%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET659+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 : n010.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 1.44s 0.70s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 44
% Syntax : Number of formulae : 218 ( 21 unt; 26 def)
% Number of atoms : 735 ( 57 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 870 ( 353 ~; 365 |; 55 &)
% ( 44 <=>; 52 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 27 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 7 con; 0-3 aty)
% Number of variables : 308 ( 291 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(C,domain_of(B))
<=> ? [D] :
( member(ordered_pair(C,D),B)
& ilf_type(D,set_type) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,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(f7,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(f9,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( B = C
<=> ( subset(C,B)
& subset(B,C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,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(f16,axiom,
? [B] : ilf_type(B,binary_relation_type),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,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(f22,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,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(f27,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(f30,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,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(f33,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(range(B,C,D),subset_type(C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( ! [E] :
( ilf_type(E,set_type)
=> ( member(E,C)
=> ? [F] :
( member(ordered_pair(E,F),D)
& ilf_type(F,set_type) ) ) )
<=> domain(C,B,D) = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( ! [E] :
( ilf_type(E,set_type)
=> ( member(E,C)
=> ? [F] :
( member(ordered_pair(E,F),D)
& ilf_type(F,set_type) ) ) )
<=> domain(C,B,D) = C ) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f37,plain,
! [B] :
( ! [C] :
( ( member(C,domain_of(B))
<=> ? [D] :
( member(ordered_pair(C,D),B)
& ilf_type(D,set_type) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,binary_relation_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f38,plain,
! [B] :
( ! [C] :
( ( ( ! [D] :
( ~ member(ordered_pair(C,D),B)
| ~ ilf_type(D,set_type) )
| member(C,domain_of(B)) )
& ( ? [D] :
( member(ordered_pair(C,D),B)
& ilf_type(D,set_type) )
| ~ member(C,domain_of(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,binary_relation_type) ),
inference(NNF_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
! [B] :
( ! [C] :
( ( ( ! [D] :
( ~ member(ordered_pair(C,D),B)
| ~ ilf_type(D,set_type) )
| member(C,domain_of(B)) )
& ( ( member(ordered_pair(C,sK0_skl(C,B)),B)
& ilf_type(sK0_skl(C,B),set_type) )
| ~ member(C,domain_of(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,binary_relation_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f38]) ).
fof(f41,plain,
! [X0,X1] :
( member(ordered_pair(X1,sK0_skl(X1,X0)),X0)
| ~ member(X1,domain_of(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ member(ordered_pair(X1,X2),X0)
| ~ ilf_type(X2,set_type)
| member(X1,domain_of(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f54,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)],[f5]) ).
fof(f55,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)],[f54]) ).
fof(f56,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)],[f55]) ).
fof(f57,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)],[f56]) ).
fof(f58,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)],[f56]) ).
fof(f61,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)],[f7]) ).
fof(f63,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)],[f61]) ).
fof(f67,plain,
! [B] :
( ! [C] :
( ( B = C
<=> ( subset(C,B)
& subset(B,C) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f68,plain,
! [B] :
( ! [C] :
( ( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f67]) ).
fof(f71,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f82,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)],[f15]) ).
fof(f83,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)],[f82]) ).
fof(f86,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)],[f83]) ).
fof(f87,plain,
ilf_type(sK3_skl,binary_relation_type),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(B,sK3_skl)],[f16]) ).
fof(f88,plain,
ilf_type(sK3_skl,binary_relation_type),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f89,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(f90,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)],[f89]) ).
fof(f91,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)],[f90]) ).
fof(f104,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)],[f20]) ).
fof(f105,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)],[f104]) ).
fof(f106,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK6_skl(C,B),C)
& member(sK6_skl(C,B),B)
& ilf_type(sK6_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,[sK6_skl]),skolemize(D,sK6_skl(C,B))],[f105]) ).
fof(f109,plain,
! [X0,X1] :
( member(sK6_skl(X1,X0),X0)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f110,plain,
! [X0,X1] :
( ~ member(sK6_skl(X1,X0),X1)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f113,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)],[f22]) ).
fof(f114,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)],[f113]) ).
fof(f115,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK7_skl(C,B),C)
& member(sK7_skl(C,B),B)
& ilf_type(sK7_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,[sK7_skl]),skolemize(D,sK7_skl(C,B))],[f114]) ).
fof(f116,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f120,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f121,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f123,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)],[f24]) ).
fof(f124,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)],[f123]) ).
