%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET650+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 : n012.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 0.02s 0.34s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 93 ( 8 unt; 7 def)
% Number of atoms : 373 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 477 ( 197 ~; 203 |; 34 &)
% ( 15 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 176 ( 166 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( member(B,domain_of(C))
<=> ? [D] :
( member(ordered_pair(B,D),C)
& ilf_type(D,set_type) ) ) ) ),
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] :
( member(ordered_pair(D,B),C)
& ilf_type(D,set_type) ) ) ) ),
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(E,C)
& member(D,B) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,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(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)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
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(range_of(D),C)
& subset(domain_of(D),B) ) ) ) ),
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(range_of(D),C)
& subset(domain_of(D),B) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
! [B] :
( ! [C] :
( ( member(B,domain_of(C))
<=> ? [D] :
( member(ordered_pair(B,D),C)
& ilf_type(D,set_type) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f30,plain,
! [B] :
( ! [C] :
( ( ( ! [D] :
( ~ member(ordered_pair(B,D),C)
| ~ ilf_type(D,set_type) )
| member(B,domain_of(C)) )
& ( ? [D] :
( member(ordered_pair(B,D),C)
& ilf_type(D,set_type) )
| ~ member(B,domain_of(C)) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [B] :
( ! [C] :
( ( ( ! [D] :
( ~ member(ordered_pair(B,D),C)
| ~ ilf_type(D,set_type) )
| member(B,domain_of(C)) )
& ( ( member(ordered_pair(B,sK0_skl(C,B)),C)
& ilf_type(sK0_skl(C,B),set_type) )
| ~ member(B,domain_of(C)) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f30]) ).
fof(f33,plain,
! [X0,X1] :
( member(ordered_pair(X0,sK0_skl(X1,X0)),X1)
| ~ member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f35,plain,
! [B] :
( ! [C] :
( ( member(B,range_of(C))
<=> ? [D] :
( member(ordered_pair(D,B),C)
& ilf_type(D,set_type) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f36,plain,
! [B] :
( ! [C] :
( ( ( ! [D] :
( ~ member(ordered_pair(D,B),C)
| ~ ilf_type(D,set_type) )
| member(B,range_of(C)) )
& ( ? [D] :
( member(ordered_pair(D,B),C)
& ilf_type(D,set_type) )
| ~ member(B,range_of(C)) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [B] :
( ! [C] :
( ( ( ! [D] :
( ~ member(ordered_pair(D,B),C)
| ~ ilf_type(D,set_type) )
| member(B,range_of(C)) )
& ( ( member(ordered_pair(sK1_skl(C,B),B),C)
& ilf_type(sK1_skl(C,B),set_type) )
| ~ member(B,range_of(C)) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B))],[f36]) ).
fof(f39,plain,
! [X0,X1] :
( member(ordered_pair(sK1_skl(X1,X0),X0),X1)
| ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f41,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ! [F] :
( ( member(E,C)
& member(D,B) )
| ~ member(ordered_pair(D,E),F)
| ~ ilf_type(F,relation_type(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(f42,plain,
! [X0,X1,X2,X3,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(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)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(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)],[f41]) ).
fof(f60,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)],[f8]) ).
fof(f62,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)],[f60]) ).
fof(f66,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)],[f10]) ).
fof(f67,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)],[f66]) ).
fof(f68,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK5_skl(C,B),C)
& member(sK5_skl(C,B),B)
& ilf_type(sK5_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,[sK5_skl]),skolemize(D,sK5_skl(C,B))],[f67]) ).
fof(f71,plain,
! [X0,X1] :
( member(sK5_skl(X1,X0),X0)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f72,plain,
! [X0,X1] :
( ~ member(sK5_skl(X1,X0),X1)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
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(f119,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(f120,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)],[f119]) ).
fof(f129,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f130,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)],[f28]) ).
fof(f131,plain,
( ( ~ subset(range_of(sK16_skl),sK15_skl)
| ~ subset(domain_of(sK16_skl),sK14_skl) )
& ilf_type(sK16_skl,relation_type(sK14_skl,sK15_skl))
& ilf_type(sK15_skl,set_type)
& ilf_type(sK14_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl]),skolemize(B,sK14_skl),skolemize(C,sK15_skl),skolemize(D,sK16_skl)],[f130]) ).
