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[121]) ).
thf(230,plain,
! [A: $i] :
( ( A @ ( A @ subset ) )
| ~ $true ),
inference(rewrite,[status(thm)],[122,103]) ).
thf(231,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(simp,[status(thm)],[230]) ).
thf(18,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',p24) ).
thf(104,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)],[18]) ).
thf(20,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( B @ ( A @ relation_type ) @ ( B @ ( A @ cross_product ) @ ilf_type ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
thf(114,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( B @ ( A @ relation_type ) @ ( B @ ( A @ cross_product ) @ ilf_type ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(29,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',p17) ).
thf(146,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)],[29]) ).
thf(264,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk2 @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( B @ relation_like )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[177,256]) ).
thf(265,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk2 @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( B @ relation_like ) ),
inference(simp,[status(thm)],[264]) ).
thf(269,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type )
!= binary_relation_type )
| ( ( A @ sk2 )
!= B )
| ( B @ relation_like ) ),
inference(simp,[status(thm)],[265]) ).
thf(273,plain,
! [A: $i] :
( ( ( A @ subset_type )
!= binary_relation_type )
| ( A @ sk2 @ relation_like ) ),
inference(simp,[status(thm)],[269]) ).
thf(26,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',p9) ).
thf(136,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)],[26]) ).
thf(266,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk3 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( A @ relation_like )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,256]) ).
thf(267,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk3 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( A @ relation_like ) ),
inference(simp,[status(thm)],[266]) ).
thf(268,plain,
sk3 @ relation_like,
inference(pattern_uni,[status(thm)],[267:[bind(A,$thf( sk3 ))]]) ).
thf(314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ ( A @ cross_product ) @ sk7 @ sk5 ) ) @ member ) )
!= ( C @ ( D @ member ) ) )
| ~ $true
| ~ ( C @ empty )
| ( B @ ( A @ cross_product ) @ empty ) ),
inference(paramod_ordered,[status(thm)],[298,154]) ).
thf(315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( B @ ( A @ cross_product ) @ sk7 @ sk5 ) ) @ member ) )
!= ( C @ ( D @ member ) ) )
| ~ ( C @ empty )
| ( B @ ( A @ cross_product ) @ empty ) ),
inference(simp,[status(thm)],[314]) ).
thf(316,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ( A @ ( B @ cross_product ) @ empty ) ),
inference(pattern_uni,[status(thm)],[315:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( G @ ( F @ ( F @ ( G @ cross_product ) @ sk7 @ sk5 ) ) ))]]) ).
thf(332,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ( A @ ( B @ cross_product ) @ empty ) ),
inference(simp,[status(thm)],[316]) ).
thf(25,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 ) )
=> ( ( D @ ( C @ cross_product ) @ ( B @ ( A @ ordered_pair ) @ member ) )
<=> ( ( D @ ( B @ member ) )
& ( C @ ( A @ member ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
thf(131,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 ) )
=> ( ( ( ( D @ ( B @ member ) )
& ( C @ ( A @ member ) ) )
=> ( D @ ( C @ cross_product ) @ ( B @ ( A @ ordered_pair ) @ member ) ) )
& ( ( D @ ( C @ cross_product ) @ ( B @ ( A @ ordered_pair ) @ member ) )
=> ( ( D @ ( B @ member ) )
& ( C @ ( A @ member ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(11,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',p21) ).
thf(68,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)],[11]) ).
thf(157,plain,
! [A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( sk1 @ ( sk1 @ cross_product ) @ ( sk1 @ identity_relation_of @ subset ) ) )
| ~ $true
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(paramod_ordered,[status(thm)],[37,33]) ).
thf(158,plain,
! [A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( sk1 @ ( sk1 @ cross_product ) @ ( sk1 @ identity_relation_of @ subset ) ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(164,plain,
! [A: $i] :
( ( A
!= ( sk1 @ ( sk1 @ cross_product ) ) )
| ( A
!= ( sk1 @ identity_relation_of ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(166,plain,
( ( ( sk1 @ ( sk1 @ cross_product ) )
!= ( sk1 @ identity_relation_of ) )
| ~ ( binary_relation_type @ ( sk1 @ identity_relation_of @ ilf_type ) ) ),
inference(simp,[status(thm)],[164]) ).
thf(221,plain,
( ( ( sk1 @ ( sk1 @ cross_product ) )
!= ( sk1 @ identity_relation_of ) )
| ~ $true ),
inference(rewrite,[status(thm)],[166,220]) ).
thf(222,plain,
( ( sk1 @ ( sk1 @ cross_product ) )
!= ( sk1 @ identity_relation_of ) ),
inference(simp,[status(thm)],[221]) ).
thf(12763,plain,
$false,
inference(e,[status(thm)],[352,142,125,229,53,256,123,95,177,154,272,42,37,189,152,78,211,106,121,61,89,116,74,220,102,38,33,298,34,313,144,187,274,39,103,91,66,299,241,167,231,104,40,114,36,146,30,273,136,268,332,131,68,277,254,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET665+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.11 % 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
% 0.21/0.47 % Computer : n011.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Sat Sep 26 08:02:59 UTC 2026
% 0.21/0.48 % CPUTime :
% 0.21/0.48 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.44/1.33 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.00/1.66 % [INFO] Parsing done (326ms).
% 2.00/1.68 % [INFO] Running in sequential loop mode.
% 3.29/2.31 % [INFO] eprover registered as external prover.
% 3.29/2.32 % [INFO] Scanning for conjecture ...
% 3.50/2.48 % [INFO] Found a conjecture (or negated_conjecture) and 27 axioms. Running axiom selection ...
% 3.89/2.60 % [INFO] Axiom selection finished. Selected 27 axioms (removed 0 axioms).
% 4.13/2.70 % [INFO] Problem is first-order (TPTP FOF).
% 4.13/2.73 % [INFO] Type checking passed.
% 4.13/2.73 % [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 ...
% 79.81/20.19 % External prover 'e' found a proof!
% 79.81/20.19 % [INFO] Killing All external provers ...
% 79.81/20.20 % Time passed: 19506ms (effective reasoning time: 18505ms)
% 79.81/20.20 % 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)>
% 79.32/20.20 % Axioms used in derivation (27): p27, p12, p18, p15, p26, p3, p22, p11, p2, p17, p9, p1, p24, p13, p16, p20, p10, p19, p4, p7, p5, p23, p21, p25, p14, p6, p8
% 79.32/20.20 % No. of inferences in proof: 160
% 79.32/20.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 19506 ms resp. 18505 ms w/o parsing
% 79.69/20.38 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 79.69/20.38 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------