%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET665+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 : n026.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 02:10:23 PM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 120 ( 10 unt; 9 def)
% Number of atoms : 437 ( 9 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 543 ( 226 ~; 228 |; 35 &)
% ( 25 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 10 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 179 ( 174 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ( member(ordered_pair(D,E),B)
=> member(ordered_pair(D,E),C) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( member(ordered_pair(C,D),identity_relation_of(B))
<=> ( C = D
& member(C,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)
=> ( member(ordered_pair(B,C),cross_product(D,E))
<=> ( member(C,E)
& member(B,D) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B] :
( ilf_type(B,set_type)
=> ilf_type(identity_relation_of(B),binary_relation_type) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,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(f17,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(f20,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(f21,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(f23,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(f25,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(f27,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
! [B] :
( ilf_type(B,set_type)
=> subset(identity_relation_of(B),cross_product(B,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> subset(identity_relation_of(B),cross_product(B,B)) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f30,plain,
! [B] :
( ! [C] :
( ( subset(B,C)
<=> ! [D] :
( ! [E] :
( member(ordered_pair(D,E),C)
| ~ member(ordered_pair(D,E),B)
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,binary_relation_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f31,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ? [E] :
( ~ member(ordered_pair(D,E),C)
& member(ordered_pair(D,E),B)
& ilf_type(E,set_type) )
& ilf_type(D,set_type) )
| subset(B,C) )
& ( ! [D] :
( ! [E] :
( member(ordered_pair(D,E),C)
| ~ member(ordered_pair(D,E),B)
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) )
| ~ subset(B,C) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,binary_relation_type) ),
inference(NNF_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(ordered_pair(sK0_skl(C,B),sK1_skl(C,B)),C)
& member(ordered_pair(sK0_skl(C,B),sK1_skl(C,B)),B)
& ilf_type(sK1_skl(C,B),set_type)
& ilf_type(sK0_skl(C,B),set_type) )
| subset(B,C) )
& ( ! [D] :
( ! [E] :
( member(ordered_pair(D,E),C)
| ~ member(ordered_pair(D,E),B)
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) )
| ~ subset(B,C) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,binary_relation_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(D,sK0_skl(C,B)),skolemize(E,sK1_skl(C,B))],[f31]) ).
fof(f36,plain,
! [X0,X1] :
( member(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)
| subset(X0,X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f37,plain,
! [X0,X1] :
( ~ member(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X1)
| subset(X0,X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f38,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( member(ordered_pair(C,D),identity_relation_of(B))
<=> ( C = D
& member(C,B) ) )
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f39,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( ( C != D
| ~ member(C,B)
| member(ordered_pair(C,D),identity_relation_of(B)) )
& ( ( C = D
& member(C,B) )
| ~ member(ordered_pair(C,D),identity_relation_of(B)) ) )
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( member(X1,X0)
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f43,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ( member(ordered_pair(B,C),cross_product(D,E))
<=> ( member(C,E)
& member(B,D) ) )
| ~ 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(f44,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ( ( ~ member(C,E)
| ~ member(B,D)
| member(ordered_pair(B,C),cross_product(D,E)) )
& ( ( member(C,E)
& member(B,D) )
| ~ member(ordered_pair(B,C),cross_product(D,E)) ) )
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f43]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( ~ member(X1,X3)
| ~ member(X0,X2)
| member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ 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)],[f44]) ).
fof(f66,plain,
! [B] :
( ilf_type(identity_relation_of(B),binary_relation_type)
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f67,plain,
! [X0] :
( ilf_type(identity_relation_of(X0),binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
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)],[f11]) ).
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(f94,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)],[f17]) ).
fof(f95,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)],[f94]) ).
fof(f97,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)],[f95]) ).
fof(f110,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)],[f20]) ).
fof(f111,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)],[f110]) ).
fof(f112,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)],[f21]) ).
fof(f113,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)],[f112]) ).
fof(f114,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK11_skl(C,B),C)
& member(sK11_skl(C,B),B)
& ilf_type(sK11_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,[sK11_skl]),skolemize(D,sK11_skl(C,B))],[f113]) ).
fof(f117,plain,
! [X0,X1] :
( member(sK11_skl(X1,X0),X0)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f118,plain,
! [X0,X1] :
( ~ member(sK11_skl(X1,X0),X1)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f122,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)],[f23]) ).
fof(f123,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)],[f122]) ).
fof(f125,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)],[f123]) ).
fof(f129,plain,
! [B] :
( ( empty(B)
<=> ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) ) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f130,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)],[f129]) ).
