%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET651+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:10:21 PM UTC 2026
% Result : Theorem 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 23
% Syntax : Number of formulae : 131 ( 17 unt; 10 def)
% Number of atoms : 460 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 558 ( 229 ~; 228 |; 38 &)
% ( 22 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 11 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-2 aty)
% Number of variables : 206 ( 199 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> subset(B,cross_product(domain_of(B),range_of(B))) ),
file('/export/starexec/sandbox/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)
=> ( ( subset(D,E)
& subset(B,C) )
=> subset(cross_product(B,D),cross_product(C,E)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) )
& ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(range_of(D),C)
& subset(domain_of(D),B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,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/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,D))
=> ( subset(domain_of(E),C)
=> ilf_type(E,relation_type(C,D)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,D))
=> ( subset(domain_of(E),C)
=> ilf_type(E,relation_type(C,D)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f31,plain,
! [B] :
( subset(B,cross_product(domain_of(B),range_of(B)))
| ~ ilf_type(B,binary_relation_type) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f32,plain,
! [X0] :
( subset(X0,cross_product(domain_of(X0),range_of(X0)))
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( subset(cross_product(B,D),cross_product(C,E))
| ~ subset(D,E)
| ~ subset(B,C)
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [B] :
( ! [C] :
( ( ! [E] :
( ilf_type(E,subset_type(cross_product(B,C)))
| ~ ilf_type(E,relation_type(B,C)) )
& ! [D] :
( ilf_type(D,relation_type(B,C))
| ~ ilf_type(D,subset_type(cross_product(B,C))) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f41,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( subset(range_of(D),C)
& subset(domain_of(D),B) )
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f43,plain,
! [X0,X1,X2] :
( subset(range_of(X2),X1)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f52,plain,
! [B] :
( ! [C] :
( ( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f53,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ subset(B,C) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK2_skl(C,B),C)
& member(sK2_skl(C,B),B)
& ilf_type(sK2_skl(C,B),set_type) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ subset(B,C) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(D,sK2_skl(C,B))],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f65,plain,
! [B] :
( ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f66,plain,
! [B] :
( ( ( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) )
& ( ( ilf_type(B,set_type)
& relation_like(B) )
| ~ ilf_type(B,binary_relation_type) ) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f65]) ).
fof(f69,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f72,plain,
! [B] :
( ! [C] :
( ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f73,plain,
! [B] :
( ! [C] :
( ( ( ~ ilf_type(C,member_type(power_set(B)))
| ilf_type(C,subset_type(B)) )
& ( ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,subset_type(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f72]) ).
fof(f75,plain,
! [X0,X1] :
( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f81,plain,
! [B] :
( ! [C] :
( ( member(B,power_set(C))
<=> ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f82,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) )
| member(B,power_set(C)) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f81]) ).
fof(f83,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK5_skl(C,B),C)
& member(sK5_skl(C,B),B)
& ilf_type(sK5_skl(C,B),set_type) )
| member(B,power_set(C)) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(D,sK5_skl(C,B))],[f82]) ).
fof(f86,plain,
! [X0,X1] :
( member(sK5_skl(X1,X0),X0)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f87,plain,
! [X0,X1] :
( ~ member(sK5_skl(X1,X0),X1)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f91,plain,
! [B] :
( ! [C] :
( ( ilf_type(B,member_type(C))
<=> member(B,C) )
| ~ ilf_type(C,set_type)
| empty(C) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f92,plain,
! [B] :
( ! [C] :
( ( ( ~ member(B,C)
| ilf_type(B,member_type(C)) )
& ( member(B,C)
| ~ ilf_type(B,member_type(C)) ) )
| ~ ilf_type(C,set_type)
| empty(C) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f91]) ).
fof(f94,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f107,plain,
! [B] :
( ! [C] :
( ! [D] :
( relation_like(D)
| ~ ilf_type(D,subset_type(cross_product(B,C))) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f108,plain,
! [X0,X1,X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
! [B] :
( ( empty(B)
<=> ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) ) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f110,plain,
! [B] :
( ( ( ? [C] :
( member(C,B)
& ilf_type(C,set_type) )
| empty(B) )
& ( ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) )
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f109]) ).