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)],[f124]) ).
fof(f139,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)],[f27]) ).
fof(f140,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)],[f139]) ).
fof(f149,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)],[f30]) ).
fof(f150,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)],[f149]) ).
fof(f151,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)],[f31]) ).
fof(f152,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)],[f151]) ).
fof(f153,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)],[f32]) ).
fof(f154,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)],[f153]) ).
fof(f155,plain,
! [B] :
( ! [C] :
( ! [D] :
( ilf_type(range(B,C,D),subset_type(C))
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f156,plain,
! [X0,X1,X2] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f157,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f158,plain,
? [B] :
( ? [C] :
( ? [D] :
( ( ! [E] :
( ? [F] :
( member(ordered_pair(E,F),D)
& ilf_type(F,set_type) )
| ~ member(E,C)
| ~ ilf_type(E,set_type) )
<~> domain(C,B,D) = C )
& ilf_type(D,relation_type(C,B)) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f159,plain,
? [B] :
( ? [C] :
( ? [D] :
( ( domain(C,B,D) != C
| ? [E] :
( ! [F] :
( ~ member(ordered_pair(E,F),D)
| ~ ilf_type(F,set_type) )
& member(E,C)
& ilf_type(E,set_type) ) )
& ( domain(C,B,D) = C
| ! [E] :
( ? [F] :
( member(ordered_pair(E,F),D)
& ilf_type(F,set_type) )
| ~ member(E,C)
| ~ ilf_type(E,set_type) ) )
& ilf_type(D,relation_type(C,B)) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f158]) ).
fof(f160,plain,
( ( domain(sK14_skl,sK13_skl,sK15_skl) != sK14_skl
| ( ! [F] :
( ~ member(ordered_pair(sK17_skl,F),sK15_skl)
| ~ ilf_type(F,set_type) )
& member(sK17_skl,sK14_skl)
& ilf_type(sK17_skl,set_type) ) )
& ( domain(sK14_skl,sK13_skl,sK15_skl) = sK14_skl
| ! [E] :
( ( member(ordered_pair(E,sK16_skl(E)),sK15_skl)
& ilf_type(sK16_skl(E),set_type) )
| ~ member(E,sK14_skl)
| ~ ilf_type(E,set_type) ) )
& ilf_type(sK15_skl,relation_type(sK14_skl,sK13_skl))
& ilf_type(sK14_skl,set_type)
& ilf_type(sK13_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl,sK16_skl,sK17_skl]),skolemize(B,sK13_skl),skolemize(C,sK14_skl),skolemize(D,sK15_skl),skolemize(F,sK16_skl(E)),skolemize(E,sK17_skl)],[f159]) ).
fof(f163,plain,
ilf_type(sK15_skl,relation_type(sK14_skl,sK13_skl)),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f165,plain,
! [X0] :
( domain(sK14_skl,sK13_skl,sK15_skl) = sK14_skl
| member(ordered_pair(X0,sK16_skl(X0)),sK15_skl)
| ~ member(X0,sK14_skl)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f167,plain,
( domain(sK14_skl,sK13_skl,sK15_skl) != sK14_skl
| member(sK17_skl,sK14_skl) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f168,plain,
! [X0] :
( domain(sK14_skl,sK13_skl,sK15_skl) != sK14_skl
| ~ member(ordered_pair(sK17_skl,X0),sK15_skl)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f169,definition,
! [X0] :
( sQ0_spl
<=> ~ ilf_type(X0,set_type) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f170,plain,
! [X0] :
( ~ sQ0_spl
| ~ ilf_type(X0,set_type) ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,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(f175,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f57,f169,f172]) ).
fof(f176,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(f179,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f58,f169,f176]) ).
fof(f183,definition,
( sQ4_spl
<=> domain(sK14_skl,sK13_skl,sK15_skl) = sK14_skl ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( ~ sQ4_spl
| domain(sK14_skl,sK13_skl,sK15_skl) = sK14_skl ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f185,plain,
( sQ4_spl
| domain(sK14_skl,sK13_skl,sK15_skl) != sK14_skl ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f187,definition,
! [X0] :
( sQ5_spl
<=> ( member(ordered_pair(X0,sK16_skl(X0)),sK15_skl)
| ~ member(X0,sK14_skl)
| ~ ilf_type(X0,set_type) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f188,plain,
! [X0] :
( ~ sQ5_spl
| member(ordered_pair(X0,sK16_skl(X0)),sK15_skl)
| ~ member(X0,sK14_skl)
| ~ ilf_type(X0,set_type) ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,plain,
( sQ4_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f165,f187,f183]) ).
