%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET664+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:30:40 AM UTC 2026
% Result : Theorem 89.76s 32.65s
% Output : Refutation 90.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of formulae : 96 ( 19 unt; 0 typ; 4 def)
% Number of atoms : 366 ( 60 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 1122 ( 153 ~; 142 |; 21 &; 735 @)
% ( 2 <=>; 69 =>; 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 : 19 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 181 ( 2 ^; 175 !; 0 ?; 181 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ilf_type_decl,type,
ilf_type: $i > $i > $o ).
thf(set_type_decl,type,
set_type: $i ).
thf(relation_type_decl,type,
relation_type: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(subset_type_decl,type,
subset_type: $i > $i ).
thf(relation_like_decl,type,
relation_like: $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(binary_relation_type_decl,type,
binary_relation_type: $i ).
thf(domain_of_decl,type,
domain_of: $i > $i ).
thf(range_of_decl,type,
range_of: $i > $i ).
thf(cross_product_decl,type,
cross_product: $i > $i > $i ).
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(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( A @ ( B @ relation_type ) @ ( C @ ilf_type ) )
=> ( ( empty_set @ ( B @ relation_type ) @ ( C @ ilf_type ) )
=> ( C = empty_set ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( sk1 @ ( A @ relation_type ) @ ( B @ ilf_type ) )
=> ( ( empty_set @ ( A @ relation_type ) @ ( B @ ilf_type ) )
=> ( B = empty_set ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( sk1 @ ( sk2 @ relation_type ) @ ( A @ ilf_type ) )
=> ( ( empty_set @ ( sk2 @ relation_type ) @ ( A @ ilf_type ) )
=> ( A = empty_set ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( set_type @ ( C @ ilf_type ) )
=> ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( A @ ( B @ relation_type ) @ ( C @ ilf_type ) )
=> ( ( empty_set @ ( B @ relation_type ) @ ( C @ ilf_type ) )
=> ( C = empty_set ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_27) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( A @ ( B @ relation_type ) @ ( C @ ilf_type ) )
=> ( ( empty_set @ ( B @ relation_type ) @ ( C @ ilf_type ) )
=> ( C = empty_set ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
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 ) )
=> ( ( empty_set @ ( B @ relation_type ) @ ( C @ ilf_type ) )
=> ( C = empty_set ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(38,plain,
( ( sk3 != empty_set )
& ( empty_set @ ( sk2 @ relation_type ) @ ( sk3 @ ilf_type ) )
& ( sk1 @ ( sk2 @ relation_type ) @ ( sk3 @ ilf_type ) )
& ( set_type @ ( sk2 @ ilf_type ) )
& ( set_type @ ( sk1 @ ilf_type ) ) ),
inference(cnf,[status(esa)],[37]) ).
thf(41,plain,
empty_set @ ( sk2 @ relation_type ) @ ( sk3 @ ilf_type ),
inference(cnfConj,[status(thm)],[38]) ).
thf(11,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ( ( B @ ( C @ range_of @ subset ) )
& ( A @ ( C @ domain_of @ subset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
thf(69,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 @ ( C @ range_of @ subset ) )
& ( A @ ( C @ domain_of @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ range_of @ subset ) )
| ~ ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( A @ ( C @ domain_of @ subset ) )
| ~ ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ range_of @ subset ) )
| ~ ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(18,axiom,
! [A: $i] : ( set_type @ ( A @ ilf_type ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33) ).
thf(111,plain,
! [A: $i] : ( set_type @ ( A @ ilf_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(112,plain,
! [A: $i] : ( set_type @ ( A @ ilf_type ) ),
inference(cnf,[status(esa)],[111]) ).
thf(1759,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ range_of @ subset ) )
| ~ ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[72,112]) ).
thf(1760,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ range_of @ subset ) )
| ~ ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[1759]) ).
thf(1808,plain,
! [C: $i,B: $i,A: $i] :
( ( ( empty_set @ ( sk2 @ relation_type ) @ ( sk3 @ ilf_type ) )
!= ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) ) )
| ( B @ ( C @ range_of @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41,1760]) ).