fof(f111,plain,
! [B] :
( ( ( ( member(sK10_skl(B),B)
& ilf_type(sK10_skl(B),set_type) )
| empty(B) )
& ( ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) )
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(C,sK10_skl(B))],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f117,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f118,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ~ ilf_type(E,relation_type(C,D))
& subset(domain_of(E),C)
& ilf_type(E,relation_type(B,D)) )
& ilf_type(D,set_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f119,plain,
( ~ ilf_type(sK14_skl,relation_type(sK12_skl,sK13_skl))
& subset(domain_of(sK14_skl),sK12_skl)
& ilf_type(sK14_skl,relation_type(sK11_skl,sK13_skl))
& ilf_type(sK13_skl,set_type)
& ilf_type(sK12_skl,set_type)
& ilf_type(sK11_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl,sK14_skl]),skolemize(B,sK11_skl),skolemize(C,sK12_skl),skolemize(D,sK13_skl),skolemize(E,sK14_skl)],[f118]) ).
fof(f123,plain,
ilf_type(sK14_skl,relation_type(sK11_skl,sK13_skl)),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f124,plain,
subset(domain_of(sK14_skl),sK12_skl),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f125,plain,
~ ilf_type(sK14_skl,relation_type(sK12_skl,sK13_skl)),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f126,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f69]) ).
fof(f130,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f117]) ).
fof(f131,plain,
! [X0,X1,X2,X3] :
( subset(cross_product(X3,X1),cross_product(X0,X2))
| ~ subset(X1,X2)
| ~ subset(X3,X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f34,f117]) ).
fof(f135,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f126,f117]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f36,f117]) ).
fof(f143,plain,
! [X0,X1,X2] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f142,f117]) ).
fof(f144,plain,
! [X0,X1,X2] :
( ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f37,f117]) ).
fof(f146,plain,
~ ilf_type(sK14_skl,subset_type(cross_product(sK12_skl,sK13_skl))),
inference(resolution,[status(thm)],[f143,f125]) ).
fof(f148,definition,
( sQ0_spl
<=> ilf_type(sK13_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( sQ0_spl
| ~ ilf_type(sK13_skl,set_type) ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f155,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f150,f117]) ).
fof(f156,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f155]) ).
fof(f194,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f112,f117]) ).
fof(f195,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f194,f117]) ).
fof(f201,plain,
! [X0,X1,X2] :
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f117]) ).
fof(f202,plain,
! [X0,X1,X2] :
( subset(range_of(X1),X0)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f117]) ).
fof(f203,plain,
! [X0,X1] :
( member(sK5_skl(X0,X1),X1)
| member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f86,f117]) ).
fof(f204,plain,
! [X0,X1] :
( member(sK5_skl(X1,X0),X0)
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f203,f117]) ).
fof(f205,plain,
! [X0,X1,X2] :
( member(sK5_skl(X1,X0),X2)
| ~ ilf_type(sK5_skl(X1,X0),set_type)
| ~ subset(X0,X2)
| ~ ilf_type(X2,set_type)
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f204,f130]) ).
fof(f206,plain,
! [X0,X1,X2] :
( member(sK5_skl(X1,X0),X2)
| ~ ilf_type(sK5_skl(X1,X0),set_type)
| ~ subset(X0,X2)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f205,f117]) ).
fof(f216,plain,
! [X0,X1,X2] :
( member(sK5_skl(X1,X0),X2)
| ~ subset(X0,X2)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f206,f117]) ).
fof(f217,plain,
! [X0,X1,X2,X3] :
( member(sK5_skl(X1,X0),X3)
| ~ ilf_type(sK5_skl(X1,X0),set_type)
| ~ subset(X2,X3)
| ~ ilf_type(X3,set_type)
| ~ subset(X0,X2)
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f216,f130]) ).
fof(f218,plain,
! [X0,X1,X2,X3] :
( member(sK5_skl(X1,X0),X3)
| ~ ilf_type(sK5_skl(X1,X0),set_type)
| ~ subset(X2,X3)
| ~ subset(X0,X2)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f217,f117]) ).
