TSTP Solution File: SET650+3 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET650+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:34:55 EDT 2023
% Result : Theorem 0.15s 0.40s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 129 ( 13 unt; 0 def)
% Number of atoms : 493 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 619 ( 255 ~; 266 |; 45 &)
% ( 16 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-2 aty)
% Number of variables : 282 (; 271 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( member(B,domain_of(C))
<=> ? [D] :
( ilf_type(D,set_type)
& member(ordered_pair(B,D),C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( member(B,range_of(C))
<=> ? [D] :
( ilf_type(D,set_type)
& member(ordered_pair(D,B),C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ! [F] :
( ilf_type(F,relation_type(B,C))
=> ( member(ordered_pair(D,E),F)
=> ( member(D,B)
& member(E,C) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( relation_like(B)
& ilf_type(B,set_type) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> relation_like(D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(domain_of(D),B)
& subset(range_of(D),C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(domain_of(D),B)
& subset(range_of(D),C) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,binary_relation_type)
| ( member(B,domain_of(C))
<=> ? [D] :
( ilf_type(D,set_type)
& member(ordered_pair(B,D),C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f30,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,binary_relation_type)
| ( ( ~ member(B,domain_of(C))
| ? [D] :
( ilf_type(D,set_type)
& member(ordered_pair(B,D),C) ) )
& ( member(B,domain_of(C))
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(ordered_pair(B,D),C) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f29]) ).
fof(f31,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,binary_relation_type)
| ( ( ~ member(B,domain_of(C))
| ( ilf_type(sk0_0(C,B),set_type)
& member(ordered_pair(B,sk0_0(C,B)),C) ) )
& ( member(B,domain_of(C))
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(ordered_pair(B,D),C) ) ) ) ) ),
inference(skolemization,[status(esa)],[f30]) ).
fof(f33,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(X0,domain_of(X1))
| member(ordered_pair(X0,sk0_0(X1,X0)),X1) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f35,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,binary_relation_type)
| ( member(B,range_of(C))
<=> ? [D] :
( ilf_type(D,set_type)
& member(ordered_pair(D,B),C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f36,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,binary_relation_type)
| ( ( ~ member(B,range_of(C))
| ? [D] :
( ilf_type(D,set_type)
& member(ordered_pair(D,B),C) ) )
& ( member(B,range_of(C))
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(ordered_pair(D,B),C) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f35]) ).
fof(f37,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,binary_relation_type)
| ( ( ~ member(B,range_of(C))
| ( ilf_type(sk0_1(C,B),set_type)
& member(ordered_pair(sk0_1(C,B),B),C) ) )
& ( member(B,range_of(C))
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(ordered_pair(D,B),C) ) ) ) ) ),
inference(skolemization,[status(esa)],[f36]) ).
fof(f39,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ member(X0,range_of(X1))
| member(ordered_pair(sk0_1(X1,X0),X0),X1) ),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f41,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( ~ ilf_type(E,set_type)
| ! [F] :
( ~ ilf_type(F,relation_type(B,C))
| ~ member(ordered_pair(D,E),F)
| ( member(D,B)
& member(E,C) ) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f42,plain,
! [X0,X1,X2,X3,X4] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| member(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| member(X3,X1) ),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f60,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f66,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( subset(B,C)
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f67,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ subset(B,C)
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( subset(B,C)
| ? [D] :
( ilf_type(D,set_type)
& member(D,B)
& ~ member(D,C) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f66]) ).
fof(f68,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ subset(B,C)
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( subset(B,C)
| ( ilf_type(sk0_5(C,B),set_type)
& member(sk0_5(C,B),B)
& ~ member(sk0_5(C,B),C) ) ) ) ) ),
inference(skolemization,[status(esa)],[f67]) ).
fof(f71,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| subset(X0,X1)
| member(sk0_5(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f68]) ).
fof(f72,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| subset(X0,X1)
| ~ member(sk0_5(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f68]) ).
fof(f77,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ilf_type(B,binary_relation_type)
<=> ( relation_like(B)
& ilf_type(B,set_type) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f78,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ( ~ ilf_type(B,binary_relation_type)
| ( relation_like(B)
& ilf_type(B,set_type) ) )
& ( ilf_type(B,binary_relation_type)
| ~ relation_like(B)
| ~ ilf_type(B,set_type) ) ) ),
inference(NNF_transformation,[status(esa)],[f77]) ).
