%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET649+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.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 08:30:38 AM UTC 2026
% Result : Theorem 114.40s 29.27s
% Output : Refutation 107.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 42
% Syntax : Number of formulae : 1097 ( 233 unt; 0 typ; 15 def)
% Number of atoms : 4004 ( 821 equ; 0 cnn)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 17392 (1681 ~;1569 |; 79 &;13897 @)
% ( 9 <=>; 157 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 30 usr; 8 con; 0-2 aty)
% Number of variables : 1708 ( 18 ^;1652 !; 23 ?;1708 :)
% ( 0 !>; 0 ?*; 0 @-; 15 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ilf_type_decl,type,
ilf_type: $i > $i > $o ).
thf(set_type_decl,type,
set_type: $i ).
thf(binary_relation_type_decl,type,
binary_relation_type: $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(domain_of_decl,type,
domain_of: $i > $i ).
thf(range_of_decl,type,
range_of: $i > $i ).
thf(relation_type_decl,type,
relation_type: $i > $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(member_decl,type,
member: $i > $i > $o ).
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(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(cross_product_decl,type,
cross_product: $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 > $i > $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 > $i ).
thf(sk9_decl,type,
sk9: $i > $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( binary_relation_type @ ( C @ ilf_type ) )
=> ( ( ( B @ ( C @ range_of @ subset ) )
& ( A @ ( C @ domain_of @ subset ) ) )
=> ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( binary_relation_type @ ( B @ ilf_type ) )
=> ( ( ( A @ ( B @ range_of @ subset ) )
& ( sk1 @ ( B @ domain_of @ subset ) ) )
=> ( A @ ( sk1 @ relation_type ) @ ( B @ ilf_type ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( ( ( sk2 @ ( A @ range_of @ subset ) )
& ( sk1 @ ( A @ domain_of @ subset ) ) )
=> ( sk2 @ ( sk1 @ 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] :
~ ( ( set_type @ ( B @ ilf_type ) )
=> ~ ( A @ ( B @ member ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( set_type @ ( C @ ilf_type ) )
=> ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( B @ ( A @ ( C @ ordered_pair ) @ member ) )
& ( set_type @ ( C @ ilf_type ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( set_type @ ( C @ ilf_type ) )
=> ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i] :
@+[B: $i] : ( A @ member_type @ ( B @ ilf_type ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] : ( binary_relation_type @ ( A @ ilf_type ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i] :
@+[B: $i] : ( A @ subset_type @ ( B @ ilf_type ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( A
= ( D @ ( C @ ordered_pair ) ) )
& ( set_type @ ( D @ ilf_type ) ) )
& ( set_type @ ( C @ ilf_type ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( A
= ( C @ ( B @ ( A @ sk12 ) @ ordered_pair ) ) )
& ( set_type @ ( C @ ilf_type ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [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(sk15_def,definition,
( sk15
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( B @ ( C @ ( A @ ordered_pair ) @ member ) )
& ( set_type @ ( C @ ilf_type ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( binary_relation_type @ ( C @ ilf_type ) )
=> ( ( ( B @ ( C @ range_of @ subset ) )
& ( A @ ( C @ domain_of @ subset ) ) )
=> ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_11) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( binary_relation_type @ ( C @ ilf_type ) )
=> ( ( ( B @ ( C @ range_of @ subset ) )
& ( A @ ( C @ domain_of @ subset ) ) )
=> ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(29,plain,
~ ! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( binary_relation_type @ ( C @ ilf_type ) )
=> ( ( ( B @ ( C @ range_of @ subset ) )
& ( A @ ( C @ domain_of @ subset ) ) )
=> ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(30,plain,
( ~ ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) )
& ( sk2 @ ( sk3 @ range_of @ subset ) )
& ( sk1 @ ( sk3 @ domain_of @ subset ) )
& ( binary_relation_type @ ( sk3 @ ilf_type ) )
& ( set_type @ ( sk2 @ ilf_type ) )
& ( set_type @ ( sk1 @ ilf_type ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(33,plain,
sk2 @ ( sk3 @ range_of @ subset ),
inference(cnfConj,[status(thm)],[30]) ).
thf(15,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 @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( D @ ( B @ cross_product ) @ ( C @ ( A @ cross_product ) @ subset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
thf(77,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 @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( D @ ( B @ cross_product ) @ ( C @ ( A @ cross_product ) @ subset ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(78,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ cross_product ) @ ( C @ ( A @ cross_product ) @ subset ) )
| ~ ( D @ ( C @ subset ) )
| ~ ( B @ ( A @ subset ) )
| ~ ( set_type @ ( D @ ilf_type ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[77]) ).
thf(26,axiom,
! [A: $i] : ( set_type @ ( A @ ilf_type ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
thf(110,plain,
! [A: $i] : ( set_type @ ( A @ ilf_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(111,plain,
! [A: $i] : ( set_type @ ( A @ ilf_type ) ),
inference(cnf,[status(esa)],[110]) ).
thf(247,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ cross_product ) @ ( C @ ( A @ cross_product ) @ subset ) )
| ~ ( D @ ( C @ subset ) )
| ~ ( B @ ( A @ subset ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[78,111]) ).
thf(248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ cross_product ) @ ( C @ ( A @ cross_product ) @ subset ) )
| ~ ( D @ ( C @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[247]) ).
thf(276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ range_of @ subset ) )
!= ( D @ ( C @ subset ) ) )
| ( D @ ( B @ cross_product ) @ ( C @ ( A @ cross_product ) @ subset ) )
| ~ $true
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[33,248]) ).
thf(277,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ range_of @ subset ) )
!= ( D @ ( C @ subset ) ) )
| ( D @ ( B @ cross_product ) @ ( C @ ( A @ cross_product ) @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[276]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[277:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk3 @ range_of )),bind(D,$thf( sk2 ))]]) ).
thf(695,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ range_of @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,278]) ).
thf(696,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ range_of @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[695]) ).
thf(697,plain,
sk2 @ ( sk2 @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[696:[bind(A,$thf( sk3 @ range_of )),bind(B,$thf( sk2 ))]]) ).
thf(737,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,278]) ).
thf(738,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[737]) ).
thf(739,plain,
sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[738:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ cross_product ) ))]]) ).
thf(822,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[739,278]) ).
thf(823,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[822]) ).
thf(824,plain,
sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[823:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) ))]]) ).
thf(35,plain,
sk1 @ ( sk3 @ domain_of @ subset ),
inference(cnfConj,[status(thm)],[30]) ).
thf(282,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ subset ) )
!= ( D @ ( C @ subset ) ) )
| ( D @ ( B @ cross_product ) @ ( C @ ( A @ cross_product ) @ subset ) )
| ~ $true
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[35,248]) ).
thf(283,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ subset ) )
!= ( D @ ( C @ subset ) ) )
| ( D @ ( B @ cross_product ) @ ( C @ ( A @ cross_product ) @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[282]) ).
thf(284,plain,
! [B: $i,A: $i] :
( ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[283:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk3 @ domain_of )),bind(D,$thf( sk1 ))]]) ).
thf(1022,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[824,284]) ).
thf(1023,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1022]) ).
thf(1024,plain,
sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1023:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(23,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) )
=> ( C @ relation_like ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
thf(101,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)],[23]) ).
thf(32,plain,
binary_relation_type @ ( sk3 @ ilf_type ),
inference(cnfConj,[status(thm)],[30]) ).
thf(13,axiom,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( A @ range_of @ ( A @ domain_of @ cross_product ) @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
thf(73,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( A @ range_of @ ( A @ domain_of @ cross_product ) @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(74,plain,
! [A: $i] :
( ( A @ range_of @ ( A @ domain_of @ cross_product ) @ ( A @ subset ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[73]) ).
thf(231,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk3 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( A @ range_of @ ( A @ domain_of @ cross_product ) @ ( A @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32,74]) ).
thf(232,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk3 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( A @ range_of @ ( A @ domain_of @ cross_product ) @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(233,plain,
sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ ( sk3 @ subset ),
inference(pattern_uni,[status(thm)],[232:[bind(A,$thf( sk3 ))]]) ).
thf(683,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ ( sk3 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[233,278]) ).
thf(684,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ ( sk3 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[683]) ).
thf(685,plain,
sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[684:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) ))]]) ).
thf(767,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[685,278]) ).
thf(768,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[767]) ).
thf(769,plain,
sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[768:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ cross_product ) )),bind(B,$thf( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) ))]]) ).
thf(1025,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[769,284]) ).
thf(1026,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1025]) ).
thf(1027,plain,
sk1 @ ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1026:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2776,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1027,284]) ).
thf(2777,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2776]) ).
thf(2778,plain,
sk1 @ ( sk1 @ ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2777:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(701,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35,278]) ).
thf(702,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[701]) ).
thf(703,plain,
sk2 @ ( sk1 @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[702:[bind(A,$thf( sk3 @ domain_of )),bind(B,$thf( sk1 ))]]) ).
thf(747,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[703,278]) ).
thf(748,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[747]) ).
thf(749,plain,
sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[748:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ cross_product ) ))]]) ).
thf(844,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[749,278]) ).
thf(845,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[844]) ).
thf(846,plain,
sk2 @ ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[845:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) ))]]) ).
thf(5,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( A @ subset_type @ ( B @ ilf_type ) )
<=> ( A @ power_set @ member_type @ ( B @ ilf_type ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).
thf(44,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)],[5]) ).
thf(45,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)],[44]) ).
thf(46,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)],[45]) ).
thf(304,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)],[46,111]) ).
thf(305,plain,
! [B: $i,A: $i] :
( ( A @ power_set @ member_type @ ( B @ ilf_type ) )
| ~ ( A @ subset_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[304]) ).
thf(312,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk3 @ ilf_type ) )
!= ( A @ subset_type @ ( B @ ilf_type ) ) )
| ( A @ power_set @ member_type @ ( B @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32,305]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk3 @ ilf_type ) )
!= ( A @ subset_type @ ( B @ ilf_type ) ) )
| ( A @ power_set @ member_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[312]) ).
thf(326,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type )
!= binary_relation_type )
| ( sk3 != B )
| ( A @ power_set @ member_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[313]) ).
thf(333,plain,
! [A: $i] :
( ( ( A @ subset_type )
!= binary_relation_type )
| ( A @ power_set @ member_type @ ( sk3 @ ilf_type ) ) ),
inference(simp,[status(thm)],[326]) ).
thf(6,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( B @ power_set @ ( A @ member ) )
<=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).
thf(48,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)],[6]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ power_set @ ( A @ member ) )
| ~ ( B @ ( A @ ( B @ sk6 ) @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B @ power_set @ ( A @ member ) )
| ( A @ ( A @ ( B @ sk6 ) @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B @ power_set @ ( A @ member ) )
| ( set_type @ ( A @ ( B @ sk6 ) @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( B @ power_set @ ( A @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[48]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( B @ power_set @ ( A @ member ) )
| ( A @ ( A @ ( B @ sk6 ) @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[49]) ).
thf(709,plain,
! [B: $i,A: $i] :
( ( B @ power_set @ ( A @ member ) )
| ( A @ ( A @ ( B @ sk6 ) @ member ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[52,111]) ).
thf(710,plain,
! [B: $i,A: $i] :
( ( B @ power_set @ ( A @ member ) )
| ( A @ ( A @ ( B @ sk6 ) @ member ) ) ),
inference(simp,[status(thm)],[709]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( B @ power_set @ ( A @ member ) )
| ~ ( B @ ( A @ ( B @ sk6 ) @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[49]) ).
thf(848,plain,
! [B: $i,A: $i] :
( ( B @ power_set @ ( A @ member ) )
| ~ ( B @ ( A @ ( B @ sk6 ) @ member ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[53,111]) ).
thf(849,plain,
! [B: $i,A: $i] :
( ( B @ power_set @ ( A @ member ) )
| ~ ( B @ ( A @ ( B @ sk6 ) @ member ) ) ),
inference(simp,[status(thm)],[848]) ).
thf(859,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk6 ) @ member ) )
!= ( D @ ( C @ ( D @ sk6 ) @ member ) ) )
| ( D @ power_set @ ( C @ member ) )
| ~ $true
| ( B @ power_set @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[710,849]) ).
thf(860,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk6 ) @ member ) )
!= ( D @ ( C @ ( D @ sk6 ) @ member ) ) )
| ( D @ power_set @ ( C @ member ) )
| ( B @ power_set @ ( A @ member ) ) ),
inference(simp,[status(thm)],[859]) ).
thf(861,plain,
! [A: $i] :
( ( A @ power_set @ ( A @ member ) )
| ( A @ power_set @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[860:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(867,plain,
! [A: $i] : ( A @ power_set @ ( A @ member ) ),
inference(simp,[status(thm)],[861]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( B @ power_set @ ( A @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[49]) ).
thf(537,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ $true
| ~ ( B @ power_set @ ( A @ member ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[50,111]) ).
thf(538,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ power_set @ ( A @ member ) ) ),
inference(simp,[status(thm)],[537]) ).
thf(4,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( ( A @ empty )
<=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ~ ( A @ ( B @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
thf(39,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)],[4]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( ( A @ empty )
| ( A @ ( A @ sk5 @ member ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( A @ empty )
| ( set_type @ ( A @ sk5 @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ~ ( A @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( A @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[39]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( A @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[40]) ).
thf(201,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ $true
| ~ ( A @ empty )
| ~ $true ),
inference(rewrite,[status(thm)],[41,111]) ).
thf(202,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[201]) ).
thf(551,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ member ) )
!= ( D @ ( E @ member ) ) )
| ~ $true
| ~ ( D @ empty )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ power_set @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[538,202]) ).
thf(552,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ member ) )
!= ( D @ ( E @ member ) ) )
| ~ ( D @ empty )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ power_set @ ( A @ member ) ) ),
inference(simp,[status(thm)],[551]) ).
thf(553,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ power_set @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[552:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(887,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ ( A @ member ) )
!= ( B @ ( D @ member ) ) )
| ~ ( C @ empty )
| ~ $true
| ~ ( C @ power_set @ ( B @ member ) ) ),
inference(paramod_ordered,[status(thm)],[867,553]) ).
thf(888,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ ( A @ member ) )
!= ( B @ ( D @ member ) ) )
| ~ ( C @ empty )
| ~ ( C @ power_set @ ( B @ member ) ) ),
inference(simp,[status(thm)],[887]) ).
thf(889,plain,
! [B: $i,A: $i] :
( ~ ( A @ empty )
| ~ ( A @ power_set @ ( B @ power_set @ member ) ) ),
inference(pattern_uni,[status(thm)],[888:[bind(A,$thf( E )),bind(B,$thf( E @ power_set )),bind(C,$thf( C )),bind(D,$thf( E ))]]) ).
thf(892,plain,
! [B: $i,A: $i] :
( ~ ( A @ empty )
| ~ ( A @ power_set @ ( B @ power_set @ member ) ) ),
inference(simp,[status(thm)],[889]) ).
thf(11,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( set_type @ ( B @ ( A @ ordered_pair ) @ ilf_type ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14) ).
thf(69,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)],[11]) ).
thf(992,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[703,284]) ).
thf(993,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[992]) ).
thf(994,plain,
sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[993:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ cross_product ) ))]]) ).
thf(1144,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[994,278]) ).
thf(1145,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1144]) ).
thf(1146,plain,
sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1145:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) ))]]) ).
thf(2197,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1146,284]) ).
thf(2198,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2197]) ).
thf(2199,plain,
sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2198:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(16,axiom,
? [A: $i] : ( binary_relation_type @ ( A @ ilf_type ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11) ).
thf(79,plain,
? [A: $i] : ( binary_relation_type @ ( A @ ilf_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(80,plain,
binary_relation_type @ ( sk10 @ ilf_type ),
inference(cnf,[status(esa)],[79]) ).
thf(236,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( A @ range_of @ ( A @ domain_of @ cross_product ) @ ( A @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[80,74]) ).
thf(237,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( A @ range_of @ ( A @ domain_of @ cross_product ) @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[236]) ).
thf(238,plain,
sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ ( sk10 @ subset ),
inference(pattern_uni,[status(thm)],[237:[bind(A,$thf( sk10 ))]]) ).
thf(986,plain,
! [B: $i,A: $i] :
( ( ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ ( sk10 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[238,284]) ).
thf(987,plain,
! [B: $i,A: $i] :
( ( ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ ( sk10 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[986]) ).
thf(988,plain,
sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[987:[bind(A,$thf( sk10 )),bind(B,$thf( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) ))]]) ).
thf(1101,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[988,278]) ).
thf(1102,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1101]) ).
thf(1103,plain,
sk2 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1102:[bind(A,$thf( sk3 @ domain_of @ ( sk10 @ cross_product ) )),bind(B,$thf( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) ))]]) ).
thf(1663,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1103,278]) ).
thf(1664,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1663]) ).
thf(1665,plain,
sk2 @ ( sk2 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1664:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(47,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)],[45]) ).
thf(409,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)],[47,111]) ).
thf(410,plain,
! [B: $i,A: $i] :
( ( A @ subset_type @ ( B @ ilf_type ) )
| ~ ( A @ power_set @ member_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[409]) ).
thf(416,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk3 @ ilf_type ) )
!= ( A @ power_set @ member_type @ ( B @ ilf_type ) ) )
| ( A @ subset_type @ ( B @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32,410]) ).
thf(417,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk3 @ ilf_type ) )
!= ( A @ power_set @ member_type @ ( B @ ilf_type ) ) )
| ( A @ subset_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[416]) ).
thf(433,plain,
! [B: $i,A: $i] :
( ( ( A @ power_set @ member_type )
!= binary_relation_type )
| ( sk3 != B )
| ( A @ subset_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[417]) ).
thf(439,plain,
! [A: $i] :
( ( ( A @ power_set @ member_type )
!= binary_relation_type )
| ( A @ subset_type @ ( sk3 @ ilf_type ) ) ),
inference(simp,[status(thm)],[433]) ).
thf(24,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) ) )
& ! [C: $i] :
( ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) )
=> ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
thf(103,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)],[24]) ).
thf(104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cross_product ) @ subset_type @ ( D @ ilf_type ) )
| ~ ( B @ ( A @ relation_type ) @ ( D @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
| ~ ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[103]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
| ~ ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[104]) ).
thf(5336,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
| ~ ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[105,111]) ).
thf(5337,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
| ~ ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[5336]) ).
thf(34,plain,
~ ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(5380,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ~ $true
| ~ ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) ) ),
inference(paramod_ordered,[status(thm)],[5337,34]) ).
thf(5381,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ~ ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[5380]) ).
thf(5382,plain,
~ ( sk2 @ ( sk1 @ cross_product ) @ subset_type @ ( sk3 @ ilf_type ) ),
inference(pattern_uni,[status(thm)],[5381:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(5507,plain,
! [A: $i] :
( ( ( A @ subset_type @ ( sk3 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ cross_product ) @ subset_type @ ( sk3 @ ilf_type ) ) )
| ~ $true
| ( ( A @ power_set @ member_type )
!= binary_relation_type ) ),
inference(paramod_ordered,[status(thm)],[439,5382]) ).
thf(5508,plain,
! [A: $i] :
( ( ( A @ subset_type @ ( sk3 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ cross_product ) @ subset_type @ ( sk3 @ ilf_type ) ) )
| ( ( A @ power_set @ member_type )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[5507]) ).
thf(5509,plain,
( ( sk2 @ ( sk1 @ cross_product ) @ power_set @ member_type )
!= binary_relation_type ),
inference(pattern_uni,[status(thm)],[5508:[bind(A,$thf( sk2 @ ( sk1 @ cross_product ) ))]]) ).
thf(22,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ? [B: $i] : ( A @ subset_type @ ( B @ ilf_type ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p16) ).
thf(99,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ? [B: $i] : ( A @ subset_type @ ( B @ ilf_type ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(100,plain,
! [A: $i] :
( ( A @ subset_type @ ( A @ sk11 @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[99]) ).
thf(222,plain,
! [A: $i] :
( ( A @ subset_type @ ( A @ sk11 @ ilf_type ) )
| ~ $true ),
inference(rewrite,[status(thm)],[100,111]) ).
thf(223,plain,
! [A: $i] : ( A @ subset_type @ ( A @ sk11 @ ilf_type ) ),
inference(simp,[status(thm)],[222]) ).
thf(316,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk11 @ ilf_type ) )
!= ( B @ subset_type @ ( C @ ilf_type ) ) )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[223,305]) ).
thf(317,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk11 @ ilf_type ) )
!= ( B @ subset_type @ ( C @ ilf_type ) ) )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[316]) ).
thf(318,plain,
! [A: $i] : ( A @ power_set @ member_type @ ( A @ sk11 @ ilf_type ) ),
inference(pattern_uni,[status(thm)],[317:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk11 ))]]) ).
thf(337,plain,
! [A: $i] : ( A @ power_set @ member_type @ ( A @ sk11 @ ilf_type ) ),
inference(simp,[status(thm)],[318]) ).
thf(17,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( ( set_type @ ( B @ ilf_type ) )
& ~ ( B @ empty ) )
=> ( ( B @ member_type @ ( A @ ilf_type ) )
<=> ( B @ ( A @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
thf(81,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)],[17]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( ( B @ member_type @ ( A @ ilf_type ) )
| ~ ( B @ ( A @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ( B @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B @ ( A @ member ) )
| ~ ( B @ member_type @ ( A @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ( B @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[81]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( B @ member_type @ ( A @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ( B @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[82]) ).
thf(3249,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( B @ member_type @ ( A @ ilf_type ) )
| ~ $true
| ( B @ empty )
| ~ $true ),
inference(rewrite,[status(thm)],[83,111]) ).
thf(3250,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( B @ member_type @ ( A @ ilf_type ) )
| ( B @ empty ) ),
inference(simp,[status(thm)],[3249]) ).
