%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET648+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 : n008.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 08:30:37 AM UTC 2026
% Result : Theorem 80.17s 16.76s
% Output : Refutation 67.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 34
% Syntax : Number of formulae : 165 ( 32 unt; 0 typ; 7 def)
% Number of atoms : 617 ( 67 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 1956 ( 221 ~; 168 |; 48 &;1366 @)
% ( 9 <=>; 144 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 7 con; 0-2 aty)
% Number of variables : 287 ( 6 ^; 254 !; 20 ?; 287 :)
% ( 0 !>; 0 ?*; 0 @-; 7 @+)
% 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(range_of_decl,type,
range_of: $i > $i ).
thf(relation_type_decl,type,
relation_type: $i > $i > $i ).
thf(domain_of_decl,type,
domain_of: $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 > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( binary_relation_type @ ( B @ ilf_type ) )
=> ( ( A @ ( B @ range_of @ subset ) )
=> ( A @ ( B @ domain_of @ relation_type ) @ ( B @ ilf_type ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( ( sk1 @ ( A @ range_of @ subset ) )
=> ( sk1 @ ( A @ domain_of @ relation_type ) @ ( A @ ilf_type ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( set_type @ ( B @ ilf_type ) )
=> ~ ( A @ ( B @ member ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( set_type @ ( C @ ilf_type ) )
=> ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i] :
@+[B: $i] : ( A @ subset_type @ ( B @ ilf_type ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] : ( binary_relation_type @ ( A @ ilf_type ) ) ) ) ).
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(65,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(23,axiom,
? [A: $i] : ( binary_relation_type @ ( A @ ilf_type ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11) ).
thf(101,plain,
? [A: $i] : ( binary_relation_type @ ( A @ ilf_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(102,plain,
binary_relation_type @ ( sk10 @ ilf_type ),
inference(cnf,[status(esa)],[101]) ).
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(71,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(72,plain,
! [A: $i] :
( ( A @ range_of @ ( A @ domain_of @ cross_product ) @ ( A @ subset ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[71]) ).
thf(167,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)],[102,72]) ).
thf(168,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk10 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( A @ range_of @ ( A @ domain_of @ cross_product ) @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[167]) ).
thf(169,plain,
sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ ( sk10 @ subset ),
inference(pattern_uni,[status(thm)],[168:[bind(A,$thf( sk10 ))]]) ).
thf(24,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(103,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)],[24]) ).
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(35,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(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(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(67,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(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(59,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(60,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk7 ) @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk7 ) @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B @ ( A @ subset ) )
| ( set_type @ ( A @ ( B @ sk7 ) @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( set_type @ ( C @ ilf_type ) )
| ~ ( B @ ( A @ subset ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[59]) ).
thf(61,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)],[60]) ).
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(185,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ $true
| ~ ( B @ ( A @ subset ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[61,111]) ).
thf(186,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[185]) ).
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(37,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(38,plain,
! [B: $i,A: $i] :
( ( ( A @ empty )
| ( A @ ( A @ sk4 @ member ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( A @ empty )
| ( set_type @ ( A @ sk4 @ 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)],[37]) ).
thf(41,plain,
! [A: $i] :
( ( A @ empty )
| ( A @ ( A @ sk4 @ member ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[38]) ).
thf(245,plain,
! [A: $i] :
( ( A @ empty )
| ( A @ ( A @ sk4 @ member ) )
| ~ $true ),
inference(rewrite,[status(thm)],[41,111]) ).
thf(246,plain,
! [A: $i] :
( ( A @ empty )
| ( A @ ( A @ sk4 @ member ) ) ),
inference(simp,[status(thm)],[245]) ).
thf(1,conjecture,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( binary_relation_type @ ( B @ ilf_type ) )
=> ( ( A @ ( B @ range_of @ subset ) )
=> ( A @ ( B @ domain_of @ relation_type ) @ ( B @ ilf_type ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_10) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( binary_relation_type @ ( B @ ilf_type ) )
=> ( ( A @ ( B @ range_of @ subset ) )
=> ( A @ ( B @ domain_of @ relation_type ) @ ( B @ ilf_type ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(29,plain,
~ ! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( binary_relation_type @ ( B @ ilf_type ) )
=> ( ( A @ ( B @ range_of @ subset ) )
=> ( A @ ( B @ domain_of @ relation_type ) @ ( B @ ilf_type ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(30,plain,
( ~ ( sk1 @ ( sk2 @ domain_of @ relation_type ) @ ( sk2 @ ilf_type ) )
& ( sk1 @ ( sk2 @ range_of @ subset ) )
& ( binary_relation_type @ ( sk2 @ ilf_type ) )
& ( set_type @ ( sk1 @ ilf_type ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(32,plain,
binary_relation_type @ ( sk2 @ ilf_type ),
inference(cnfConj,[status(thm)],[30]) ).