fof(f195,definition,
( sQ7_spl
<=> member(sK17_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( ~ sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f167,f195,f183]) ).
fof(f199,definition,
! [X0] :
( sQ8_spl
<=> ( ~ member(ordered_pair(sK17_skl,X0),sK15_skl)
| ~ ilf_type(X0,set_type) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f200,plain,
! [X0] :
( ~ sQ8_spl
| ~ member(ordered_pair(sK17_skl,X0),sK15_skl)
| ~ ilf_type(X0,set_type) ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,plain,
( ~ sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f168,f199,f183]) ).
fof(f207,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f86]) ).
fof(f208,plain,
! [X0] :
( ~ sQ8_spl
| ~ member(ordered_pair(sK17_skl,X0),sK15_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f200,f157]) ).
fof(f209,plain,
! [X0] :
( ~ sQ5_spl
| member(ordered_pair(X0,sK16_skl(X0)),sK15_skl)
| ~ member(X0,sK14_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f188,f157]) ).
fof(f213,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)],[f152,f157]) ).
fof(f214,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f157]) ).
fof(f215,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f214]) ).
fof(f221,plain,
! [X0] : ~ empty(power_set(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f121,f157]) ).
fof(f223,definition,
( sQ9_spl
<=> ilf_type(sK13_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( sQ9_spl
| ~ ilf_type(sK13_skl,set_type) ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,definition,
( sQ10_spl
<=> ilf_type(sK15_skl,relation_type(sK14_skl,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f228,plain,
( sQ10_spl
| ~ ilf_type(sK15_skl,relation_type(sK14_skl,sK13_skl)) ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f233,plain,
! [X0,X1] :
( member(ordered_pair(X1,sK0_skl(X1,X0)),X0)
| ~ member(X1,domain_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f41,f157]) ).
fof(f234,plain,
! [X0,X1,X2] :
( ~ member(ordered_pair(X1,X2),X0)
| ~ ilf_type(X2,set_type)
| member(X1,domain_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f42,f157]) ).
fof(f445,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f207,f157]) ).
fof(f2042,definition,
( sQ15_spl
<=> ilf_type(domain_of(sK3_skl),set_type) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f2044,plain,
( sQ15_spl
| ~ ilf_type(domain_of(sK3_skl),set_type) ),
inference(component_clause,[status(thm)],[f2042]) ).
fof(f2049,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2044,f157]) ).
fof(f2050,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f2049]) ).
fof(f2054,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X1 = X0
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f71,f157]) ).
fof(f2055,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f2054,f157]) ).
fof(f2057,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)],[f63,f157]) ).
fof(f2058,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)],[f91,f157]) ).
fof(f2062,definition,
( sQ17_spl
<=> ilf_type(sK0_skl(sK12_skl(domain_of(sK3_skl)),sK3_skl),set_type) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f2064,plain,
( sQ17_spl
| ~ ilf_type(sK0_skl(sK12_skl(domain_of(sK3_skl)),sK3_skl),set_type) ),
inference(component_clause,[status(thm)],[f2062]) ).
fof(f2065,definition,
( sQ18_spl
<=> ilf_type(sK3_skl,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f2067,plain,
( sQ18_spl
| ~ ilf_type(sK3_skl,binary_relation_type) ),
inference(component_clause,[status(thm)],[f2065]) ).
fof(f2076,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2064,f157]) ).
fof(f2077,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f2076]) ).
fof(f2078,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2067,f88]) ).
fof(f2079,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f2078]) ).
fof(f2439,plain,
! [X0,X1] :
( member(sK6_skl(X0,X1),X1)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f109,f157]) ).
fof(f2440,plain,
! [X0,X1] :
( member(sK6_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f2439,f157]) ).
fof(f2442,plain,
! [X0,X1] :
( ~ member(sK6_skl(X0,X1),X0)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f110,f157]) ).
fof(f2443,plain,
! [X0,X1] :
( ~ member(sK6_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f2442,f157]) ).
fof(f2446,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)],[f140,f157]) ).
fof(f2516,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,f157]) ).
fof(f2517,plain,
! [X0,X1] :
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[f2516,f157]) ).