thf(1809,plain,
! [C: $i,B: $i,A: $i] :
( ( ( empty_set @ ( sk2 @ relation_type ) @ ( sk3 @ ilf_type ) )
!= ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) ) )
| ( B @ ( C @ range_of @ subset ) ) ),
inference(simp,[status(thm)],[1808]) ).
thf(1810,plain,
empty_set @ ( sk3 @ range_of @ subset ),
inference(pattern_uni,[status(thm)],[1809:[bind(A,$thf( sk2 )),bind(B,$thf( empty_set )),bind(C,$thf( sk3 ))]]) ).
thf(7,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( set_type @ ( C @ ilf_type ) )
=> ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
thf(54,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)],[7]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk4 ) @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) )
& ( ( B @ ( A @ subset ) )
| ( set_type @ ( A @ ( B @ sk4 ) @ 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)],[54]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk4 ) @ member ) )
| ~ ( set_type @ ( B @ ilf_type ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[55]) ).
thf(669,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk4 ) @ member ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[58,112]) ).
thf(670,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(simp,[status(thm)],[669]) ).
thf(56,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)],[55]) ).
thf(327,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ $true
| ~ ( B @ ( A @ subset ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[56,112]) ).
thf(328,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[327]) ).
thf(33,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ~ ( empty_set @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
thf(162,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ~ ( empty_set @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(163,plain,
! [A: $i] :
( ~ ( empty_set @ ( A @ member ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[162]) ).
thf(317,plain,
! [A: $i] :
( ~ ( empty_set @ ( A @ member ) )
| ~ $true ),
inference(rewrite,[status(thm)],[163,112]) ).
thf(318,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(simp,[status(thm)],[317]) ).
thf(332,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ member ) )
!= ( empty_set @ ( D @ member ) ) )
| ~ $true
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[328,318]) ).
thf(333,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ member ) )
!= ( empty_set @ ( D @ member ) ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[332]) ).
thf(334,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ ( empty_set @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[333:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(339,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ ( empty_set @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[334]) ).
thf(677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk4 ) @ member ) )
!= ( C @ ( D @ member ) ) )
| ~ $true
| ~ ( empty_set @ ( C @ subset ) )
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[670,339]) ).
thf(678,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk4 ) @ member ) )
!= ( C @ ( D @ member ) ) )
| ~ ( empty_set @ ( C @ subset ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[677]) ).
thf(679,plain,
! [B: $i,A: $i] :
( ~ ( empty_set @ ( B @ subset ) )
| ( A @ ( B @ subset ) ) ),
inference(pattern_uni,[status(thm)],[678:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ sk4 ) ))]]) ).
thf(696,plain,
! [B: $i,A: $i] :
( ~ ( empty_set @ ( B @ subset ) )
| ( A @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[679]) ).
thf(1997,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ ( sk3 @ range_of @ subset ) )
!= ( empty_set @ ( B @ subset ) ) )
| ~ $true
| ( A @ ( B @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[1810,696]) ).
thf(1998,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ ( sk3 @ range_of @ subset ) )
!= ( empty_set @ ( B @ subset ) ) )
| ( A @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[1997]) ).
thf(1999,plain,
! [A: $i] : ( A @ ( sk3 @ range_of @ subset ) ),
inference(pattern_uni,[status(thm)],[1998:[bind(A,$thf( A )),bind(B,$thf( sk3 @ range_of ))]]) ).
thf(17,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
thf(108,plain,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(109,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( empty_set @ ( A @ subset ) )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(cnf,[status(esa)],[108]) ).
thf(110,plain,
! [A: $i] :
( ~ ( empty_set @ ( A @ subset ) )
| ~ ( set_type @ ( A @ ilf_type ) )
| ( A = empty_set ) ),
inference(lifteq,[status(thm)],[109]) ).
thf(11864,plain,
! [A: $i] :
( ~ ( empty_set @ ( A @ subset ) )
| ~ $true
| ( A = empty_set ) ),
inference(rewrite,[status(thm)],[110,112]) ).
thf(11865,plain,
! [A: $i] :
( ~ ( empty_set @ ( A @ subset ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[11864]) ).
thf(11959,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk3 @ range_of @ subset ) )
!= ( empty_set @ ( B @ subset ) ) )
| ~ $true
| ( B = empty_set ) ),
inference(paramod_ordered,[status(thm)],[1999,11865]) ).