thf(176,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk2 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( A @ range_of @ ( A @ domain_of @ cross_product ) @ ( A @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32,72]) ).
thf(177,plain,
! [A: $i] :
( ( ( binary_relation_type @ ( sk2 @ ilf_type ) )
!= ( binary_relation_type @ ( A @ ilf_type ) ) )
| ( A @ range_of @ ( A @ domain_of @ cross_product ) @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[176]) ).
thf(178,plain,
sk2 @ range_of @ ( sk2 @ domain_of @ cross_product ) @ ( sk2 @ subset ),
inference(pattern_uni,[status(thm)],[177:[bind(A,$thf( sk2 ))]]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( A @ empty )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[38]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ $true
| ~ ( A @ empty )
| ~ $true ),
inference(rewrite,[status(thm)],[39,111]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[160]) ).
thf(202,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ member ) )
!= ( D @ ( E @ member ) ) )
| ~ $true
| ~ ( D @ empty )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[186,161]) ).
thf(203,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ member ) )
!= ( D @ ( E @ member ) ) )
| ~ ( D @ empty )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[202]) ).
thf(204,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[203:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(229,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ range_of @ ( sk2 @ domain_of @ cross_product ) @ ( sk2 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ~ ( B @ empty )
| ~ ( A @ ( C @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[178,204]) ).
thf(230,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ range_of @ ( sk2 @ domain_of @ cross_product ) @ ( sk2 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ~ ( B @ empty )
| ~ ( A @ ( C @ member ) ) ),
inference(simp,[status(thm)],[229]) ).
thf(231,plain,
! [A: $i] :
( ~ ( sk2 @ range_of @ ( sk2 @ domain_of @ cross_product ) @ empty )
| ~ ( sk2 @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[230:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 @ range_of @ ( sk2 @ domain_of @ cross_product ) )),bind(C,$thf( C ))]]) ).
thf(235,plain,
! [A: $i] :
( ~ ( sk2 @ range_of @ ( sk2 @ domain_of @ cross_product ) @ empty )
| ~ ( sk2 @ ( A @ member ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(324,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk4 @ member ) )
!= ( sk2 @ ( B @ member ) ) )
| ~ ( sk2 @ range_of @ ( sk2 @ domain_of @ cross_product ) @ empty )
| ~ $true
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[246,235]) ).
thf(325,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk4 @ member ) )
!= ( sk2 @ ( B @ member ) ) )
| ~ ( sk2 @ range_of @ ( sk2 @ domain_of @ cross_product ) @ empty )
| ( A @ empty ) ),
inference(simp,[status(thm)],[324]) ).
thf(326,plain,
( ~ ( sk2 @ range_of @ ( sk2 @ domain_of @ cross_product ) @ empty )
| ( sk2 @ empty ) ),
inference(pattern_uni,[status(thm)],[325:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 @ sk4 ))]]) ).
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(69,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(33,plain,
sk1 @ ( sk2 @ range_of @ subset ),
inference(cnfConj,[status(thm)],[30]) ).
thf(221,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ range_of @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ~ ( B @ empty )
| ~ ( A @ ( C @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,204]) ).
thf(222,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ range_of @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ~ ( B @ empty )
| ~ ( A @ ( C @ member ) ) ),
inference(simp,[status(thm)],[221]) ).
thf(223,plain,
! [A: $i] :
( ~ ( sk1 @ empty )
| ~ ( sk2 @ range_of @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[222:[bind(A,$thf( sk2 @ range_of )),bind(B,$thf( sk1 )),bind(C,$thf( C ))]]) ).
thf(228,plain,
! [A: $i] :
( ~ ( sk1 @ empty )
| ~ ( sk2 @ range_of @ ( A @ member ) ) ),
inference(simp,[status(thm)],[223]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk4 @ member ) )
!= ( sk2 @ range_of @ ( B @ member ) ) )
| ~ ( sk1 @ empty )
| ~ $true
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[246,228]) ).
thf(248,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk4 @ member ) )
!= ( sk2 @ range_of @ ( B @ member ) ) )
| ~ ( sk1 @ empty )
| ( A @ empty ) ),
inference(simp,[status(thm)],[247]) ).
thf(249,plain,
( ~ ( sk1 @ empty )
| ( sk2 @ range_of @ empty ) ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( sk2 @ range_of )),bind(B,$thf( sk2 @ range_of @ sk4 ))]]) ).