fof(f131,plain,
! [B] :
( ( ( ( member(sK13_skl(B),B)
& ilf_type(sK13_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,[sK13_skl]),skolemize(C,sK13_skl(B))],[f130]) ).
fof(f132,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f137,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f138,plain,
? [B] :
( ~ subset(identity_relation_of(B),cross_product(B,B))
& ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f139,plain,
( ~ subset(identity_relation_of(sK14_skl),cross_product(sK14_skl,sK14_skl))
& ilf_type(sK14_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(B,sK14_skl)],[f138]) ).
fof(f141,plain,
~ subset(identity_relation_of(sK14_skl),cross_product(sK14_skl,sK14_skl)),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f147,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f81]) ).
fof(f150,plain,
! [X0] : ilf_type(identity_relation_of(X0),binary_relation_type),
inference(forward_subsumption_resolution,[status(thm)],[f67,f137]) ).
fof(f154,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ member(ordered_pair(X0,X1),identity_relation_of(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f41,f137]) ).
fof(f159,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),identity_relation_of(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f40,f137]) ).
fof(f168,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f147,f137]) ).
fof(f172,plain,
( member(ordered_pair(sK0_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl))),identity_relation_of(sK14_skl))
| ~ ilf_type(cross_product(sK14_skl,sK14_skl),binary_relation_type)
| ~ ilf_type(identity_relation_of(sK14_skl),binary_relation_type) ),
inference(resolution,[status(thm)],[f36,f141]) ).
fof(f174,definition,
( sQ0_spl
<=> ilf_type(identity_relation_of(sK14_skl),binary_relation_type) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( sQ0_spl
| ~ ilf_type(identity_relation_of(sK14_skl),binary_relation_type) ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,definition,
( sQ1_spl
<=> ilf_type(cross_product(sK14_skl,sK14_skl),binary_relation_type) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f179,plain,
( sQ1_spl
| ~ ilf_type(cross_product(sK14_skl,sK14_skl),binary_relation_type) ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,definition,
( sQ2_spl
<=> member(ordered_pair(sK0_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl))),identity_relation_of(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( ~ sQ2_spl
| member(ordered_pair(sK0_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl))),identity_relation_of(sK14_skl)) ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f183,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f172,f174,f177,f180]) ).
fof(f184,plain,
( ~ sQ2_spl
| member(sK0_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),sK14_skl)
| ~ ilf_type(sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),set_type)
| ~ ilf_type(sK0_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),set_type) ),
inference(resolution,[status(thm)],[f181,f159]) ).
fof(f185,plain,
( ~ sQ2_spl
| sK0_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)) = sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl))
| ~ ilf_type(sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),set_type)
| ~ ilf_type(sK0_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),set_type) ),
inference(resolution,[status(thm)],[f181,f154]) ).
fof(f186,definition,
( sQ3_spl
<=> ilf_type(sK0_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),set_type) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( sQ3_spl
| ~ ilf_type(sK0_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),set_type) ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,definition,
( sQ4_spl
<=> ilf_type(sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),set_type) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( sQ4_spl
| ~ ilf_type(sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),set_type) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,definition,
( sQ5_spl
<=> member(sK0_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( ~ sQ5_spl
| member(sK0_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),sK14_skl) ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,plain,
( ~ sQ2_spl
| sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f184,f186,f189,f192,f180]) ).
fof(f196,definition,
( sQ6_spl
<=> sK0_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)) = sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f197,plain,
( ~ sQ6_spl
| sK0_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)) = sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)) ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,plain,
( ~ sQ2_spl
| sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f185,f186,f189,f196,f180]) ).
fof(f200,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f137]) ).
fof(f201,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f200]) ).
fof(f202,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f188,f137]) ).
fof(f203,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f204,plain,
( sQ1_spl
| ~ relation_like(cross_product(sK14_skl,sK14_skl)) ),
inference(resolution,[status(thm)],[f179,f168]) ).
fof(f207,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| member(sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),sK14_skl) ),
inference(forward_demodulation,[status(thm)],[f197,f193]) ).
fof(f214,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,X2)
| ~ member(X3,X1)
| member(ordered_pair(X3,X0),cross_product(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f47,f137]) ).
fof(f216,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(ordered_pair(X2,X0),cross_product(X3,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f214,f137]) ).
fof(f219,plain,
! [X0,X1,X2,X3] :
( ~ member(X2,X0)
| ~ member(X1,X3)
| member(ordered_pair(X1,X2),cross_product(X3,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f216,f137]) ).
fof(f222,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f132,f137]) ).
fof(f233,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)],[f111,f137]) ).
