%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET681+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 : n007.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 02:10:26 PM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 32
% Syntax : Number of formulae : 162 ( 20 unt; 21 def)
% Number of atoms : 558 ( 26 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 679 ( 283 ~; 275 |; 51 &)
% ( 33 <=>; 36 =>; 0 <=; 1 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 22 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 225 ( 209 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f4,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,set_type)
=> ( F = ordered_pair(D,E)
<=> F = unordered_pair(unordered_pair(D,E),singleton(D)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,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(f8,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(f10,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,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(f26,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(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/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ! [E] :
( ilf_type(E,member_type(B))
=> ( member(E,range(C,B,D))
<=> ? [F] :
( member(ordered_pair(F,E),D)
& ilf_type(F,member_type(C)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ! [E] :
( ilf_type(E,member_type(B))
=> ( member(E,range(C,B,D))
<=> ? [F] :
( member(ordered_pair(F,E),D)
& ilf_type(F,member_type(C)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f34,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)],[f1]) ).
fof(f35,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)],[f34]) ).
fof(f36,plain,
! [B] :
( ! [C] :
( ( ( ! [D] :
( ~ member(ordered_pair(D,B),C)
| ~ ilf_type(D,set_type) )
| member(B,range_of(C)) )
& ( ( member(ordered_pair(sK0_skl(C,B),B),C)
& ilf_type(sK0_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,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f35]) ).
fof(f38,plain,
! [X0,X1] :
( member(ordered_pair(sK0_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)],[f36]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X2,set_type)
| member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f43,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(f44,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)],[f43]) ).
fof(f45,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)],[f43]) ).
fof(f46,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ! [F] :
( ( F = ordered_pair(D,E)
<=> F = unordered_pair(unordered_pair(D,E),singleton(D)) )
| ~ ilf_type(F,set_type) )
| ~ 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)],[f4]) ).
fof(f47,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ! [F] :
( ( ( F != unordered_pair(unordered_pair(D,E),singleton(D))
| F = ordered_pair(D,E) )
& ( F = unordered_pair(unordered_pair(D,E),singleton(D))
| F != ordered_pair(D,E) ) )
| ~ ilf_type(F,set_type) )
| ~ 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)],[f46]) ).
fof(f48,plain,
( ! [D] :
( ! [E] :
( ! [F] :
( ( ( F != unordered_pair(unordered_pair(D,E),singleton(D))
| F = ordered_pair(D,E) )
& ( F = unordered_pair(unordered_pair(D,E),singleton(D))
| F != ordered_pair(D,E) ) )
| ~ ilf_type(F,set_type) )
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) )
| ! [C] : ~ ilf_type(C,set_type)
| ! [B] : ~ ilf_type(B,set_type) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4] :
( X4 = unordered_pair(unordered_pair(X2,X3),singleton(X2))
| X4 != ordered_pair(X2,X3)
| ~ ilf_type(X4,set_type)
| ~ 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)],[f48]) ).
fof(f50,plain,
! [X0,X1,X2,X3,X4] :
( X4 != unordered_pair(unordered_pair(X2,X3),singleton(X2))
| X4 = ordered_pair(X2,X3)
| ~ ilf_type(X4,set_type)
| ~ 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)],[f48]) ).
fof(f53,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)],[f6]) ).
fof(f55,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)],[f53]) ).
fof(f59,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)],[f8]) ).
fof(f60,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)],[f59]) ).
fof(f61,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)],[f60]) ).
fof(f62,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)],[f60]) ).
fof(f66,plain,
! [B] :
( ( empty(B)
<=> ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) ) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f67,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)],[f66]) ).
fof(f68,plain,
! [B] :
( ( ( ( member(sK3_skl(B),B)
& ilf_type(sK3_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,[sK3_skl]),skolemize(C,sK3_skl(B))],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f84,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)],[f17]) ).
fof(f85,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)],[f84]) ).
fof(f88,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)],[f85]) ).
fof(f127,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)],[f26]) ).
fof(f128,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)],[f127]) ).
fof(f133,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(f134,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)],[f133]) ).