thf(34,plain,
~ ( sk1 @ ( sk2 @ domain_of @ relation_type ) @ ( sk2 @ ilf_type ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(139,plain,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
!= ( sk1 @ ( sk2 @ domain_of @ relation_type ) @ ( sk2 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,34]) ).
thf(140,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
!= ( sk1 @ ( sk2 @ domain_of @ relation_type ) @ ( sk2 @ ilf_type ) ) ),
inference(simp,[status(thm)],[139]) ).
thf(141,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ domain_of @ relation_type ) )
!= set_type )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[140]) ).
thf(142,plain,
( ( sk1 @ ( sk2 @ domain_of @ relation_type ) )
!= set_type ),
inference(simp,[status(thm)],[141]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ relation_type ) @ ( A @ ( B @ sk3 ) @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ relation_type ) @ ( A @ ( B @ sk3 ) @ ilf_type ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[36,111]) ).
thf(144,plain,
! [B: $i,A: $i] : ( A @ ( B @ relation_type ) @ ( A @ ( B @ sk3 ) @ ilf_type ) ),
inference(simp,[status(thm)],[143]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ relation_type ) @ ( A @ ( B @ sk3 ) @ ilf_type ) )
!= ( sk1 @ ( sk2 @ domain_of @ relation_type ) @ ( sk2 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[144,34]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ relation_type ) @ ( A @ ( B @ sk3 ) @ ilf_type ) )
!= ( sk1 @ ( sk2 @ domain_of @ relation_type ) @ ( sk2 @ ilf_type ) ) ),
inference(simp,[status(thm)],[145]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ relation_type ) )
!= ( sk1 @ ( sk2 @ domain_of @ relation_type ) ) )
| ( ( A @ ( B @ sk3 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[146]) ).
thf(152,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( B
!= ( sk2 @ domain_of ) )
| ( ( A @ ( B @ sk3 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[147]) ).
thf(153,plain,
( ( sk1 @ ( sk2 @ domain_of @ sk3 ) )
!= sk2 ),
inference(simp,[status(thm)],[152]) ).
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(42,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(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(52,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(43,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)],[42]) ).
thf(44,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)],[43]) ).
thf(331,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)],[44,111]) ).
thf(332,plain,
! [B: $i,A: $i] :
( ( A @ power_set @ member_type @ ( B @ ilf_type ) )
| ~ ( A @ subset_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[331]) ).
thf(341,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk2 @ ilf_type ) )
!= ( A @ subset_type @ ( B @ ilf_type ) ) )
| ( A @ power_set @ member_type @ ( B @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32,332]) ).
thf(342,plain,
! [B: $i,A: $i] :
( ( ( binary_relation_type @ ( sk2 @ ilf_type ) )
!= ( A @ subset_type @ ( B @ ilf_type ) ) )
| ( A @ power_set @ member_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[341]) ).
thf(352,plain,
! [B: $i,A: $i] :
( ( ( A @ subset_type )
!= binary_relation_type )
| ( sk2 != B )
| ( A @ power_set @ member_type @ ( B @ ilf_type ) ) ),
inference(simp,[status(thm)],[342]) ).
thf(357,plain,
! [A: $i] :
( ( ( A @ subset_type )
!= binary_relation_type )
| ( A @ power_set @ member_type @ ( sk2 @ ilf_type ) ) ),
inference(simp,[status(thm)],[352]) ).
thf(8,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( A @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17) ).
thf(57,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( A @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(58,plain,
! [A: $i] :
( ( A @ ( A @ subset ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[57]) ).
thf(156,plain,
! [A: $i] :
( ( A @ ( A @ subset ) )
| ~ $true ),
inference(rewrite,[status(thm)],[58,111]) ).
thf(157,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(simp,[status(thm)],[156]) ).
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(46,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(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(212,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ ( sk10 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ~ ( B @ empty )
| ~ ( A @ ( C @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[169,204]) ).
thf(213,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ ( sk10 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ~ ( B @ empty )
| ~ ( A @ ( C @ member ) ) ),
inference(simp,[status(thm)],[212]) ).
thf(214,plain,
! [A: $i] :
( ~ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ empty )
| ~ ( sk10 @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[213:[bind(A,$thf( sk10 )),bind(B,$thf( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) )),bind(C,$thf( C ))]]) ).
thf(225,plain,
! [A: $i] :
( ~ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ empty )
| ~ ( sk10 @ ( A @ member ) ) ),
inference(simp,[status(thm)],[214]) ).
thf(310,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk4 @ member ) )
!= ( sk10 @ ( B @ member ) ) )
| ~ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ empty )
| ~ $true
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[246,225]) ).
thf(311,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk4 @ member ) )
!= ( sk10 @ ( B @ member ) ) )
| ~ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ empty )
| ( A @ empty ) ),
inference(simp,[status(thm)],[310]) ).
thf(312,plain,
( ~ ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ empty )
| ( sk10 @ empty ) ),
inference(pattern_uni,[status(thm)],[311:[bind(A,$thf( sk10 )),bind(B,$thf( sk10 @ sk4 ))]]) ).