thf(3346,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( A @ sk11 @ ilf_type ) )
!= ( C @ member_type @ ( B @ ilf_type ) ) )
| ( C @ ( B @ member ) )
| ~ $true
| ( C @ empty ) ),
inference(paramod_ordered,[status(thm)],[337,3250]) ).
thf(3347,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( A @ sk11 @ ilf_type ) )
!= ( C @ member_type @ ( B @ ilf_type ) ) )
| ( C @ ( B @ member ) )
| ( C @ empty ) ),
inference(simp,[status(thm)],[3346]) ).
thf(3348,plain,
! [A: $i] :
( ( A @ power_set @ ( A @ sk11 @ member ) )
| ( A @ power_set @ empty ) ),
inference(pattern_uni,[status(thm)],[3347:[bind(A,$thf( E )),bind(B,$thf( E @ sk11 )),bind(C,$thf( E @ power_set ))]]) ).
thf(3370,plain,
! [A: $i] :
( ( A @ power_set @ ( A @ sk11 @ member ) )
| ( A @ power_set @ empty ) ),
inference(simp,[status(thm)],[3348]) ).
thf(21,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( ( set_type @ ( A @ power_set @ ilf_type ) )
& ~ ( A @ power_set @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
thf(95,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)],[21]) ).
thf(96,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)],[95]) ).
thf(97,plain,
! [A: $i] :
( ~ ( A @ power_set @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[96]) ).
thf(193,plain,
! [A: $i] :
( ~ ( A @ power_set @ empty )
| ~ $true ),
inference(rewrite,[status(thm)],[97,111]) ).
thf(194,plain,
! [A: $i] :
~ ( A @ power_set @ empty ),
inference(simp,[status(thm)],[193]) ).
thf(6921,plain,
! [A: $i] :
( ( A @ power_set @ ( A @ sk11 @ member ) )
| $false ),
inference(rewrite,[status(thm)],[3370,194]) ).
thf(6922,plain,
! [A: $i] : ( A @ power_set @ ( A @ sk11 @ member ) ),
inference(simp,[status(thm)],[6921]) ).
thf(43,plain,
! [A: $i] :
( ( A @ empty )
| ( A @ ( A @ sk5 @ member ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[40]) ).
thf(217,plain,
! [A: $i] :
( ( A @ empty )
| ( A @ ( A @ sk5 @ member ) )
| ~ $true ),
inference(rewrite,[status(thm)],[43,111]) ).
thf(218,plain,
! [A: $i] :
( ( A @ empty )
| ( A @ ( A @ sk5 @ member ) ) ),
inference(simp,[status(thm)],[217]) ).
thf(548,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk5 @ member ) )
!= ( B @ ( D @ member ) ) )
| ( C @ ( D @ member ) )
| ~ $true
| ~ ( C @ power_set @ ( B @ member ) )
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[218,538]) ).
thf(549,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk5 @ member ) )
!= ( B @ ( D @ member ) ) )
| ( C @ ( D @ member ) )
| ~ ( C @ power_set @ ( B @ member ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[548]) ).
thf(550,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk5 @ member ) )
| ~ ( A @ power_set @ ( B @ member ) )
| ( B @ empty ) ),
inference(pattern_uni,[status(thm)],[549:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( E @ sk5 ))]]) ).
thf(565,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk5 @ member ) )
| ~ ( A @ power_set @ ( B @ member ) )
| ( B @ empty ) ),
inference(simp,[status(thm)],[550]) ).
thf(6936,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ ( A @ sk11 @ member ) )
!= ( B @ power_set @ ( C @ member ) ) )
| ( B @ ( C @ sk5 @ member ) )
| ~ $true
| ( C @ empty ) ),
inference(paramod_ordered,[status(thm)],[6922,565]) ).
thf(6937,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ ( A @ sk11 @ member ) )
!= ( B @ power_set @ ( C @ member ) ) )
| ( B @ ( C @ sk5 @ member ) )
| ( C @ empty ) ),
inference(simp,[status(thm)],[6936]) ).
thf(6938,plain,
! [A: $i] :
( ( A @ ( A @ sk11 @ sk5 @ member ) )
| ( A @ sk11 @ empty ) ),
inference(pattern_uni,[status(thm)],[6937:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk11 ))]]) ).
thf(7004,plain,
! [A: $i] :
( ( A @ ( A @ sk11 @ sk5 @ member ) )
| ( A @ sk11 @ empty ) ),
inference(simp,[status(thm)],[6938]) ).
thf(9,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12) ).
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)],[9]) ).
thf(62,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk8 ) @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk8 ) @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B @ ( A @ subset ) )
| ( set_type @ ( A @ ( B @ sk8 ) @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( B @ ( A @ subset ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[61]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( B @ ( A @ subset ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[62]) ).
thf(1718,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ $true
| ~ ( B @ ( A @ subset ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[63,111]) ).
thf(1719,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[1718]) ).
thf(1840,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35,1719]) ).
thf(1841,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(simp,[status(thm)],[1840]) ).
thf(1842,plain,
! [A: $i] :
( ( sk1 @ ( A @ member ) )
| ~ ( sk3 @ domain_of @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[1841:[bind(A,$thf( sk3 @ domain_of )),bind(B,$thf( sk1 )),bind(C,$thf( C ))]]) ).
thf(1912,plain,
! [A: $i] :
( ( sk1 @ ( A @ member ) )
| ~ ( sk3 @ domain_of @ ( A @ member ) ) ),
inference(simp,[status(thm)],[1842]) ).
thf(2504,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk5 @ member ) )
!= ( sk3 @ domain_of @ ( B @ member ) ) )
| ( sk1 @ ( B @ member ) )
| ~ $true
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[218,1912]) ).
thf(2505,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk5 @ member ) )
!= ( sk3 @ domain_of @ ( B @ member ) ) )
| ( sk1 @ ( B @ member ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[2504]) ).
thf(2506,plain,
( ( sk1 @ ( sk3 @ domain_of @ sk5 @ member ) )
| ( sk3 @ domain_of @ empty ) ),
inference(pattern_uni,[status(thm)],[2505:[bind(A,$thf( sk3 @ domain_of )),bind(B,$thf( sk3 @ domain_of @ sk5 ))]]) ).
thf(2707,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk5 @ member ) )
!= ( A @ ( B @ member ) ) )
| ~ $true
| ~ ( A @ empty )
| ( sk3 @ domain_of @ empty ) ),
inference(paramod_ordered,[status(thm)],[2506,202]) ).
thf(2708,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk5 @ member ) )
!= ( A @ ( B @ member ) ) )
| ~ ( A @ empty )
| ( sk3 @ domain_of @ empty ) ),
inference(simp,[status(thm)],[2707]) ).
thf(2709,plain,
( ~ ( sk1 @ empty )
| ( sk3 @ domain_of @ empty ) ),
inference(pattern_uni,[status(thm)],[2708:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ domain_of @ sk5 ))]]) ).
thf(2925,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ domain_of @ empty )
!= ( A @ empty ) )
| ~ ( A @ ( B @ member ) )
| ~ $true
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[2709,202]) ).
thf(2926,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ domain_of @ empty )
!= ( A @ empty ) )
| ~ ( A @ ( B @ member ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[2925]) ).
thf(2927,plain,
! [A: $i] :
( ~ ( sk3 @ domain_of @ ( A @ member ) )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[2926:[bind(A,$thf( sk3 @ domain_of )),bind(B,$thf( B ))]]) ).
thf(2992,plain,
! [A: $i] :
( ~ ( sk3 @ domain_of @ ( A @ member ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[2927]) ).
thf(8481,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ sk5 @ member ) )
!= ( sk3 @ domain_of @ ( B @ member ) ) )
| ~ $true
| ~ ( sk1 @ empty )
| ( A @ sk11 @ empty ) ),
inference(paramod_ordered,[status(thm)],[7004,2992]) ).
thf(8482,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ sk5 @ member ) )
!= ( sk3 @ domain_of @ ( B @ member ) ) )
| ~ ( sk1 @ empty )
| ( A @ sk11 @ empty ) ),
inference(simp,[status(thm)],[8481]) ).
thf(8483,plain,
( ~ ( sk1 @ empty )
| ( sk3 @ domain_of @ sk11 @ empty ) ),
inference(pattern_uni,[status(thm)],[8482:[bind(A,$thf( sk3 @ domain_of )),bind(B,$thf( sk3 @ domain_of @ sk11 @ sk5 ))]]) ).
thf(27,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( ( A @ relation_like )
<=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( A @ ( B @ member ) )
=> ? [C: $i] :
( ? [D: $i] :
( ( B
= ( D @ ( C @ ordered_pair ) ) )
& ( set_type @ ( D @ ilf_type ) ) )
& ( set_type @ ( C @ ilf_type ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18) ).
thf(112,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)],[27]) ).
thf(113,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ relation_like )
| ( ( A @ sk14 )
!= ( D @ ( C @ ordered_pair ) ) )
| ~ ( set_type @ ( D @ ilf_type ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( A @ relation_like )
| ( A @ ( A @ sk14 @ member ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( A @ relation_like )
| ( set_type @ ( A @ sk14 @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B
= ( A @ ( B @ sk13 ) @ ( A @ ( B @ sk12 ) @ ordered_pair ) ) )
| ~ ( A @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( A @ relation_like )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( set_type @ ( A @ ( B @ sk13 ) @ ilf_type ) )
| ~ ( A @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( A @ relation_like )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( set_type @ ( A @ ( B @ sk12 ) @ ilf_type ) )
| ~ ( A @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( A @ relation_like )
| ~ ( set_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[112]) ).
thf(114,plain,
! [A: $i] :
( ( A @ relation_like )
| ( A @ ( A @ sk14 @ member ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[113]) ).
thf(403,plain,
! [A: $i] :
( ( A @ relation_like )
| ( A @ ( A @ sk14 @ member ) )
| ~ $true ),
inference(rewrite,[status(thm)],[114,111]) ).
thf(404,plain,
! [A: $i] :
( ( A @ relation_like )
| ( A @ ( A @ sk14 @ member ) ) ),
inference(simp,[status(thm)],[403]) ).
thf(405,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk14 @ member ) )
!= ( B @ ( C @ member ) ) )
| ~ $true
| ~ ( B @ empty )
| ( A @ relation_like ) ),
inference(paramod_ordered,[status(thm)],[404,202]) ).
thf(406,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk14 @ member ) )
!= ( B @ ( C @ member ) ) )
| ~ ( B @ empty )
| ( A @ relation_like ) ),
inference(simp,[status(thm)],[405]) ).
thf(407,plain,
! [A: $i] :
( ~ ( A @ empty )
| ( A @ relation_like ) ),
inference(pattern_uni,[status(thm)],[406:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk14 ))]]) ).
thf(408,plain,
! [A: $i] :
( ~ ( A @ empty )
| ( A @ relation_like ) ),
inference(simp,[status(thm)],[407]) ).
thf(8694,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ sk11 @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A @ relation_like )
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[8483,408]) ).
thf(8695,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ sk11 @ empty )
!= ( A @ empty ) )
| ( A @ relation_like )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[8694]) ).
thf(8696,plain,
( ( sk3 @ domain_of @ sk11 @ relation_like )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[8695:[bind(A,$thf( sk3 @ domain_of @ sk11 ))]]) ).
thf(19,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( ( binary_relation_type @ ( A @ ilf_type ) )
<=> ( ( set_type @ ( A @ ilf_type ) )
& ( A @ relation_like ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
thf(87,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)],[19]) ).
thf(88,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)],[87]) ).
thf(91,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) )
| ~ ( A @ relation_like )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[88]) ).
thf(92,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
| ~ ( A @ relation_like )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(4118,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
| ~ ( A @ relation_like )
| ~ $true ),
inference(rewrite,[status(thm)],[92,111]) ).
thf(4119,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
| ~ ( A @ relation_like ) ),
inference(simp,[status(thm)],[4118]) ).
thf(9129,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ sk11 @ relation_like )
!= ( A @ relation_like ) )
| ( binary_relation_type @ ( A @ ilf_type ) )
| ~ $true
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[8696,4119]) ).
thf(9130,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ sk11 @ relation_like )
!= ( A @ relation_like ) )
| ( binary_relation_type @ ( A @ ilf_type ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[9129]) ).
thf(9131,plain,
( ( binary_relation_type @ ( sk3 @ domain_of @ sk11 @ ilf_type ) )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[9130:[bind(A,$thf( sk3 @ domain_of @ sk11 ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
& ~ ( A @ empty ) )
=> ? [B: $i] : ( A @ member_type @ ( B @ ilf_type ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23) ).
thf(67,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)],[10]) ).
thf(68,plain,
! [A: $i] :
( ( A @ member_type @ ( A @ sk9 @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) )
| ( A @ empty ) ),
inference(cnf,[status(esa)],[67]) ).
thf(480,plain,
! [A: $i] :
( ( A @ member_type @ ( A @ sk9 @ ilf_type ) )
| ~ $true
| ( A @ empty ) ),
inference(rewrite,[status(thm)],[68,111]) ).
thf(481,plain,
! [A: $i] :
( ( A @ member_type @ ( A @ sk9 @ ilf_type ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[480]) ).
thf(1013,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ range_of @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,284]) ).
thf(1014,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ range_of @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1013]) ).
thf(1015,plain,
sk1 @ ( sk2 @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1014:[bind(A,$thf( sk3 @ range_of )),bind(B,$thf( sk2 ))]]) ).
thf(1064,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1015,284]) ).
thf(1065,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1064]) ).
thf(1066,plain,
sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1065:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ cross_product ) ))]]) ).
thf(1161,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1066,284]) ).
thf(1162,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1161]) ).
thf(1163,plain,
sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1162:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) ))]]) ).
thf(2248,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1163,284]) ).
thf(2249,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2248]) ).
thf(2250,plain,
sk1 @ ( sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2249:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2490,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk6 ) @ member ) )
!= ( sk3 @ domain_of @ ( C @ member ) ) )
| ( sk1 @ ( C @ member ) )
| ~ $true
| ( B @ power_set @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[710,1912]) ).
thf(2491,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk6 ) @ member ) )
!= ( sk3 @ domain_of @ ( C @ member ) ) )
| ( sk1 @ ( C @ member ) )
| ( B @ power_set @ ( A @ member ) ) ),
inference(simp,[status(thm)],[2490]) ).
thf(2492,plain,
! [A: $i] :
( ( sk1 @ ( sk3 @ domain_of @ ( A @ sk6 ) @ member ) )
| ( A @ power_set @ ( sk3 @ domain_of @ member ) ) ),
inference(pattern_uni,[status(thm)],[2491:[bind(A,$thf( sk3 @ domain_of )),bind(B,$thf( D )),bind(C,$thf( sk3 @ domain_of @ ( D @ sk6 ) ))]]) ).
thf(2515,plain,
! [A: $i] :
( ( sk1 @ ( sk3 @ domain_of @ ( A @ sk6 ) @ member ) )
| ( A @ power_set @ ( sk3 @ domain_of @ member ) ) ),
inference(simp,[status(thm)],[2492]) ).
thf(3121,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ ( A @ sk6 ) @ member ) )
!= ( C @ ( B @ ( C @ sk6 ) @ member ) ) )
| ( C @ power_set @ ( B @ member ) )
| ~ $true
| ( A @ power_set @ ( sk3 @ domain_of @ member ) ) ),
inference(paramod_ordered,[status(thm)],[2515,849]) ).
thf(3122,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ ( A @ sk6 ) @ member ) )
!= ( C @ ( B @ ( C @ sk6 ) @ member ) ) )
| ( C @ power_set @ ( B @ member ) )
| ( A @ power_set @ ( sk3 @ domain_of @ member ) ) ),
inference(simp,[status(thm)],[3121]) ).
thf(3123,plain,
( ( sk1 @ power_set @ ( sk3 @ domain_of @ member ) )
| ( sk1 @ power_set @ ( sk3 @ domain_of @ member ) ) ),
inference(pattern_uni,[status(thm)],[3122:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ domain_of )),bind(C,$thf( sk1 ))]]) ).
thf(3170,plain,
sk1 @ power_set @ ( sk3 @ domain_of @ member ),
inference(simp,[status(thm)],[3123]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( B @ member_type @ ( A @ ilf_type ) )
| ~ ( B @ ( A @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ( B @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[82]) ).
thf(3622,plain,
! [B: $i,A: $i] :
( ( B @ member_type @ ( A @ ilf_type ) )
| ~ ( B @ ( A @ member ) )
| ~ $true
| ( B @ empty )
| ~ $true ),
inference(rewrite,[status(thm)],[84,111]) ).
thf(3623,plain,
! [B: $i,A: $i] :
( ( B @ member_type @ ( A @ ilf_type ) )
| ~ ( B @ ( A @ member ) )
| ( B @ empty ) ),
inference(simp,[status(thm)],[3622]) ).
thf(3651,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ power_set @ ( sk3 @ domain_of @ member ) )
!= ( B @ ( A @ member ) ) )
| ( B @ member_type @ ( A @ ilf_type ) )
| ~ $true
| ( B @ empty ) ),
inference(paramod_ordered,[status(thm)],[3170,3623]) ).
thf(3652,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ power_set @ ( sk3 @ domain_of @ member ) )
!= ( B @ ( A @ member ) ) )
| ( B @ member_type @ ( A @ ilf_type ) )
| ( B @ empty ) ),
inference(simp,[status(thm)],[3651]) ).
thf(3653,plain,
( ( sk1 @ power_set @ member_type @ ( sk3 @ domain_of @ ilf_type ) )
| ( sk1 @ power_set @ empty ) ),
inference(pattern_uni,[status(thm)],[3652:[bind(A,$thf( sk3 @ domain_of )),bind(B,$thf( sk1 @ power_set ))]]) ).
thf(4042,plain,
( ( sk1 @ power_set @ member_type @ ( sk3 @ domain_of @ ilf_type ) )
| $false ),
inference(rewrite,[status(thm)],[3653,194]) ).
thf(4043,plain,
sk1 @ power_set @ member_type @ ( sk3 @ domain_of @ ilf_type ),
inference(simp,[status(thm)],[4042]) ).
thf(7,axiom,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( A @ range_of @ ( B @ member ) )
<=> ? [C: $i] :
( ( A @ ( B @ ( C @ ordered_pair ) @ member ) )
& ( set_type @ ( C @ ilf_type ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8) ).
thf(54,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( ? [C: $i] :
( ( A @ ( B @ ( C @ ordered_pair ) @ member ) )
& ( set_type @ ( C @ ilf_type ) ) )
=> ( A @ range_of @ ( B @ member ) ) )
& ( ( A @ range_of @ ( B @ member ) )
=> ? [C: $i] :
( ( A @ ( B @ ( C @ ordered_pair ) @ member ) )
& ( set_type @ ( C @ ilf_type ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ range_of @ ( B @ member ) )
| ~ ( A @ ( B @ ( C @ ordered_pair ) @ member ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) )
& ( ( A @ ( B @ ( A @ ( B @ sk7 ) @ ordered_pair ) @ member ) )
| ~ ( A @ range_of @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) )
& ( ( set_type @ ( A @ ( B @ sk7 ) @ ilf_type ) )
| ~ ( A @ range_of @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[54]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( B @ sk7 ) @ ordered_pair ) @ member ) )
| ~ ( A @ range_of @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[55]) ).
thf(1174,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( B @ sk7 ) @ ordered_pair ) @ member ) )
| ~ ( A @ range_of @ ( B @ member ) )
| ~ $true
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(rewrite,[status(thm)],[57,111]) ).
thf(1175,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( B @ sk7 ) @ ordered_pair ) @ member ) )
| ~ ( A @ range_of @ ( B @ member ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(simp,[status(thm)],[1174]) ).
thf(1195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ sk7 ) @ ordered_pair ) @ member ) )
!= ( C @ ( D @ member ) ) )
| ~ $true
| ~ ( C @ empty )
| ~ ( A @ range_of @ ( B @ member ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(paramod_ordered,[status(thm)],[1175,202]) ).
thf(1196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ sk7 ) @ ordered_pair ) @ member ) )
!= ( C @ ( D @ member ) ) )
| ~ ( C @ empty )
| ~ ( A @ range_of @ ( B @ member ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(simp,[status(thm)],[1195]) ).
thf(1197,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( B @ range_of @ ( A @ member ) )
| ~ ( binary_relation_type @ ( B @ ilf_type ) ) ),
inference(pattern_uni,[status(thm)],[1196:[bind(A,$thf( H )),bind(B,$thf( F )),bind(C,$thf( H )),bind(D,$thf( F @ ( H @ ( F @ sk7 ) @ ordered_pair ) ))]]) ).
thf(1290,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( B @ range_of @ ( A @ member ) )
| ~ ( binary_relation_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[1197]) ).
thf(1043,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[739,284]) ).
thf(1044,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1043]) ).
thf(1045,plain,
sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1044:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) ))]]) ).
thf(2097,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1045,284]) ).
thf(2098,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2097]) ).
thf(2099,plain,
sk1 @ ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2098:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(509,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( sk3 @ ilf_type ) )
!= ( B @ subset_type @ ( C @ ilf_type ) ) )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) )
| ~ $true
| ( ( A @ power_set @ member_type )
!= binary_relation_type ) ),
inference(paramod_ordered,[status(thm)],[439,305]) ).
thf(510,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( sk3 @ ilf_type ) )
!= ( B @ subset_type @ ( C @ ilf_type ) ) )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) )
| ( ( A @ power_set @ member_type )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[509]) ).
thf(511,plain,
! [A: $i] :
( ( A @ power_set @ member_type @ ( sk3 @ ilf_type ) )
| ( ( A @ power_set @ member_type )
!= binary_relation_type ) ),
inference(pattern_uni,[status(thm)],[510:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 ))]]) ).
thf(1392,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk3 @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ~ ( B @ empty )
| ~ ( B @ range_of @ ( A @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32,1290]) ).
thf(1393,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk3 @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ~ ( B @ empty )
| ~ ( B @ range_of @ ( A @ member ) ) ),
inference(simp,[status(thm)],[1392]) ).