fof(f2519,plain,
! [X0,X1] :
( ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| member(X1,power_set(X0))
| empty(power_set(X0)) ),
inference(resolution,[status(thm)],[f2517,f2058]) ).
fof(f2521,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2519,f221]) ).
fof(f2523,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2521,f157]) ).
fof(f2526,plain,
! [X0,X1,X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| member(domain(X0,X1,X2),power_set(X0)) ),
inference(resolution,[status(thm)],[f2523,f213]) ).
fof(f2529,plain,
! [X0,X1,X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| member(domain(X0,X1,X2),power_set(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2526,f157]) ).
fof(f2538,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f116,f157]) ).
fof(f2539,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f2538,f157]) ).
fof(f2540,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2539,f157]) ).
fof(f2547,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ member(sK6_skl(X1,X2),X0)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f2540,f2443]) ).
fof(f2566,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f228,f163]) ).
fof(f2567,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f2566]) ).
fof(f2574,plain,
! [X0] :
( ~ sQ5_spl
| ~ ilf_type(sK16_skl(X0),set_type)
| member(X0,domain_of(sK15_skl))
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ member(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f209,f234]) ).
fof(f2578,definition,
( sQ23_spl
<=> ilf_type(sK15_skl,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f2580,plain,
( sQ23_spl
| ~ ilf_type(sK15_skl,binary_relation_type) ),
inference(component_clause,[status(thm)],[f2578]) ).
fof(f2582,definition,
! [X0] :
( sQ24_spl
<=> ( ~ ilf_type(sK16_skl(X0),set_type)
| member(X0,domain_of(sK15_skl))
| ~ member(X0,sK14_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f2583,plain,
! [X0] :
( ~ sQ24_spl
| ~ ilf_type(sK16_skl(X0),set_type)
| member(X0,domain_of(sK15_skl))
| ~ member(X0,sK14_skl) ),
inference(component_clause,[status(thm)],[f2582]) ).
fof(f2585,plain,
( ~ sQ5_spl
| ~ sQ23_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f2574,f2582,f2578,f187]) ).
fof(f2586,plain,
( sQ23_spl
| ~ relation_like(sK15_skl) ),
inference(resolution,[status(thm)],[f2580,f445]) ).
fof(f2589,plain,
! [X0,X1] :
( sQ23_spl
| ~ ilf_type(sK15_skl,subset_type(cross_product(X1,X0)))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f2586,f2446]) ).
fof(f2592,plain,
! [X0,X1] :
( sQ23_spl
| ~ ilf_type(sK15_skl,subset_type(cross_product(X0,X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f2589,f157]) ).
fof(f2593,plain,
! [X0,X1] :
( sQ23_spl
| ~ ilf_type(sK15_skl,relation_type(X1,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f2592,f2057]) ).
fof(f2595,plain,
! [X0,X1] :
( sQ23_spl
| ~ ilf_type(sK15_skl,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2593,f157]) ).
fof(f2596,definition,
( sQ25_spl
<=> ilf_type(sK15_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f2598,plain,
( sQ25_spl
| ~ ilf_type(sK15_skl,set_type) ),
inference(component_clause,[status(thm)],[f2596]) ).
fof(f2604,plain,
! [X0] :
( ~ sQ24_spl
| member(X0,domain_of(sK15_skl))
| ~ member(X0,sK14_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f2583,f157]) ).
fof(f2608,plain,
! [X0] :
( ~ sQ24_spl
| subset(sK14_skl,X0)
| member(sK6_skl(X0,sK14_skl),domain_of(sK15_skl)) ),
inference(resolution,[status(thm)],[f2604,f2440]) ).
fof(f2645,plain,
( sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2598,f157]) ).
fof(f2646,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f2645]) ).
fof(f2652,plain,
( sQ23_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f163,f2595]) ).
fof(f2654,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f2652]) ).
fof(f2674,definition,
( sQ34_spl
<=> ilf_type(sK14_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f2676,plain,
( sQ34_spl
| ~ ilf_type(sK14_skl,set_type) ),
inference(component_clause,[status(thm)],[f2674]) ).
fof(f2704,plain,
( sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2676,f157]) ).
fof(f2705,plain,
sQ34_spl,
inference(contradiction_clause,[status(thm)],[f2704]) ).
fof(f2739,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)],[f150,f157]) ).
fof(f2740,plain,
! [X0,X1,X2] :
( domain(X1,X2,X0) = domain_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f2739,f157]) ).
fof(f2741,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)],[f154,f157]) ).