thf(11960,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk3 @ range_of @ subset ) )
!= ( empty_set @ ( B @ subset ) ) )
| ( B = empty_set ) ),
inference(simp,[status(thm)],[11959]) ).
thf(11961,plain,
( ( sk3 @ range_of )
= empty_set ),
inference(pattern_uni,[status(thm)],[11960:[bind(A,$thf( empty_set )),bind(B,$thf( sk3 @ range_of ))]]) ).
thf(25,axiom,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( ( ( ( A @ range_of )
= empty_set )
| ( ( A @ domain_of )
= empty_set ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
thf(132,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
=> ( ( ( ( A @ range_of )
= empty_set )
| ( ( A @ domain_of )
= empty_set ) )
=> ( A = empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(133,plain,
! [A: $i] :
( ( ( A = empty_set )
| ( ( A @ range_of )
!= empty_set )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) )
& ( ( A = empty_set )
| ( ( A @ domain_of )
!= empty_set )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ) ),
inference(cnf,[status(esa)],[132]) ).
thf(135,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( A @ range_of )
!= empty_set )
| ~ ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(cnfConj,[status(thm)],[133]) ).
thf(137,plain,
! [A: $i] :
( ~ ( binary_relation_type @ ( A @ ilf_type ) )
| ( A = empty_set )
| ( ( A @ range_of )
!= empty_set ) ),
inference(lifteq,[status(thm)],[135]) ).
thf(17726,plain,
! [A: $i] :
( ( ( sk3 @ range_of )
!= ( A @ range_of ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) )
| ( A = empty_set )
| ( empty_set != empty_set ) ),
inference(paramod_ordered,[status(thm)],[11961,137]) ).
thf(17727,plain,
! [A: $i] :
( ( ( sk3 @ range_of )
!= ( A @ range_of ) )
| ~ ( binary_relation_type @ ( A @ ilf_type ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[17726]) ).
thf(17728,plain,
( ~ ( binary_relation_type @ ( sk3 @ ilf_type ) )
| ( sk3 = empty_set ) ),
inference(pattern_uni,[status(thm)],[17727:[bind(A,$thf( sk3 ))]]) ).
thf(20,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ( ! [C: $i] :
( ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) )
=> ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) ) )
& ! [C: $i] :
( ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) )
=> ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
thf(115,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)],[20]) ).
thf(116,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)],[115]) ).
thf(118,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)],[116]) ).
thf(119,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)],[118]) ).
thf(14506,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)],[119,112]) ).
thf(14507,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)],[14506]) ).
thf(14578,plain,
! [C: $i,B: $i,A: $i] :
( ( ( empty_set @ ( sk2 @ relation_type ) @ ( sk3 @ ilf_type ) )
!= ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) ) )
| ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41,14507]) ).
thf(14579,plain,
! [C: $i,B: $i,A: $i] :
( ( ( empty_set @ ( sk2 @ relation_type ) @ ( sk3 @ ilf_type ) )
!= ( B @ ( A @ relation_type ) @ ( C @ ilf_type ) ) )
| ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[14578]) ).
thf(14580,plain,
empty_set @ ( sk2 @ cross_product ) @ subset_type @ ( sk3 @ ilf_type ),
inference(pattern_uni,[status(thm)],[14579:[bind(A,$thf( sk2 )),bind(B,$thf( empty_set )),bind(C,$thf( sk3 ))]]) ).
thf(19,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ! [B: $i] :
( ( set_type @ ( B @ ilf_type ) )
=> ! [C: $i] :
( ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) )
=> ( C @ relation_like ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p28) ).
thf(113,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)],[19]) ).
thf(114,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)],[113]) ).
thf(13341,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)],[114,112]) ).
thf(13342,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ relation_like )
| ~ ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) ) ),
inference(simp,[status(thm)],[13341]) ).
thf(14819,plain,
! [C: $i,B: $i,A: $i] :
( ( ( empty_set @ ( sk2 @ cross_product ) @ subset_type @ ( sk3 @ ilf_type ) )
!= ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) ) )
| ( C @ relation_like )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14580,13342]) ).