thf(1394,plain,
! [A: $i] :
( ~ ( sk3 @ empty )
| ~ ( sk3 @ range_of @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[1393:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(1480,plain,
! [B: $i,A: $i] :
( ( ( A @ power_set @ ( A @ member ) )
!= ( sk3 @ range_of @ ( B @ member ) ) )
| ~ ( sk3 @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[867,1394]) ).
thf(1481,plain,
! [B: $i,A: $i] :
( ( ( A @ power_set @ ( A @ member ) )
!= ( sk3 @ range_of @ ( B @ member ) ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[1480]) ).
thf(1482,plain,
! [B: $i,A: $i] :
( ( ( A @ power_set )
!= ( sk3 @ range_of ) )
| ( A != B )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[1481]) ).
thf(1486,plain,
! [A: $i] :
( ( ( A @ power_set )
!= ( sk3 @ range_of ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[1482]) ).
thf(28,axiom,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( A @ domain_of @ ( B @ member ) )
<=> ? [C: $i] :
( ( A @ ( C @ ( B @ ordered_pair ) @ member ) )
& ( set_type @ ( C @ ilf_type ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
thf(123,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( ? [C: $i] :
( ( A @ ( C @ ( B @ ordered_pair ) @ member ) )
& ( set_type @ ( C @ ilf_type ) ) )
=> ( A @ domain_of @ ( B @ member ) ) )
& ( ( A @ domain_of @ ( B @ member ) )
=> ? [C: $i] :
( ( A @ ( C @ ( B @ ordered_pair ) @ member ) )
& ( set_type @ ( C @ ilf_type ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(124,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ domain_of @ ( B @ member ) )
| ~ ( A @ ( C @ ( B @ ordered_pair ) @ member ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) )
& ( ( A @ ( A @ ( B @ sk15 ) @ ( B @ ordered_pair ) @ member ) )
| ~ ( A @ domain_of @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) )
& ( ( set_type @ ( A @ ( B @ sk15 ) @ ilf_type ) )
| ~ ( A @ domain_of @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[123]) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ domain_of @ ( B @ member ) )
| ~ ( A @ ( C @ ( B @ ordered_pair ) @ member ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[124]) ).
thf(8056,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ domain_of @ ( B @ member ) )
| ~ ( A @ ( C @ ( B @ ordered_pair ) @ member ) )
| ~ $true
| ~ $true
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(rewrite,[status(thm)],[127,111]) ).
thf(8057,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ domain_of @ ( B @ member ) )
| ~ ( A @ ( C @ ( B @ ordered_pair ) @ member ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(simp,[status(thm)],[8056]) ).
thf(1037,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35,284]) ).
thf(1038,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1037]) ).
thf(1039,plain,
sk1 @ ( sk1 @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1038:[bind(A,$thf( sk3 @ domain_of )),bind(B,$thf( sk1 ))]]) ).
thf(1079,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1039,284]) ).
thf(1080,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1079]) ).
thf(1081,plain,
sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1080:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ cross_product ) ))]]) ).
thf(1325,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1081,284]) ).
thf(1326,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1325]) ).
thf(1327,plain,
sk1 @ ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1326:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) ))]]) ).
thf(1088,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1039,278]) ).
thf(1089,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1088]) ).
thf(1090,plain,
sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1089:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ cross_product ) ))]]) ).
thf(1347,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1090,278]) ).
thf(1348,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1347]) ).
thf(1349,plain,
sk2 @ ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1348:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) ))]]) ).
thf(2578,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1349,284]) ).
thf(2579,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2578]) ).
thf(2580,plain,
sk1 @ ( sk2 @ ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2579:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk8 ) @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[62]) ).
thf(2265,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk8 ) @ member ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[65,111]) ).
thf(2266,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk8 ) @ member ) ) ),
inference(simp,[status(thm)],[2265]) ).
thf(2501,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk8 ) @ member ) )
!= ( sk3 @ domain_of @ ( C @ member ) ) )
| ( sk1 @ ( C @ member ) )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[2266,1912]) ).
thf(2502,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk8 ) @ member ) )
!= ( sk3 @ domain_of @ ( C @ member ) ) )
| ( sk1 @ ( C @ member ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[2501]) ).
thf(2503,plain,
! [A: $i] :
( ( sk1 @ ( sk3 @ domain_of @ ( A @ sk8 ) @ member ) )
| ( A @ ( sk3 @ domain_of @ subset ) ) ),
inference(pattern_uni,[status(thm)],[2502:[bind(A,$thf( sk3 @ domain_of )),bind(B,$thf( D )),bind(C,$thf( sk3 @ domain_of @ ( D @ sk8 ) ))]]) ).
thf(2513,plain,
! [A: $i] :
( ( sk1 @ ( sk3 @ domain_of @ ( A @ sk8 ) @ member ) )
| ( A @ ( sk3 @ domain_of @ subset ) ) ),
inference(simp,[status(thm)],[2503]) ).
thf(2848,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ ( A @ sk8 ) @ member ) )
!= ( B @ ( C @ member ) ) )
| ~ $true
| ~ ( B @ empty )
| ( A @ ( sk3 @ domain_of @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[2513,202]) ).
thf(2849,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ ( A @ sk8 ) @ member ) )
!= ( B @ ( C @ member ) ) )
| ~ ( B @ empty )
| ( A @ ( sk3 @ domain_of @ subset ) ) ),
inference(simp,[status(thm)],[2848]) ).
thf(2850,plain,
! [A: $i] :
( ~ ( sk1 @ empty )
| ( A @ ( sk3 @ domain_of @ subset ) ) ),
inference(pattern_uni,[status(thm)],[2849:[bind(A,$thf( D )),bind(B,$thf( sk1 )),bind(C,$thf( sk3 @ domain_of @ ( D @ sk8 ) ))]]) ).
thf(2901,plain,
! [A: $i] :
( ~ ( sk1 @ empty )
| ( A @ ( sk3 @ domain_of @ subset ) ) ),
inference(simp,[status(thm)],[2850]) ).
thf(8,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( A @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17) ).
thf(59,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( A @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(60,plain,
! [A: $i] :
( ( A @ ( A @ subset ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[59]) ).
thf(207,plain,
! [A: $i] :
( ( A @ ( A @ subset ) )
| ~ $true ),
inference(rewrite,[status(thm)],[60,111]) ).
thf(208,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(simp,[status(thm)],[207]) ).
thf(680,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk2 @ ( C @ cross_product ) @ ( sk3 @ range_of @ ( B @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[208,278]) ).
thf(681,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk2 @ ( C @ cross_product ) @ ( sk3 @ range_of @ ( B @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[680]) ).
thf(682,plain,
! [A: $i] : ( sk2 @ ( A @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ),
inference(pattern_uni,[status(thm)],[681:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(832,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk2 @ ( C @ cross_product ) @ ( sk3 @ range_of @ ( B @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[682,278]) ).
thf(833,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk2 @ ( C @ cross_product ) @ ( sk3 @ range_of @ ( B @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[832]) ).
thf(834,plain,
! [A: $i] : ( sk2 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ subset ) ),
inference(pattern_uni,[status(thm)],[833:[bind(A,$thf( G )),bind(B,$thf( sk3 @ range_of @ ( G @ cross_product ) )),bind(C,$thf( sk2 @ ( G @ cross_product ) ))]]) ).
thf(835,plain,
! [A: $i] : ( sk2 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ subset ) ),
inference(simp,[status(thm)],[834]) ).
thf(1049,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk1 @ ( C @ cross_product ) @ ( sk3 @ domain_of @ ( B @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[835,284]) ).
thf(1050,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk1 @ ( C @ cross_product ) @ ( sk3 @ domain_of @ ( B @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1049]) ).
thf(1051,plain,
! [A: $i] : ( sk1 @ ( sk2 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) ),
inference(pattern_uni,[status(thm)],[1050:[bind(A,$thf( L )),bind(B,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( L @ cross_product ) @ cross_product ) )),bind(C,$thf( sk2 @ ( sk2 @ ( L @ cross_product ) @ cross_product ) ))]]) ).
thf(1063,plain,
! [A: $i] : ( sk1 @ ( sk2 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) ),
inference(simp,[status(thm)],[1051]) ).
thf(1338,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1090,284]) ).
thf(1339,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1338]) ).
thf(1340,plain,
sk1 @ ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1339:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) ))]]) ).
thf(2573,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1340,278]) ).
thf(2574,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2573]) ).
thf(2575,plain,
sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2574:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(674,plain,
! [B: $i,A: $i] :
( ( ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ ( sk10 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[238,278]) ).
thf(675,plain,
! [B: $i,A: $i] :
( ( ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ ( sk10 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[674]) ).
thf(676,plain,
sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[675:[bind(A,$thf( sk10 )),bind(B,$thf( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) ))]]) ).
thf(1052,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[676,284]) ).
thf(1053,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1052]) ).
thf(1054,plain,
sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1053:[bind(A,$thf( sk3 @ range_of @ ( sk10 @ cross_product ) )),bind(B,$thf( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) ))]]) ).
thf(1497,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1054,278]) ).
thf(1498,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1497]) ).
thf(1499,plain,
sk2 @ ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1498:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(3047,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1499,278]) ).
thf(3048,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[3047]) ).
thf(3049,plain,
sk2 @ ( sk2 @ ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[3048:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(1135,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[994,284]) ).
thf(1136,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1135]) ).
thf(1137,plain,
sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1136:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) ))]]) ).
thf(3,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ? [C: $i] : ( A @ ( B @ relation_type ) @ ( C @ ilf_type ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5) ).
thf(37,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)],[3]) ).
thf(38,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)],[37]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ relation_type ) @ ( A @ ( B @ sk4 ) @ ilf_type ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[38,111]) ).
thf(185,plain,
! [B: $i,A: $i] : ( A @ ( B @ relation_type ) @ ( A @ ( B @ sk4 ) @ ilf_type ) ),
inference(simp,[status(thm)],[184]) ).
thf(1019,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[697,284]) ).
thf(1020,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1019]) ).
thf(1021,plain,
sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1020:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ cross_product ) ))]]) ).
thf(1148,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1021,284]) ).
thf(1149,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1148]) ).
thf(1150,plain,
sk1 @ ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1149:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) ))]]) ).
thf(2214,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1150,284]) ).
thf(2215,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2214]) ).
thf(2216,plain,
sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2215:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(1465,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk14 @ member ) )
!= ( sk3 @ range_of @ ( B @ member ) ) )
| ~ ( sk3 @ empty )
| ~ $true
| ( A @ relation_like ) ),
inference(paramod_ordered,[status(thm)],[404,1394]) ).
thf(1466,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk14 @ member ) )
!= ( sk3 @ range_of @ ( B @ member ) ) )
| ~ ( sk3 @ empty )
| ( A @ relation_like ) ),
inference(simp,[status(thm)],[1465]) ).
thf(1467,plain,
( ~ ( sk3 @ empty )
| ( sk3 @ range_of @ relation_like ) ),
inference(pattern_uni,[status(thm)],[1466:[bind(A,$thf( sk3 @ range_of )),bind(B,$thf( sk3 @ range_of @ sk14 ))]]) ).
thf(2951,plain,
( ( ( sk3 @ domain_of @ empty )
!= ( sk3 @ empty ) )
| ~ $true
| ( sk3 @ range_of @ relation_like )
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[2709,1467]) ).
thf(2952,plain,
( ( ( sk3 @ domain_of @ empty )
!= ( sk3 @ empty ) )
| ( sk3 @ range_of @ relation_like )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[2951]) ).
thf(2985,plain,
( ( ( sk3 @ domain_of )
!= sk3 )
| ~ ( sk1 @ empty )
| ( sk3 @ range_of @ relation_like ) ),
inference(simp,[status(thm)],[2952]) ).
thf(1477,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk5 @ member ) )
!= ( sk3 @ range_of @ ( B @ member ) ) )
| ~ ( sk3 @ empty )
| ~ $true
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[218,1394]) ).
thf(1478,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk5 @ member ) )
!= ( sk3 @ range_of @ ( B @ member ) ) )
| ~ ( sk3 @ empty )
| ( A @ empty ) ),
inference(simp,[status(thm)],[1477]) ).
thf(1479,plain,
( ~ ( sk3 @ empty )
| ( sk3 @ range_of @ empty ) ),
inference(pattern_uni,[status(thm)],[1478:[bind(A,$thf( sk3 @ range_of )),bind(B,$thf( sk3 @ range_of @ sk5 ))]]) ).
thf(1402,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ~ ( B @ empty )
| ~ ( B @ range_of @ ( A @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[80,1290]) ).
thf(1403,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ~ ( B @ empty )
| ~ ( B @ range_of @ ( A @ member ) ) ),
inference(simp,[status(thm)],[1402]) ).
thf(1404,plain,
! [A: $i] :
( ~ ( sk10 @ empty )
| ~ ( sk10 @ range_of @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[1403:[bind(A,$thf( A )),bind(B,$thf( sk10 ))]]) ).
thf(3217,plain,
! [A: $i] :
( ( ( sk1 @ power_set @ ( sk3 @ domain_of @ member ) )
!= ( sk10 @ range_of @ ( A @ member ) ) )
| ~ ( sk10 @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3170,1404]) ).
thf(3218,plain,
! [A: $i] :
( ( ( sk1 @ power_set @ ( sk3 @ domain_of @ member ) )
!= ( sk10 @ range_of @ ( A @ member ) ) )
| ~ ( sk10 @ empty ) ),
inference(simp,[status(thm)],[3217]) ).
thf(3225,plain,
! [A: $i] :
( ( ( sk1 @ power_set )
!= ( sk10 @ range_of ) )
| ( ( sk3 @ domain_of )
!= A )
| ~ ( sk10 @ empty ) ),
inference(simp,[status(thm)],[3218]) ).
thf(3243,plain,
( ( ( sk1 @ power_set )
!= ( sk10 @ range_of ) )
| ~ ( sk10 @ empty ) ),
inference(simp,[status(thm)],[3225]) ).
thf(3462,plain,
( ( ( sk3 @ range_of @ empty )
!= ( sk10 @ empty ) )
| ( ( sk1 @ power_set )
!= ( sk10 @ range_of ) )
| ~ $true
| ~ ( sk3 @ empty ) ),
inference(paramod_ordered,[status(thm)],[1479,3243]) ).
thf(3463,plain,
( ( ( sk3 @ range_of @ empty )
!= ( sk10 @ empty ) )
| ( ( sk1 @ power_set )
!= ( sk10 @ range_of ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[3462]) ).
thf(3466,plain,
( ( ( sk3 @ range_of )
!= sk10 )
| ( ( sk1 @ power_set )
!= ( sk10 @ range_of ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[3463]) ).
thf(3581,plain,
! [A: $i] :
( ( ( sk1 @ power_set @ ( sk3 @ domain_of @ member ) )
!= ( sk3 @ domain_of @ ( A @ member ) ) )
| ~ $true
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[3170,2992]) ).
thf(3582,plain,
! [A: $i] :
( ( ( sk1 @ power_set @ ( sk3 @ domain_of @ member ) )
!= ( sk3 @ domain_of @ ( A @ member ) ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[3581]) ).
thf(3605,plain,
! [A: $i] :
( ( ( sk1 @ power_set )
!= ( sk3 @ domain_of ) )
| ( ( sk3 @ domain_of )
!= A )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[3582]) ).
thf(3617,plain,
( ( ( sk1 @ power_set )
!= ( sk3 @ domain_of ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[3605]) ).
thf(1073,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1015,278]) ).
thf(1074,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1073]) ).
thf(1075,plain,
sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1074:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ cross_product ) ))]]) ).
thf(1321,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1075,278]) ).
thf(1322,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1321]) ).
thf(1323,plain,
sk2 @ ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1322:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) ))]]) ).
thf(186,plain,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,34]) ).
thf(187,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) ),
inference(simp,[status(thm)],[186]) ).
thf(188,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ relation_type ) )
!= set_type )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[187]) ).
thf(189,plain,
( ( sk2 @ ( sk1 @ relation_type ) )
!= set_type ),
inference(simp,[status(thm)],[188]) ).
thf(102,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ relation_like )
| ~ ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[101]) ).
thf(5098,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ relation_like )
| ~ ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[102,111]) ).
thf(5099,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ relation_like )
| ~ ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[5098]) ).
thf(5133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk11 @ ilf_type ) )
!= ( C @ ( B @ cross_product ) @ subset_type @ ( D @ ilf_type ) ) )
| ( D @ relation_like )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[223,5099]) ).
thf(5134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk11 @ ilf_type ) )
!= ( C @ ( B @ cross_product ) @ subset_type @ ( D @ ilf_type ) ) )
| ( D @ relation_like ) ),
inference(simp,[status(thm)],[5133]) ).
thf(5135,plain,
! [B: $i,A: $i] : ( B @ ( A @ cross_product ) @ sk11 @ relation_like ),
inference(pattern_uni,[status(thm)],[5134:[bind(A,$thf( G @ ( F @ cross_product ) )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( G @ ( F @ cross_product ) @ sk11 ))]]) ).
thf(5174,plain,
! [B: $i,A: $i] : ( B @ ( A @ cross_product ) @ sk11 @ relation_like ),
inference(simp,[status(thm)],[5135]) ).
thf(5196,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cross_product ) @ sk11 @ relation_like )
!= ( C @ relation_like ) )
| ( binary_relation_type @ ( C @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5174,4119]) ).
thf(5197,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cross_product ) @ sk11 @ relation_like )
!= ( C @ relation_like ) )
| ( binary_relation_type @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[5196]) ).
thf(5198,plain,
! [B: $i,A: $i] : ( binary_relation_type @ ( B @ ( A @ cross_product ) @ sk11 @ ilf_type ) ),
inference(pattern_uni,[status(thm)],[5197:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ cross_product ) @ sk11 ))]]) ).
thf(5199,plain,
! [B: $i,A: $i] : ( binary_relation_type @ ( B @ ( A @ cross_product ) @ sk11 @ ilf_type ) ),
inference(simp,[status(thm)],[5198]) ).
thf(1702,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[846,284]) ).
thf(1703,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1702]) ).
thf(1704,plain,
sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1703:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2484,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk14 @ member ) )
!= ( sk3 @ domain_of @ ( B @ member ) ) )
| ( sk1 @ ( B @ member ) )
| ~ $true
| ( A @ relation_like ) ),
inference(paramod_ordered,[status(thm)],[404,1912]) ).
thf(2485,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk14 @ member ) )
!= ( sk3 @ domain_of @ ( B @ member ) ) )
| ( sk1 @ ( B @ member ) )
| ( A @ relation_like ) ),
inference(simp,[status(thm)],[2484]) ).
thf(2486,plain,
( ( sk1 @ ( sk3 @ domain_of @ sk14 @ member ) )
| ( sk3 @ domain_of @ relation_like ) ),
inference(pattern_uni,[status(thm)],[2485:[bind(A,$thf( sk3 @ domain_of )),bind(B,$thf( sk3 @ domain_of @ sk14 ))]]) ).
thf(2633,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk14 @ member ) )
!= ( A @ ( B @ member ) ) )
| ~ $true
| ~ ( A @ empty )
| ( sk3 @ domain_of @ relation_like ) ),
inference(paramod_ordered,[status(thm)],[2486,202]) ).
thf(2634,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk14 @ member ) )
!= ( A @ ( B @ member ) ) )
| ~ ( A @ empty )
| ( sk3 @ domain_of @ relation_like ) ),
inference(simp,[status(thm)],[2633]) ).
thf(2635,plain,
( ~ ( sk1 @ empty )
| ( sk3 @ domain_of @ relation_like ) ),
inference(pattern_uni,[status(thm)],[2634:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ domain_of @ sk14 ))]]) ).
thf(3672,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ ( A @ member ) )
!= ( C @ ( B @ member ) ) )
| ( C @ member_type @ ( B @ ilf_type ) )
| ~ $true
| ( C @ empty ) ),
inference(paramod_ordered,[status(thm)],[867,3623]) ).
thf(3673,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ ( A @ member ) )
!= ( C @ ( B @ member ) ) )
| ( C @ member_type @ ( B @ ilf_type ) )
| ( C @ empty ) ),
inference(simp,[status(thm)],[3672]) ).
thf(3674,plain,
! [A: $i] :
( ( A @ power_set @ member_type @ ( A @ ilf_type ) )
| ( A @ power_set @ empty ) ),
inference(pattern_uni,[status(thm)],[3673:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ power_set ))]]) ).
thf(3684,plain,
! [A: $i] :
( ( A @ power_set @ member_type @ ( A @ ilf_type ) )
| ( A @ power_set @ empty ) ),
inference(simp,[status(thm)],[3674]) ).
thf(7353,plain,
! [A: $i] :
( ( A @ power_set @ member_type @ ( A @ ilf_type ) )
| $false ),
inference(rewrite,[status(thm)],[3684,194]) ).
thf(7354,plain,
! [A: $i] : ( A @ power_set @ member_type @ ( A @ ilf_type ) ),
inference(simp,[status(thm)],[7353]) ).
thf(7378,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( A @ ilf_type ) )
!= ( B @ power_set @ member_type @ ( C @ ilf_type ) ) )
| ( B @ subset_type @ ( C @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7354,410]) ).
thf(7379,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( A @ ilf_type ) )
!= ( B @ power_set @ member_type @ ( C @ ilf_type ) ) )
| ( B @ subset_type @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[7378]) ).
thf(7380,plain,
! [A: $i] : ( A @ subset_type @ ( A @ ilf_type ) ),
inference(pattern_uni,[status(thm)],[7379:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(7428,plain,
! [A: $i] :
( ( ( A @ subset_type @ ( A @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7380,34]) ).
thf(7429,plain,
! [A: $i] :
( ( A @ subset_type @ ( A @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) ),
inference(simp,[status(thm)],[7428]) ).
thf(7452,plain,
! [A: $i] :
( ( ( A @ subset_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[7429]) ).