fof(f134,plain,
ilf_type(sK16_skl,relation_type(sK14_skl,sK15_skl)),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f135,plain,
( ~ subset(range_of(sK16_skl),sK15_skl)
| ~ subset(domain_of(sK16_skl),sK14_skl) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f136,definition,
( sQ0_spl
<=> subset(domain_of(sK16_skl),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f139,definition,
( sQ1_spl
<=> subset(range_of(sK16_skl),sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f135,f136,f139]) ).
fof(f143,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f81]) ).
fof(f152,plain,
! [X0,X1,X2,X3,X4] :
( member(X1,X4)
| ~ member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X3,relation_type(X4,X0))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f42,f129]) ).
fof(f153,plain,
! [X0,X1,X2,X3,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X3,relation_type(X4,X0))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f129]) ).
fof(f156,plain,
! [X0,X1] :
( member(ordered_pair(X1,sK0_skl(X0,X1)),X0)
| ~ member(X1,domain_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f33,f129]) ).
fof(f158,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ ilf_type(X0,relation_type(X3,X2))
| ~ ilf_type(sK0_skl(X0,X1),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,domain_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[f156,f152]) ).
fof(f162,plain,
! [X0,X1,X2,X3] :
( member(X1,X2)
| ~ ilf_type(X0,relation_type(X2,X3))
| ~ ilf_type(sK0_skl(X0,X1),set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X1,domain_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f158,f129]) ).
fof(f167,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f143,f129]) ).
fof(f192,plain,
! [X0,X1] :
( member(ordered_pair(sK1_skl(X0,X1),X1),X0)
| ~ member(X1,range_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f39,f129]) ).
fof(f193,plain,
! [X0,X1,X2,X3] :
( member(X1,X2)
| ~ ilf_type(X0,relation_type(X3,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK1_skl(X0,X1),set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,range_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[f192,f153]) ).
fof(f199,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ ilf_type(X0,relation_type(X2,X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK1_skl(X0,X1),set_type)
| ~ member(X1,range_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f193,f129]) ).
fof(f265,plain,
! [X0,X1,X2,X3] :
( member(X1,X2)
| ~ ilf_type(X0,relation_type(X2,X3))
| ~ ilf_type(sK0_skl(X0,X1),set_type)
| ~ member(X1,domain_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f162,f129]) ).
fof(f266,plain,
! [X0,X1,X2,X3] :
( member(X1,X2)
| ~ ilf_type(X0,relation_type(X2,X3))
| ~ member(X1,domain_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[f265,f129]) ).
fof(f267,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ ilf_type(X0,relation_type(X2,X3))
| ~ ilf_type(X1,set_type)
| ~ member(X1,range_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f199,f129]) ).
fof(f268,plain,
! [X0] :
( member(X0,sK15_skl)
| ~ ilf_type(X0,set_type)
| ~ member(X0,range_of(sK16_skl))
| ~ ilf_type(sK16_skl,binary_relation_type) ),
inference(resolution,[status(thm)],[f267,f134]) ).
fof(f269,definition,
( sQ5_spl
<=> ilf_type(sK16_skl,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f271,plain,
( sQ5_spl
| ~ ilf_type(sK16_skl,binary_relation_type) ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f272,definition,
! [X0] :
( sQ6_spl
<=> ( member(X0,sK15_skl)
| ~ ilf_type(X0,set_type)
| ~ member(X0,range_of(sK16_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f273,plain,
! [X0] :
( ~ sQ6_spl
| member(X0,sK15_skl)
| ~ ilf_type(X0,set_type)
| ~ member(X0,range_of(sK16_skl)) ),
inference(component_clause,[status(thm)],[f272]) ).
fof(f275,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f268,f269,f272]) ).
fof(f276,plain,
( sQ5_spl
| ~ relation_like(sK16_skl) ),
inference(resolution,[status(thm)],[f271,f167]) ).
fof(f280,plain,
! [X0,X1] :
( member(sK5_skl(X0,X1),X1)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f71,f129]) ).
fof(f395,plain,
! [X0] :
( member(X0,sK14_skl)
| ~ member(X0,domain_of(sK16_skl))
| ~ ilf_type(sK16_skl,binary_relation_type) ),
inference(resolution,[status(thm)],[f266,f134]) ).
fof(f397,definition,
! [X0] :
( sQ10_spl
<=> ( member(X0,sK14_skl)
| ~ member(X0,domain_of(sK16_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f398,plain,
! [X0] :
( ~ sQ10_spl
| member(X0,sK14_skl)
| ~ member(X0,domain_of(sK16_skl)) ),
inference(component_clause,[status(thm)],[f397]) ).