fof(f81,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f78]) ).
fof(f84,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f85,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) )
& ( ilf_type(C,subset_type(B))
| ~ ilf_type(C,member_type(power_set(B))) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,subset_type(X0))
| ilf_type(X1,member_type(power_set(X0))) ),
inference(cnf_transformation,[status(esa)],[f85]) ).
fof(f87,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) ),
inference(cnf_transformation,[status(esa)],[f85]) ).
fof(f93,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( member(B,power_set(C))
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f94,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ member(B,power_set(C))
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( member(B,power_set(C))
| ? [D] :
( ilf_type(D,set_type)
& member(D,B)
& ~ member(D,C) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f93]) ).
fof(f95,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ member(B,power_set(C))
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( member(B,power_set(C))
| ( ilf_type(sk0_8(C,B),set_type)
& member(sk0_8(C,B),B)
& ~ member(sk0_8(C,B),C) ) ) ) ) ),
inference(skolemization,[status(esa)],[f94]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f95]) ).
fof(f98,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1))
| member(sk0_8(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f95]) ).
fof(f99,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1))
| ~ member(sk0_8(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f95]) ).
fof(f100,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f101,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[status(esa)],[f100]) ).
fof(f103,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( empty(C)
| ~ ilf_type(C,set_type)
| ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f104,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( empty(C)
| ~ ilf_type(C,set_type)
| ( ( ~ ilf_type(B,member_type(C))
| member(B,C) )
& ( ilf_type(B,member_type(C))
| ~ member(B,C) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f103]) ).
fof(f105,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,member_type(X1))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f104]) ).
fof(f106,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| empty(X1)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f104]) ).
fof(f119,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f23]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(cnf_transformation,[status(esa)],[f119]) ).
fof(f129,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f130,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,relation_type(B,C))
& ( ~ subset(domain_of(D),B)
| ~ subset(range_of(D),C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f28]) ).
fof(f131,plain,
( ilf_type(sk0_14,set_type)
& ilf_type(sk0_15,set_type)
& ilf_type(sk0_16,relation_type(sk0_14,sk0_15))
& ( ~ subset(domain_of(sk0_16),sk0_14)
| ~ subset(range_of(sk0_16),sk0_15) ) ),
inference(skolemization,[status(esa)],[f130]) ).
fof(f134,plain,
ilf_type(sk0_16,relation_type(sk0_14,sk0_15)),
inference(cnf_transformation,[status(esa)],[f131]) ).
fof(f135,plain,
( ~ subset(domain_of(sk0_16),sk0_14)
| ~ subset(range_of(sk0_16),sk0_15) ),
inference(cnf_transformation,[status(esa)],[f131]) ).
fof(f136,plain,
( spl0_0
<=> subset(domain_of(sk0_16),sk0_14) ),
introduced(split_symbol_definition) ).
fof(f139,plain,
( spl0_1
<=> subset(range_of(sk0_16),sk0_15) ),
introduced(split_symbol_definition) ).
fof(f142,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f135,f136,f139]) ).
fof(f143,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(duplicate_literals_removal,[status(esa)],[f81]) ).
fof(f148,plain,
! [X0,X1,X2,X3,X4] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X4,X0))
| ~ member(ordered_pair(X1,X2),X3)
| member(X1,X4) ),
inference(forward_subsumption_resolution,[status(thm)],[f42,f129]) ).
fof(f149,plain,
! [X0,X1,X2,X3,X4] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X4,X0))
| ~ member(ordered_pair(X1,X2),X3)
| member(X2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f129]) ).
fof(f154,plain,
! [X0] : ~ empty(power_set(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f101,f129]) ).
fof(f158,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f143,f129]) ).
fof(f169,plain,
! [X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ member(X1,domain_of(X0))
| member(ordered_pair(X1,sk0_0(X0,X1)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f33,f129]) ).
fof(f171,plain,
! [X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ member(X1,range_of(X0))
| member(ordered_pair(sk0_1(X0,X1),X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f39,f129]) ).
fof(f310,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| subset(X1,X0)
| member(sk0_5(X0,X1),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f71,f129]) ).
fof(f311,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_5(X1,X0),X0) ),
inference(resolution,[status(thm)],[f310,f129]) ).
fof(f324,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| subset(X1,X0)
| ~ member(sk0_5(X0,X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f72,f129]) ).