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(132,plain,
( ( ( sk1 @ ( sk2 @ domain_of @ relation_type ) @ ( sk2 @ ilf_type ) )
!= ( binary_relation_type @ ( sk2 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32,34]) ).
thf(133,plain,
( ( sk1 @ ( sk2 @ domain_of @ relation_type ) @ ( sk2 @ ilf_type ) )
!= ( binary_relation_type @ ( sk2 @ ilf_type ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(136,plain,
( ( ( sk1 @ ( sk2 @ domain_of @ relation_type ) )
!= binary_relation_type )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[133]) ).
thf(137,plain,
( ( sk1 @ ( sk2 @ domain_of @ relation_type ) )
!= binary_relation_type ),
inference(simp,[status(thm)],[136]) ).
thf(16,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( B @ ( A @ subset ) )
=> ( ( B @ ( C @ cross_product ) @ ( A @ ( C @ cross_product ) @ subset ) )
& ( C @ ( 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 ) )
=> ( ( B @ ( A @ subset ) )
=> ( ( B @ ( C @ cross_product ) @ ( A @ ( C @ cross_product ) @ subset ) )
& ( C @ ( B @ cross_product ) @ ( C @ ( A @ cross_product ) @ subset ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
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(73,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(25,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(105,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)],[25]) ).
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 @ sk9 @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[99]) ).
thf(162,plain,
! [A: $i] :
( ( A @ subset_type @ ( A @ sk9 @ ilf_type ) )
| ~ $true ),
inference(rewrite,[status(thm)],[100,111]) ).
thf(163,plain,
! [A: $i] : ( A @ subset_type @ ( A @ sk9 @ ilf_type ) ),
inference(simp,[status(thm)],[162]) ).
thf(164,plain,
! [A: $i] :
( ( ( A @ subset_type @ ( A @ sk9 @ ilf_type ) )
!= ( sk1 @ ( sk2 @ domain_of @ relation_type ) @ ( sk2 @ ilf_type ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[163,34]) ).
thf(165,plain,
! [A: $i] :
( ( A @ subset_type @ ( A @ sk9 @ ilf_type ) )
!= ( sk1 @ ( sk2 @ domain_of @ relation_type ) @ ( sk2 @ ilf_type ) ) ),
inference(simp,[status(thm)],[164]) ).
thf(166,plain,
! [A: $i] :
( ( ( A @ subset_type )
!= ( sk1 @ ( sk2 @ domain_of @ relation_type ) ) )
| ( ( A @ sk9 )
!= sk2 ) ),
inference(simp,[status(thm)],[165]) ).
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(148,plain,
! [A: $i] :
( ~ ( A @ power_set @ empty )
| ~ $true ),
inference(rewrite,[status(thm)],[97,111]) ).
thf(149,plain,
! [A: $i] :
~ ( A @ power_set @ empty ),
inference(simp,[status(thm)],[148]) ).
thf(303,plain,
! [A: $i] :
( ( ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ empty )
!= ( sk2 @ range_of @ empty ) )
| ~ $true
| ~ ( sk10 @ ( A @ member ) )
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[249,225]) ).
thf(304,plain,
! [A: $i] :
( ( ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) @ empty )
!= ( sk2 @ range_of @ empty ) )
| ~ ( sk10 @ ( A @ member ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[303]) ).
thf(313,plain,
! [A: $i] :
( ( ( sk10 @ range_of @ ( sk10 @ domain_of @ cross_product ) )
!= ( sk2 @ range_of ) )
| ~ ( sk10 @ ( A @ member ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[304]) ).
