%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET649+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 : 10
% Number of leaves : 27
% Syntax : Number of formulae : 125 ( 19 unt; 16 def)
% Number of atoms : 416 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 491 ( 200 ~; 199 |; 33 &)
% ( 24 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 20 usr; 17 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 135 ( 130 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> subset(B,cross_product(domain_of(B),range_of(B))) ),
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)
=> ( ( subset(D,E)
& subset(B,C) )
=> subset(cross_product(B,D),cross_product(C,E)) ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,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(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(f20,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(f21,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,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/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,binary_relation_type)
=> ( ( subset(range_of(D),C)
& subset(domain_of(D),B) )
=> ilf_type(D,relation_type(B,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,binary_relation_type)
=> ( ( subset(range_of(D),C)
& subset(domain_of(D),B) )
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
! [B] :
( ! [C] :
( ! [D] :
( subset(B,D)
| ~ subset(C,D)
| ~ subset(B,C)
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f30,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
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(f64,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)],[f12]) ).
fof(f65,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)],[f64]) ).
fof(f66,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK4_skl(C,B),C)
& member(sK4_skl(C,B),B)
& ilf_type(sK4_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,[sK4_skl]),skolemize(D,sK4_skl(C,B))],[f65]) ).
fof(f67,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)],[f66]) ).
fof(f75,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(f76,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)],[f75]) ).
fof(f78,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)],[f76]) ).
fof(f95,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)],[f20]) ).
fof(f96,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)],[f95]) ).
fof(f97,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK9_skl(C,B),C)
& member(sK9_skl(C,B),B)
& ilf_type(sK9_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,[sK9_skl]),skolemize(D,sK9_skl(C,B))],[f96]) ).
fof(f100,plain,
! [X0,X1] :
( member(sK9_skl(X1,X0),X0)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f101,plain,
! [X0,X1] :
( ~ member(sK9_skl(X1,X0),X1)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f102,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f103,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f105,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)],[f22]) ).
fof(f106,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)],[f105]) ).
fof(f108,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)],[f106]) ).
fof(f120,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f121,plain,
? [B] :
( ? [C] :
( ? [D] :
( ~ ilf_type(D,relation_type(B,C))
& subset(range_of(D),C)
& subset(domain_of(D),B)
& ilf_type(D,binary_relation_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f122,plain,
( ~ ilf_type(sK14_skl,relation_type(sK12_skl,sK13_skl))
& subset(range_of(sK14_skl),sK13_skl)
& subset(domain_of(sK14_skl),sK12_skl)
& ilf_type(sK14_skl,binary_relation_type)
& ilf_type(sK13_skl,set_type)
& ilf_type(sK12_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl,sK14_skl]),skolemize(B,sK12_skl),skolemize(C,sK13_skl),skolemize(D,sK14_skl)],[f121]) ).
fof(f125,plain,
ilf_type(sK14_skl,binary_relation_type),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f126,plain,
subset(domain_of(sK14_skl),sK12_skl),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f127,plain,
subset(range_of(sK14_skl),sK13_skl),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f128,plain,
~ ilf_type(sK14_skl,relation_type(sK12_skl,sK13_skl)),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f131,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ subset(X0,X1)
| ~ subset(X2,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f30,f120]) ).
fof(f132,plain,
! [X0] : ~ empty(power_set(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f103,f120]) ).
fof(f139,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,f120]) ).
fof(f140,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,f120]) ).
fof(f141,plain,
! [X0,X1,X2] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f140,f120]) ).
fof(f145,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)],[f67,f120]) ).
fof(f159,plain,
! [X0,X1] :
( member(sK9_skl(X0,X1),X1)
| member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f100,f120]) ).
fof(f160,plain,
! [X0,X1] :
( ~ member(sK9_skl(X0,X1),X0)
| member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f101,f120]) ).
fof(f163,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)],[f108,f120]) ).
fof(f165,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)],[f78,f120]) ).
fof(f166,plain,
! [X0,X1] :
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(resolution,[status(thm)],[f165,f120]) ).
fof(f167,plain,
! [X0,X1,X2] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,member_type(power_set(cross_product(X1,X2)))) ),
inference(resolution,[status(thm)],[f166,f141]) ).
fof(f168,plain,
~ ilf_type(sK14_skl,member_type(power_set(cross_product(sK12_skl,sK13_skl)))),
inference(resolution,[status(thm)],[f167,f128]) ).
fof(f171,plain,
( ~ member(sK14_skl,power_set(cross_product(sK12_skl,sK13_skl)))
| ~ ilf_type(power_set(cross_product(sK12_skl,sK13_skl)),set_type)
| empty(power_set(cross_product(sK12_skl,sK13_skl))) ),
inference(resolution,[status(thm)],[f168,f163]) ).