thf(7464,plain,
( ( sk2 @ ( sk1 @ relation_type ) )
!= ( sk3 @ subset_type ) ),
inference(simp,[status(thm)],[7452]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',p1) ).
thf(93,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)],[20]) ).
thf(89,plain,
! [A: $i] :
( ( A @ relation_like )
| ~ ( binary_relation_type @ ( A @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[88]) ).
thf(3918,plain,
! [A: $i] :
( ( A @ relation_like )
| ~ ( binary_relation_type @ ( A @ ilf_type ) )
| ~ $true ),
inference(rewrite,[status(thm)],[89,111]) ).
thf(3919,plain,
! [A: $i] :
( ( A @ relation_like )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(simp,[status(thm)],[3918]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk15 ) @ ( B @ ordered_pair ) @ member ) )
| ~ ( A @ domain_of @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[124]) ).
thf(7559,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk15 ) @ ( B @ ordered_pair ) @ member ) )
| ~ ( A @ domain_of @ ( B @ member ) )
| ~ $true
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(rewrite,[status(thm)],[126,111]) ).
thf(7560,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk15 ) @ ( B @ ordered_pair ) @ member ) )
| ~ ( A @ domain_of @ ( B @ member ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(simp,[status(thm)],[7559]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk8 ) @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[62]) ).
thf(2519,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk8 ) @ member ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[66,111]) ).
thf(2520,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk8 ) @ member ) ) ),
inference(simp,[status(thm)],[2519]) ).
thf(2959,plain,
! [A: $i] :
( ( ( A @ power_set @ empty )
!= ( sk3 @ domain_of @ empty ) )
| ~ $true
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[2709,194]) ).
thf(2960,plain,
! [A: $i] :
( ( ( A @ power_set @ empty )
!= ( sk3 @ domain_of @ empty ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[2959]) ).
thf(2989,plain,
! [A: $i] :
( ( ( A @ power_set )
!= ( sk3 @ domain_of ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[2960]) ).
thf(1028,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[685,284]) ).
thf(1029,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1028]) ).
thf(1030,plain,
sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1029:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ cross_product ) )),bind(B,$thf( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) ))]]) ).
thf(1360,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1030,278]) ).
thf(1361,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1360]) ).
thf(1362,plain,
sk2 @ ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1361:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2827,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1362,284]) ).
thf(2828,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2827]) ).
thf(2829,plain,
sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2828:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(8447,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ sk5 @ member ) )
!= ( sk3 @ range_of @ ( B @ member ) ) )
| ~ ( sk3 @ empty )
| ~ $true
| ( A @ sk11 @ empty ) ),
inference(paramod_ordered,[status(thm)],[7004,1394]) ).
thf(8448,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ sk5 @ member ) )
!= ( sk3 @ range_of @ ( B @ member ) ) )
| ~ ( sk3 @ empty )
| ( A @ sk11 @ empty ) ),
inference(simp,[status(thm)],[8447]) ).
thf(8449,plain,
( ~ ( sk3 @ empty )
| ( sk3 @ range_of @ sk11 @ empty ) ),
inference(pattern_uni,[status(thm)],[8448:[bind(A,$thf( sk3 @ range_of )),bind(B,$thf( sk3 @ range_of @ sk11 @ sk5 ))]]) ).
thf(8522,plain,
! [A: $i] :
( ( ( sk3 @ range_of @ sk11 @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A @ relation_like )
| ~ ( sk3 @ empty ) ),
inference(paramod_ordered,[status(thm)],[8449,408]) ).
thf(8523,plain,
! [A: $i] :
( ( ( sk3 @ range_of @ sk11 @ empty )
!= ( A @ empty ) )
| ( A @ relation_like )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[8522]) ).
thf(8524,plain,
( ( sk3 @ range_of @ sk11 @ relation_like )
| ~ ( sk3 @ empty ) ),
inference(pattern_uni,[status(thm)],[8523:[bind(A,$thf( sk3 @ range_of @ sk11 ))]]) ).
thf(9101,plain,
! [A: $i] :
( ( ( sk3 @ range_of @ sk11 @ relation_like )
!= ( A @ relation_like ) )
| ( binary_relation_type @ ( A @ ilf_type ) )
| ~ $true
| ~ ( sk3 @ empty ) ),
inference(paramod_ordered,[status(thm)],[8524,4119]) ).
thf(9102,plain,
! [A: $i] :
( ( ( sk3 @ range_of @ sk11 @ relation_like )
!= ( A @ relation_like ) )
| ( binary_relation_type @ ( A @ ilf_type ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[9101]) ).
thf(9103,plain,
( ( binary_relation_type @ ( sk3 @ range_of @ sk11 @ ilf_type ) )
| ~ ( sk3 @ empty ) ),
inference(pattern_uni,[status(thm)],[9102:[bind(A,$thf( sk3 @ range_of @ sk11 ))]]) ).
thf(411,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( sk3 @ ilf_type ) )
!= ( B @ power_set @ member_type @ ( C @ ilf_type ) ) )
| ( B @ subset_type @ ( C @ ilf_type ) )
| ~ $true
| ( ( A @ subset_type )
!= binary_relation_type ) ),
inference(paramod_ordered,[status(thm)],[333,410]) ).
thf(412,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( sk3 @ ilf_type ) )
!= ( B @ power_set @ member_type @ ( C @ ilf_type ) ) )
| ( B @ subset_type @ ( C @ ilf_type ) )
| ( ( A @ subset_type )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[411]) ).
thf(413,plain,
! [A: $i] :
( ( A @ subset_type @ ( sk3 @ ilf_type ) )
| ( ( A @ subset_type )
!= binary_relation_type ) ),
inference(pattern_uni,[status(thm)],[412:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 ))]]) ).
thf(5524,plain,
! [A: $i] :
( ( ( A @ subset_type @ ( sk3 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ cross_product ) @ subset_type @ ( sk3 @ ilf_type ) ) )
| ~ $true
| ( ( A @ subset_type )
!= binary_relation_type ) ),
inference(paramod_ordered,[status(thm)],[413,5382]) ).
thf(5525,plain,
! [A: $i] :
( ( ( A @ subset_type @ ( sk3 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ cross_product ) @ subset_type @ ( sk3 @ ilf_type ) ) )
| ( ( A @ subset_type )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[5524]) ).
thf(5526,plain,
( ( sk2 @ ( sk1 @ cross_product ) @ subset_type )
!= binary_relation_type ),
inference(pattern_uni,[status(thm)],[5525:[bind(A,$thf( sk2 @ ( sk1 @ cross_product ) ))]]) ).
thf(3196,plain,
! [A: $i] :
( ( ( sk1 @ power_set @ ( sk3 @ domain_of @ member ) )
!= ( sk3 @ range_of @ ( A @ member ) ) )
| ~ ( sk3 @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3170,1394]) ).
thf(3197,plain,
! [A: $i] :
( ( ( sk1 @ power_set @ ( sk3 @ domain_of @ member ) )
!= ( sk3 @ range_of @ ( A @ member ) ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[3196]) ).
thf(3229,plain,
! [A: $i] :
( ( ( sk1 @ power_set )
!= ( sk3 @ range_of ) )
| ( ( sk3 @ domain_of )
!= A )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[3197]) ).
thf(3246,plain,
( ( ( sk1 @ power_set )
!= ( sk3 @ range_of ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[3229]) ).
thf(3470,plain,
( ( ( sk3 @ domain_of @ empty )
!= ( sk3 @ empty ) )
| ( ( sk1 @ power_set )
!= ( sk3 @ range_of ) )
| ~ $true
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[2709,3246]) ).
thf(3471,plain,
( ( ( sk3 @ domain_of @ empty )
!= ( sk3 @ empty ) )
| ( ( sk1 @ power_set )
!= ( sk3 @ range_of ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[3470]) ).
thf(3473,plain,
( ( ( sk3 @ domain_of )
!= sk3 )
| ( ( sk1 @ power_set )
!= ( sk3 @ range_of ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[3471]) ).
thf(1001,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ ( sk3 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[233,284]) ).
thf(1002,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ ( sk3 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1001]) ).
thf(1003,plain,
sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1002:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) ))]]) ).
thf(1114,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1003,278]) ).
thf(1115,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1114]) ).
thf(1116,plain,
sk2 @ ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1115:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ cross_product ) )),bind(B,$thf( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) ))]]) ).
thf(1680,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1116,284]) ).
thf(1681,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1680]) ).
thf(1682,plain,
sk1 @ ( sk2 @ ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1681:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2365,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1323,284]) ).
thf(2366,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2365]) ).
thf(2367,plain,
sk1 @ ( sk2 @ ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2366:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(234,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk11 @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( B @ range_of @ ( B @ domain_of @ cross_product ) @ ( B @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[223,74]) ).
thf(235,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk11 @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( B @ range_of @ ( B @ domain_of @ cross_product ) @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[234]) ).
thf(241,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type )
!= binary_relation_type )
| ( ( A @ sk11 )
!= B )
| ( B @ range_of @ ( B @ domain_of @ cross_product ) @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(243,plain,
! [A: $i] :
( ( ( A @ subset_type )
!= binary_relation_type )
| ( A @ sk11 @ range_of @ ( A @ sk11 @ domain_of @ cross_product ) @ ( A @ sk11 @ subset ) ) ),
inference(simp,[status(thm)],[241]) ).
thf(4046,plain,
! [A: $i] :
( ( ( sk1 @ power_set @ member_type @ ( sk3 @ domain_of @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( A @ relation_like )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4043,3919]) ).
thf(4047,plain,
! [A: $i] :
( ( ( sk1 @ power_set @ member_type @ ( sk3 @ domain_of @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( A @ relation_like ) ),
inference(simp,[status(thm)],[4046]) ).
thf(4067,plain,
! [A: $i] :
( ( ( sk1 @ power_set @ member_type )
!= binary_relation_type )
| ( ( sk3 @ domain_of )
!= A )
| ( A @ relation_like ) ),
inference(simp,[status(thm)],[4047]) ).
thf(4074,plain,
( ( ( sk1 @ power_set @ member_type )
!= binary_relation_type )
| ( sk3 @ domain_of @ relation_like ) ),
inference(simp,[status(thm)],[4067]) ).
thf(5294,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ relation_like )
!= ( A @ relation_like ) )
| ( binary_relation_type @ ( A @ ilf_type ) )
| ~ $true
| ( ( sk1 @ power_set @ member_type )
!= binary_relation_type ) ),
inference(paramod_ordered,[status(thm)],[4074,4119]) ).
thf(5295,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ relation_like )
!= ( A @ relation_like ) )
| ( binary_relation_type @ ( A @ ilf_type ) )
| ( ( sk1 @ power_set @ member_type )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[5294]) ).
thf(5296,plain,
( ( binary_relation_type @ ( sk3 @ domain_of @ ilf_type ) )
| ( ( sk1 @ power_set @ member_type )
!= binary_relation_type ) ),
inference(pattern_uni,[status(thm)],[5295:[bind(A,$thf( sk3 @ domain_of ))]]) ).
thf(8553,plain,
( ( ( sk3 @ range_of @ sk11 @ empty )
!= ( sk10 @ empty ) )
| ( ( sk1 @ power_set )
!= ( sk10 @ range_of ) )
| ~ $true
| ~ ( sk3 @ empty ) ),
inference(paramod_ordered,[status(thm)],[8449,3243]) ).
thf(8554,plain,
( ( ( sk3 @ range_of @ sk11 @ empty )
!= ( sk10 @ empty ) )
| ( ( sk1 @ power_set )
!= ( sk10 @ range_of ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[8553]) ).
thf(8655,plain,
( ( ( sk3 @ range_of @ sk11 )
!= sk10 )
| ( ( sk1 @ power_set )
!= ( sk10 @ range_of ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[8554]) ).
thf(1689,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1116,278]) ).
thf(1690,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1689]) ).
thf(1691,plain,
sk2 @ ( sk2 @ ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1690:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(3221,plain,
! [A: $i] :
( ( ( sk1 @ power_set @ ( sk3 @ domain_of @ member ) )
!= ( sk3 @ domain_of @ ( A @ member ) ) )
| ( sk1 @ ( A @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3170,1912]) ).
thf(3222,plain,
! [A: $i] :
( ( ( sk1 @ power_set @ ( sk3 @ domain_of @ member ) )
!= ( sk3 @ domain_of @ ( A @ member ) ) )
| ( sk1 @ ( A @ member ) ) ),
inference(simp,[status(thm)],[3221]) ).
thf(3227,plain,
! [A: $i] :
( ( ( sk1 @ power_set )
!= ( sk3 @ domain_of ) )
| ( ( sk3 @ domain_of )
!= A )
| ( sk1 @ ( A @ member ) ) ),
inference(simp,[status(thm)],[3222]) ).
thf(3244,plain,
( ( ( sk1 @ power_set )
!= ( sk3 @ domain_of ) )
| ( sk1 @ ( sk3 @ domain_of @ member ) ) ),
inference(simp,[status(thm)],[3227]) ).
thf(7519,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ member ) )
!= ( sk10 @ range_of @ ( A @ member ) ) )
| ~ ( sk10 @ empty )
| ~ $true
| ( ( sk1 @ power_set )
!= ( sk3 @ domain_of ) ) ),
inference(paramod_ordered,[status(thm)],[3244,1404]) ).
thf(7520,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ member ) )
!= ( sk10 @ range_of @ ( A @ member ) ) )
| ~ ( sk10 @ empty )
| ( ( sk1 @ power_set )
!= ( sk3 @ domain_of ) ) ),
inference(simp,[status(thm)],[7519]) ).
thf(7535,plain,
! [A: $i] :
( ( ( sk10 @ range_of )
!= sk1 )
| ( ( sk3 @ domain_of )
!= A )
| ~ ( sk10 @ empty )
| ( ( sk1 @ power_set )
!= ( sk3 @ domain_of ) ) ),
inference(simp,[status(thm)],[7520]) ).
thf(7550,plain,
( ( ( sk10 @ range_of )
!= sk1 )
| ~ ( sk10 @ empty )
| ( ( sk1 @ power_set )
!= ( sk3 @ domain_of ) ) ),
inference(simp,[status(thm)],[7535]) ).
thf(18,axiom,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( set_type @ ( A @ range_of @ ilf_type ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9) ).
thf(85,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( set_type @ ( A @ range_of @ ilf_type ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1092,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[988,284]) ).
thf(1093,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1092]) ).
thf(1094,plain,
sk1 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1093:[bind(A,$thf( sk3 @ domain_of @ ( sk10 @ cross_product ) )),bind(B,$thf( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) ))]]) ).
thf(1641,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1094,284]) ).
thf(1642,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1641]) ).
thf(1643,plain,
sk1 @ ( sk1 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1642:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(3052,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1643,284]) ).
thf(3053,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[3052]) ).
thf(3054,plain,
sk1 @ ( sk1 @ ( sk1 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[3053:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2788,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1027,278]) ).
thf(2789,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2788]) ).
thf(2790,plain,
sk2 @ ( sk1 @ ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2789:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2719,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk5 @ member ) )
!= ( sk3 @ range_of @ ( A @ member ) ) )
| ~ ( sk3 @ empty )
| ~ $true
| ( sk3 @ domain_of @ empty ) ),
inference(paramod_ordered,[status(thm)],[2506,1394]) ).
thf(2720,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk5 @ member ) )
!= ( sk3 @ range_of @ ( A @ member ) ) )
| ~ ( sk3 @ empty )
| ( sk3 @ domain_of @ empty ) ),
inference(simp,[status(thm)],[2719]) ).
thf(2751,plain,
! [A: $i] :
( ( ( sk3 @ range_of )
!= sk1 )
| ( ( sk3 @ domain_of @ sk5 )
!= A )
| ~ ( sk3 @ empty )
| ( sk3 @ domain_of @ empty ) ),
inference(simp,[status(thm)],[2720]) ).
thf(2773,plain,
( ( ( sk3 @ range_of )
!= sk1 )
| ~ ( sk3 @ empty )
| ( sk3 @ domain_of @ empty ) ),
inference(simp,[status(thm)],[2751]) ).
thf(989,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk1 @ ( C @ cross_product ) @ ( sk3 @ domain_of @ ( B @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[208,284]) ).
thf(990,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk1 @ ( C @ cross_product ) @ ( sk3 @ domain_of @ ( B @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[989]) ).
thf(991,plain,
! [A: $i] : ( sk1 @ ( A @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ),
inference(pattern_uni,[status(thm)],[990:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(1127,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk2 @ ( C @ cross_product ) @ ( sk3 @ range_of @ ( B @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[991,278]) ).
thf(1128,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk2 @ ( C @ cross_product ) @ ( sk3 @ range_of @ ( B @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1127]) ).
thf(1129,plain,
! [A: $i] : ( sk2 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ subset ) ),
inference(pattern_uni,[status(thm)],[1128:[bind(A,$thf( G )),bind(B,$thf( sk3 @ domain_of @ ( G @ cross_product ) )),bind(C,$thf( sk1 @ ( G @ cross_product ) ))]]) ).
thf(1133,plain,
! [A: $i] : ( sk2 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ subset ) ),
inference(simp,[status(thm)],[1129]) ).
thf(2006,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk2 @ ( C @ cross_product ) @ ( sk3 @ range_of @ ( B @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1133,278]) ).
thf(2007,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk2 @ ( C @ cross_product ) @ ( sk3 @ range_of @ ( B @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2006]) ).
thf(2008,plain,
! [A: $i] : ( sk2 @ ( sk2 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) ),
inference(pattern_uni,[status(thm)],[2007:[bind(A,$thf( L )),bind(B,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( L @ cross_product ) @ cross_product ) )),bind(C,$thf( sk2 @ ( sk1 @ ( L @ cross_product ) @ cross_product ) ))]]) ).
thf(2011,plain,
! [A: $i] : ( sk2 @ ( sk2 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) ),
inference(simp,[status(thm)],[2008]) ).
thf(3035,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1499,284]) ).
thf(3036,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[3035]) ).
thf(3037,plain,
sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[3036:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( B @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ~ $true
| ~ ( A @ subset_type @ ( B @ ilf_type ) ) ),
inference(paramod_ordered,[status(thm)],[305,34]) ).
thf(315,plain,
! [B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( B @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ~ ( A @ subset_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[314]) ).
thf(327,plain,
! [B: $i,A: $i] :
( ( ( A @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ( B != sk3 )
| ~ ( A @ subset_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[315]) ).
thf(334,plain,
! [A: $i] :
( ( ( A @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ~ ( A @ subset_type @ ( sk3 @ ilf_type ) ) ),
inference(simp,[status(thm)],[327]) ).
thf(1040,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[749,284]) ).
thf(1041,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1040]) ).
thf(1042,plain,
sk1 @ ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1041:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) ))]]) ).
thf(803,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( A @ ( C @ member ) )
!= ( B @ power_set @ ( A @ member ) ) )
| ~ ( B @ empty )
| ~ ( B @ power_set @ ( A @ member ) ) ),
inference(eqfactor_ordered,[status(thm)],[553]) ).
thf(804,plain,
! [A: $i] :
( ~ ( A @ empty )
| ~ ( A @ power_set @ ( A @ power_set @ member ) ) ),
inference(pattern_uni,[status(thm)],[803:[bind(A,$thf( D @ power_set )),bind(B,$thf( D )),bind(C,$thf( D @ power_set ))]]) ).
thf(808,plain,
! [A: $i] :
( ~ ( A @ empty )
| ~ ( A @ power_set @ ( A @ power_set @ member ) ) ),
inference(simp,[status(thm)],[804]) ).
thf(939,plain,
! [B: $i,A: $i] :
( ( ( A @ power_set @ ( A @ member ) )
!= ( B @ power_set @ ( B @ power_set @ member ) ) )
| ~ ( B @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[867,808]) ).
thf(940,plain,
! [B: $i,A: $i] :
( ( ( A @ power_set @ ( A @ member ) )
!= ( B @ power_set @ ( B @ power_set @ member ) ) )
| ~ ( B @ empty ) ),
inference(simp,[status(thm)],[939]) ).
thf(945,plain,
! [B: $i,A: $i] :
( ( ( A @ power_set )
!= ( B @ power_set ) )
| ( A
!= ( B @ power_set ) )
| ~ ( B @ empty ) ),
inference(simp,[status(thm)],[940]) ).
thf(947,plain,
! [A: $i] :
( ( ( A @ power_set @ power_set )
!= ( A @ power_set ) )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[945]) ).
thf(1517,plain,
! [A: $i] :
( ( ( sk3 @ range_of @ empty )
!= ( A @ empty ) )
| ( ( A @ power_set @ power_set )
!= ( A @ power_set ) )
| ~ $true
| ~ ( sk3 @ empty ) ),
inference(paramod_ordered,[status(thm)],[1479,947]) ).
thf(1518,plain,
! [A: $i] :
( ( ( sk3 @ range_of @ empty )
!= ( A @ empty ) )
| ( ( A @ power_set @ power_set )
!= ( A @ power_set ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[1517]) ).
thf(1519,plain,
( ( ( sk3 @ range_of @ power_set @ power_set )
!= ( sk3 @ range_of @ power_set ) )
| ~ ( sk3 @ empty ) ),
inference(pattern_uni,[status(thm)],[1518:[bind(A,$thf( sk3 @ range_of ))]]) ).
thf(8606,plain,
! [A: $i] :
( ( ( sk3 @ range_of @ sk11 @ empty )
!= ( A @ power_set @ empty ) )
| ~ $true
| ~ ( sk3 @ empty ) ),
inference(paramod_ordered,[status(thm)],[8449,194]) ).
thf(8607,plain,
! [A: $i] :
( ( ( sk3 @ range_of @ sk11 @ empty )
!= ( A @ power_set @ empty ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[8606]) ).
thf(8645,plain,
! [A: $i] :
( ( ( sk3 @ range_of @ sk11 )
!= ( A @ power_set ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[8607]) ).