fof(f325,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_5(X1,X0),X1) ),
inference(resolution,[status(thm)],[f324,f129]) ).
fof(f328,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| relation_like(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f129]) ).
fof(f329,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| relation_like(X0) ),
inference(resolution,[status(thm)],[f328,f129]) ).
fof(f345,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| member(X1,power_set(X0))
| member(sk0_8(X0,X1),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f98,f129]) ).
fof(f346,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sk0_8(X1,X0),X0) ),
inference(resolution,[status(thm)],[f345,f129]) ).
fof(f359,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| member(X1,power_set(X0))
| ~ member(sk0_8(X0,X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f99,f129]) ).
fof(f360,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sk0_8(X1,X0),X1) ),
inference(resolution,[status(thm)],[f359,f129]) ).
fof(f361,plain,
! [X0] :
( member(X0,power_set(X0))
| member(X0,power_set(X0)) ),
inference(resolution,[status(thm)],[f360,f346]) ).
fof(f362,plain,
! [X0] : member(X0,power_set(X0)),
inference(duplicate_literals_removal,[status(esa)],[f361]) ).
fof(f371,plain,
! [X0,X1] :
( empty(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,member_type(X0))
| member(X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f105,f129]) ).
fof(f372,plain,
! [X0,X1] :
( empty(X0)
| ~ ilf_type(X1,member_type(X0))
| member(X1,X0) ),
inference(resolution,[status(thm)],[f371,f129]) ).
fof(f389,plain,
! [X0,X1] :
( empty(X0)
| ~ ilf_type(X0,set_type)
| ilf_type(X1,member_type(X0))
| ~ member(X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f106,f129]) ).
fof(f390,plain,
! [X0,X1] :
( empty(X0)
| ilf_type(X1,member_type(X0))
| ~ member(X1,X0) ),
inference(resolution,[status(thm)],[f389,f129]) ).
fof(f391,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f86,f129]) ).
fof(f392,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(resolution,[status(thm)],[f391,f129]) ).
fof(f401,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ilf_type(X1,relation_type(X2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f61,f129]) ).
fof(f402,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f401,f129]) ).
fof(f675,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| empty(power_set(X1))
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f392,f372]) ).
fof(f676,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f675,f154]) ).
fof(f725,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f87,f129]) ).
fof(f726,plain,
! [X0,X1] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(resolution,[status(thm)],[f725,f129]) ).
fof(f729,plain,
! [X0,X1] :
( ilf_type(X0,subset_type(X1))
| empty(power_set(X1))
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f726,f390]) ).
fof(f730,plain,
! [X0,X1] :
( ilf_type(X0,subset_type(X1))
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f729,f154]) ).
fof(f745,plain,
! [X0] : ilf_type(X0,subset_type(X0)),
inference(resolution,[status(thm)],[f730,f362]) ).
fof(f746,plain,
! [X0,X1] : ilf_type(cross_product(X0,X1),relation_type(X0,X1)),
inference(resolution,[status(thm)],[f745,f402]) ).
fof(f784,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,X0))
| ilf_type(X1,subset_type(cross_product(X2,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f62,f129]) ).
fof(f785,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f784,f129]) ).
fof(f786,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| member(X2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f96,f129]) ).
fof(f787,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ member(X1,power_set(X0))
| ~ member(X2,X1)
| member(X2,X0) ),
inference(resolution,[status(thm)],[f786,f129]) ).
fof(f788,plain,
! [X0,X1,X2] :
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f787,f129]) ).
fof(f879,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(resolution,[status(thm)],[f785,f329]) ).
fof(f880,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| member(X0,power_set(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f785,f676]) ).
fof(f887,plain,
relation_like(sk0_16),
inference(resolution,[status(thm)],[f879,f134]) ).
fof(f888,plain,
ilf_type(sk0_16,binary_relation_type),
inference(resolution,[status(thm)],[f887,f158]) ).
fof(f892,plain,
! [X0] :
( ~ member(X0,range_of(sk0_16))
| member(ordered_pair(sk0_1(sk0_16,X0),X0),sk0_16) ),
inference(resolution,[status(thm)],[f888,f171]) ).
fof(f893,plain,
! [X0] :
( ~ member(X0,domain_of(sk0_16))
| member(ordered_pair(X0,sk0_0(sk0_16,X0)),sk0_16) ),
inference(resolution,[status(thm)],[f888,f169]) ).