thf(14820,plain,
! [C: $i,B: $i,A: $i] :
( ( ( empty_set @ ( sk2 @ cross_product ) @ subset_type @ ( sk3 @ ilf_type ) )
!= ( B @ ( A @ cross_product ) @ subset_type @ ( C @ ilf_type ) ) )
| ( C @ relation_like ) ),
inference(simp,[status(thm)],[14819]) ).
thf(14821,plain,
sk3 @ relation_like,
inference(pattern_uni,[status(thm)],[14820:[bind(A,$thf( sk2 )),bind(B,$thf( empty_set )),bind(C,$thf( sk3 ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( set_type @ ( A @ ilf_type ) )
=> ( ( binary_relation_type @ ( A @ ilf_type ) )
<=> ( ( set_type @ ( A @ ilf_type ) )
& ( A @ relation_like ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
thf(63,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)],[10]) ).
thf(64,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)],[63]) ).
thf(67,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)],[64]) ).
thf(68,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
| ~ ( A @ relation_like )
| ~ ( set_type @ ( A @ ilf_type ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(1244,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
| ~ ( A @ relation_like )
| ~ $true ),
inference(rewrite,[status(thm)],[68,112]) ).
thf(1245,plain,
! [A: $i] :
( ( binary_relation_type @ ( A @ ilf_type ) )
| ~ ( A @ relation_like ) ),
inference(simp,[status(thm)],[1244]) ).
thf(14894,plain,
! [A: $i] :
( ( ( sk3 @ relation_like )
!= ( A @ relation_like ) )
| ( binary_relation_type @ ( A @ ilf_type ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14821,1245]) ).
thf(14895,plain,
! [A: $i] :
( ( ( sk3 @ relation_like )
!= ( A @ relation_like ) )
| ( binary_relation_type @ ( A @ ilf_type ) ) ),
inference(simp,[status(thm)],[14894]) ).
thf(14896,plain,
binary_relation_type @ ( sk3 @ ilf_type ),
inference(pattern_uni,[status(thm)],[14895:[bind(A,$thf( sk3 ))]]) ).
thf(18631,plain,
( ~ $true
| ( sk3 = empty_set ) ),
inference(rewrite,[status(thm)],[17728,14896]) ).
thf(18632,plain,
sk3 = empty_set,
inference(simp,[status(thm)],[18631]) ).
thf(42,plain,
sk3 != empty_set,
inference(cnfConj,[status(thm)],[38]) ).
thf(44,plain,
sk3 != empty_set,
inference(lifteq,[status(thm)],[42]) ).
thf(18633,plain,
$false,
inference(simplifyReflect,[status(thm)],[18632,44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET664+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.23/10.51 % Computer : n004.cluster.edu
% 0.23/10.51 % Model : x86_64 x86_64
% 0.23/10.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/10.51 % Memory : 8046.5625MB
% 0.23/10.51 % OS : Linux 6.8.0-71-generic
% 0.23/10.51 % CPULimit : 300
% 0.23/10.51 % WCLimit : 300
% 0.23/10.51 % DateTime : Sat Sep 26 08:03:18 UTC 2026
% 0.23/10.51 % CPUTime :
% 0.23/10.52 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.36/11.35 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.82/11.69 % [INFO] Parsing done (330ms).
% 2.18/11.71 % [INFO] Running in sequential loop mode.
% 3.13/12.33 % [INFO] eprover registered as external prover.
% 3.13/12.34 % [INFO] Scanning for conjecture ...
% 3.47/12.50 % [INFO] Found a conjecture (or negated_conjecture) and 34 axioms. Running axiom selection ...
% 3.63/12.62 % [INFO] Axiom selection finished. Selected 34 axioms (removed 0 axioms).
% 3.90/12.73 % [INFO] Problem is first-order (TPTP FOF).
% 3.90/12.75 % [INFO] Type checking passed.
% 3.90/12.76 % [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 ...
% 89.76/32.63 % [INFO] Killing All external provers ...
% 89.76/32.64 % Time passed: 21918ms (effective reasoning time: 20918ms)
% 89.76/32.64 % 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)>
% 89.76/32.64 % Axioms used in derivation (9): p19, p4, p2, p28, p1, p13, p6, p3, p33
% 89.76/32.64 % No. of inferences in proof: 92
% 89.76/32.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 21918 ms resp. 20918 ms w/o parsing
% 90.30/32.75 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 90.30/32.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------