thf(190,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ relation_type ) @ ( A @ ( B @ sk4 ) @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[185,34]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ relation_type ) @ ( A @ ( B @ sk4 ) @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) ),
inference(simp,[status(thm)],[190]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ relation_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ( ( A @ ( B @ sk4 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[191]) ).
thf(2394,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1327,278]) ).
thf(2395,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2394]) ).
thf(2396,plain,
sk2 @ ( sk1 @ ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2395:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(3669,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk5 @ member ) )
!= ( C @ ( B @ member ) ) )
| ( C @ member_type @ ( B @ ilf_type ) )
| ~ $true
| ( C @ empty )
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[218,3623]) ).
thf(3670,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk5 @ member ) )
!= ( C @ ( B @ member ) ) )
| ( C @ member_type @ ( B @ ilf_type ) )
| ( C @ empty )
| ( A @ empty ) ),
inference(simp,[status(thm)],[3669]) ).
thf(3671,plain,
! [A: $i] :
( ( A @ member_type @ ( A @ sk5 @ ilf_type ) )
| ( A @ empty )
| ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[3670:[bind(A,$thf( D )),bind(B,$thf( D @ sk5 )),bind(C,$thf( D ))]]) ).
thf(3682,plain,
! [A: $i] :
( ( A @ member_type @ ( A @ sk5 @ ilf_type ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[3671]) ).
thf(484,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ member_type @ ( A @ sk9 @ ilf_type ) )
!= ( B @ power_set @ member_type @ ( C @ ilf_type ) ) )
| ( B @ subset_type @ ( C @ ilf_type ) )
| ~ $true
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[481,410]) ).
thf(485,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ member_type @ ( A @ sk9 @ ilf_type ) )
!= ( B @ power_set @ member_type @ ( C @ ilf_type ) ) )
| ( B @ subset_type @ ( C @ ilf_type ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[484]) ).
thf(486,plain,
! [A: $i] :
( ( A @ subset_type @ ( A @ power_set @ sk9 @ ilf_type ) )
| ( A @ power_set @ empty ) ),
inference(pattern_uni,[status(thm)],[485:[bind(A,$thf( E @ power_set )),bind(B,$thf( E )),bind(C,$thf( E @ power_set @ sk9 ))]]) ).
thf(497,plain,
! [A: $i] :
( ( A @ subset_type @ ( A @ power_set @ sk9 @ ilf_type ) )
| ( A @ power_set @ empty ) ),
inference(simp,[status(thm)],[486]) ).
thf(588,plain,
! [A: $i] :
( ( A @ subset_type @ ( A @ power_set @ sk9 @ ilf_type ) )
| $false ),
inference(rewrite,[status(thm)],[497,194]) ).
thf(589,plain,
! [A: $i] : ( A @ subset_type @ ( A @ power_set @ sk9 @ ilf_type ) ),
inference(simp,[status(thm)],[588]) ).
thf(598,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ power_set @ sk9 @ ilf_type ) )
!= ( B @ subset_type @ ( C @ ilf_type ) ) )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[589,305]) ).
thf(599,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ power_set @ sk9 @ ilf_type ) )
!= ( B @ subset_type @ ( C @ ilf_type ) ) )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[598]) ).
thf(600,plain,
! [A: $i] : ( A @ power_set @ member_type @ ( A @ power_set @ sk9 @ ilf_type ) ),
inference(pattern_uni,[status(thm)],[599:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ power_set @ sk9 ))]]) ).
thf(605,plain,
! [A: $i] : ( A @ power_set @ member_type @ ( A @ power_set @ sk9 @ ilf_type ) ),
inference(simp,[status(thm)],[600]) ).
thf(3302,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( A @ power_set @ sk9 @ ilf_type ) )
!= ( C @ member_type @ ( B @ ilf_type ) ) )
| ( C @ ( B @ member ) )
| ~ $true
| ( C @ empty ) ),
inference(paramod_ordered,[status(thm)],[605,3250]) ).
thf(3303,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( A @ power_set @ sk9 @ ilf_type ) )
!= ( C @ member_type @ ( B @ ilf_type ) ) )
| ( C @ ( B @ member ) )
| ( C @ empty ) ),
inference(simp,[status(thm)],[3302]) ).
thf(3304,plain,
! [A: $i] :
( ( A @ power_set @ ( A @ power_set @ sk9 @ member ) )
| ( A @ power_set @ empty ) ),
inference(pattern_uni,[status(thm)],[3303:[bind(A,$thf( F )),bind(B,$thf( F @ power_set @ sk9 )),bind(C,$thf( F @ power_set ))]]) ).
thf(3385,plain,
! [A: $i] :
( ( A @ power_set @ ( A @ power_set @ sk9 @ member ) )
| ( A @ power_set @ empty ) ),
inference(simp,[status(thm)],[3304]) ).
thf(9733,plain,
! [A: $i] :
( ( A @ power_set @ ( A @ power_set @ sk9 @ member ) )
| $false ),
inference(rewrite,[status(thm)],[3385,194]) ).
thf(9734,plain,
! [A: $i] : ( A @ power_set @ ( A @ power_set @ sk9 @ member ) ),
inference(simp,[status(thm)],[9733]) ).
thf(1134,plain,
! [A: $i] :
( ( ( A @ power_set )
!= A )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[947]) ).
thf(2953,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ empty )
!= ( A @ empty ) )
| ( ( A @ power_set )
!= A )
| ~ $true
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[2709,1134]) ).
thf(2954,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ empty )
!= ( A @ empty ) )
| ( ( A @ power_set )
!= A )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[2953]) ).
thf(2955,plain,
( ( ( sk3 @ domain_of @ power_set )
!= ( sk3 @ domain_of ) )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[2954:[bind(A,$thf( sk3 @ domain_of ))]]) ).
thf(3086,plain,
( ( ( sk3 @ range_of @ empty )
!= ( sk1 @ empty ) )
| ( ( sk3 @ domain_of @ power_set )
!= ( sk3 @ domain_of ) )
| ~ $true
| ~ ( sk3 @ empty ) ),
inference(paramod_ordered,[status(thm)],[1479,2955]) ).
thf(3087,plain,
( ( ( sk3 @ range_of @ empty )
!= ( sk1 @ empty ) )
| ( ( sk3 @ domain_of @ power_set )
!= ( sk3 @ domain_of ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[3086]) ).
thf(3090,plain,
( ( ( sk3 @ range_of )
!= sk1 )
| ( ( sk3 @ domain_of @ power_set )
!= ( sk3 @ domain_of ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[3087]) ).
thf(4153,plain,
! [A: $i] :
( ( ( sk3 @ range_of @ relation_like )
!= ( A @ relation_like ) )
| ( binary_relation_type @ ( A @ ilf_type ) )
| ~ $true
| ~ ( sk3 @ empty ) ),
inference(paramod_ordered,[status(thm)],[1467,4119]) ).
thf(4154,plain,
! [A: $i] :
( ( ( sk3 @ range_of @ relation_like )
!= ( A @ relation_like ) )
| ( binary_relation_type @ ( A @ ilf_type ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[4153]) ).
thf(4155,plain,
( ( binary_relation_type @ ( sk3 @ range_of @ ilf_type ) )
| ~ ( sk3 @ empty ) ),
inference(pattern_uni,[status(thm)],[4154:[bind(A,$thf( sk3 @ range_of ))]]) ).
thf(757,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[676,278]) ).
thf(758,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[757]) ).
thf(759,plain,
sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[758:[bind(A,$thf( sk3 @ range_of @ ( sk10 @ cross_product ) )),bind(B,$thf( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) ))]]) ).
thf(902,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[759,278]) ).
thf(903,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[902]) ).
thf(904,plain,
sk2 @ ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[903:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2607,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[904,278]) ).
thf(2608,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2607]) ).
thf(2609,plain,
sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2608:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(1157,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1021,278]) ).
thf(1158,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1157]) ).
thf(1159,plain,
sk2 @ ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1158:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) ))]]) ).
thf(1654,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1103,284]) ).
thf(1655,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1654]) ).
thf(1656,plain,
sk1 @ ( sk2 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1655:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(1170,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1066,278]) ).
thf(1171,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1170]) ).
thf(1172,plain,
sk2 @ ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1171:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) ))]]) ).
thf(2343,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1172,278]) ).
thf(2344,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2343]) ).
thf(2345,plain,
sk2 @ ( sk2 @ ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2344:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2226,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1150,278]) ).
thf(2227,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2226]) ).
thf(2228,plain,
sk2 @ ( sk1 @ ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2227:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(4061,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ power_set @ member_type @ ( sk3 @ domain_of @ ilf_type ) )
!= ( A @ power_set @ member_type @ ( B @ ilf_type ) ) )
| ( A @ subset_type @ ( B @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4043,410]) ).
thf(4062,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ power_set @ member_type @ ( sk3 @ domain_of @ ilf_type ) )
!= ( A @ power_set @ member_type @ ( B @ ilf_type ) ) )
| ( A @ subset_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[4061]) ).
thf(4063,plain,
sk1 @ subset_type @ ( sk3 @ domain_of @ ilf_type ),
inference(pattern_uni,[status(thm)],[4062:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ domain_of ))]]) ).
thf(2209,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1146,278]) ).
thf(2210,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2209]) ).
thf(2211,plain,
sk2 @ ( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2210:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2243,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1159,278]) ).
thf(2244,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2243]) ).
thf(2245,plain,
sk2 @ ( sk2 @ ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2244:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(3464,plain,
( ( ( sk3 @ domain_of @ empty )
!= ( sk10 @ empty ) )
| ( ( sk1 @ power_set )
!= ( sk10 @ range_of ) )
| ~ $true
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[2709,3243]) ).
thf(3465,plain,
( ( ( sk3 @ domain_of @ empty )
!= ( sk10 @ empty ) )
| ( ( sk1 @ power_set )
!= ( sk10 @ range_of ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[3464]) ).
thf(3467,plain,
( ( ( sk3 @ domain_of )
!= sk10 )
| ( ( sk1 @ power_set )
!= ( sk10 @ range_of ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[3465]) ).
thf(2839,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1362,278]) ).
thf(2840,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2839]) ).
thf(2841,plain,
sk2 @ ( sk2 @ ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2840:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( A @ subset_type @ ( B @ ilf_type ) ) )
| ( A @ power_set @ member_type @ ( B @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[80,305]) ).
thf(320,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( A @ subset_type @ ( B @ ilf_type ) ) )
| ( A @ power_set @ member_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[319]) ).
thf(323,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type )
!= binary_relation_type )
| ( sk10 != B )
| ( A @ power_set @ member_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[320]) ).
thf(330,plain,
! [A: $i] :
( ( ( A @ subset_type )
!= binary_relation_type )
| ( A @ power_set @ member_type @ ( sk10 @ ilf_type ) ) ),
inference(simp,[status(thm)],[323]) ).
thf(418,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( sk10 @ ilf_type ) )
!= ( B @ power_set @ member_type @ ( C @ ilf_type ) ) )
| ( B @ subset_type @ ( C @ ilf_type ) )
| ~ $true
| ( ( A @ subset_type )
!= binary_relation_type ) ),
inference(paramod_ordered,[status(thm)],[330,410]) ).
thf(419,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ power_set @ member_type @ ( sk10 @ ilf_type ) )
!= ( B @ power_set @ member_type @ ( C @ ilf_type ) ) )
| ( B @ subset_type @ ( C @ ilf_type ) )
| ( ( A @ subset_type )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[418]) ).
thf(420,plain,
! [A: $i] :
( ( A @ subset_type @ ( sk10 @ ilf_type ) )
| ( ( A @ subset_type )
!= binary_relation_type ) ),
inference(pattern_uni,[status(thm)],[419:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk10 ))]]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ range_of @ ( B @ member ) )
| ~ ( A @ ( B @ ( C @ ordered_pair ) @ member ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[55]) ).
thf(1540,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ range_of @ ( B @ member ) )
| ~ ( A @ ( B @ ( C @ ordered_pair ) @ member ) )
| ~ $true
| ~ $true
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(rewrite,[status(thm)],[58,111]) ).
thf(1541,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ range_of @ ( B @ member ) )
| ~ ( A @ ( B @ ( C @ ordered_pair ) @ member ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(simp,[status(thm)],[1540]) ).
thf(8528,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ range_of @ sk11 @ empty )
!= ( A @ empty ) )
| ~ ( A @ ( B @ member ) )
| ~ $true
| ~ ( sk3 @ empty ) ),
inference(paramod_ordered,[status(thm)],[8449,202]) ).
thf(8529,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ range_of @ sk11 @ empty )
!= ( A @ empty ) )
| ~ ( A @ ( B @ member ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[8528]) ).
thf(8530,plain,
! [A: $i] :
( ~ ( sk3 @ range_of @ sk11 @ ( A @ member ) )
| ~ ( sk3 @ empty ) ),
inference(pattern_uni,[status(thm)],[8529:[bind(A,$thf( sk3 @ range_of @ sk11 )),bind(B,$thf( B ))]]) ).
thf(8690,plain,
! [A: $i] :
( ~ ( sk3 @ range_of @ sk11 @ ( A @ member ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[8530]) ).
thf(10279,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ sk5 @ member ) )
!= ( sk3 @ range_of @ sk11 @ ( B @ member ) ) )
| ~ $true
| ~ ( sk3 @ empty )
| ( A @ sk11 @ empty ) ),
inference(paramod_ordered,[status(thm)],[7004,8690]) ).
thf(10280,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ sk5 @ member ) )
!= ( sk3 @ range_of @ sk11 @ ( B @ member ) ) )
| ~ ( sk3 @ empty )
| ( A @ sk11 @ empty ) ),
inference(simp,[status(thm)],[10279]) ).
thf(10281,plain,
( ~ ( sk3 @ empty )
| ( sk3 @ range_of @ sk11 @ sk11 @ empty ) ),
inference(pattern_uni,[status(thm)],[10280:[bind(A,$thf( sk3 @ range_of @ sk11 )),bind(B,$thf( sk3 @ range_of @ sk11 @ sk11 @ sk5 ))]]) ).
thf(1522,plain,
! [A: $i] :
( ( ( sk3 @ range_of @ empty )
!= ( A @ empty ) )
| ( ( A @ power_set )
!= A )
| ~ $true
| ~ ( sk3 @ empty ) ),
inference(paramod_ordered,[status(thm)],[1479,1134]) ).
thf(1523,plain,
! [A: $i] :
( ( ( sk3 @ range_of @ empty )
!= ( A @ empty ) )
| ( ( A @ power_set )
!= A )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[1522]) ).
thf(1524,plain,
( ( ( sk3 @ range_of @ power_set )
!= ( sk3 @ range_of ) )
| ~ ( sk3 @ empty ) ),
inference(pattern_uni,[status(thm)],[1523:[bind(A,$thf( sk3 @ range_of ))]]) ).
thf(2949,plain,
( ( ( sk3 @ domain_of @ empty )
!= ( sk3 @ empty ) )
| ( ( sk3 @ range_of @ power_set )
!= ( sk3 @ range_of ) )
| ~ $true
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[2709,1524]) ).
thf(2950,plain,
( ( ( sk3 @ domain_of @ empty )
!= ( sk3 @ empty ) )
| ( ( sk3 @ range_of @ power_set )
!= ( sk3 @ range_of ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[2949]) ).
thf(2973,plain,
( ( ( sk3 @ domain_of )
!= sk3 )
| ( ( sk3 @ range_of @ power_set )
!= ( sk3 @ range_of ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[2950]) ).
thf(5547,plain,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( sk2 @ ( sk1 @ cross_product ) @ subset_type @ ( sk3 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,5382]) ).
thf(5548,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
!= ( sk2 @ ( sk1 @ cross_product ) @ subset_type @ ( sk3 @ ilf_type ) ) ),
inference(simp,[status(thm)],[5547]) ).
thf(5570,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ cross_product ) @ subset_type )
!= set_type )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[5548]) ).
thf(5577,plain,
( ( sk2 @ ( sk1 @ cross_product ) @ subset_type )
!= set_type ),
inference(simp,[status(thm)],[5570]) ).
thf(1016,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk1 @ ( C @ cross_product ) @ ( sk3 @ domain_of @ ( B @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[682,284]) ).
thf(1017,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk1 @ ( C @ cross_product ) @ ( sk3 @ domain_of @ ( B @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1016]) ).
thf(1018,plain,
! [A: $i] : ( sk1 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ subset ) ),
inference(pattern_uni,[status(thm)],[1017:[bind(A,$thf( G )),bind(B,$thf( sk3 @ range_of @ ( G @ cross_product ) )),bind(C,$thf( sk2 @ ( G @ cross_product ) ))]]) ).
thf(1062,plain,
! [A: $i] : ( sk1 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ subset ) ),
inference(simp,[status(thm)],[1018]) ).
thf(1954,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk1 @ ( C @ cross_product ) @ ( sk3 @ domain_of @ ( B @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1062,284]) ).
thf(1955,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk1 @ ( C @ cross_product ) @ ( sk3 @ domain_of @ ( B @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1954]) ).
thf(1956,plain,
! [A: $i] : ( sk1 @ ( sk1 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) ),
inference(pattern_uni,[status(thm)],[1955:[bind(A,$thf( L )),bind(B,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( L @ cross_product ) @ cross_product ) )),bind(C,$thf( sk1 @ ( sk2 @ ( L @ cross_product ) @ cross_product ) ))]]) ).
thf(1970,plain,
! [A: $i] : ( sk1 @ ( sk1 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) ),
inference(simp,[status(thm)],[1956]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) )
| ~ ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[104]) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) )
| ~ ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(5644,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) )
| ~ ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[107,111]) ).
thf(5645,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) )
| ~ ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[5644]) ).
thf(5656,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ relation_type ) @ ( A @ ( B @ sk4 ) @ ilf_type ) )
!= ( D @ ( C @ relation_type ) @ ( E @ ilf_type ) ) )
| ( D @ ( C @ cross_product ) @ subset_type @ ( E @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[185,5645]) ).
thf(5657,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ relation_type ) @ ( A @ ( B @ sk4 ) @ ilf_type ) )
!= ( D @ ( C @ relation_type ) @ ( E @ ilf_type ) ) )
| ( D @ ( C @ cross_product ) @ subset_type @ ( E @ ilf_type ) ) ),
inference(simp,[status(thm)],[5656]) ).
thf(5658,plain,
! [B: $i,A: $i] : ( B @ ( A @ cross_product ) @ subset_type @ ( B @ ( A @ sk4 ) @ ilf_type ) ),
inference(pattern_uni,[status(thm)],[5657:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( G @ ( F @ sk4 ) ))]]) ).
thf(5790,plain,
! [B: $i,A: $i] : ( B @ ( A @ cross_product ) @ subset_type @ ( B @ ( A @ sk4 ) @ ilf_type ) ),
inference(simp,[status(thm)],[5658]) ).
thf(5884,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cross_product ) @ subset_type @ ( B @ ( A @ sk4 ) @ ilf_type ) )
!= ( D @ ( C @ cross_product ) @ subset_type @ ( E @ ilf_type ) ) )
| ( E @ relation_like )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5790,5099]) ).
thf(5885,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cross_product ) @ subset_type @ ( B @ ( A @ sk4 ) @ ilf_type ) )
!= ( D @ ( C @ cross_product ) @ subset_type @ ( E @ ilf_type ) ) )
| ( E @ relation_like ) ),
inference(simp,[status(thm)],[5884]) ).
thf(5886,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk4 ) @ relation_like ),
inference(pattern_uni,[status(thm)],[5885:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( G @ ( F @ sk4 ) ))]]) ).
thf(5919,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk4 ) @ relation_like ),
inference(simp,[status(thm)],[5886]) ).
thf(1488,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1054,284]) ).
thf(1489,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1488]) ).
thf(1490,plain,
sk1 @ ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1489:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(3030,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1490,278]) ).
thf(3031,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[3030]) ).
thf(3032,plain,
sk2 @ ( sk1 @ ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[3031:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(380,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk11 @ ilf_type ) )
!= ( B @ subset_type @ ( sk3 @ ilf_type ) ) )
| ( ( B @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[223,334]) ).
thf(381,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk11 @ ilf_type ) )
!= ( B @ subset_type @ ( sk3 @ ilf_type ) ) )
| ( ( B @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) ) ),
inference(simp,[status(thm)],[380]) ).
thf(393,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type )
!= ( B @ subset_type ) )
| ( ( A @ sk11 )
!= sk3 )
| ( ( B @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) ) ),
inference(simp,[status(thm)],[381]) ).
thf(1501,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ range_of @ empty )
!= ( A @ empty ) )
| ~ $true
| ~ ( A @ power_set @ ( B @ power_set @ member ) )
| ~ ( sk3 @ empty ) ),
inference(paramod_ordered,[status(thm)],[1479,892]) ).
thf(1502,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ range_of @ empty )
!= ( A @ empty ) )
| ~ ( A @ power_set @ ( B @ power_set @ member ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[1501]) ).
thf(1503,plain,
! [A: $i] :
( ~ ( sk3 @ range_of @ power_set @ ( A @ power_set @ member ) )
| ~ ( sk3 @ empty ) ),
inference(pattern_uni,[status(thm)],[1502:[bind(A,$thf( sk3 @ range_of )),bind(B,$thf( B ))]]) ).
thf(1539,plain,
! [A: $i] :
( ~ ( sk3 @ range_of @ power_set @ ( A @ power_set @ member ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[1503]) ).
thf(362,plain,
! [A: $i] :
( ( ( A @ power_set @ member_type @ ( sk3 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ~ $true
| ( ( A @ subset_type )
!= binary_relation_type ) ),
inference(paramod_ordered,[status(thm)],[333,34]) ).
thf(363,plain,
! [A: $i] :
( ( ( A @ power_set @ member_type @ ( sk3 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ( ( A @ subset_type )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[362]) ).
thf(367,plain,
! [A: $i] :
( ( ( A @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ( sk3 != sk3 )
| ( ( A @ subset_type )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[363]) ).
