%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET667+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 : n015.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 02:10:24 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 26
% Syntax : Number of formulae : 139 ( 13 unt; 15 def)
% Number of atoms : 428 ( 12 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 495 ( 206 ~; 204 |; 27 &)
% ( 21 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 16 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 175 ( 170 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,binary_relation_type)
=> ( member(ordered_pair(B,C),D)
=> ( member(C,range_of(D))
& member(B,domain_of(D)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(C,B)
<=> member(ordered_pair(C,C),identity_relation_of(B)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,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(f7,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(f24,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(f27,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> domain(B,C,D) = domain_of(D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(domain(B,C,D),subset_type(B)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> range(B,C,D) = range_of(D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,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,C))
=> ( subset(identity_relation_of(D),E)
=> ( subset(D,range(B,C,E))
& subset(D,domain(B,C,E)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,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,C))
=> ( subset(identity_relation_of(D),E)
=> ( subset(D,range(B,C,E))
& subset(D,domain(B,C,E)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f34,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( member(C,range_of(D))
& member(B,domain_of(D)) )
| ~ member(ordered_pair(B,C),D)
| ~ ilf_type(D,binary_relation_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f35,plain,
! [X0,X1,X2] :
( member(X0,domain_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( member(X1,range_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
! [B] :
( ! [C] :
( ( member(C,B)
<=> member(ordered_pair(C,C),identity_relation_of(B)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f38,plain,
! [B] :
( ! [C] :
( ( ( ~ member(ordered_pair(C,C),identity_relation_of(B))
| member(C,B) )
& ( member(ordered_pair(C,C),identity_relation_of(B))
| ~ member(C,B) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f48,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)],[f5]) ).
fof(f50,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)],[f48]) ).
fof(f54,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)],[f7]) ).
fof(f55,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)],[f54]) ).
fof(f56,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK1_skl(C,B),C)
& member(sK1_skl(C,B),B)
& ilf_type(sK1_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,[sK1_skl]),skolemize(D,sK1_skl(C,B))],[f55]) ).
fof(f57,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)],[f56]) ).
fof(f59,plain,
! [X0,X1] :
( member(sK1_skl(X1,X0),X0)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f60,plain,
! [X0,X1] :
( ~ member(sK1_skl(X1,X0),X1)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f77,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(f78,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)],[f77]) ).
fof(f81,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)],[f78]) ).
fof(f121,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)],[f24]) ).
fof(f122,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)],[f121]) ).
fof(f131,plain,
! [B] :
( ! [C] :
( ! [D] :
( domain(B,C,D) = domain_of(D)
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f132,plain,
! [X0,X1,X2] :
( domain(X0,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [B] :
( ! [C] :
( ! [D] :
( ilf_type(domain(B,C,D),subset_type(B))
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ilf_type(domain(X0,X1,X2),subset_type(X0))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [B] :
( ! [C] :
( ! [D] :
( range(B,C,D) = range_of(D)
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f136,plain,
! [X0,X1,X2] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f139,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f140,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ( ~ subset(D,range(B,C,E))
| ~ subset(D,domain(B,C,E)) )
& subset(identity_relation_of(D),E)
& ilf_type(E,relation_type(B,C)) )
& ilf_type(D,set_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f141,plain,
( ( ~ subset(sK14_skl,range(sK12_skl,sK13_skl,sK15_skl))
| ~ subset(sK14_skl,domain(sK12_skl,sK13_skl,sK15_skl)) )
& subset(identity_relation_of(sK14_skl),sK15_skl)
& ilf_type(sK15_skl,relation_type(sK12_skl,sK13_skl))
& ilf_type(sK14_skl,set_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,sK15_skl]),skolemize(B,sK12_skl),skolemize(C,sK13_skl),skolemize(D,sK14_skl),skolemize(E,sK15_skl)],[f140]) ).
fof(f145,plain,
ilf_type(sK15_skl,relation_type(sK12_skl,sK13_skl)),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f146,plain,
subset(identity_relation_of(sK14_skl),sK15_skl),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f147,plain,
( ~ subset(sK14_skl,range(sK12_skl,sK13_skl,sK15_skl))
| ~ subset(sK14_skl,domain(sK12_skl,sK13_skl,sK15_skl)) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f148,definition,
( sQ0_spl
<=> subset(sK14_skl,domain(sK12_skl,sK13_skl,sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( sQ0_spl
| ~ subset(sK14_skl,domain(sK12_skl,sK13_skl,sK15_skl)) ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f151,definition,
( sQ1_spl
<=> subset(sK14_skl,range(sK12_skl,sK13_skl,sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( sQ1_spl
| ~ subset(sK14_skl,range(sK12_skl,sK13_skl,sK15_skl)) ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f147,f148,f151]) ).