fof(f137,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f138,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ( member(E,range(C,B,D))
<~> ? [F] :
( member(ordered_pair(F,E),D)
& ilf_type(F,member_type(C)) ) )
& ilf_type(E,member_type(B)) )
& ilf_type(D,relation_type(C,B)) )
& ilf_type(C,set_type)
& ~ empty(C) )
& ilf_type(B,set_type)
& ~ empty(B) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f139,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ( ! [F] :
( ~ member(ordered_pair(F,E),D)
| ~ ilf_type(F,member_type(C)) )
| ~ member(E,range(C,B,D)) )
& ( ? [F] :
( member(ordered_pair(F,E),D)
& ilf_type(F,member_type(C)) )
| member(E,range(C,B,D)) )
& ilf_type(E,member_type(B)) )
& ilf_type(D,relation_type(C,B)) )
& ilf_type(C,set_type)
& ~ empty(C) )
& ilf_type(B,set_type)
& ~ empty(B) ),
inference(NNF_transformation,[status(thm)],[f138]) ).
fof(f140,plain,
( ( ! [F] :
( ~ member(ordered_pair(F,sK14_skl),sK13_skl)
| ~ ilf_type(F,member_type(sK12_skl)) )
| ~ member(sK14_skl,range(sK12_skl,sK11_skl,sK13_skl)) )
& ( ( member(ordered_pair(sK15_skl,sK14_skl),sK13_skl)
& ilf_type(sK15_skl,member_type(sK12_skl)) )
| member(sK14_skl,range(sK12_skl,sK11_skl,sK13_skl)) )
& ilf_type(sK14_skl,member_type(sK11_skl))
& ilf_type(sK13_skl,relation_type(sK12_skl,sK11_skl))
& ilf_type(sK12_skl,set_type)
& ~ empty(sK12_skl)
& ilf_type(sK11_skl,set_type)
& ~ empty(sK11_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl,sK14_skl,sK15_skl]),skolemize(B,sK11_skl),skolemize(C,sK12_skl),skolemize(D,sK13_skl),skolemize(E,sK14_skl),skolemize(F,sK15_skl)],[f139]) ).
fof(f141,plain,
~ empty(sK11_skl),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f143,plain,
~ empty(sK12_skl),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f145,plain,
ilf_type(sK13_skl,relation_type(sK12_skl,sK11_skl)),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f146,plain,
ilf_type(sK14_skl,member_type(sK11_skl)),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f148,plain,
( member(ordered_pair(sK15_skl,sK14_skl),sK13_skl)
| member(sK14_skl,range(sK12_skl,sK11_skl,sK13_skl)) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f149,plain,
! [X0] :
( ~ member(ordered_pair(X0,sK14_skl),sK13_skl)
| ~ ilf_type(X0,member_type(sK12_skl))
| ~ member(sK14_skl,range(sK12_skl,sK11_skl,sK13_skl)) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f150,definition,
! [X0] :
( sQ0_spl
<=> ~ ilf_type(X0,set_type) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f151,plain,
! [X0] :
( ~ sQ0_spl
| ~ ilf_type(X0,set_type) ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,definition,
! [X2,X3,X4] :
( sQ1_spl
<=> ( X4 = unordered_pair(unordered_pair(X2,X3),singleton(X2))
| X4 != ordered_pair(X2,X3)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f150,f153]) ).
fof(f157,definition,
! [X2,X3,X4] :
( sQ2_spl
<=> ( X4 != unordered_pair(unordered_pair(X2,X3),singleton(X2))
| X4 = ordered_pair(X2,X3)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f50,f150,f157]) ).
fof(f161,definition,
( sQ3_spl
<=> member(sK14_skl,range(sK12_skl,sK11_skl,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( ~ sQ3_spl
| member(sK14_skl,range(sK12_skl,sK11_skl,sK13_skl)) ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f163,plain,
( sQ3_spl
| ~ member(sK14_skl,range(sK12_skl,sK11_skl,sK13_skl)) ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f168,definition,
( sQ5_spl
<=> member(ordered_pair(sK15_skl,sK14_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f169,plain,
( ~ sQ5_spl
| member(ordered_pair(sK15_skl,sK14_skl),sK13_skl) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,plain,
( sQ5_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f148,f161,f168]) ).