fof(f270,plain,
! [X0,X1,X2,X3] :
( member(sK5_skl(X1,X0),X3)
| ~ subset(X2,X3)
| ~ subset(X0,X2)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f218,f117]) ).
fof(f277,plain,
! [X0,X1] :
( ~ member(sK5_skl(X0,X1),X0)
| member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f87,f117]) ).
fof(f278,plain,
! [X0,X1] :
( ~ member(sK5_skl(X1,X0),X1)
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f277,f117]) ).
fof(f299,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f94,f117]) ).
fof(f300,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[f299,f117]) ).
fof(f301,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f300,f195]) ).
fof(f305,plain,
! [X0,X1] :
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f75,f117]) ).
fof(f306,plain,
! [X0,X1] :
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(resolution,[status(thm)],[f305,f117]) ).
fof(f317,plain,
~ ilf_type(sK14_skl,member_type(power_set(cross_product(sK12_skl,sK13_skl)))),
inference(resolution,[status(thm)],[f306,f146]) ).
fof(f320,plain,
~ member(sK14_skl,power_set(cross_product(sK12_skl,sK13_skl))),
inference(resolution,[status(thm)],[f317,f301]) ).
fof(f321,plain,
~ member(sK5_skl(cross_product(sK12_skl,sK13_skl),sK14_skl),cross_product(sK12_skl,sK13_skl)),
inference(resolution,[status(thm)],[f320,f278]) ).
fof(f362,plain,
! [X0] :
( ~ subset(X0,cross_product(sK12_skl,sK13_skl))
| ~ subset(sK14_skl,X0)
| member(sK14_skl,power_set(cross_product(sK12_skl,sK13_skl))) ),
inference(resolution,[status(thm)],[f321,f270]) ).
fof(f366,definition,
( sQ11_spl
<=> member(sK14_skl,power_set(cross_product(sK12_skl,sK13_skl))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f367,plain,
( ~ sQ11_spl
| member(sK14_skl,power_set(cross_product(sK12_skl,sK13_skl))) ),
inference(component_clause,[status(thm)],[f366]) ).
fof(f369,definition,
! [X0] :
( sQ12_spl
<=> ( ~ subset(X0,cross_product(sK12_skl,sK13_skl))
| ~ subset(sK14_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f370,plain,
! [X0] :
( ~ sQ12_spl
| ~ subset(X0,cross_product(sK12_skl,sK13_skl))
| ~ subset(sK14_skl,X0) ),
inference(component_clause,[status(thm)],[f369]) ).
fof(f372,plain,
( sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f362,f366,f369]) ).
fof(f377,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f367,f320]) ).
fof(f378,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f377]) ).
fof(f399,plain,
( ~ sQ12_spl
| ~ ilf_type(sK14_skl,binary_relation_type)
| ~ subset(cross_product(domain_of(sK14_skl),range_of(sK14_skl)),cross_product(sK12_skl,sK13_skl)) ),
inference(resolution,[status(thm)],[f370,f32]) ).
fof(f405,definition,
( sQ17_spl
<=> subset(cross_product(domain_of(sK14_skl),range_of(sK14_skl)),cross_product(sK12_skl,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f407,plain,
( sQ17_spl
| ~ subset(cross_product(domain_of(sK14_skl),range_of(sK14_skl)),cross_product(sK12_skl,sK13_skl)) ),
inference(component_clause,[status(thm)],[f405]) ).
fof(f408,definition,
( sQ18_spl
<=> ilf_type(sK14_skl,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f410,plain,
( sQ18_spl
| ~ ilf_type(sK14_skl,binary_relation_type) ),
inference(component_clause,[status(thm)],[f408]) ).
fof(f411,plain,
( ~ sQ12_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f399,f405,f408,f369]) ).
