%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET680+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 : n019.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 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 47
% Syntax : Number of formulae : 232 ( 23 unt; 31 def)
% Number of atoms : 766 ( 26 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 904 ( 370 ~; 378 |; 61 &)
% ( 47 <=>; 47 =>; 0 <=; 1 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 37 ( 35 usr; 32 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 7 con; 0-3 aty)
% Number of variables : 283 ( 264 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( member(B,domain_of(C))
<=> ? [D] :
( member(ordered_pair(B,D),C)
& ilf_type(D,set_type) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(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(f9,axiom,
! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ? [C] : ilf_type(C,member_type(B)) ),
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(f19,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(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(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(f27,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> domain(B,C,D) = domain_of(D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(domain(B,C,D),subset_type(B)) ) ) ),
file('/export/starexec/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(B,C))
=> ! [E] :
( ilf_type(E,member_type(B))
=> ( member(E,domain(B,C,D))
<=> ? [F] :
( member(ordered_pair(E,F),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(B,C))
=> ! [E] :
( ilf_type(E,member_type(B))
=> ( member(E,domain(B,C,D))
<=> ? [F] :
( member(ordered_pair(E,F),D)
& ilf_type(F,member_type(C)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f34,plain,
! [B] :
( ! [C] :
( ( member(B,domain_of(C))
<=> ? [D] :
( member(ordered_pair(B,D),C)
& ilf_type(D,set_type) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f35,plain,
! [B] :
( ! [C] :
( ( ( ! [D] :
( ~ member(ordered_pair(B,D),C)
| ~ ilf_type(D,set_type) )
| member(B,domain_of(C)) )
& ( ? [D] :
( member(ordered_pair(B,D),C)
& ilf_type(D,set_type) )
| ~ member(B,domain_of(C)) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [B] :
( ! [C] :
( ( ( ! [D] :
( ~ member(ordered_pair(B,D),C)
| ~ ilf_type(D,set_type) )
| member(B,domain_of(C)) )
& ( ( member(ordered_pair(B,sK0_skl(C,B)),C)
& ilf_type(sK0_skl(C,B),set_type) )
| ~ member(B,domain_of(C)) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f35]) ).
fof(f38,plain,
! [X0,X1] :
( member(ordered_pair(X0,sK0_skl(X1,X0)),X1)
| ~ member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ member(ordered_pair(X0,X2),X1)
| ~ ilf_type(X2,set_type)
| member(X0,domain_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(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(f63,plain,
! [B] :
( ? [C] : ilf_type(C,member_type(B))
| ~ ilf_type(B,set_type)
| empty(B) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f64,plain,
! [B] :
( ilf_type(sK2_skl(B),member_type(B))
| ~ ilf_type(B,set_type)
| empty(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(C,sK2_skl(B))],[f63]) ).
fof(f65,plain,
! [X0] :
( ilf_type(sK2_skl(X0),member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
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(f71,plain,
! [X0] :
( member(sK3_skl(X0),X0)
| 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(f91,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)],[f19]) ).
fof(f92,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)],[f91]) ).
fof(f93,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)],[f92]) ).
fof(f94,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)],[f92]) ).
fof(f106,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(f107,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)],[f106]) ).
fof(f108,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))],[f107]) ).
fof(f109,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)],[f108]) ).
fof(f112,plain,
! [X0,X1] :
( ~ member(sK7_skl(X1,X0),X1)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f113,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(f114,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
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(f129,plain,
! [B] :
( ! [C] :
( ! [D] :
( domain(B,C,D) = domain_of(D)
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f130,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)],[f129]) ).
fof(f131,plain,
! [B] :
( ! [C] :
( ! [D] :
( ilf_type(domain(B,C,D),subset_type(B))
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f132,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)],[f131]) ).