fof(f179,definition,
( sQ2_spl
<=> empty(power_set(cross_product(sK12_skl,sK13_skl))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ2_spl
| empty(power_set(cross_product(sK12_skl,sK13_skl))) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,definition,
( sQ3_spl
<=> ilf_type(power_set(cross_product(sK12_skl,sK13_skl)),set_type) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( sQ3_spl
| ~ ilf_type(power_set(cross_product(sK12_skl,sK13_skl)),set_type) ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,definition,
( sQ4_spl
<=> member(sK14_skl,power_set(cross_product(sK12_skl,sK13_skl))) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( sQ4_spl
| ~ member(sK14_skl,power_set(cross_product(sK12_skl,sK13_skl))) ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f171,f179,f182,f185]) ).
fof(f191,plain,
( sQ4_spl
| ~ member(sK9_skl(cross_product(sK12_skl,sK13_skl),sK14_skl),cross_product(sK12_skl,sK13_skl))
| ~ ilf_type(cross_product(sK12_skl,sK13_skl),set_type) ),
inference(resolution,[status(thm)],[f187,f160]) ).
fof(f194,definition,
( sQ5_spl
<=> ilf_type(cross_product(sK12_skl,sK13_skl),set_type) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( sQ5_spl
| ~ ilf_type(cross_product(sK12_skl,sK13_skl),set_type) ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f197,definition,
( sQ6_spl
<=> member(sK9_skl(cross_product(sK12_skl,sK13_skl),sK14_skl),cross_product(sK12_skl,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f199,plain,
( sQ6_spl
| ~ member(sK9_skl(cross_product(sK12_skl,sK13_skl),sK14_skl),cross_product(sK12_skl,sK13_skl)) ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,plain,
( sQ4_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f191,f194,f197,f185]) ).
fof(f209,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f120]) ).
fof(f210,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f209]) ).
fof(f211,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f180,f132]) ).
fof(f212,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f211]) ).
fof(f213,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f196,f120]) ).
fof(f214,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f213]) ).
fof(f235,plain,
! [X0] :
( sQ6_spl
| ~ member(sK9_skl(cross_product(sK12_skl,sK13_skl),sK14_skl),X0)
| ~ ilf_type(sK9_skl(cross_product(sK12_skl,sK13_skl),sK14_skl),set_type)
| ~ subset(X0,cross_product(sK12_skl,sK13_skl))
| ~ ilf_type(cross_product(sK12_skl,sK13_skl),set_type) ),
inference(resolution,[status(thm)],[f199,f145]) ).
fof(f243,definition,
! [X0] :
( sQ13_spl
<=> ( ~ member(sK9_skl(cross_product(sK12_skl,sK13_skl),sK14_skl),X0)
| ~ subset(X0,cross_product(sK12_skl,sK13_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f244,plain,
! [X0] :
( ~ sQ13_spl
| ~ member(sK9_skl(cross_product(sK12_skl,sK13_skl),sK14_skl),X0)
| ~ subset(X0,cross_product(sK12_skl,sK13_skl)) ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f246,definition,
( sQ14_spl
<=> ilf_type(sK9_skl(cross_product(sK12_skl,sK13_skl),sK14_skl),set_type) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f248,plain,
( sQ14_spl
| ~ ilf_type(sK9_skl(cross_product(sK12_skl,sK13_skl),sK14_skl),set_type) ),
inference(component_clause,[status(thm)],[f246]) ).
fof(f249,plain,
( sQ6_spl
| ~ sQ14_spl
| sQ13_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f235,f194,f243,f246,f197]) ).
fof(f416,plain,
( ~ sQ13_spl
| member(sK14_skl,power_set(cross_product(sK12_skl,sK13_skl)))
| ~ ilf_type(cross_product(sK12_skl,sK13_skl),set_type)
| ~ subset(sK14_skl,cross_product(sK12_skl,sK13_skl)) ),
inference(resolution,[status(thm)],[f244,f159]) ).
fof(f422,definition,
( sQ42_spl
<=> subset(sK14_skl,cross_product(sK12_skl,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f424,plain,
( sQ42_spl
| ~ subset(sK14_skl,cross_product(sK12_skl,sK13_skl)) ),
inference(component_clause,[status(thm)],[f422]) ).
fof(f425,plain,
( ~ sQ13_spl
| sQ4_spl
| ~ sQ5_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f416,f422,f194,f185,f243]) ).
fof(f434,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f248,f120]) ).
fof(f435,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f434]) ).
fof(f450,plain,
! [X0] :
( sQ42_spl
| ~ subset(X0,cross_product(sK12_skl,sK13_skl))
| ~ subset(sK14_skl,X0)
| ~ ilf_type(cross_product(sK12_skl,sK13_skl),set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f424,f131]) ).