fof(f157,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f81]) ).
fof(f160,plain,
! [X0,X1] :
( member(ordered_pair(X0,X0),identity_relation_of(X1))
| ~ member(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f39,f139]) ).
fof(f165,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f157,f139]) ).
fof(f167,plain,
! [X0,X1,X2] :
( member(X2,domain_of(X1))
| ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f35,f139]) ).
fof(f168,plain,
! [X0,X1,X2] :
( member(X0,range_of(X1))
| ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f36,f139]) ).
fof(f170,plain,
! [X0,X1,X2] :
( domain(X2,X0,X1) = domain_of(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f132,f139]) ).
fof(f171,plain,
! [X0,X1,X2] :
( domain(X1,X2,X0) = domain_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f170,f139]) ).
fof(f172,plain,
domain(sK12_skl,sK13_skl,sK15_skl) = domain_of(sK15_skl),
inference(resolution,[status(thm)],[f171,f145]) ).
fof(f173,plain,
( sQ0_spl
| ~ subset(sK14_skl,domain_of(sK15_skl)) ),
inference(backward_demodulation,[status(thm)],[f172,f150]) ).
fof(f174,plain,
! [X0,X1,X2] :
( range(X2,X0,X1) = range_of(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f136,f139]) ).
fof(f175,plain,
! [X0,X1,X2] :
( range(X1,X2,X0) = range_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f174,f139]) ).
fof(f176,plain,
range(sK12_skl,sK13_skl,sK15_skl) = range_of(sK15_skl),
inference(resolution,[status(thm)],[f175,f145]) ).
fof(f185,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)],[f57,f139]) ).
fof(f186,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f185,f139]) ).
fof(f187,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f186,f139]) ).
fof(f198,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)],[f50,f139]) ).
fof(f203,plain,
! [X0,X1,X2] :
( ilf_type(domain(X2,X0,X1),subset_type(X2))
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f134,f139]) ).
fof(f204,plain,
! [X0,X1,X2] :
( ilf_type(domain(X1,X2,X0),subset_type(X1))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f203,f139]) ).
fof(f207,plain,
( ilf_type(domain_of(sK15_skl),subset_type(sK12_skl))
| ~ ilf_type(sK15_skl,relation_type(sK12_skl,sK13_skl)) ),
inference(paramodulation,[status(thm)],[f172,f204]) ).
fof(f209,definition,
( sQ2_spl
<=> ilf_type(sK15_skl,relation_type(sK12_skl,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f211,plain,
( sQ2_spl
| ~ ilf_type(sK15_skl,relation_type(sK12_skl,sK13_skl)) ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f212,definition,
( sQ3_spl
<=> ilf_type(domain_of(sK15_skl),subset_type(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f215,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f207,f209,f212]) ).
fof(f217,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f211,f145]) ).
fof(f218,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f217]) ).
fof(f258,plain,
! [X0,X1] :
( member(sK1_skl(X0,X1),X1)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f59,f139]) ).
fof(f259,plain,
! [X0,X1] :
( ~ member(sK1_skl(X0,X1),X0)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f60,f139]) ).
fof(f260,plain,
! [X0,X1] :
( ~ member(sK1_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f259,f139]) ).
fof(f261,plain,
( sQ0_spl
| ~ member(sK1_skl(domain_of(sK15_skl),sK14_skl),domain_of(sK15_skl)) ),
inference(resolution,[status(thm)],[f260,f173]) ).
fof(f263,plain,
! [X0] :
( sQ0_spl
| ~ member(ordered_pair(sK1_skl(domain_of(sK15_skl),sK14_skl),X0),sK15_skl)
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f261,f167]) ).
fof(f267,definition,
! [X0] :
( sQ6_spl
<=> ( ~ member(ordered_pair(sK1_skl(domain_of(sK15_skl),sK14_skl),X0),sK15_skl)
| ~ ilf_type(X0,set_type) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f268,plain,
! [X0] :
( ~ sQ6_spl
| ~ member(ordered_pair(sK1_skl(domain_of(sK15_skl),sK14_skl),X0),sK15_skl)
| ~ ilf_type(X0,set_type) ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f270,definition,
( sQ7_spl
<=> ilf_type(sK15_skl,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f272,plain,
( sQ7_spl
| ~ ilf_type(sK15_skl,binary_relation_type) ),
inference(component_clause,[status(thm)],[f270]) ).