fof(f137,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f138,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ( member(E,domain(B,C,D))
<~> ? [F] :
( member(ordered_pair(E,F),D)
& ilf_type(F,member_type(C)) ) )
& ilf_type(E,member_type(B)) )
& ilf_type(D,relation_type(B,C)) )
& 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(E,F),D)
| ~ ilf_type(F,member_type(C)) )
| ~ member(E,domain(B,C,D)) )
& ( ? [F] :
( member(ordered_pair(E,F),D)
& ilf_type(F,member_type(C)) )
| member(E,domain(B,C,D)) )
& ilf_type(E,member_type(B)) )
& ilf_type(D,relation_type(B,C)) )
& 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(sK14_skl,F),sK13_skl)
| ~ ilf_type(F,member_type(sK12_skl)) )
| ~ member(sK14_skl,domain(sK11_skl,sK12_skl,sK13_skl)) )
& ( ( member(ordered_pair(sK14_skl,sK15_skl),sK13_skl)
& ilf_type(sK15_skl,member_type(sK12_skl)) )
| member(sK14_skl,domain(sK11_skl,sK12_skl,sK13_skl)) )
& ilf_type(sK14_skl,member_type(sK11_skl))
& ilf_type(sK13_skl,relation_type(sK11_skl,sK12_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(sK11_skl,sK12_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(sK14_skl,sK15_skl),sK13_skl)
| member(sK14_skl,domain(sK11_skl,sK12_skl,sK13_skl)) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f149,plain,
! [X0] :
( ~ member(ordered_pair(sK14_skl,X0),sK13_skl)
| ~ ilf_type(X0,member_type(sK12_skl))
| ~ member(sK14_skl,domain(sK11_skl,sK12_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,domain(sK11_skl,sK12_skl,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( ~ sQ3_spl
| member(sK14_skl,domain(sK11_skl,sK12_skl,sK13_skl)) ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f163,plain,
( sQ3_spl
| ~ member(sK14_skl,domain(sK11_skl,sK12_skl,sK13_skl)) ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f168,definition,
( sQ5_spl
<=> member(ordered_pair(sK14_skl,sK15_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f169,plain,
( ~ sQ5_spl
| member(ordered_pair(sK14_skl,sK15_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(sK14_skl,X0),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(sK14_skl,X0),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] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f88]) ).
fof(f178,plain,
! [X0,X1,X2,X3,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X3,relation_type(X4,X0))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f45,f137]) ).
fof(f179,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)],[f61,f137]) ).
fof(f180,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f137]) ).
fof(f181,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f180]) ).
fof(f184,plain,
( member(sK14_skl,sK11_skl)
| ~ ilf_type(sK11_skl,set_type)
| empty(sK11_skl) ),
inference(resolution,[status(thm)],[f146,f179]) ).
fof(f185,definition,
( sQ7_spl
<=> empty(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( ~ sQ7_spl
| empty(sK11_skl) ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,definition,
( sQ8_spl
<=> ilf_type(sK11_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( sQ8_spl
| ~ ilf_type(sK11_skl,set_type) ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f191,definition,
( sQ9_spl
<=> member(sK14_skl,sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( sQ9_spl
| ~ sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f184,f185,f188,f191]) ).
fof(f195,plain,
! [X0,X1] :
( member(ordered_pair(X1,sK0_skl(X0,X1)),X0)
| ~ member(X1,domain_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f38,f137]) ).
fof(f196,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)],[f39,f137]) ).
fof(f200,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)],[f62,f137]) ).
fof(f201,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[f200,f137]) ).
fof(f202,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f69,f137]) ).
fof(f203,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)],[f93,f137]) ).
fof(f204,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)],[f94,f137]) ).
fof(f205,plain,
! [X0] : ~ empty(power_set(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f114,f137]) ).
fof(f206,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)],[f55,f137]) ).
fof(f207,plain,
! [X0,X1,X2] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f206,f137]) ).
fof(f209,plain,
! [X0] :
( ilf_type(sK2_skl(X0),member_type(X0))
| empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f65,f137]) ).
fof(f211,plain,
! [X0] :
( member(sK2_skl(X0),X0)
| ~ ilf_type(X0,set_type)
| empty(X0)
| empty(X0) ),
inference(resolution,[status(thm)],[f209,f179]) ).
fof(f213,plain,
! [X0] :
( member(sK2_skl(X0),X0)
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f211]) ).
fof(f214,plain,
! [X0] :
( member(sK2_skl(X0),X0)
| empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f213,f137]) ).
fof(f215,plain,
! [X0] :
( member(sK3_skl(X0),X0)
| empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f71,f137]) ).
fof(f216,plain,
! [X0] :
( member(ordered_pair(sK3_skl(domain_of(X0)),sK0_skl(X0,sK3_skl(domain_of(X0)))),X0)
| ~ ilf_type(X0,binary_relation_type)
| empty(domain_of(X0)) ),
inference(resolution,[status(thm)],[f215,f195]) ).