fof(f968,plain,
member(sk0_16,power_set(cross_product(sk0_14,sk0_15))),
inference(resolution,[status(thm)],[f880,f134]) ).
fof(f973,plain,
! [X0] :
( ~ member(X0,sk0_16)
| member(X0,cross_product(sk0_14,sk0_15)) ),
inference(resolution,[status(thm)],[f968,f788]) ).
fof(f1005,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X0,X1),sk0_16)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(cross_product(sk0_14,sk0_15),relation_type(X3,X2))
| member(X1,X2) ),
inference(resolution,[status(thm)],[f973,f149]) ).
fof(f1006,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X0,X1),sk0_16)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(cross_product(sk0_14,sk0_15),relation_type(X2,X3))
| member(X1,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f1005,f129]) ).
fof(f1007,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X0,X1),sk0_16)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(cross_product(sk0_14,sk0_15),relation_type(X3,X2))
| member(X0,X3) ),
inference(resolution,[status(thm)],[f973,f148]) ).
fof(f1008,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X0,X1),sk0_16)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(cross_product(sk0_14,sk0_15),relation_type(X2,X3))
| member(X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1007,f129]) ).
fof(f4390,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X0,X1),sk0_16)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(cross_product(sk0_14,sk0_15),relation_type(X2,X3))
| member(X1,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f1006,f129]) ).
fof(f4391,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sk0_16)
| ~ ilf_type(X1,set_type)
| member(X1,sk0_15) ),
inference(resolution,[status(thm)],[f4390,f746]) ).
fof(f4392,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sk0_16)
| member(X1,sk0_15) ),
inference(forward_subsumption_resolution,[status(thm)],[f4391,f129]) ).
fof(f4393,plain,
! [X0] :
( member(X0,sk0_15)
| ~ member(X0,range_of(sk0_16)) ),
inference(resolution,[status(thm)],[f4392,f892]) ).
fof(f4505,plain,
! [X0] :
( member(sk0_5(X0,range_of(sk0_16)),sk0_15)
| subset(range_of(sk0_16),X0) ),
inference(resolution,[status(thm)],[f4393,f311]) ).
fof(f4676,plain,
( subset(range_of(sk0_16),sk0_15)
| subset(range_of(sk0_16),sk0_15) ),
inference(resolution,[status(thm)],[f4505,f325]) ).
fof(f4677,plain,
spl0_1,
inference(split_clause,[status(thm)],[f4676,f139]) ).
fof(f6142,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X0,X1),sk0_16)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(cross_product(sk0_14,sk0_15),relation_type(X2,X3))
| member(X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1008,f129]) ).
fof(f6143,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sk0_16)
| ~ ilf_type(X1,set_type)
| member(X0,sk0_14) ),
inference(resolution,[status(thm)],[f6142,f746]) ).
fof(f6144,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sk0_16)
| member(X0,sk0_14) ),
inference(forward_subsumption_resolution,[status(thm)],[f6143,f129]) ).
fof(f6147,plain,
! [X0] :
( member(X0,sk0_14)
| ~ member(X0,domain_of(sk0_16)) ),
inference(resolution,[status(thm)],[f6144,f893]) ).
fof(f6286,plain,
! [X0] :
( member(sk0_5(X0,domain_of(sk0_16)),sk0_14)
| subset(domain_of(sk0_16),X0) ),
inference(resolution,[status(thm)],[f6147,f311]) ).
fof(f6434,plain,
( subset(domain_of(sk0_16),sk0_14)
| subset(domain_of(sk0_16),sk0_14) ),
inference(resolution,[status(thm)],[f6286,f325]) ).
fof(f6435,plain,
spl0_0,
inference(split_clause,[status(thm)],[f6434,f136]) ).
fof(f6438,plain,
$false,
inference(sat_refutation,[status(thm)],[f142,f4677,f6435]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SET650+3 : TPTP v8.1.2. Released v2.2.0.
% 0.05/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31 % Computer : n017.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Tue May 30 09:47:55 EDT 2023
% 0.09/0.31 % CPUTime :
% 0.15/0.31 % Drodi V3.5.1
% 0.15/0.40 % Refutation found
% 0.15/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.44/0.63 % Elapsed time: 0.105008 seconds
% 0.44/0.63 % CPU time: 0.267502 seconds
% 0.44/0.63 % Memory used: 25.315 MB
%------------------------------------------------------------------------------