fof(f273,plain,
( sQ0_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f263,f267,f270,f148]) ).
fof(f274,definition,
( sQ8_spl
<=> ilf_type(sK1_skl(domain_of(sK15_skl),sK14_skl),set_type) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f276,plain,
( sQ8_spl
| ~ ilf_type(sK1_skl(domain_of(sK15_skl),sK14_skl),set_type) ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f285,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f276,f139]) ).
fof(f286,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f285]) ).
fof(f287,plain,
( sQ1_spl
| ~ subset(sK14_skl,range_of(sK15_skl)) ),
inference(forward_demodulation,[status(thm)],[f176,f153]) ).
fof(f289,plain,
( sQ1_spl
| ~ member(sK1_skl(range_of(sK15_skl),sK14_skl),range_of(sK15_skl)) ),
inference(resolution,[status(thm)],[f287,f260]) ).
fof(f290,plain,
! [X0] :
( sQ1_spl
| ~ member(ordered_pair(X0,sK1_skl(range_of(sK15_skl),sK14_skl)),sK15_skl)
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(sK1_skl(range_of(sK15_skl),sK14_skl),set_type) ),
inference(resolution,[status(thm)],[f289,f168]) ).
fof(f294,definition,
( sQ11_spl
<=> ilf_type(sK1_skl(range_of(sK15_skl),sK14_skl),set_type) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f296,plain,
( sQ11_spl
| ~ ilf_type(sK1_skl(range_of(sK15_skl),sK14_skl),set_type) ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f297,definition,
! [X0] :
( sQ12_spl
<=> ~ member(ordered_pair(X0,sK1_skl(range_of(sK15_skl),sK14_skl)),sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f298,plain,
! [X0] :
( ~ sQ12_spl
| ~ member(ordered_pair(X0,sK1_skl(range_of(sK15_skl),sK14_skl)),sK15_skl) ),
inference(component_clause,[status(thm)],[f297]) ).
fof(f300,plain,
( sQ1_spl
| sQ12_spl
| ~ sQ7_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f290,f294,f270,f297,f151]) ).
fof(f309,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f296,f139]) ).
fof(f310,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f309]) ).
fof(f312,plain,
( sQ7_spl
| ~ relation_like(sK15_skl) ),
inference(resolution,[status(thm)],[f272,f165]) ).
fof(f346,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)],[f122,f139]) ).
fof(f347,plain,
! [X0,X1] :
( sQ7_spl
| ~ ilf_type(sK15_skl,subset_type(cross_product(X1,X0)))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f346,f312]) ).
fof(f348,plain,
! [X0,X1] :
( sQ7_spl
| ~ ilf_type(sK15_skl,subset_type(cross_product(X0,X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f347,f139]) ).
fof(f349,plain,
! [X0,X1] :
( sQ7_spl
| ~ ilf_type(sK15_skl,relation_type(X1,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f348,f198]) ).
fof(f350,plain,
! [X0,X1] :
( sQ7_spl
| ~ ilf_type(sK15_skl,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f349,f139]) ).
fof(f351,plain,
( sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f145,f350]) ).
fof(f353,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f351]) ).
fof(f365,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ member(ordered_pair(X1,sK1_skl(range_of(sK15_skl),sK14_skl)),X0)
| ~ subset(X0,sK15_skl) ),
inference(resolution,[status(thm)],[f298,f187]) ).
fof(f370,plain,
! [X0] :
( ~ sQ12_spl
| ~ member(ordered_pair(X0,sK1_skl(range_of(sK15_skl),sK14_skl)),identity_relation_of(sK14_skl)) ),
inference(resolution,[status(thm)],[f365,f146]) ).
fof(f373,plain,
( ~ sQ12_spl
| ~ member(sK1_skl(range_of(sK15_skl),sK14_skl),sK14_skl)
| ~ ilf_type(sK1_skl(range_of(sK15_skl),sK14_skl),set_type) ),
inference(resolution,[status(thm)],[f370,f160]) ).