fof(f2742,plain,
! [X0,X1,X2] :
( range(X1,X2,X0) = range_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f2741,f157]) ).
fof(f2754,plain,
domain(sK14_skl,sK13_skl,sK15_skl) = domain_of(sK15_skl),
inference(resolution,[status(thm)],[f2740,f163]) ).
fof(f2759,plain,
( sQ4_spl
| domain_of(sK15_skl) != sK14_skl ),
inference(backward_demodulation,[status(thm)],[f2754,f185]) ).
fof(f2760,plain,
( ~ ilf_type(sK15_skl,relation_type(sK14_skl,sK13_skl))
| member(domain_of(sK15_skl),power_set(sK14_skl)) ),
inference(paramodulation,[status(thm)],[f2754,f2529]) ).
fof(f2761,plain,
( ilf_type(domain_of(sK15_skl),subset_type(sK14_skl))
| ~ ilf_type(sK15_skl,relation_type(sK14_skl,sK13_skl))
| ~ ilf_type(sK13_skl,set_type) ),
inference(paramodulation,[status(thm)],[f2754,f213]) ).
fof(f2762,definition,
( sQ39_spl
<=> member(domain_of(sK15_skl),power_set(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f2765,plain,
( ~ sQ10_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f2760,f2762,f226]) ).
fof(f2766,definition,
( sQ40_spl
<=> ilf_type(domain_of(sK15_skl),subset_type(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f2769,plain,
( sQ40_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2761,f223,f226,f2766]) ).
fof(f2770,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f225,f157]) ).
fof(f2771,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f2770]) ).
fof(f2772,plain,
range(sK14_skl,sK13_skl,sK15_skl) = range_of(sK15_skl),
inference(resolution,[status(thm)],[f2742,f163]) ).
fof(f2789,plain,
( ~ sQ24_spl
| subset(sK14_skl,domain_of(sK15_skl))
| subset(sK14_skl,domain_of(sK15_skl)) ),
inference(resolution,[status(thm)],[f2608,f2443]) ).
fof(f2791,definition,
( sQ42_spl
<=> subset(sK14_skl,domain_of(sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f2792,plain,
( ~ sQ42_spl
| subset(sK14_skl,domain_of(sK15_skl)) ),
inference(component_clause,[status(thm)],[f2791]) ).
fof(f2794,plain,
( ~ sQ24_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f2789,f2791,f2582]) ).
fof(f2800,plain,
( ~ sQ42_spl
| ~ subset(domain_of(sK15_skl),sK14_skl)
| domain_of(sK15_skl) = sK14_skl ),
inference(resolution,[status(thm)],[f2792,f2055]) ).
fof(f2801,definition,
( sQ44_spl
<=> domain_of(sK15_skl) = sK14_skl ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f2802,plain,
( ~ sQ44_spl
| domain_of(sK15_skl) = sK14_skl ),
inference(component_clause,[status(thm)],[f2801]) ).
fof(f2804,definition,
( sQ45_spl
<=> subset(domain_of(sK15_skl),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f2806,plain,
( sQ45_spl
| ~ subset(domain_of(sK15_skl),sK14_skl) ),
inference(component_clause,[status(thm)],[f2804]) ).
fof(f2807,plain,
( ~ sQ42_spl
| ~ sQ45_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f2800,f2801,f2804,f2791]) ).
fof(f2808,plain,
( ~ sQ44_spl
| sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2802,f2759]) ).
fof(f2809,plain,
( ~ sQ44_spl
| sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f2808]) ).
fof(f2810,plain,
! [X0] :
( sQ45_spl
| ~ member(sK6_skl(sK14_skl,domain_of(sK15_skl)),X0)
| ~ member(X0,power_set(sK14_skl)) ),
inference(resolution,[status(thm)],[f2547,f2806]) ).
fof(f2813,plain,
! [X0,X1,X2] :
( ilf_type(range(X2,X0,X1),subset_type(X0))
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f157]) ).
fof(f2814,plain,
! [X0,X1,X2] :
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f2813,f157]) ).
fof(f2815,plain,
! [X0,X1,X2] :
( member(range(X1,X2,X0),power_set(X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f2814,f2523]) ).
fof(f2816,plain,
( ilf_type(range_of(sK15_skl),subset_type(sK13_skl))
| ~ ilf_type(sK15_skl,relation_type(sK14_skl,sK13_skl)) ),
inference(paramodulation,[status(thm)],[f2772,f2814]) ).