fof(f172,definition,
! [X0] :
( sQ6_spl
<=> ( ~ member(ordered_pair(X0,sK14_skl),sK13_skl)
| ~ ilf_type(X0,member_type(sK12_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f173,plain,
! [X0] :
( ~ sQ6_spl
| ~ member(ordered_pair(X0,sK14_skl),sK13_skl)
| ~ ilf_type(X0,member_type(sK12_skl)) ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,plain,
( sQ6_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f149,f161,f172]) ).
fof(f176,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f62,f69]) ).
fof(f177,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f88]) ).
fof(f179,plain,
! [X0,X1,X2] :
( range(X0,X2,X1) = range_of(X1)
| ~ ilf_type(X1,relation_type(X0,X2))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f134,f137]) ).
fof(f182,plain,
! [X0,X1,X2] :
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X0,X2)))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f128,f137]) ).
fof(f196,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f177,f137]) ).
fof(f202,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f61,f137]) ).
fof(f204,plain,
! [X0,X1,X2] :
( ilf_type(X1,subset_type(cross_product(X0,X2)))
| ~ ilf_type(X1,relation_type(X0,X2))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f55,f137]) ).
fof(f206,plain,
! [X0,X1,X2,X3,X4] :
( member(X4,X1)
| ~ member(ordered_pair(X2,X4),X3)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f45,f137]) ).
fof(f207,plain,
! [X0,X1,X2,X3,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X4),X3)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f44,f137]) ).
fof(f209,plain,
! [X0,X1,X2] :
( ~ member(ordered_pair(X2,X0),X1)
| member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f39,f137]) ).
fof(f210,plain,
! [X0,X1] :
( member(ordered_pair(sK0_skl(X0,X1),X1),X0)
| ~ member(X1,range_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f38,f137]) ).
fof(f211,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f137]) ).
fof(f212,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f211]) ).
fof(f213,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f137]) ).
fof(f215,plain,
! [X0,X1,X2] :
( range(X1,X2,X0) = range_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f179,f137]) ).
fof(f218,plain,
! [X0,X1,X2] :
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f182,f137]) ).
fof(f230,plain,
! [X0,X1] :
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f202,f137]) ).
fof(f232,plain,
! [X0,X1,X2] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f137]) ).
fof(f234,plain,
! [X0,X1,X2,X3,X4] :
( member(X4,X0)
| ~ member(ordered_pair(X1,X4),X2)
| ~ ilf_type(X2,relation_type(X3,X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f206,f137]) ).
fof(f235,plain,
! [X0,X1,X2,X3,X4] :
( member(X1,X3)
| ~ member(ordered_pair(X1,X4),X2)
| ~ ilf_type(X2,relation_type(X3,X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f207,f137]) ).
fof(f237,plain,
! [X0,X1,X2] :
( ~ member(ordered_pair(X2,X1),X0)
| member(X1,range_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f209,f137]) ).
fof(f243,plain,
range(sK12_skl,sK11_skl,sK13_skl) = range_of(sK13_skl),
inference(resolution,[status(thm)],[f215,f145]) ).
fof(f245,plain,
( ~ sQ3_spl
| member(sK14_skl,range_of(sK13_skl)) ),
inference(backward_demodulation,[status(thm)],[f243,f162]) ).
fof(f264,definition,
( sQ9_spl
<=> ilf_type(range_of(sK13_skl),set_type) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f266,plain,
( sQ9_spl
| ~ ilf_type(range_of(sK13_skl),set_type) ),
inference(component_clause,[status(thm)],[f264]) ).
fof(f271,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f266,f137]) ).
fof(f272,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f271]) ).
fof(f328,plain,
( member(sK14_skl,sK11_skl)
| empty(sK11_skl) ),
inference(resolution,[status(thm)],[f230,f146]) ).
fof(f331,definition,
( sQ11_spl
<=> empty(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f332,plain,
( ~ sQ11_spl
| empty(sK11_skl) ),
inference(component_clause,[status(thm)],[f331]) ).
fof(f334,definition,
( sQ12_spl
<=> member(sK14_skl,sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f335,plain,
( ~ sQ12_spl
| member(sK14_skl,sK11_skl) ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f337,plain,
( sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f328,f331,f334]) ).
fof(f338,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f332,f141]) ).