fof(f377,definition,
( sQ16_spl
<=> member(sK1_skl(range_of(sK15_skl),sK14_skl),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f379,plain,
( sQ16_spl
| ~ member(sK1_skl(range_of(sK15_skl),sK14_skl),sK14_skl) ),
inference(component_clause,[status(thm)],[f377]) ).
fof(f380,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f373,f294,f377,f297]) ).
fof(f383,plain,
( sQ16_spl
| subset(sK14_skl,range_of(sK15_skl))
| ~ ilf_type(range_of(sK15_skl),set_type) ),
inference(resolution,[status(thm)],[f379,f258]) ).
fof(f387,definition,
( sQ17_spl
<=> ilf_type(range_of(sK15_skl),set_type) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f389,plain,
( sQ17_spl
| ~ ilf_type(range_of(sK15_skl),set_type) ),
inference(component_clause,[status(thm)],[f387]) ).
fof(f390,definition,
( sQ18_spl
<=> subset(sK14_skl,range_of(sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f391,plain,
( ~ sQ18_spl
| subset(sK14_skl,range_of(sK15_skl)) ),
inference(component_clause,[status(thm)],[f390]) ).
fof(f393,plain,
( sQ16_spl
| sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f383,f387,f390,f377]) ).
fof(f403,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f389,f139]) ).
fof(f404,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f403]) ).
fof(f405,plain,
( ~ sQ18_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f391,f287]) ).
fof(f406,plain,
( ~ sQ18_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f405]) ).
fof(f407,plain,
! [X0] :
( ~ sQ6_spl
| ~ member(ordered_pair(sK1_skl(domain_of(sK15_skl),sK14_skl),X0),sK15_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f268,f139]) ).
fof(f431,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ member(ordered_pair(sK1_skl(domain_of(sK15_skl),sK14_skl),X1),X0)
| ~ subset(X0,sK15_skl) ),
inference(resolution,[status(thm)],[f407,f187]) ).
fof(f457,plain,
! [X0] :
( ~ sQ6_spl
| ~ member(ordered_pair(sK1_skl(domain_of(sK15_skl),sK14_skl),X0),identity_relation_of(sK14_skl)) ),
inference(resolution,[status(thm)],[f431,f146]) ).
fof(f465,plain,
( ~ sQ6_spl
| ~ member(sK1_skl(domain_of(sK15_skl),sK14_skl),sK14_skl)
| ~ ilf_type(sK1_skl(domain_of(sK15_skl),sK14_skl),set_type) ),
inference(resolution,[status(thm)],[f457,f160]) ).
fof(f469,definition,
( sQ22_spl
<=> member(sK1_skl(domain_of(sK15_skl),sK14_skl),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( sQ22_spl
| ~ member(sK1_skl(domain_of(sK15_skl),sK14_skl),sK14_skl) ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f472,plain,
( ~ sQ6_spl
| ~ sQ22_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f465,f274,f469,f267]) ).
fof(f475,plain,
( sQ22_spl
| subset(sK14_skl,domain_of(sK15_skl))
| ~ ilf_type(domain_of(sK15_skl),set_type) ),
inference(resolution,[status(thm)],[f471,f258]) ).
fof(f479,definition,
( sQ23_spl
<=> ilf_type(domain_of(sK15_skl),set_type) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f481,plain,
( sQ23_spl
| ~ ilf_type(domain_of(sK15_skl),set_type) ),
inference(component_clause,[status(thm)],[f479]) ).
fof(f482,definition,
( sQ24_spl
<=> subset(sK14_skl,domain_of(sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( ~ sQ24_spl
| subset(sK14_skl,domain_of(sK15_skl)) ),
inference(component_clause,[status(thm)],[f482]) ).
fof(f485,plain,
( sQ22_spl
| sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f475,f479,f482,f469]) ).
fof(f494,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f481,f139]) ).
fof(f495,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f494]) ).
fof(f496,plain,
( ~ sQ24_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f483,f173]) ).
fof(f497,plain,
( ~ sQ24_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f496]) ).
fof(f498,plain,
$false,
inference(sat_refutation,[status(thm)],[f154,f215,f218,f273,f286,f300,f310,f353,f380,f393,f404,f406,f472,f485,f495,f497]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET667+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n015.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 05:34:51 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.051621 seconds
% 0.13/0.40 % CPU time: 0.217799 seconds
% 0.13/0.40 % Total memory used: 85.691 MB
% 0.13/0.40 % Net memory used: 85.461 MB
%------------------------------------------------------------------------------