fof(f2818,definition,
( sQ46_spl
<=> ilf_type(range_of(sK15_skl),subset_type(sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f2821,plain,
( sQ46_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2816,f226,f2818]) ).
fof(f2865,plain,
( member(range_of(sK15_skl),power_set(sK13_skl))
| ~ ilf_type(sK15_skl,relation_type(sK14_skl,sK13_skl)) ),
inference(paramodulation,[status(thm)],[f2772,f2815]) ).
fof(f2867,definition,
( sQ51_spl
<=> member(range_of(sK15_skl),power_set(sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f2870,plain,
( sQ51_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2865,f226,f2867]) ).
fof(f2879,definition,
( sQ52_spl
<=> ilf_type(sK0_skl(sK12_skl(sK14_skl),sK15_skl),set_type) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f2881,plain,
( sQ52_spl
| ~ ilf_type(sK0_skl(sK12_skl(sK14_skl),sK15_skl),set_type) ),
inference(component_clause,[status(thm)],[f2879]) ).
fof(f2887,plain,
( sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2881,f157]) ).
fof(f2888,plain,
sQ52_spl,
inference(contradiction_clause,[status(thm)],[f2887]) ).
fof(f2996,definition,
( sQ65_spl
<=> ilf_type(sK0_skl(sK8_skl(sK14_skl),sK15_skl),set_type) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f2998,plain,
( sQ65_spl
| ~ ilf_type(sK0_skl(sK8_skl(sK14_skl),sK15_skl),set_type) ),
inference(component_clause,[status(thm)],[f2996]) ).
fof(f3004,plain,
( sQ65_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2998,f157]) ).
fof(f3005,plain,
sQ65_spl,
inference(contradiction_clause,[status(thm)],[f3004]) ).
fof(f3021,plain,
( sQ45_spl
| subset(domain_of(sK15_skl),sK14_skl)
| ~ member(domain_of(sK15_skl),power_set(sK14_skl)) ),
inference(resolution,[status(thm)],[f2810,f2440]) ).
fof(f3026,plain,
( sQ45_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f3021,f2762,f2804]) ).
fof(f3031,plain,
( ~ sQ4_spl
| domain_of(sK15_skl) = sK14_skl ),
inference(forward_demodulation,[status(thm)],[f2754,f184]) ).
fof(f3042,plain,
! [X0] :
( ~ sQ44_spl
| member(ordered_pair(X0,sK0_skl(X0,sK15_skl)),sK15_skl)
| ~ member(X0,sK14_skl)
| ~ ilf_type(sK15_skl,binary_relation_type) ),
inference(paramodulation,[status(thm)],[f2802,f233]) ).
fof(f3060,definition,
! [X0] :
( sQ74_spl
<=> ( member(ordered_pair(X0,sK0_skl(X0,sK15_skl)),sK15_skl)
| ~ member(X0,sK14_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f3061,plain,
! [X0] :
( ~ sQ74_spl
| member(ordered_pair(X0,sK0_skl(X0,sK15_skl)),sK15_skl)
| ~ member(X0,sK14_skl) ),
inference(component_clause,[status(thm)],[f3060]) ).
fof(f3063,plain,
( ~ sQ44_spl
| sQ74_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f3042,f2578,f3060,f2801]) ).
fof(f3077,plain,
( ~ sQ8_spl
| ~ sQ74_spl
| ~ member(sK17_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f3061,f208]) ).
fof(f3081,plain,
( ~ sQ8_spl
| ~ sQ74_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3077,f195,f3060,f199]) ).
fof(f3094,plain,
( ~ sQ4_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f3031,f2801,f183]) ).
fof(f3095,plain,
$false,
inference(sat_refutation,[status(thm)],[f175,f179,f190,f198,f202,f215,f2050,f2077,f2079,f2567,f2585,f2646,f2654,f2705,f2765,f2769,f2771,f2794,f2807,f2809,f2821,f2870,f2888,f3005,f3026,f3063,f3081,f3094]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET659+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:31:55 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 1.44/0.70 % Refutation found
% 1.44/0.70 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.44/0.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.44/0.73 % Elapsed time: 0.347092 seconds
% 1.44/0.73 % CPU time: 2.335216 seconds
% 1.44/0.73 % Total memory used: 147.752 MB
% 1.44/0.73 % Net memory used: 144.328 MB
%------------------------------------------------------------------------------