fof(f234,plain,
! [X0,X1,X2] :
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f233,f137]) ).
fof(f236,plain,
( ~ member(ordered_pair(sK0_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl))),cross_product(sK14_skl,sK14_skl))
| ~ ilf_type(cross_product(sK14_skl,sK14_skl),binary_relation_type)
| ~ ilf_type(identity_relation_of(sK14_skl),binary_relation_type) ),
inference(resolution,[status(thm)],[f37,f141]) ).
fof(f238,definition,
( sQ7_spl
<=> member(ordered_pair(sK0_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl))),cross_product(sK14_skl,sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f240,plain,
( sQ7_spl
| ~ member(ordered_pair(sK0_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl))),cross_product(sK14_skl,sK14_skl)) ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f236,f174,f177,f238]) ).
fof(f243,plain,
! [X0,X1,X2,X3] :
( ~ member(X1,X3)
| ~ member(X0,X2)
| member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f219,f137]) ).
fof(f268,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f150]) ).
fof(f269,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f268]) ).
fof(f271,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f222,f137]) ).
fof(f289,plain,
! [X0,X1] :
( member(sK11_skl(X0,X1),X1)
| member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f117,f137]) ).
fof(f290,plain,
! [X0,X1] :
( ~ member(sK11_skl(X0,X1),X0)
| member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f118,f137]) ).
fof(f291,plain,
! [X0,X1] :
( ~ member(sK11_skl(X1,X0),X1)
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f290,f137]) ).
fof(f292,plain,
! [X0] :
( member(X0,power_set(X0))
| ~ ilf_type(X0,set_type)
| member(X0,power_set(X0)) ),
inference(resolution,[status(thm)],[f291,f289]) ).
fof(f293,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| member(X0,power_set(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f292]) ).
fof(f294,plain,
! [X0] : member(X0,power_set(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f293,f137]) ).
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)],[f125,f137]) ).
fof(f300,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[f299,f137]) ).
fof(f301,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f300,f271]) ).
fof(f385,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)],[f97,f137]) ).
fof(f386,plain,
! [X0,X1] :
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(resolution,[status(thm)],[f385,f137]) ).
fof(f387,plain,
! [X0,X1,X2] :
( relation_like(X0)
| ~ ilf_type(X0,member_type(power_set(cross_product(X1,X2)))) ),
inference(resolution,[status(thm)],[f386,f234]) ).
fof(f389,plain,
! [X0,X1] :
( sQ1_spl
| ~ ilf_type(cross_product(sK14_skl,sK14_skl),member_type(power_set(cross_product(X0,X1)))) ),
inference(resolution,[status(thm)],[f387,f204]) ).
fof(f391,plain,
! [X0,X1] :
( sQ1_spl
| ~ member(cross_product(sK14_skl,sK14_skl),power_set(cross_product(X0,X1))) ),
inference(resolution,[status(thm)],[f389,f301]) ).
fof(f392,plain,
( sQ1_spl
| $false ),
inference(resolution,[status(thm)],[f391,f294]) ).
fof(f393,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f392]) ).
fof(f408,plain,
( sQ7_spl
| ~ sQ6_spl
| ~ member(ordered_pair(sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl))),cross_product(sK14_skl,sK14_skl)) ),
inference(forward_demodulation,[status(thm)],[f197,f240]) ).
fof(f409,plain,
( sQ7_spl
| ~ sQ6_spl
| ~ member(sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),sK14_skl)
| ~ member(sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),sK14_skl) ),
inference(resolution,[status(thm)],[f408,f243]) ).
fof(f410,definition,
( sQ14_spl
<=> member(sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f412,plain,
( sQ14_spl
| ~ member(sK1_skl(cross_product(sK14_skl,sK14_skl),identity_relation_of(sK14_skl)),sK14_skl) ),
inference(component_clause,[status(thm)],[f410]) ).
fof(f413,plain,
( sQ7_spl
| ~ sQ6_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f409,f410,f196,f238]) ).
fof(f414,plain,
( sQ14_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f412,f207]) ).
fof(f415,plain,
( sQ14_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f414]) ).
fof(f416,plain,
$false,
inference(sat_refutation,[status(thm)],[f183,f195,f199,f201,f203,f241,f269,f393,f413,f415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET665+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n026.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 05:34:22 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.46 % Refutation found
% 0.17/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.52 % Elapsed time: 0.076233 seconds
% 0.17/0.52 % CPU time: 0.172732 seconds
% 0.17/0.52 % Total memory used: 29.546 MB
% 0.17/0.52 % Net memory used: 29.443 MB
%------------------------------------------------------------------------------