fof(f400,plain,
( sQ10_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f395,f269,f397]) ).
fof(f451,plain,
! [X0,X1] :
( ~ member(sK5_skl(X0,X1),X0)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f72,f129]) ).
fof(f454,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)],[f120,f129]) ).
fof(f561,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)],[f62,f129]) ).
fof(f563,plain,
! [X0,X1,X2] :
( relation_like(X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f561,f454]) ).
fof(f564,plain,
! [X0,X1,X2] :
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f563]) ).
fof(f565,plain,
! [X0,X1,X2] :
( relation_like(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f564,f129]) ).
fof(f568,plain,
relation_like(sK16_skl),
inference(resolution,[status(thm)],[f565,f134]) ).
fof(f570,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f568,f276]) ).
fof(f571,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f570]) ).
fof(f572,plain,
! [X0] :
( ~ sQ6_spl
| member(X0,sK15_skl)
| ~ member(X0,range_of(sK16_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f273,f129]) ).
fof(f578,plain,
! [X0] :
( ~ sQ6_spl
| subset(range_of(sK16_skl),X0)
| ~ ilf_type(X0,set_type)
| member(sK5_skl(X0,range_of(sK16_skl)),sK15_skl) ),
inference(resolution,[status(thm)],[f572,f280]) ).
fof(f590,plain,
! [X0] :
( ~ sQ6_spl
| subset(range_of(sK16_skl),X0)
| member(sK5_skl(X0,range_of(sK16_skl)),sK15_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f578,f129]) ).
fof(f631,plain,
! [X0] :
( ~ sQ10_spl
| subset(domain_of(sK16_skl),X0)
| ~ ilf_type(X0,set_type)
| member(sK5_skl(X0,domain_of(sK16_skl)),sK14_skl) ),
inference(resolution,[status(thm)],[f398,f280]) ).
fof(f643,plain,
! [X0] :
( ~ sQ10_spl
| subset(domain_of(sK16_skl),X0)
| member(sK5_skl(X0,domain_of(sK16_skl)),sK14_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f631,f129]) ).
fof(f685,plain,
( ~ sQ6_spl
| subset(range_of(sK16_skl),sK15_skl)
| ~ ilf_type(sK15_skl,set_type)
| subset(range_of(sK16_skl),sK15_skl) ),
inference(resolution,[status(thm)],[f590,f451]) ).
fof(f686,definition,
( sQ44_spl
<=> ilf_type(sK15_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f688,plain,
( sQ44_spl
| ~ ilf_type(sK15_skl,set_type) ),
inference(component_clause,[status(thm)],[f686]) ).
fof(f689,plain,
( ~ sQ6_spl
| ~ sQ44_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f685,f139,f686,f272]) ).
fof(f691,plain,
( ~ sQ10_spl
| subset(domain_of(sK16_skl),sK14_skl)
| ~ ilf_type(sK14_skl,set_type)
| subset(domain_of(sK16_skl),sK14_skl) ),
inference(resolution,[status(thm)],[f643,f451]) ).
fof(f692,definition,
( sQ45_spl
<=> ilf_type(sK14_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f694,plain,
( sQ45_spl
| ~ ilf_type(sK14_skl,set_type) ),
inference(component_clause,[status(thm)],[f692]) ).
fof(f695,plain,
( ~ sQ10_spl
| ~ sQ45_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f691,f136,f692,f397]) ).
fof(f696,plain,
( sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f688,f129]) ).
fof(f697,plain,
sQ44_spl,
inference(contradiction_clause,[status(thm)],[f696]) ).
fof(f698,plain,
( sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f694,f129]) ).
fof(f699,plain,
sQ45_spl,
inference(contradiction_clause,[status(thm)],[f698]) ).
fof(f700,plain,
$false,
inference(sat_refutation,[status(thm)],[f142,f275,f400,f571,f689,f695,f697,f699]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET650+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Mon Sep 21 05:31:23 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.31 % Drodi V4.1.1
% 0.02/0.34 % Refutation found
% 0.02/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.02/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.36 % Elapsed time: 0.055120 seconds
% 0.09/0.36 % CPU time: 0.190191 seconds
% 0.09/0.36 % Total memory used: 79.822 MB
% 0.09/0.36 % Net memory used: 79.626 MB
%------------------------------------------------------------------------------