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(347,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk9 @ ilf_type ) )
!= ( B @ subset_type @ ( C @ ilf_type ) ) )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[163,332]) ).
thf(348,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ subset_type @ ( A @ sk9 @ ilf_type ) )
!= ( B @ subset_type @ ( C @ ilf_type ) ) )
| ( B @ power_set @ member_type @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[347]) ).
thf(349,plain,
! [A: $i] : ( A @ power_set @ member_type @ ( A @ sk9 @ ilf_type ) ),
inference(pattern_uni,[status(thm)],[348:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk9 ))]]) ).
thf(362,plain,
! [A: $i] : ( A @ power_set @ member_type @ ( A @ sk9 @ ilf_type ) ),
inference(simp,[status(thm)],[349]) ).
thf(199,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ range_of @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,186]) ).
thf(200,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ range_of @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(simp,[status(thm)],[199]) ).
thf(201,plain,
! [A: $i] :
( ( sk1 @ ( A @ member ) )
| ~ ( sk2 @ range_of @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[200:[bind(A,$thf( sk2 @ range_of )),bind(B,$thf( sk1 )),bind(C,$thf( C ))]]) ).
thf(208,plain,
! [A: $i] :
( ( sk1 @ ( A @ member ) )
| ~ ( sk2 @ range_of @ ( A @ member ) ) ),
inference(simp,[status(thm)],[201]) ).
thf(253,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk4 @ member ) )
!= ( sk2 @ range_of @ ( B @ member ) ) )
| ( sk1 @ ( B @ member ) )
| ~ $true
| ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[246,208]) ).
thf(254,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk4 @ member ) )
!= ( sk2 @ range_of @ ( B @ member ) ) )
| ( sk1 @ ( B @ member ) )
| ( A @ empty ) ),
inference(simp,[status(thm)],[253]) ).
thf(255,plain,
( ( sk1 @ ( sk2 @ range_of @ sk4 @ member ) )
| ( sk2 @ range_of @ empty ) ),
inference(pattern_uni,[status(thm)],[254:[bind(A,$thf( sk2 @ range_of )),bind(B,$thf( sk2 @ range_of @ sk4 ))]]) ).
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(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(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(15,axiom,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
& ( A @ empty ) )
=> ( A @ relation_like ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25) ).
thf(75,plain,
! [A: $i] :
( ( ( set_type @ ( A @ ilf_type ) )
& ( A @ empty ) )
=> ( A @ relation_like ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(274,plain,
! [A: $i] :
( ( ( A @ power_set @ empty )
!= ( sk2 @ range_of @ empty ) )
| ~ $true
| ~ ( sk1 @ empty ) ),
inference(paramod_ordered,[status(thm)],[249,149]) ).
thf(275,plain,
! [A: $i] :
( ( ( A @ power_set @ empty )
!= ( sk2 @ range_of @ empty ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[274]) ).
thf(277,plain,
! [A: $i] :
( ( ( A @ power_set )
!= ( sk2 @ range_of ) )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[275]) ).
thf(18703,plain,
$false,
inference(e,[status(thm)],[65,169,103,35,95,67,72,186,326,111,69,101,249,142,153,42,37,52,110,357,157,46,93,228,57,29,147,312,85,102,137,33,225,77,73,105,166,161,149,32,34,59,204,71,313,144,81,362,208,255,112,123,99,87,75,235,246,332,163,178,277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET648+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.22/0.46 % Computer : n008.cluster.edu
% 0.22/0.46 % Model : x86_64 x86_64
% 0.22/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.46 % Memory : 8046.5625MB
% 0.22/0.46 % OS : Linux 6.8.0-71-generic
% 0.22/0.46 % CPULimit : 300
% 0.22/0.47 % WCLimit : 300
% 0.22/0.47 % DateTime : Sat Sep 26 08:03:39 UTC 2026
% 0.22/0.47 % CPUTime :
% 0.22/0.47 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
% 1.45/1.34 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.98/1.67 % [INFO] Parsing done (320ms).
% 1.98/1.69 % [INFO] Running in sequential loop mode.
% 3.15/2.27 % [INFO] eprover registered as external prover.
% 3.15/2.28 % [INFO] Scanning for conjecture ...
% 3.57/2.40 % [INFO] Found a conjecture (or negated_conjecture) and 26 axioms. Running axiom selection ...
% 3.78/2.53 % [INFO] Axiom selection finished. Selected 26 axioms (removed 0 axioms).
% 4.03/2.62 % [INFO] Problem is first-order (TPTP FOF).
% 4.03/2.65 % [INFO] Type checking passed.
% 4.03/2.65 % [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 ...
% 80.17/16.75 % External prover 'e' found a proof!
% 80.17/16.75 % [INFO] Killing All external provers ...
% 80.17/16.76 % Time passed: 16067ms (effective reasoning time: 15053ms)
% 80.17/16.76 % 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)>
% 80.17/16.76 % 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
% 80.17/16.76 % No. of inferences in proof: 158
% 80.17/16.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 16067 ms resp. 15053 ms w/o parsing
% 67.86/16.87 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 67.86/16.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------