fof(f339,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f338]) ).
fof(f347,plain,
ilf_type(sK13_skl,subset_type(cross_product(sK12_skl,sK11_skl))),
inference(resolution,[status(thm)],[f232,f145]) ).
fof(f352,plain,
( ~ sQ12_spl
| ilf_type(sK14_skl,member_type(sK11_skl))
| ~ ilf_type(sK11_skl,set_type) ),
inference(resolution,[status(thm)],[f335,f213]) ).
fof(f360,definition,
( sQ15_spl
<=> ilf_type(sK11_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f362,plain,
( sQ15_spl
| ~ ilf_type(sK11_skl,set_type) ),
inference(component_clause,[status(thm)],[f360]) ).
fof(f363,definition,
( sQ16_spl
<=> ilf_type(sK14_skl,member_type(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f366,plain,
( ~ sQ12_spl
| sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f352,f360,f363,f334]) ).
fof(f367,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f362,f137]) ).
fof(f368,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f367]) ).
fof(f372,plain,
! [X0,X1] :
( member(X1,sK11_skl)
| ~ member(ordered_pair(X0,X1),sK13_skl)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK11_skl,set_type) ),
inference(resolution,[status(thm)],[f234,f145]) ).
fof(f374,definition,
! [X0,X1] :
( sQ17_spl
<=> ( member(X1,sK11_skl)
| ~ member(ordered_pair(X0,X1),sK13_skl)
| ~ ilf_type(X0,set_type) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f377,plain,
( sQ17_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f372,f360,f374]) ).
fof(f380,plain,
! [X0,X1] :
( member(X0,sK12_skl)
| ~ member(ordered_pair(X0,X1),sK13_skl)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK11_skl,set_type) ),
inference(resolution,[status(thm)],[f235,f145]) ).
fof(f382,definition,
! [X0,X1] :
( sQ18_spl
<=> ( member(X0,sK12_skl)
| ~ member(ordered_pair(X0,X1),sK13_skl)
| ~ ilf_type(X0,set_type) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f383,plain,
! [X0,X1] :
( ~ sQ18_spl
| member(X0,sK12_skl)
| ~ member(ordered_pair(X0,X1),sK13_skl)
| ~ ilf_type(X0,set_type) ),
inference(component_clause,[status(thm)],[f382]) ).
fof(f385,plain,
( sQ18_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f380,f360,f382]) ).
fof(f386,plain,
! [X0,X1] :
( ~ sQ18_spl
| member(X0,sK12_skl)
| ~ member(ordered_pair(X0,X1),sK13_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f383,f137]) ).
fof(f395,plain,
( ~ sQ3_spl
| member(ordered_pair(sK0_skl(sK13_skl,sK14_skl),sK14_skl),sK13_skl)
| ~ ilf_type(sK13_skl,binary_relation_type) ),
inference(resolution,[status(thm)],[f210,f245]) ).
fof(f397,definition,
( sQ19_spl
<=> ilf_type(sK13_skl,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f399,plain,
( sQ19_spl
| ~ ilf_type(sK13_skl,binary_relation_type) ),
inference(component_clause,[status(thm)],[f397]) ).
fof(f400,definition,
( sQ20_spl
<=> member(ordered_pair(sK0_skl(sK13_skl,sK14_skl),sK14_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( ~ sQ20_spl
| member(ordered_pair(sK0_skl(sK13_skl,sK14_skl),sK14_skl),sK13_skl) ),
inference(component_clause,[status(thm)],[f400]) ).
fof(f403,plain,
( ~ sQ3_spl
| sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f395,f397,f400,f161]) ).
fof(f404,plain,
( sQ3_spl
| ~ member(sK14_skl,range_of(sK13_skl)) ),
inference(forward_demodulation,[status(thm)],[f243,f163]) ).
fof(f406,definition,
( sQ21_spl
<=> empty(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f407,plain,
( ~ sQ21_spl
| empty(sK12_skl) ),
inference(component_clause,[status(thm)],[f406]) ).
fof(f413,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f407,f143]) ).
fof(f414,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f413]) ).
fof(f415,plain,
( ~ sQ5_spl
| member(sK14_skl,range_of(sK13_skl))
| ~ ilf_type(sK13_skl,binary_relation_type) ),
inference(resolution,[status(thm)],[f169,f237]) ).