thf(371,plain,
! [A: $i] :
( ( ( A @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ( ( A @ subset_type )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[367]) ).
thf(982,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[824,278]) ).
thf(983,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[982]) ).
thf(984,plain,
sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[983:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(3257,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ member_type @ ( A @ sk9 @ ilf_type ) )
!= ( C @ member_type @ ( B @ ilf_type ) ) )
| ( C @ ( B @ member ) )
| ~ $true
| ( C @ empty )
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[481,3250]) ).
thf(3258,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ member_type @ ( A @ sk9 @ ilf_type ) )
!= ( C @ member_type @ ( B @ ilf_type ) ) )
| ( C @ ( B @ member ) )
| ( C @ empty )
| ( A @ empty ) ),
inference(simp,[status(thm)],[3257]) ).
thf(3259,plain,
! [A: $i] :
( ( A @ ( A @ sk9 @ member ) )
| ( A @ empty )
| ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[3258:[bind(A,$thf( D )),bind(B,$thf( D @ sk9 )),bind(C,$thf( D ))]]) ).
thf(3390,plain,
! [A: $i] :
( ( A @ ( A @ sk9 @ member ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[3259]) ).
thf(1118,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk1 @ ( C @ cross_product ) @ ( sk3 @ domain_of @ ( B @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[991,284]) ).
thf(1119,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk1 @ ( C @ cross_product ) @ ( sk3 @ domain_of @ ( B @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1118]) ).
thf(1120,plain,
! [A: $i] : ( sk1 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ subset ) ),
inference(pattern_uni,[status(thm)],[1119:[bind(A,$thf( G )),bind(B,$thf( sk3 @ domain_of @ ( G @ cross_product ) )),bind(C,$thf( sk1 @ ( G @ cross_product ) ))]]) ).
thf(1130,plain,
! [A: $i] : ( sk1 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ subset ) ),
inference(simp,[status(thm)],[1120]) ).
thf(1974,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk1 @ ( C @ cross_product ) @ ( sk3 @ domain_of @ ( B @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1130,284]) ).
thf(1975,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk1 @ ( C @ cross_product ) @ ( sk3 @ domain_of @ ( B @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1974]) ).
thf(1976,plain,
! [A: $i] : ( sk1 @ ( sk1 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) ),
inference(pattern_uni,[status(thm)],[1975:[bind(A,$thf( L )),bind(B,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( L @ cross_product ) @ cross_product ) )),bind(C,$thf( sk1 @ ( sk1 @ ( L @ cross_product ) @ cross_product ) ))]]) ).
thf(1991,plain,
! [A: $i] : ( sk1 @ ( sk1 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) ),
inference(simp,[status(thm)],[1976]) ).
thf(227,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ relation_type ) @ ( A @ ( B @ sk4 ) @ ilf_type ) )
!= ( binary_relation_type @ ( C @ ilf_type ) ) )
| ( C @ range_of @ ( C @ domain_of @ cross_product ) @ ( C @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[185,74]) ).
thf(228,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ relation_type ) @ ( A @ ( B @ sk4 ) @ ilf_type ) )
!= ( binary_relation_type @ ( C @ ilf_type ) ) )
| ( C @ range_of @ ( C @ domain_of @ cross_product ) @ ( C @ subset ) ) ),
inference(simp,[status(thm)],[227]) ).
thf(239,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ relation_type ) )
!= binary_relation_type )
| ( ( A @ ( B @ sk4 ) )
!= C )
| ( C @ range_of @ ( C @ domain_of @ cross_product ) @ ( C @ subset ) ) ),
inference(simp,[status(thm)],[228]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ relation_type ) )
!= binary_relation_type )
| ( A @ ( B @ sk4 ) @ range_of @ ( A @ ( B @ sk4 ) @ domain_of @ cross_product ) @ ( A @ ( B @ sk4 ) @ subset ) ) ),
inference(simp,[status(thm)],[239]) ).
thf(2961,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ empty )
!= ( A @ empty ) )
| ~ $true
| ~ ( A @ power_set @ ( A @ power_set @ member ) )
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[2709,808]) ).
thf(2962,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ empty )
!= ( A @ empty ) )
| ~ ( A @ power_set @ ( A @ power_set @ member ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[2961]) ).
thf(2963,plain,
( ~ ( sk3 @ domain_of @ power_set @ ( sk3 @ domain_of @ power_set @ member ) )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[2962:[bind(A,$thf( sk3 @ domain_of ))]]) ).
thf(5893,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cross_product ) @ subset_type @ ( B @ ( A @ sk4 ) @ ilf_type ) )
!= ( C @ subset_type @ ( D @ ilf_type ) ) )
| ( C @ power_set @ member_type @ ( D @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5790,305]) ).
thf(5894,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cross_product ) @ subset_type @ ( B @ ( A @ sk4 ) @ ilf_type ) )
!= ( C @ subset_type @ ( D @ ilf_type ) ) )
| ( C @ power_set @ member_type @ ( D @ ilf_type ) ) ),
inference(simp,[status(thm)],[5893]) ).
thf(5895,plain,
! [B: $i,A: $i] : ( B @ ( A @ cross_product ) @ power_set @ member_type @ ( B @ ( A @ sk4 ) @ ilf_type ) ),
inference(pattern_uni,[status(thm)],[5894:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( H @ ( G @ cross_product ) )),bind(D,$thf( H @ ( G @ sk4 ) ))]]) ).
thf(5909,plain,
! [B: $i,A: $i] : ( B @ ( A @ cross_product ) @ power_set @ member_type @ ( B @ ( A @ sk4 ) @ ilf_type ) ),
inference(simp,[status(thm)],[5895]) ).
thf(4129,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ relation_like )
!= ( A @ relation_like ) )
| ( binary_relation_type @ ( A @ ilf_type ) )
| ~ $true
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[2635,4119]) ).
thf(4130,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ relation_like )
!= ( A @ relation_like ) )
| ( binary_relation_type @ ( A @ ilf_type ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[4129]) ).
thf(4131,plain,
( ( binary_relation_type @ ( sk3 @ domain_of @ ilf_type ) )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[4130:[bind(A,$thf( sk3 @ domain_of ))]]) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ relation_like )
| ( ( A @ sk14 )
!= ( C @ ( B @ ordered_pair ) ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[113]) ).
thf(120,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ relation_like )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) )
| ( ( A @ sk14 )
!= ( C @ ( B @ ordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[115]) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ relation_like )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) )
| ( ( A @ sk14 )
!= ( C @ ( B @ ordered_pair ) ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(6823,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ relation_like )
| ~ $true
| ~ $true
| ~ $true
| ( ( A @ sk14 )
!= ( C @ ( B @ ordered_pair ) ) ) ),
inference(rewrite,[status(thm)],[121,111]) ).
thf(6824,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ relation_like )
| ( ( A @ sk14 )
!= ( C @ ( B @ ordered_pair ) ) ) ),
inference(simp,[status(thm)],[6823]) ).
thf(596,plain,
! [A: $i] :
( ( ( A @ subset_type @ ( A @ power_set @ sk9 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[589,34]) ).
thf(597,plain,
! [A: $i] :
( ( A @ subset_type @ ( A @ power_set @ sk9 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) ),
inference(simp,[status(thm)],[596]) ).
thf(601,plain,
! [A: $i] :
( ( ( A @ subset_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ( ( A @ power_set @ sk9 )
!= sk3 ) ),
inference(simp,[status(thm)],[597]) ).
thf(4082,plain,
! [A: $i] :
( ( ( sk1 @ subset_type @ ( sk3 @ domain_of @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( A @ relation_like )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4063,3919]) ).
thf(4083,plain,
! [A: $i] :
( ( ( sk1 @ subset_type @ ( sk3 @ domain_of @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( A @ relation_like ) ),
inference(simp,[status(thm)],[4082]) ).
thf(4109,plain,
! [A: $i] :
( ( ( sk1 @ subset_type )
!= binary_relation_type )
| ( ( sk3 @ domain_of )
!= A )
| ( A @ relation_like ) ),
inference(simp,[status(thm)],[4083]) ).
thf(4116,plain,
( ( ( sk1 @ subset_type )
!= binary_relation_type )
| ( sk3 @ domain_of @ relation_like ) ),
inference(simp,[status(thm)],[4109]) ).
thf(1471,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk6 ) @ member ) )
!= ( sk3 @ range_of @ ( C @ member ) ) )
| ~ ( sk3 @ empty )
| ~ $true
| ( B @ power_set @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[710,1394]) ).
thf(1472,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk6 ) @ member ) )
!= ( sk3 @ range_of @ ( C @ member ) ) )
| ~ ( sk3 @ empty )
| ( B @ power_set @ ( A @ member ) ) ),
inference(simp,[status(thm)],[1471]) ).
thf(1473,plain,
! [A: $i] :
( ~ ( sk3 @ empty )
| ( A @ power_set @ ( sk3 @ range_of @ member ) ) ),
inference(pattern_uni,[status(thm)],[1472:[bind(A,$thf( sk3 @ range_of )),bind(B,$thf( D )),bind(C,$thf( sk3 @ range_of @ ( D @ sk6 ) ))]]) ).
thf(1483,plain,
! [A: $i] :
( ~ ( sk3 @ empty )
| ( A @ power_set @ ( sk3 @ range_of @ member ) ) ),
inference(simp,[status(thm)],[1473]) ).
thf(2026,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1042,278]) ).
thf(2027,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2026]) ).
thf(2028,plain,
sk2 @ ( sk1 @ ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2027:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(3521,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk9 @ member ) )
!= ( sk3 @ domain_of @ ( B @ member ) ) )
| ( sk1 @ ( B @ member ) )
| ~ $true
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[3390,1912]) ).
thf(3522,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk9 @ member ) )
!= ( sk3 @ domain_of @ ( B @ member ) ) )
| ( sk1 @ ( B @ member ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[3521]) ).
thf(3523,plain,
( ( sk1 @ ( sk3 @ domain_of @ sk9 @ member ) )
| ( sk3 @ domain_of @ empty ) ),
inference(pattern_uni,[status(thm)],[3522:[bind(A,$thf( sk3 @ domain_of )),bind(B,$thf( sk3 @ domain_of @ sk9 ))]]) ).
thf(5920,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk4 ) @ relation_like )
!= ( C @ relation_like ) )
| ( binary_relation_type @ ( C @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5919,4119]) ).
thf(5921,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk4 ) @ relation_like )
!= ( C @ relation_like ) )
| ( binary_relation_type @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[5920]) ).
thf(5922,plain,
! [B: $i,A: $i] : ( binary_relation_type @ ( B @ ( A @ sk4 ) @ ilf_type ) ),
inference(pattern_uni,[status(thm)],[5921:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ sk4 ) ))]]) ).
thf(5923,plain,
! [B: $i,A: $i] : ( binary_relation_type @ ( B @ ( A @ sk4 ) @ ilf_type ) ),
inference(simp,[status(thm)],[5922]) ).
thf(2014,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1042,284]) ).
thf(2015,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2014]) ).
thf(2016,plain,
sk1 @ ( sk1 @ ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2015:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(1650,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1094,278]) ).
thf(1651,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1650]) ).
thf(1652,plain,
sk2 @ ( sk1 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1651:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(3943,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( A @ relation_like )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[80,3919]) ).
thf(3944,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( A @ relation_like ) ),
inference(simp,[status(thm)],[3943]) ).
thf(3945,plain,
sk10 @ relation_like,
inference(pattern_uni,[status(thm)],[3944:[bind(A,$thf( sk10 ))]]) ).
thf(12,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( set_type @ ( B @ ( A @ cross_product ) @ ilf_type ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).
thf(71,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)],[12]) ).
thf(1105,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1003,284]) ).
thf(1106,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1105]) ).
thf(1107,plain,
sk1 @ ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1106:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ cross_product ) )),bind(B,$thf( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) ))]]) ).
thf(1667,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1107,284]) ).
thf(1668,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1667]) ).
thf(1669,plain,
sk1 @ ( sk1 @ ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1668:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(5394,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk11 @ ilf_type ) )
!= ( C @ ( B @ cross_product ) @ subset_type @ ( D @ ilf_type ) ) )
| ( C @ ( B @ relation_type ) @ ( D @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[223,5337]) ).
thf(5395,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk11 @ ilf_type ) )
!= ( C @ ( B @ cross_product ) @ subset_type @ ( D @ ilf_type ) ) )
| ( C @ ( B @ relation_type ) @ ( D @ ilf_type ) ) ),
inference(simp,[status(thm)],[5394]) ).
thf(5396,plain,
! [B: $i,A: $i] : ( B @ ( A @ relation_type ) @ ( B @ ( A @ cross_product ) @ sk11 @ ilf_type ) ),
inference(pattern_uni,[status(thm)],[5395:[bind(A,$thf( G @ ( F @ cross_product ) )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( G @ ( F @ cross_product ) @ sk11 ))]]) ).
thf(5471,plain,
! [B: $i,A: $i] : ( B @ ( A @ relation_type ) @ ( B @ ( A @ cross_product ) @ sk11 @ ilf_type ) ),
inference(simp,[status(thm)],[5396]) ).
thf(7430,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ ilf_type ) )
!= ( C @ ( B @ cross_product ) @ subset_type @ ( D @ ilf_type ) ) )
| ( D @ relation_like )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7380,5099]) ).
thf(7431,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ ilf_type ) )
!= ( C @ ( B @ cross_product ) @ subset_type @ ( D @ ilf_type ) ) )
| ( D @ relation_like ) ),
inference(simp,[status(thm)],[7430]) ).
thf(7432,plain,
! [B: $i,A: $i] : ( B @ ( A @ cross_product ) @ relation_like ),
inference(pattern_uni,[status(thm)],[7431:[bind(A,$thf( F @ ( E @ cross_product ) )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ cross_product ) ))]]) ).
thf(7455,plain,
! [B: $i,A: $i] : ( B @ ( A @ cross_product ) @ relation_like ),
inference(simp,[status(thm)],[7432]) ).
thf(3660,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ ( A @ sk8 ) @ member ) )
!= ( C @ ( B @ member ) ) )
| ( C @ member_type @ ( B @ ilf_type ) )
| ~ $true
| ( C @ empty )
| ( A @ ( sk3 @ domain_of @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[2513,3623]) ).
thf(3661,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ ( A @ sk8 ) @ member ) )
!= ( C @ ( B @ member ) ) )
| ( C @ member_type @ ( B @ ilf_type ) )
| ( C @ empty )
| ( A @ ( sk3 @ domain_of @ subset ) ) ),
inference(simp,[status(thm)],[3660]) ).
thf(3662,plain,
! [A: $i] :
( ( sk1 @ member_type @ ( sk3 @ domain_of @ ( A @ sk8 ) @ ilf_type ) )
| ( sk1 @ empty )
| ( A @ ( sk3 @ domain_of @ subset ) ) ),
inference(pattern_uni,[status(thm)],[3661:[bind(A,$thf( D )),bind(B,$thf( sk3 @ domain_of @ ( D @ sk8 ) )),bind(C,$thf( sk1 ))]]) ).
thf(3678,plain,
! [A: $i] :
( ( sk1 @ member_type @ ( sk3 @ domain_of @ ( A @ sk8 ) @ ilf_type ) )
| ( sk1 @ empty )
| ( A @ ( sk3 @ domain_of @ subset ) ) ),
inference(simp,[status(thm)],[3662]) ).
thf(3760,plain,
( ( ( sk3 @ range_of @ empty )
!= ( sk1 @ empty ) )
| ( ( sk1 @ power_set )
!= ( sk3 @ domain_of ) )
| ~ $true
| ~ ( sk3 @ empty ) ),
inference(paramod_ordered,[status(thm)],[1479,3617]) ).
thf(3761,plain,
( ( ( sk3 @ range_of @ empty )
!= ( sk1 @ empty ) )
| ( ( sk1 @ power_set )
!= ( sk3 @ domain_of ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[3760]) ).
thf(3764,plain,
( ( ( sk3 @ range_of )
!= sk1 )
| ( ( sk1 @ power_set )
!= ( sk3 @ domain_of ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[3761]) ).
thf(1046,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[759,284]) ).
thf(1047,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1046]) ).
thf(1048,plain,
sk1 @ ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1047:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(3064,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1643,278]) ).
thf(3065,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[3064]) ).
thf(3066,plain,
sk2 @ ( sk1 @ ( sk1 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[3065:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk1 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(4092,plain,
( ( ( sk1 @ subset_type @ ( sk3 @ domain_of @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4063,34]) ).
thf(4093,plain,
( ( sk1 @ subset_type @ ( sk3 @ domain_of @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) ),
inference(simp,[status(thm)],[4092]) ).
thf(4107,plain,
( ( ( sk2 @ ( sk1 @ relation_type ) )
!= ( sk1 @ subset_type ) )
| ( ( sk3 @ domain_of )
!= sk3 ) ),
inference(simp,[status(thm)],[4093]) ).
thf(1966,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk2 @ ( C @ cross_product ) @ ( sk3 @ range_of @ ( B @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1062,278]) ).
thf(1967,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk2 @ ( C @ cross_product ) @ ( sk3 @ range_of @ ( B @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1966]) ).
thf(1968,plain,
! [A: $i] : ( sk2 @ ( sk1 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) ),
inference(pattern_uni,[status(thm)],[1967:[bind(A,$thf( L )),bind(B,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( L @ cross_product ) @ cross_product ) )),bind(C,$thf( sk1 @ ( sk2 @ ( L @ cross_product ) @ cross_product ) ))]]) ).
thf(1969,plain,
! [A: $i] : ( sk2 @ ( sk1 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) ),
inference(simp,[status(thm)],[1968]) ).
thf(1351,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1030,284]) ).
thf(1352,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1351]) ).
thf(1353,plain,
sk1 @ ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1352:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2822,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1353,278]) ).
thf(2823,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2822]) ).
thf(2824,plain,
sk2 @ ( sk1 @ ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2823:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2180,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1137,284]) ).
thf(2181,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2180]) ).
thf(2182,plain,
sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2181:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2810,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1353,284]) ).
thf(2811,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2810]) ).
thf(2812,plain,
sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2811:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(340,plain,
! [A: $i] :
( ( ( A @ power_set @ member_type @ ( A @ sk11 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[337,34]) ).
thf(341,plain,
! [A: $i] :
( ( A @ power_set @ member_type @ ( A @ sk11 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) ),
inference(simp,[status(thm)],[340]) ).
thf(345,plain,
! [A: $i] :
( ( ( A @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ( ( A @ sk11 )
!= sk3 ) ),
inference(simp,[status(thm)],[341]) ).
thf(2109,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1045,278]) ).
thf(2110,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2109]) ).
thf(2111,plain,
sk2 @ ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2110:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(5138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ power_set @ sk9 @ ilf_type ) )
!= ( C @ ( B @ cross_product ) @ subset_type @ ( D @ ilf_type ) ) )
| ( D @ relation_like )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[589,5099]) ).
thf(5139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ power_set @ sk9 @ ilf_type ) )
!= ( C @ ( B @ cross_product ) @ subset_type @ ( D @ ilf_type ) ) )
| ( D @ relation_like ) ),
inference(simp,[status(thm)],[5138]) ).
thf(5140,plain,
! [B: $i,A: $i] : ( B @ ( A @ cross_product ) @ power_set @ sk9 @ relation_like ),
inference(pattern_uni,[status(thm)],[5139:[bind(A,$thf( H @ ( G @ cross_product ) )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( H @ ( G @ cross_product ) @ power_set @ sk9 ))]]) ).
thf(5175,plain,
! [B: $i,A: $i] : ( B @ ( A @ cross_product ) @ power_set @ sk9 @ relation_like ),
inference(simp,[status(thm)],[5140]) ).
thf(134,plain,
( ( ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) )
!= ( binary_relation_type @ ( sk3 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32,34]) ).
thf(135,plain,
( ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) )
!= ( binary_relation_type @ ( sk3 @ ilf_type ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(139,plain,
( ( ( sk2 @ ( sk1 @ relation_type ) )
!= binary_relation_type )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[135]) ).
thf(140,plain,
( ( sk2 @ ( sk1 @ relation_type ) )
!= binary_relation_type ),
inference(simp,[status(thm)],[139]) ).
thf(1334,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1081,278]) ).
thf(1335,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1334]) ).
thf(1336,plain,
sk2 @ ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1335:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) ))]]) ).
thf(2444,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1336,284]) ).
thf(2445,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2444]) ).
thf(2446,plain,
sk1 @ ( sk2 @ ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2445:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(617,plain,
! [A: $i] :
( ( ( A @ power_set @ member_type @ ( A @ power_set @ sk9 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[605,34]) ).
thf(618,plain,
! [A: $i] :
( ( A @ power_set @ member_type @ ( A @ power_set @ sk9 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) ),
inference(simp,[status(thm)],[617]) ).
thf(621,plain,
! [A: $i] :
( ( ( A @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ( ( A @ power_set @ sk9 )
!= sk3 ) ),
inference(simp,[status(thm)],[618]) ).
thf(2739,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk5 @ member ) )
!= ( sk10 @ range_of @ ( A @ member ) ) )
| ~ ( sk10 @ empty )
| ~ $true
| ( sk3 @ domain_of @ empty ) ),
inference(paramod_ordered,[status(thm)],[2506,1404]) ).
thf(2740,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk5 @ member ) )
!= ( sk10 @ range_of @ ( A @ member ) ) )
| ~ ( sk10 @ empty )
| ( sk3 @ domain_of @ empty ) ),
inference(simp,[status(thm)],[2739]) ).
thf(2746,plain,
! [A: $i] :
( ( ( sk10 @ range_of )
!= sk1 )
| ( ( sk3 @ domain_of @ sk5 )
!= A )
| ~ ( sk10 @ empty )
| ( sk3 @ domain_of @ empty ) ),
inference(simp,[status(thm)],[2740]) ).