fof(f474,plain,
( sQ17_spl
| ~ subset(range_of(sK14_skl),sK13_skl)
| ~ subset(domain_of(sK14_skl),sK12_skl)
| ~ ilf_type(sK13_skl,set_type)
| ~ ilf_type(range_of(sK14_skl),set_type)
| ~ ilf_type(sK12_skl,set_type) ),
inference(resolution,[status(thm)],[f407,f131]) ).
fof(f479,definition,
( sQ29_spl
<=> ilf_type(sK12_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f481,plain,
( sQ29_spl
| ~ ilf_type(sK12_skl,set_type) ),
inference(component_clause,[status(thm)],[f479]) ).
fof(f482,definition,
( sQ30_spl
<=> ilf_type(range_of(sK14_skl),set_type) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f484,plain,
( sQ30_spl
| ~ ilf_type(range_of(sK14_skl),set_type) ),
inference(component_clause,[status(thm)],[f482]) ).
fof(f485,definition,
( sQ31_spl
<=> subset(domain_of(sK14_skl),sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f487,plain,
( sQ31_spl
| ~ subset(domain_of(sK14_skl),sK12_skl) ),
inference(component_clause,[status(thm)],[f485]) ).
fof(f488,definition,
( sQ32_spl
<=> subset(range_of(sK14_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f490,plain,
( sQ32_spl
| ~ subset(range_of(sK14_skl),sK13_skl) ),
inference(component_clause,[status(thm)],[f488]) ).
fof(f491,plain,
( sQ17_spl
| ~ sQ32_spl
| ~ sQ31_spl
| ~ sQ0_spl
| ~ sQ30_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f474,f479,f482,f148,f485,f488,f405]) ).
fof(f503,plain,
! [X0] :
( sQ32_spl
| ~ ilf_type(sK14_skl,relation_type(X0,sK13_skl))
| ~ ilf_type(sK13_skl,set_type) ),
inference(resolution,[status(thm)],[f490,f202]) ).
fof(f508,definition,
! [X0] :
( sQ35_spl
<=> ~ ilf_type(sK14_skl,relation_type(X0,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f509,plain,
! [X0] :
( ~ sQ35_spl
| ~ ilf_type(sK14_skl,relation_type(X0,sK13_skl)) ),
inference(component_clause,[status(thm)],[f508]) ).
fof(f511,plain,
( sQ32_spl
| sQ35_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f503,f148,f508,f488]) ).
fof(f521,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f487,f124]) ).
fof(f522,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f521]) ).
fof(f523,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f481,f117]) ).
fof(f524,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f523]) ).
fof(f533,plain,
( ~ sQ35_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f123,f509]) ).
fof(f535,plain,
~ sQ35_spl,
inference(contradiction_clause,[status(thm)],[f533]) ).
fof(f536,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f484,f117]) ).
fof(f537,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f536]) ).
fof(f538,plain,
( sQ18_spl
| ~ relation_like(sK14_skl) ),
inference(resolution,[status(thm)],[f410,f135]) ).
fof(f540,plain,
! [X0,X1] :
( sQ18_spl
| ~ ilf_type(sK14_skl,subset_type(cross_product(X1,X0)))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f538,f201]) ).
fof(f544,plain,
! [X0,X1] :
( sQ18_spl
| ~ ilf_type(sK14_skl,subset_type(cross_product(X0,X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f540,f117]) ).
fof(f556,plain,
! [X0,X1] :
( sQ18_spl
| ~ ilf_type(sK14_skl,relation_type(X1,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f544,f144]) ).
fof(f558,plain,
! [X0,X1] :
( sQ18_spl
| ~ ilf_type(sK14_skl,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f556,f117]) ).
fof(f559,plain,
( sQ18_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f123,f558]) ).
fof(f561,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f559]) ).
fof(f562,plain,
$false,
inference(sat_refutation,[status(thm)],[f156,f372,f378,f411,f491,f511,f522,f524,f535,f537,f561]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET651+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:31:25 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.44 % Elapsed time: 0.078722 seconds
% 0.14/0.44 % CPU time: 0.284159 seconds
% 0.14/0.44 % Total memory used: 85.770 MB
% 0.14/0.44 % Net memory used: 85.364 MB
%------------------------------------------------------------------------------