fof(f420,definition,
( sQ23_spl
<=> member(sK14_skl,range_of(sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f421,plain,
( ~ sQ23_spl
| member(sK14_skl,range_of(sK13_skl)) ),
inference(component_clause,[status(thm)],[f420]) ).
fof(f423,plain,
( ~ sQ5_spl
| sQ23_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f415,f397,f420,f168]) ).
fof(f428,definition,
( sQ25_spl
<=> relation_like(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f430,plain,
( sQ25_spl
| ~ relation_like(sK13_skl) ),
inference(component_clause,[status(thm)],[f428]) ).
fof(f435,definition,
( sQ27_spl
<=> ilf_type(sK13_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f437,plain,
( sQ27_spl
| ~ ilf_type(sK13_skl,set_type) ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f442,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f437,f137]) ).
fof(f443,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f442]) ).
fof(f463,definition,
( sQ31_spl
<=> ilf_type(sK12_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( sQ31_spl
| ~ ilf_type(sK12_skl,set_type) ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f493,plain,
relation_like(sK13_skl),
inference(resolution,[status(thm)],[f347,f218]) ).
fof(f495,plain,
( sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f493,f430]) ).
fof(f496,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f495]) ).
fof(f500,plain,
ilf_type(sK13_skl,binary_relation_type),
inference(resolution,[status(thm)],[f493,f196]) ).
fof(f501,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f399]) ).
fof(f502,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f501]) ).
fof(f503,plain,
( ~ sQ23_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f421,f404]) ).
fof(f504,plain,
( ~ sQ23_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f503]) ).
fof(f505,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f465,f137]) ).
fof(f506,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f505]) ).
fof(f566,plain,
( ~ sQ6_spl
| ~ sQ20_spl
| ~ ilf_type(sK0_skl(sK13_skl,sK14_skl),member_type(sK12_skl)) ),
inference(resolution,[status(thm)],[f401,f173]) ).
fof(f567,plain,
( ~ sQ18_spl
| ~ sQ20_spl
| member(sK0_skl(sK13_skl,sK14_skl),sK12_skl) ),
inference(resolution,[status(thm)],[f401,f386]) ).
fof(f569,plain,
( ~ sQ20_spl
| member(sK14_skl,range_of(sK13_skl))
| ~ ilf_type(sK13_skl,binary_relation_type) ),
inference(resolution,[status(thm)],[f401,f237]) ).
fof(f574,plain,
( ~ sQ20_spl
| sQ23_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f569,f397,f420,f400]) ).
fof(f669,plain,
( ~ sQ18_spl
| ~ sQ20_spl
| ilf_type(sK0_skl(sK13_skl,sK14_skl),member_type(sK12_skl))
| ~ ilf_type(sK12_skl,set_type) ),
inference(resolution,[status(thm)],[f567,f213]) ).
fof(f674,definition,
( sQ41_spl
<=> ilf_type(sK0_skl(sK13_skl,sK14_skl),member_type(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f675,plain,
( ~ sQ41_spl
| ilf_type(sK0_skl(sK13_skl,sK14_skl),member_type(sK12_skl)) ),
inference(component_clause,[status(thm)],[f674]) ).
fof(f677,plain,
( ~ sQ18_spl
| ~ sQ20_spl
| sQ41_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f669,f463,f674,f400,f382]) ).
fof(f678,plain,
( ~ sQ41_spl
| ~ sQ6_spl
| ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f675,f566]) ).
fof(f679,plain,
( ~ sQ41_spl
| ~ sQ6_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f678]) ).
fof(f680,plain,
$false,
inference(sat_refutation,[status(thm)],[f156,f160,f171,f175,f212,f272,f337,f339,f366,f368,f377,f385,f403,f414,f423,f443,f496,f502,f504,f506,f574,f677,f679]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET681+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 05:30:05 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.44 % Elapsed time: 0.065158 seconds
% 0.14/0.44 % CPU time: 0.279219 seconds
% 0.14/0.44 % Total memory used: 82.384 MB
% 0.14/0.44 % Net memory used: 82.055 MB
%------------------------------------------------------------------------------