thf(2770,plain,
( ( ( sk10 @ range_of )
!= sk1 )
| ~ ( sk10 @ empty )
| ( sk3 @ domain_of @ empty ) ),
inference(simp,[status(thm)],[2746]) ).
thf(6042,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ empty )
!= ( A @ empty ) )
| ( ( A @ power_set )
!= A )
| ~ $true
| ( ( sk10 @ range_of )
!= sk1 )
| ~ ( sk10 @ empty ) ),
inference(paramod_ordered,[status(thm)],[2770,1134]) ).
thf(6043,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ empty )
!= ( A @ empty ) )
| ( ( A @ power_set )
!= A )
| ( ( sk10 @ range_of )
!= sk1 )
| ~ ( sk10 @ empty ) ),
inference(simp,[status(thm)],[6042]) ).
thf(6044,plain,
( ( ( sk3 @ domain_of @ power_set )
!= ( sk3 @ domain_of ) )
| ( ( sk10 @ range_of )
!= sk1 )
| ~ ( sk10 @ empty ) ),
inference(pattern_uni,[status(thm)],[6043:[bind(A,$thf( sk3 @ domain_of ))]]) ).
thf(25,axiom,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
& ( A @ empty ) )
=> ( A @ relation_like ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25) ).
thf(108,plain,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
& ( A @ empty ) )
=> ( A @ relation_like ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1312,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1075,284]) ).
thf(1313,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1312]) ).
thf(1314,plain,
sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1313:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) ))]]) ).
thf(2348,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1314,284]) ).
thf(2349,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2348]) ).
thf(2350,plain,
sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2349:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(8774,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ sk11 @ empty )
!= ( A @ empty ) )
| ( ( A @ power_set )
!= A )
| ~ $true
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[8483,1134]) ).
thf(8775,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ sk11 @ empty )
!= ( A @ empty ) )
| ( ( A @ power_set )
!= A )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[8774]) ).
thf(8776,plain,
( ( ( sk3 @ domain_of @ sk11 @ power_set )
!= ( sk3 @ domain_of @ sk11 ) )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[8775:[bind(A,$thf( sk3 @ domain_of @ sk11 ))]]) ).
thf(5512,plain,
( ( ( sk1 @ subset_type @ ( sk3 @ domain_of @ ilf_type ) )
!= ( sk2 @ ( sk1 @ cross_product ) @ subset_type @ ( sk3 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4063,5382]) ).
thf(5513,plain,
( ( sk1 @ subset_type @ ( sk3 @ domain_of @ ilf_type ) )
!= ( sk2 @ ( sk1 @ cross_product ) @ subset_type @ ( sk3 @ ilf_type ) ) ),
inference(simp,[status(thm)],[5512]) ).
thf(5569,plain,
( ( ( sk2 @ ( sk1 @ cross_product ) @ subset_type )
!= ( sk1 @ subset_type ) )
| ( ( sk3 @ domain_of )
!= sk3 ) ),
inference(simp,[status(thm)],[5513]) ).
thf(6223,plain,
( ( ( sk2 @ ( sk1 @ cross_product ) )
!= sk1 )
| ( ( sk3 @ domain_of )
!= sk3 ) ),
inference(simp,[status(thm)],[5569]) ).
thf(2590,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1349,278]) ).
thf(2591,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2590]) ).
thf(2592,plain,
sk2 @ ( sk2 @ ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2591:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ subset ) )
| ~ ( C @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[93]) ).
thf(4303,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ subset ) )
| ~ ( C @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) )
| ~ $true
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[94,111]) ).
thf(4304,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ subset ) )
| ~ ( C @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[4303]) ).
thf(224,plain,
! [A: $i] :
( ( ( A @ subset_type @ ( A @ sk11 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[223,34]) ).
thf(225,plain,
! [A: $i] :
( ( A @ subset_type @ ( A @ sk11 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(226,plain,
! [A: $i] :
( ( ( A @ subset_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ( ( A @ sk11 )
!= sk3 ) ),
inference(simp,[status(thm)],[225]) ).
thf(8486,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ sk5 @ member ) )
!= ( sk3 @ domain_of @ ( B @ member ) ) )
| ( sk1 @ ( B @ member ) )
| ~ $true
| ( A @ sk11 @ empty ) ),
inference(paramod_ordered,[status(thm)],[7004,1912]) ).
thf(8487,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ sk5 @ member ) )
!= ( sk3 @ domain_of @ ( B @ member ) ) )
| ( sk1 @ ( B @ member ) )
| ( A @ sk11 @ empty ) ),
inference(simp,[status(thm)],[8486]) ).
thf(8488,plain,
( ( sk1 @ ( sk3 @ domain_of @ sk11 @ sk5 @ member ) )
| ( sk3 @ domain_of @ sk11 @ empty ) ),
inference(pattern_uni,[status(thm)],[8487:[bind(A,$thf( sk3 @ domain_of )),bind(B,$thf( sk3 @ domain_of @ sk11 @ sk5 ))]]) ).
thf(9052,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk11 @ sk5 @ member ) )
!= ( B @ ( A @ member ) ) )
| ( B @ member_type @ ( A @ ilf_type ) )
| ~ $true
| ( B @ empty )
| ( sk3 @ domain_of @ sk11 @ empty ) ),
inference(paramod_ordered,[status(thm)],[8488,3623]) ).
thf(9053,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk11 @ sk5 @ member ) )
!= ( B @ ( A @ member ) ) )
| ( B @ member_type @ ( A @ ilf_type ) )
| ( B @ empty )
| ( sk3 @ domain_of @ sk11 @ empty ) ),
inference(simp,[status(thm)],[9052]) ).
thf(9054,plain,
( ( sk1 @ member_type @ ( sk3 @ domain_of @ sk11 @ sk5 @ ilf_type ) )
| ( sk1 @ empty )
| ( sk3 @ domain_of @ sk11 @ empty ) ),
inference(pattern_uni,[status(thm)],[9053:[bind(A,$thf( sk3 @ domain_of @ sk11 @ sk5 )),bind(B,$thf( sk1 ))]]) ).
thf(912,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[769,278]) ).
thf(913,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[912]) ).
thf(914,plain,
sk2 @ ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[913:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2612,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[914,284]) ).
thf(2613,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2612]) ).
thf(2614,plain,
sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2613:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(3934,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk3 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( A @ relation_like )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32,3919]) ).
thf(3935,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk3 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( A @ relation_like ) ),
inference(simp,[status(thm)],[3934]) ).
thf(3936,plain,
sk3 @ relation_like,
inference(pattern_uni,[status(thm)],[3935:[bind(A,$thf( sk3 ))]]) ).
thf(922,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk2 @ ( C @ cross_product ) @ ( sk3 @ range_of @ ( B @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[835,278]) ).
thf(923,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk2 @ ( C @ cross_product ) @ ( sk3 @ range_of @ ( B @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[922]) ).
thf(924,plain,
! [A: $i] : ( sk2 @ ( sk2 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) ),
inference(pattern_uni,[status(thm)],[923:[bind(A,$thf( L )),bind(B,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( L @ cross_product ) @ cross_product ) )),bind(C,$thf( sk2 @ ( sk2 @ ( L @ cross_product ) @ cross_product ) ))]]) ).
thf(927,plain,
! [A: $i] : ( sk2 @ ( sk2 @ ( sk2 @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) ),
inference(simp,[status(thm)],[924]) ).
thf(2331,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1172,284]) ).
thf(2332,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2331]) ).
thf(2333,plain,
sk1 @ ( sk2 @ ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2332:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2595,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[904,284]) ).
thf(2596,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2595]) ).
thf(2597,plain,
sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2596:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(7425,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ ilf_type ) )
!= ( C @ ( B @ cross_product ) @ subset_type @ ( D @ ilf_type ) ) )
| ( C @ ( B @ relation_type ) @ ( D @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7380,5337]) ).
thf(7426,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ ilf_type ) )
!= ( C @ ( B @ cross_product ) @ subset_type @ ( D @ ilf_type ) ) )
| ( C @ ( B @ relation_type ) @ ( D @ ilf_type ) ) ),
inference(simp,[status(thm)],[7425]) ).
thf(7427,plain,
! [B: $i,A: $i] : ( B @ ( A @ relation_type ) @ ( B @ ( A @ cross_product ) @ ilf_type ) ),
inference(pattern_uni,[status(thm)],[7426:[bind(A,$thf( F @ ( E @ cross_product ) )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ cross_product ) ))]]) ).
thf(7454,plain,
! [B: $i,A: $i] : ( B @ ( A @ relation_type ) @ ( B @ ( A @ cross_product ) @ ilf_type ) ),
inference(simp,[status(thm)],[7427]) ).
thf(1986,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk2 @ ( C @ cross_product ) @ ( sk3 @ range_of @ ( B @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1130,278]) ).
thf(1987,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk2 @ ( C @ cross_product ) @ ( sk3 @ range_of @ ( B @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1986]) ).
thf(1988,plain,
! [A: $i] : ( sk2 @ ( sk1 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) ),
inference(pattern_uni,[status(thm)],[1987:[bind(A,$thf( L )),bind(B,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( L @ cross_product ) @ cross_product ) )),bind(C,$thf( sk1 @ ( sk1 @ ( L @ cross_product ) @ cross_product ) ))]]) ).
thf(1990,plain,
! [A: $i] : ( sk2 @ ( sk1 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) ),
inference(simp,[status(thm)],[1988]) ).
thf(507,plain,
! [A: $i] :
( ( ( A @ subset_type @ ( sk3 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ~ $true
| ( ( A @ power_set @ member_type )
!= binary_relation_type ) ),
inference(paramod_ordered,[status(thm)],[439,34]) ).
thf(508,plain,
! [A: $i] :
( ( ( A @ subset_type @ ( sk3 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ( ( A @ power_set @ member_type )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[507]) ).
thf(513,plain,
! [A: $i] :
( ( ( A @ subset_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ( sk3 != sk3 )
| ( ( A @ power_set @ member_type )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[508]) ).
thf(516,plain,
! [A: $i] :
( ( ( A @ subset_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ( ( A @ power_set @ member_type )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[513]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ ( B @ sk13 ) @ ( A @ ( B @ sk12 ) @ ordered_pair ) ) )
| ~ ( A @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( A @ relation_like )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[113]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( A @ relation_like )
| ~ ( set_type @ ( A @ ilf_type ) )
| ( ( A @ ( B @ sk13 ) @ ( A @ ( B @ sk12 ) @ ordered_pair ) )
= B ) ),
inference(lifteq,[status(thm)],[116]) ).
thf(7121,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ $true
| ~ ( A @ relation_like )
| ~ $true
| ( ( A @ ( B @ sk13 ) @ ( A @ ( B @ sk12 ) @ ordered_pair ) )
= B ) ),
inference(rewrite,[status(thm)],[122,111]) ).
thf(7122,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ ( A @ relation_like )
| ( ( A @ ( B @ sk13 ) @ ( A @ ( B @ sk12 ) @ ordered_pair ) )
= B ) ),
inference(simp,[status(thm)],[7121]) ).
thf(423,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( A @ power_set @ member_type @ ( B @ ilf_type ) ) )
| ( A @ subset_type @ ( B @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[80,410]) ).
thf(424,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( A @ power_set @ member_type @ ( B @ ilf_type ) ) )
| ( A @ subset_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[423]) ).
thf(435,plain,
! [B: $i,A: $i] :
( ( ( A @ power_set @ member_type )
!= binary_relation_type )
| ( sk10 != B )
| ( A @ subset_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[424]) ).
thf(441,plain,
! [A: $i] :
( ( ( A @ power_set @ member_type )
!= binary_relation_type )
| ( A @ subset_type @ ( sk10 @ ilf_type ) ) ),
inference(simp,[status(thm)],[435]) ).
thf(578,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( sk10 @ ilf_type ) )
!= ( B @ subset_type @ ( C @ ilf_type ) ) )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) )
| ~ $true
| ( ( A @ power_set @ member_type )
!= binary_relation_type ) ),
inference(paramod_ordered,[status(thm)],[441,305]) ).
thf(579,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( sk10 @ ilf_type ) )
!= ( B @ subset_type @ ( C @ ilf_type ) ) )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) )
| ( ( A @ power_set @ member_type )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[578]) ).
thf(580,plain,
! [A: $i] :
( ( A @ power_set @ member_type @ ( sk10 @ ilf_type ) )
| ( ( A @ power_set @ member_type )
!= binary_relation_type ) ),
inference(pattern_uni,[status(thm)],[579:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk10 ))]]) ).
thf(1994,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk1 @ ( C @ cross_product ) @ ( sk3 @ domain_of @ ( B @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1133,284]) ).
thf(1995,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( sk1 @ ( C @ cross_product ) @ ( sk3 @ domain_of @ ( B @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1994]) ).
thf(1996,plain,
! [A: $i] : ( sk1 @ ( sk2 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) ),
inference(pattern_uni,[status(thm)],[1995:[bind(A,$thf( L )),bind(B,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( L @ cross_product ) @ cross_product ) )),bind(C,$thf( sk2 @ ( sk1 @ ( L @ cross_product ) @ cross_product ) ))]]) ).
thf(2012,plain,
! [A: $i] : ( sk1 @ ( sk2 @ ( sk1 @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( A @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) ),
inference(simp,[status(thm)],[1996]) ).
thf(3657,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk5 @ member ) )
!= ( B @ ( A @ member ) ) )
| ( B @ member_type @ ( A @ ilf_type ) )
| ~ $true
| ( B @ empty )
| ( sk3 @ domain_of @ empty ) ),
inference(paramod_ordered,[status(thm)],[2506,3623]) ).
thf(3658,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk5 @ member ) )
!= ( B @ ( A @ member ) ) )
| ( B @ member_type @ ( A @ ilf_type ) )
| ( B @ empty )
| ( sk3 @ domain_of @ empty ) ),
inference(simp,[status(thm)],[3657]) ).
thf(3659,plain,
( ( sk1 @ member_type @ ( sk3 @ domain_of @ sk5 @ ilf_type ) )
| ( sk1 @ empty )
| ( sk3 @ domain_of @ empty ) ),
inference(pattern_uni,[status(thm)],[3658:[bind(A,$thf( sk3 @ domain_of @ sk5 )),bind(B,$thf( sk1 ))]]) ).
thf(2665,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk14 @ member ) )
!= ( sk10 @ range_of @ ( A @ member ) ) )
| ~ ( sk10 @ empty )
| ~ $true
| ( sk3 @ domain_of @ relation_like ) ),
inference(paramod_ordered,[status(thm)],[2486,1404]) ).
thf(2666,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk14 @ member ) )
!= ( sk10 @ range_of @ ( A @ member ) ) )
| ~ ( sk10 @ empty )
| ( sk3 @ domain_of @ relation_like ) ),
inference(simp,[status(thm)],[2665]) ).
thf(2673,plain,
! [A: $i] :
( ( ( sk10 @ range_of )
!= sk1 )
| ( ( sk3 @ domain_of @ sk14 )
!= A )
| ~ ( sk10 @ empty )
| ( sk3 @ domain_of @ relation_like ) ),
inference(simp,[status(thm)],[2666]) ).
thf(2689,plain,
( ( ( sk10 @ range_of )
!= sk1 )
| ~ ( sk10 @ empty )
| ( sk3 @ domain_of @ relation_like ) ),
inference(simp,[status(thm)],[2673]) ).
thf(2645,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk14 @ member ) )
!= ( sk3 @ range_of @ ( A @ member ) ) )
| ~ ( sk3 @ empty )
| ~ $true
| ( sk3 @ domain_of @ relation_like ) ),
inference(paramod_ordered,[status(thm)],[2486,1394]) ).
thf(2646,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk14 @ member ) )
!= ( sk3 @ range_of @ ( A @ member ) ) )
| ~ ( sk3 @ empty )
| ( sk3 @ domain_of @ relation_like ) ),
inference(simp,[status(thm)],[2645]) ).
thf(2672,plain,
! [A: $i] :
( ( ( sk3 @ range_of )
!= sk1 )
| ( ( sk3 @ domain_of @ sk14 )
!= A )
| ~ ( sk3 @ empty )
| ( sk3 @ domain_of @ relation_like ) ),
inference(simp,[status(thm)],[2646]) ).
thf(2688,plain,
( ( ( sk3 @ range_of )
!= sk1 )
| ~ ( sk3 @ empty )
| ( sk3 @ domain_of @ relation_like ) ),
inference(simp,[status(thm)],[2672]) ).
thf(5497,plain,
( ( ( sk1 @ power_set @ member_type @ ( sk3 @ domain_of @ ilf_type ) )
!= ( sk2 @ ( sk1 @ cross_product ) @ subset_type @ ( sk3 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4043,5382]) ).
thf(5498,plain,
( ( sk1 @ power_set @ member_type @ ( sk3 @ domain_of @ ilf_type ) )
!= ( sk2 @ ( sk1 @ cross_product ) @ subset_type @ ( sk3 @ ilf_type ) ) ),
inference(simp,[status(thm)],[5497]) ).
thf(5555,plain,
( ( ( sk1 @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ cross_product ) @ subset_type ) )
| ( ( sk3 @ domain_of )
!= sk3 ) ),
inference(simp,[status(thm)],[5498]) ).
thf(8727,plain,
( ( ( sk3 @ domain_of @ sk11 @ empty )
!= ( sk10 @ empty ) )
| ( ( sk1 @ power_set )
!= ( sk10 @ range_of ) )
| ~ $true
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[8483,3243]) ).
thf(8728,plain,
( ( ( sk3 @ domain_of @ sk11 @ empty )
!= ( sk10 @ empty ) )
| ( ( sk1 @ power_set )
!= ( sk10 @ range_of ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[8727]) ).
thf(8845,plain,
( ( ( sk3 @ domain_of @ sk11 )
!= sk10 )
| ( ( sk1 @ power_set )
!= ( sk10 @ range_of ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[8728]) ).
thf(5200,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cross_product ) @ power_set @ sk9 @ relation_like )
!= ( C @ relation_like ) )
| ( binary_relation_type @ ( C @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5175,4119]) ).
thf(5201,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cross_product ) @ power_set @ sk9 @ relation_like )
!= ( C @ relation_like ) )
| ( binary_relation_type @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[5200]) ).
thf(5202,plain,
! [B: $i,A: $i] : ( binary_relation_type @ ( B @ ( A @ cross_product ) @ power_set @ sk9 @ ilf_type ) ),
inference(pattern_uni,[status(thm)],[5201:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G @ ( F @ cross_product ) @ power_set @ sk9 ))]]) ).
thf(5203,plain,
! [B: $i,A: $i] : ( binary_relation_type @ ( B @ ( A @ cross_product ) @ power_set @ sk9 @ ilf_type ) ),
inference(simp,[status(thm)],[5202]) ).
thf(2946,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ empty )
!= ( A @ empty ) )
| ( ( A @ power_set @ power_set )
!= ( A @ power_set ) )
| ~ $true
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[2709,947]) ).
thf(2947,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ empty )
!= ( A @ empty ) )
| ( ( A @ power_set @ power_set )
!= ( A @ power_set ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[2946]) ).
thf(2948,plain,
( ( ( sk3 @ domain_of @ power_set @ power_set )
!= ( sk3 @ domain_of @ power_set ) )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[2947:[bind(A,$thf( sk3 @ domain_of ))]]) ).
thf(7435,plain,
! [A: $i] :
( ( ( A @ subset_type @ ( A @ ilf_type ) )
!= ( sk2 @ ( sk1 @ cross_product ) @ subset_type @ ( sk3 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7380,5382]) ).
thf(7436,plain,
! [A: $i] :
( ( A @ subset_type @ ( A @ ilf_type ) )
!= ( sk2 @ ( sk1 @ cross_product ) @ subset_type @ ( sk3 @ ilf_type ) ) ),
inference(simp,[status(thm)],[7435]) ).
thf(7445,plain,
! [A: $i] :
( ( ( A @ subset_type )
!= ( sk2 @ ( sk1 @ cross_product ) @ subset_type ) )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[7436]) ).
thf(7457,plain,
( ( sk2 @ ( sk1 @ cross_product ) @ subset_type )
!= ( sk3 @ subset_type ) ),
inference(simp,[status(thm)],[7445]) ).
thf(7466,plain,
( ( sk2 @ ( sk1 @ cross_product ) )
!= sk3 ),
inference(simp,[status(thm)],[7457]) ).
thf(2377,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1323,278]) ).
thf(2378,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2377]) ).
thf(2379,plain,
sk2 @ ( sk2 @ ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2378:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(8600,plain,
! [A: $i] :
( ( ( sk3 @ range_of @ sk11 @ empty )
!= ( A @ empty ) )
| ( ( A @ power_set )
!= A )
| ~ $true
| ~ ( sk3 @ empty ) ),
inference(paramod_ordered,[status(thm)],[8449,1134]) ).
thf(8601,plain,
! [A: $i] :
( ( ( sk3 @ range_of @ sk11 @ empty )
!= ( A @ empty ) )
| ( ( A @ power_set )
!= A )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[8600]) ).
thf(8602,plain,
( ( ( sk3 @ range_of @ sk11 @ power_set )
!= ( sk3 @ range_of @ sk11 ) )
| ~ ( sk3 @ empty ) ),
inference(pattern_uni,[status(thm)],[8601:[bind(A,$thf( sk3 @ range_of @ sk11 ))]]) ).
thf(5399,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ power_set @ sk9 @ ilf_type ) )
!= ( C @ ( B @ cross_product ) @ subset_type @ ( D @ ilf_type ) ) )
| ( C @ ( B @ relation_type ) @ ( D @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[589,5337]) ).
thf(5400,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ power_set @ sk9 @ ilf_type ) )
!= ( C @ ( B @ cross_product ) @ subset_type @ ( D @ ilf_type ) ) )
| ( C @ ( B @ relation_type ) @ ( D @ ilf_type ) ) ),
inference(simp,[status(thm)],[5399]) ).