fof(f455,definition,
! [X0] :
( sQ45_spl
<=> ( ~ subset(X0,cross_product(sK12_skl,sK13_skl))
| ~ subset(sK14_skl,X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f456,plain,
! [X0] :
( ~ sQ45_spl
| ~ subset(X0,cross_product(sK12_skl,sK13_skl))
| ~ subset(sK14_skl,X0)
| ~ ilf_type(X0,set_type) ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f458,plain,
( sQ42_spl
| ~ sQ5_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f450,f455,f194,f422]) ).
fof(f459,plain,
! [X0] :
( ~ sQ45_spl
| ~ subset(X0,cross_product(sK12_skl,sK13_skl))
| ~ subset(sK14_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f456,f120]) ).
fof(f473,definition,
( sQ47_spl
<=> ilf_type(sK12_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f475,plain,
( sQ47_spl
| ~ ilf_type(sK12_skl,set_type) ),
inference(component_clause,[status(thm)],[f473]) ).
fof(f476,definition,
( sQ48_spl
<=> ilf_type(sK13_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f478,plain,
( sQ48_spl
| ~ ilf_type(sK13_skl,set_type) ),
inference(component_clause,[status(thm)],[f476]) ).
fof(f489,plain,
( sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f478,f120]) ).
fof(f490,plain,
sQ48_spl,
inference(contradiction_clause,[status(thm)],[f489]) ).
fof(f712,plain,
( ~ sQ45_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)],[f459,f32]) ).
fof(f716,definition,
( sQ83_spl
<=> subset(cross_product(domain_of(sK14_skl),range_of(sK14_skl)),cross_product(sK12_skl,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f718,plain,
( sQ83_spl
| ~ subset(cross_product(domain_of(sK14_skl),range_of(sK14_skl)),cross_product(sK12_skl,sK13_skl)) ),
inference(component_clause,[status(thm)],[f716]) ).
fof(f719,definition,
( sQ84_spl
<=> ilf_type(sK14_skl,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f721,plain,
( sQ84_spl
| ~ ilf_type(sK14_skl,binary_relation_type) ),
inference(component_clause,[status(thm)],[f719]) ).
fof(f722,plain,
( ~ sQ45_spl
| ~ sQ84_spl
| ~ sQ83_spl ),
inference(split_clause,[status(thm)],[f712,f716,f719,f455]) ).
fof(f979,plain,
( sQ84_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f721,f125]) ).
fof(f980,plain,
sQ84_spl,
inference(contradiction_clause,[status(thm)],[f979]) ).
fof(f1044,definition,
( sQ123_spl
<=> ilf_type(range_of(sK14_skl),set_type) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f1046,plain,
( sQ123_spl
| ~ ilf_type(range_of(sK14_skl),set_type) ),
inference(component_clause,[status(thm)],[f1044]) ).
fof(f1055,plain,
( sQ123_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1046,f120]) ).
fof(f1056,plain,
sQ123_spl,
inference(contradiction_clause,[status(thm)],[f1055]) ).
fof(f2967,plain,
( sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f475,f120]) ).
fof(f2968,plain,
sQ47_spl,
inference(contradiction_clause,[status(thm)],[f2967]) ).
fof(f3011,plain,
( sQ83_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)],[f718,f139]) ).
fof(f3014,definition,
( sQ318_spl
<=> subset(domain_of(sK14_skl),sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ318_spl])],[split_symbol_definition]) ).
fof(f3016,plain,
( sQ318_spl
| ~ subset(domain_of(sK14_skl),sK12_skl) ),
inference(component_clause,[status(thm)],[f3014]) ).
fof(f3017,definition,
( sQ319_spl
<=> subset(range_of(sK14_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ319_spl])],[split_symbol_definition]) ).
fof(f3019,plain,
( sQ319_spl
| ~ subset(range_of(sK14_skl),sK13_skl) ),
inference(component_clause,[status(thm)],[f3017]) ).
fof(f3020,plain,
( sQ83_spl
| ~ sQ319_spl
| ~ sQ318_spl
| ~ sQ48_spl
| ~ sQ123_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f3011,f473,f1044,f476,f3014,f3017,f716]) ).
fof(f3030,plain,
( sQ318_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3016,f126]) ).
fof(f3031,plain,
sQ318_spl,
inference(contradiction_clause,[status(thm)],[f3030]) ).
fof(f3032,plain,
( sQ319_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3019,f127]) ).
fof(f3033,plain,
sQ319_spl,
inference(contradiction_clause,[status(thm)],[f3032]) ).
fof(f3034,plain,
$false,
inference(sat_refutation,[status(thm)],[f188,f200,f210,f212,f214,f249,f425,f435,f458,f490,f722,f980,f1056,f2968,f3020,f3031,f3033]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET649+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:31:17 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % 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: 0.086219 seconds
% 0.14/0.44 % CPU time: 0.395876 seconds
% 0.14/0.44 % Total memory used: 89.209 MB
% 0.14/0.44 % Net memory used: 88.660 MB
%------------------------------------------------------------------------------