thf(5401,plain,
! [B: $i,A: $i] : ( B @ ( A @ relation_type ) @ ( B @ ( A @ cross_product ) @ power_set @ sk9 @ ilf_type ) ),
inference(pattern_uni,[status(thm)],[5400:[bind(A,$thf( H @ ( G @ cross_product ) )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( H @ ( G @ cross_product ) @ power_set @ sk9 ))]]) ).
thf(5472,plain,
! [B: $i,A: $i] : ( B @ ( A @ relation_type ) @ ( B @ ( A @ cross_product ) @ power_set @ sk9 @ ilf_type ) ),
inference(simp,[status(thm)],[5401]) ).
thf(2805,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1048,278]) ).
thf(2806,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2805]) ).
thf(2807,plain,
sk2 @ ( sk1 @ ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2806:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2456,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1336,278]) ).
thf(2457,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2456]) ).
thf(2458,plain,
sk2 @ ( sk2 @ ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2457:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2624,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[914,278]) ).
thf(2625,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2624]) ).
thf(2626,plain,
sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2625:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk2 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2192,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1137,278]) ).
thf(2193,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2192]) ).
thf(2194,plain,
sk2 @ ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2193:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(3663,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk14 @ member ) )
!= ( B @ ( A @ member ) ) )
| ( B @ member_type @ ( A @ ilf_type ) )
| ~ $true
| ( B @ empty )
| ( sk3 @ domain_of @ relation_like ) ),
inference(paramod_ordered,[status(thm)],[2486,3623]) ).
thf(3664,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk14 @ member ) )
!= ( B @ ( A @ member ) ) )
| ( B @ member_type @ ( A @ ilf_type ) )
| ( B @ empty )
| ( sk3 @ domain_of @ relation_like ) ),
inference(simp,[status(thm)],[3663]) ).
thf(3665,plain,
( ( sk1 @ member_type @ ( sk3 @ domain_of @ sk14 @ ilf_type ) )
| ( sk1 @ empty )
| ( sk3 @ domain_of @ relation_like ) ),
inference(pattern_uni,[status(thm)],[3664:[bind(A,$thf( sk3 @ domain_of @ sk14 )),bind(B,$thf( sk1 ))]]) ).
thf(2284,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk8 ) @ member ) )
!= ( sk3 @ range_of @ ( C @ member ) ) )
| ~ ( sk3 @ empty )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[2266,1394]) ).
thf(2285,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk8 ) @ member ) )
!= ( sk3 @ range_of @ ( C @ member ) ) )
| ~ ( sk3 @ empty )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[2284]) ).
thf(2286,plain,
! [A: $i] :
( ~ ( sk3 @ empty )
| ( A @ ( sk3 @ range_of @ subset ) ) ),
inference(pattern_uni,[status(thm)],[2285:[bind(A,$thf( sk3 @ range_of )),bind(B,$thf( D )),bind(C,$thf( sk3 @ range_of @ ( D @ sk8 ) ))]]) ).
thf(2325,plain,
! [A: $i] :
( ~ ( sk3 @ empty )
| ( A @ ( sk3 @ range_of @ subset ) ) ),
inference(simp,[status(thm)],[2286]) ).
thf(386,plain,
! [B: $i,A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( B @ subset_type @ ( sk3 @ ilf_type ) ) )
| ( ( B @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,334]) ).
thf(387,plain,
! [B: $i,A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( B @ subset_type @ ( sk3 @ ilf_type ) ) )
| ( ( B @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) ) ),
inference(simp,[status(thm)],[386]) ).
thf(396,plain,
! [B: $i,A: $i] :
( ( ( B @ subset_type )
!= set_type )
| ( A != sk3 )
| ( ( B @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) ) ),
inference(simp,[status(thm)],[387]) ).
thf(401,plain,
! [A: $i] :
( ( ( A @ subset_type )
!= set_type )
| ( ( A @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) ) ),
inference(simp,[status(thm)],[396]) ).
thf(2260,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1163,278]) ).
thf(2261,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2260]) ).
thf(2262,plain,
sk2 @ ( sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2261:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(4259,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ relation_like )
!= ( A @ relation_like ) )
| ( binary_relation_type @ ( A @ ilf_type ) )
| ~ $true
| ( ( sk1 @ subset_type )
!= binary_relation_type ) ),
inference(paramod_ordered,[status(thm)],[4116,4119]) ).
thf(4260,plain,
! [A: $i] :
( ( ( sk3 @ domain_of @ relation_like )
!= ( A @ relation_like ) )
| ( binary_relation_type @ ( A @ ilf_type ) )
| ( ( sk1 @ subset_type )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[4259]) ).
thf(4261,plain,
( ( binary_relation_type @ ( sk3 @ domain_of @ ilf_type ) )
| ( ( sk1 @ subset_type )
!= binary_relation_type ) ),
inference(pattern_uni,[status(thm)],[4260:[bind(A,$thf( sk3 @ domain_of ))]]) ).
thf(8539,plain,
( ( ( sk3 @ range_of @ sk11 @ empty )
!= ( sk1 @ empty ) )
| ( ( sk1 @ power_set )
!= ( sk3 @ domain_of ) )
| ~ $true
| ~ ( sk3 @ empty ) ),
inference(paramod_ordered,[status(thm)],[8449,3617]) ).
thf(8540,plain,
( ( ( sk3 @ range_of @ sk11 @ empty )
!= ( sk1 @ empty ) )
| ( ( sk1 @ power_set )
!= ( sk3 @ domain_of ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[8539]) ).
thf(8638,plain,
( ( ( sk3 @ range_of @ sk11 )
!= sk1 )
| ( ( sk1 @ power_set )
!= ( sk3 @ domain_of ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[8540]) ).
thf(7376,plain,
! [A: $i] :
( ( ( A @ power_set @ member_type @ ( A @ ilf_type ) )
!= ( sk2 @ ( sk1 @ cross_product ) @ subset_type @ ( sk3 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7354,5382]) ).
thf(7377,plain,
! [A: $i] :
( ( A @ power_set @ member_type @ ( A @ ilf_type ) )
!= ( sk2 @ ( sk1 @ cross_product ) @ subset_type @ ( sk3 @ ilf_type ) ) ),
inference(simp,[status(thm)],[7376]) ).
thf(7394,plain,
! [A: $i] :
( ( ( A @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ cross_product ) @ subset_type ) )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[7377]) ).
thf(7399,plain,
( ( sk3 @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ cross_product ) @ subset_type ) ),
inference(simp,[status(thm)],[7394]) ).
thf(2360,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1314,278]) ).
thf(2361,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2360]) ).
thf(2362,plain,
sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2361:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(7370,plain,
! [A: $i] :
( ( ( A @ power_set @ member_type @ ( A @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7354,34]) ).
thf(7371,plain,
! [A: $i] :
( ( A @ power_set @ member_type @ ( A @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) ),
inference(simp,[status(thm)],[7370]) ).
thf(7388,plain,
! [A: $i] :
( ( ( A @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[7371]) ).
thf(7406,plain,
( ( sk2 @ ( sk1 @ relation_type ) )
!= ( sk3 @ power_set @ member_type ) ),
inference(simp,[status(thm)],[7388]) ).
thf(14,axiom,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( set_type @ ( A @ domain_of @ ilf_type ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
thf(75,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( set_type @ ( A @ domain_of @ ilf_type ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(2382,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1327,284]) ).
thf(2383,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2382]) ).
thf(2384,plain,
sk1 @ ( sk1 @ ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2383:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2087,plain,
! [B: $i,A: $i] :
( ( ( A @ power_set @ ( A @ member ) )
!= ( sk10 @ range_of @ ( B @ member ) ) )
| ~ ( sk10 @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[867,1404]) ).
thf(2088,plain,
! [B: $i,A: $i] :
( ( ( A @ power_set @ ( A @ member ) )
!= ( sk10 @ range_of @ ( B @ member ) ) )
| ~ ( sk10 @ empty ) ),
inference(simp,[status(thm)],[2087]) ).
thf(2089,plain,
! [B: $i,A: $i] :
( ( ( A @ power_set )
!= ( sk10 @ range_of ) )
| ( A != B )
| ~ ( sk10 @ empty ) ),
inference(simp,[status(thm)],[2088]) ).
thf(2095,plain,
! [A: $i] :
( ( ( A @ power_set )
!= ( sk10 @ range_of ) )
| ~ ( sk10 @ empty ) ),
inference(simp,[status(thm)],[2089]) ).
thf(1676,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1107,278]) ).
thf(1677,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1676]) ).
thf(1678,plain,
sk2 @ ( sk1 @ ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1677:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(2231,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1159,284]) ).
thf(2232,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2231]) ).
thf(2233,plain,
sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2232:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk1 @ ( sk2 @ ( sk2 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(3107,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ ( A @ sk6 ) @ member ) )
!= ( B @ ( C @ member ) ) )
| ~ $true
| ~ ( B @ empty )
| ( A @ power_set @ ( sk3 @ domain_of @ member ) ) ),
inference(paramod_ordered,[status(thm)],[2515,202]) ).
thf(3108,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ ( A @ sk6 ) @ member ) )
!= ( B @ ( C @ member ) ) )
| ~ ( B @ empty )
| ( A @ power_set @ ( sk3 @ domain_of @ member ) ) ),
inference(simp,[status(thm)],[3107]) ).
thf(3109,plain,
! [A: $i] :
( ~ ( sk1 @ empty )
| ( A @ power_set @ ( sk3 @ domain_of @ member ) ) ),
inference(pattern_uni,[status(thm)],[3108:[bind(A,$thf( D )),bind(B,$thf( sk1 )),bind(C,$thf( sk3 @ domain_of @ ( D @ sk6 ) ))]]) ).
thf(3164,plain,
! [A: $i] :
( ~ ( sk1 @ empty )
| ( A @ power_set @ ( sk3 @ domain_of @ member ) ) ),
inference(simp,[status(thm)],[3109]) ).
thf(2930,plain,
( ( ( sk3 @ domain_of @ empty )
!= ( sk3 @ empty ) )
| ~ $true
| ( sk3 @ range_of @ empty )
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[2709,1479]) ).
thf(2931,plain,
( ( ( sk3 @ domain_of @ empty )
!= ( sk3 @ empty ) )
| ( sk3 @ range_of @ empty )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[2930]) ).
thf(2983,plain,
( ( ( sk3 @ domain_of )
!= sk3 )
| ~ ( sk1 @ empty )
| ( sk3 @ range_of @ empty ) ),
inference(simp,[status(thm)],[2931]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( B != sk1 )
| ( ( A @ ( B @ sk4 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[192]) ).
thf(210,plain,
( ( sk2 @ ( sk1 @ sk4 ) )
!= sk3 ),
inference(simp,[status(thm)],[209]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( B @ range_of @ ( B @ domain_of @ cross_product ) @ ( B @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,74]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( binary_relation_type @ ( B @ ilf_type ) ) )
| ( B @ range_of @ ( B @ domain_of @ cross_product ) @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[229]) ).
thf(240,plain,
! [B: $i,A: $i] :
( ( binary_relation_type != set_type )
| ( A != B )
| ( B @ range_of @ ( B @ domain_of @ cross_product ) @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(242,plain,
! [A: $i] :
( ( binary_relation_type != set_type )
| ( A @ range_of @ ( A @ domain_of @ cross_product ) @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[240]) ).
thf(504,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type @ ( sk3 @ ilf_type ) )
!= ( B @ subset_type @ ( sk3 @ ilf_type ) ) )
| ( ( B @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ~ $true
| ( ( A @ power_set @ member_type )
!= binary_relation_type ) ),
inference(paramod_ordered,[status(thm)],[439,334]) ).
thf(505,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type @ ( sk3 @ ilf_type ) )
!= ( B @ subset_type @ ( sk3 @ ilf_type ) ) )
| ( ( B @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ( ( A @ power_set @ member_type )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[504]) ).
thf(506,plain,
! [A: $i] :
( ( ( A @ power_set @ member_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ( ( A @ power_set @ member_type )
!= binary_relation_type ) ),
inference(pattern_uni,[status(thm)],[505:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(7467,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cross_product ) @ relation_like )
!= ( C @ relation_like ) )
| ( binary_relation_type @ ( C @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7455,4119]) ).
thf(7468,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cross_product ) @ relation_like )
!= ( C @ relation_like ) )
| ( binary_relation_type @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[7467]) ).
thf(7469,plain,
! [B: $i,A: $i] : ( binary_relation_type @ ( B @ ( A @ cross_product ) @ ilf_type ) ),
inference(pattern_uni,[status(thm)],[7468:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( E @ ( D @ cross_product ) ))]]) ).
thf(7474,plain,
! [B: $i,A: $i] : ( binary_relation_type @ ( B @ ( A @ cross_product ) @ ilf_type ) ),
inference(simp,[status(thm)],[7469]) ).
thf(2793,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1048,284]) ).
thf(2794,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2793]) ).
thf(2795,plain,
sk1 @ ( sk1 @ ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2794:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(1530,plain,
! [A: $i] :
( ( ( sk3 @ range_of @ empty )
!= ( A @ empty ) )
| ~ $true
| ~ ( A @ power_set @ ( A @ power_set @ member ) )
| ~ ( sk3 @ empty ) ),
inference(paramod_ordered,[status(thm)],[1479,808]) ).
thf(1531,plain,
! [A: $i] :
( ( ( sk3 @ range_of @ empty )
!= ( A @ empty ) )
| ~ ( A @ power_set @ ( A @ power_set @ member ) )
| ~ ( sk3 @ empty ) ),
inference(simp,[status(thm)],[1530]) ).
thf(1532,plain,
( ~ ( sk3 @ range_of @ power_set @ ( sk3 @ range_of @ power_set @ member ) )
| ~ ( sk3 @ empty ) ),
inference(pattern_uni,[status(thm)],[1531:[bind(A,$thf( sk3 @ range_of ))]]) ).
thf(3867,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk9 @ member ) )
!= ( B @ ( A @ member ) ) )
| ( B @ member_type @ ( A @ ilf_type ) )
| ~ $true
| ( B @ empty )
| ( sk3 @ domain_of @ empty ) ),
inference(paramod_ordered,[status(thm)],[3523,3623]) ).
thf(3868,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ domain_of @ sk9 @ member ) )
!= ( B @ ( A @ member ) ) )
| ( B @ member_type @ ( A @ ilf_type ) )
| ( B @ empty )
| ( sk3 @ domain_of @ empty ) ),
inference(simp,[status(thm)],[3867]) ).
thf(3869,plain,
( ( sk1 @ member_type @ ( sk3 @ domain_of @ sk9 @ ilf_type ) )
| ( sk1 @ empty )
| ( sk3 @ domain_of @ empty ) ),
inference(pattern_uni,[status(thm)],[3868:[bind(A,$thf( sk3 @ domain_of @ sk9 )),bind(B,$thf( sk1 ))]]) ).
thf(3018,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1490,284]) ).
thf(3019,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[3018]) ).
thf(3020,plain,
sk1 @ ( sk1 @ ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[3019:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk10 @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk2 @ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(1711,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[846,278]) ).
thf(1712,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk2 @ ( B @ cross_product ) @ ( sk3 @ range_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[1711]) ).
thf(1713,plain,
sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[1712:[bind(A,$thf( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk2 @ ( sk2 @ ( sk2 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(451,plain,
! [A: $i] :
( ( ( A @ subset_type @ ( sk3 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ~ $true
| ( ( A @ subset_type )
!= binary_relation_type ) ),
inference(paramod_ordered,[status(thm)],[413,34]) ).
thf(452,plain,
! [A: $i] :
( ( ( A @ subset_type @ ( sk3 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ( ( A @ subset_type )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[451]) ).
thf(456,plain,
! [A: $i] :
( ( ( A @ subset_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ( sk3 != sk3 )
| ( ( A @ subset_type )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[452]) ).
thf(459,plain,
! [A: $i] :
( ( ( A @ subset_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ( ( A @ subset_type )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[456]) ).
thf(4057,plain,
( ( ( sk1 @ power_set @ member_type @ ( sk3 @ domain_of @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4043,34]) ).
thf(4058,plain,
( ( sk1 @ power_set @ member_type @ ( sk3 @ domain_of @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) ),
inference(simp,[status(thm)],[4057]) ).
thf(4066,plain,
( ( ( sk2 @ ( sk1 @ relation_type ) )
!= ( sk1 @ power_set @ member_type ) )
| ( ( sk3 @ domain_of )
!= sk3 ) ),
inference(simp,[status(thm)],[4058]) ).
thf(2561,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1340,284]) ).
thf(2562,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( sk1 @ ( B @ cross_product ) @ ( sk3 @ domain_of @ ( A @ cross_product ) @ subset ) ) ),
inference(simp,[status(thm)],[2561]) ).
thf(2563,plain,
sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) @ cross_product ) @ subset ),
inference(pattern_uni,[status(thm)],[2562:[bind(A,$thf( sk3 @ domain_of @ ( sk3 @ range_of @ ( sk3 @ domain_of @ ( sk3 @ domain_of @ cross_product ) @ cross_product ) @ cross_product ) )),bind(B,$thf( sk1 @ ( sk2 @ ( sk1 @ ( sk1 @ cross_product ) @ cross_product ) @ cross_product ) ))]]) ).
thf(8784,plain,
( ( ( sk3 @ domain_of @ sk11 @ empty )
!= ( sk3 @ empty ) )
| ( ( sk1 @ power_set )
!= ( sk3 @ range_of ) )
| ~ $true
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[8483,3246]) ).
thf(8785,plain,
( ( ( sk3 @ domain_of @ sk11 @ empty )
!= ( sk3 @ empty ) )
| ( ( sk1 @ power_set )
!= ( sk3 @ range_of ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[8784]) ).
thf(8829,plain,
( ( ( sk3 @ domain_of @ sk11 )
!= sk3 )
| ( ( sk1 @ power_set )
!= ( sk3 @ range_of ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[8785]) ).
thf(489,plain,
! [A: $i] :
( ( ( A @ member_type @ ( A @ sk9 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ~ $true
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[481,34]) ).
thf(490,plain,
! [A: $i] :
( ( ( A @ member_type @ ( A @ sk9 @ ilf_type ) )
!= ( sk2 @ ( sk1 @ relation_type ) @ ( sk3 @ ilf_type ) ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[489]) ).
thf(496,plain,
! [A: $i] :
( ( ( A @ member_type )
!= ( sk2 @ ( sk1 @ relation_type ) ) )
| ( ( A @ sk9 )
!= sk3 )
| ( A @ empty ) ),
inference(simp,[status(thm)],[490]) ).
thf(25297,plain,
$false,
inference(e,[status(thm)],[1024,101,2778,846,333,892,69,2199,1665,5509,9131,481,2250,4043,408,1290,994,2099,511,202,1486,8057,1327,2580,2901,1063,538,2575,3049,1137,404,185,2216,2985,3466,565,37,110,3617,1323,4119,189,5199,1704,1479,284,2635,8483,7464,93,3919,7560,2520,2989,1362,29,2829,9103,5526,3473,1682,238,2367,61,7004,3243,988,243,849,7354,74,1394,5296,233,248,439,8655,1691,7550,85,3054,2790,2773,5174,2011,3037,1163,334,1021,1042,1519,8645,192,3250,2396,33,3682,9734,3090,4155,2609,1159,1656,1027,2345,2228,710,4063,682,2211,2245,3467,2515,2841,420,697,1541,10281,2973,2709,5577,1970,1719,5919,77,1075,5337,3032,1039,393,1150,1539,8690,371,605,984,3390,73,1991,244,1054,2963,5909,6922,4131,1146,6824,824,601,4116,1103,34,1483,32,2028,3523,904,44,5923,2016,5099,59,413,1652,3945,71,1669,54,5471,1107,8524,947,3170,7455,1090,3678,3764,1048,1349,2955,39,1175,81,1524,3066,208,4107,1969,2824,2182,2812,345,103,2111,5175,140,2446,621,769,6044,108,330,685,2770,2350,8776,1643,6223,1015,223,2592,4304,226,80,35,2506,1066,278,9054,2614,3936,589,1467,927,1134,112,1340,2333,2597,7454,553,194,1081,749,1990,516,7122,123,2513,48,1003,580,95,2012,3659,739,5790,2689,1499,3246,67,2688,441,5555,8845,5203,3623,1130,1336,2486,808,1404,2948,8696,7466,703,2992,2379,1353,8602,1094,8449,5472,2807,2266,991,7380,2458,2626,99,87,2194,218,3665,2325,759,5382,1062,401,2262,4261,914,8638,7399,2362,7406,1045,75,1030,2384,8488,2095,4074,1116,1133,1678,835,2233,867,3164,410,2983,305,210,242,1314,506,79,1172,7474,2795,3244,1532,3869,7457,3020,1713,5645,459,4066,111,337,2563,8829,5569,1490,676,496,1912]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET649+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n007.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 08:00:54 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.87/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.40/1.25 % [INFO] Parsing done (243ms).
% 1.40/1.26 % [INFO] Running in sequential loop mode.
% 2.07/1.54 % [INFO] eprover registered as external prover.
% 2.07/1.55 % [INFO] Scanning for conjecture ...
% 2.27/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 26 axioms. Running axiom selection ...
% 2.42/1.75 % [INFO] Axiom selection finished. Selected 26 axioms (removed 0 axioms).
% 2.64/1.82 % [INFO] Problem is first-order (TPTP FOF).
% 2.64/1.84 % [INFO] Type checking passed.
% 2.64/1.84 % [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 ...
% 114.40/29.26 % External prover 'e' found a proof!
% 114.40/29.26 % [INFO] Killing All external provers ...
% 114.40/29.26 % Time passed: 28709ms (effective reasoning time: 27994ms)
% 114.40/29.26 % 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)>
% 114.40/29.27 % Axioms used in derivation (26): 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
% 114.40/29.27 % No. of inferences in proof: 1082
% 114.40/29.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 28709 ms resp. 27994 ms w/o parsing
% 107.30/29.82 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 107.30/29.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------