fof(f217,plain,
! [X0] :
( member(ordered_pair(sK2_skl(domain_of(X0)),sK0_skl(X0,sK2_skl(domain_of(X0)))),X0)
| ~ ilf_type(X0,binary_relation_type)
| empty(domain_of(X0)) ),
inference(resolution,[status(thm)],[f214,f195]) ).
fof(f218,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)],[f130,f137]) ).
fof(f219,plain,
! [X0,X1,X2] :
( domain(X1,X2,X0) = domain_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f218,f137]) ).
fof(f220,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)],[f132,f137]) ).
fof(f221,plain,
! [X0,X1,X2] :
( ilf_type(domain(X1,X2,X0),subset_type(X1))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f220,f137]) ).
fof(f226,plain,
domain(sK11_skl,sK12_skl,sK13_skl) = domain_of(sK13_skl),
inference(resolution,[status(thm)],[f219,f145]) ).
fof(f240,plain,
( ~ sQ3_spl
| member(sK14_skl,domain_of(sK13_skl)) ),
inference(backward_demodulation,[status(thm)],[f226,f162]) ).
fof(f243,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f137]) ).
fof(f249,plain,
( ~ sQ3_spl
| member(ordered_pair(sK14_skl,sK0_skl(sK13_skl,sK14_skl)),sK13_skl)
| ~ ilf_type(sK13_skl,binary_relation_type) ),
inference(resolution,[status(thm)],[f240,f195]) ).
fof(f250,definition,
( sQ10_spl
<=> ilf_type(sK13_skl,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f252,plain,
( sQ10_spl
| ~ ilf_type(sK13_skl,binary_relation_type) ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f253,definition,
( sQ11_spl
<=> member(ordered_pair(sK14_skl,sK0_skl(sK13_skl,sK14_skl)),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( ~ sQ11_spl
| member(ordered_pair(sK14_skl,sK0_skl(sK13_skl,sK14_skl)),sK13_skl) ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,plain,
( ~ sQ3_spl
| sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f249,f250,f253,f161]) ).
fof(f258,definition,
( sQ12_spl
<=> empty(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( ~ sQ12_spl
| empty(sK12_skl) ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,definition,
( sQ13_spl
<=> ilf_type(sK12_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f263,plain,
( sQ13_spl
| ~ ilf_type(sK12_skl,set_type) ),
inference(component_clause,[status(thm)],[f261]) ).
fof(f268,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f263,f137]) ).
fof(f269,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f268]) ).
fof(f270,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f143]) ).
fof(f271,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f270]) ).
fof(f274,plain,
( ~ sQ5_spl
| ~ ilf_type(sK15_skl,set_type)
| member(sK14_skl,domain_of(sK13_skl))
| ~ ilf_type(sK13_skl,binary_relation_type) ),
inference(resolution,[status(thm)],[f169,f196]) ).
fof(f277,definition,
( sQ15_spl
<=> ilf_type(sK15_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f279,plain,
( sQ15_spl
| ~ ilf_type(sK15_skl,set_type) ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f284,definition,
( sQ17_spl
<=> member(sK14_skl,domain_of(sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| sQ17_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f274,f250,f284,f277,f168]) ).
fof(f291,definition,
( sQ19_spl
<=> ilf_type(sK14_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f293,plain,
( sQ19_spl
| ~ ilf_type(sK14_skl,set_type) ),
inference(component_clause,[status(thm)],[f291]) ).
fof(f299,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f279,f137]) ).
fof(f300,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f299]) ).
fof(f301,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f293,f137]) ).
fof(f302,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f301]) ).
fof(f305,plain,
( sQ10_spl
| ~ relation_like(sK13_skl) ),
inference(resolution,[status(thm)],[f252,f243]) ).
fof(f313,plain,
ilf_type(domain(sK11_skl,sK12_skl,sK13_skl),subset_type(sK11_skl)),
inference(resolution,[status(thm)],[f221,f145]) ).
fof(f315,plain,
ilf_type(domain_of(sK13_skl),subset_type(sK11_skl)),
inference(forward_demodulation,[status(thm)],[f226,f313]) ).
fof(f319,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)],[f109,f137]) ).
fof(f320,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f319,f137]) ).
fof(f321,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f320,f137]) ).
fof(f324,plain,
! [X0,X1] :
( ~ member(sK7_skl(X0,X1),X0)
| member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f112,f137]) ).
fof(f325,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ ilf_type(sK0_skl(sK13_skl,sK14_skl),member_type(sK12_skl)) ),
inference(resolution,[status(thm)],[f254,f173]) ).
fof(f328,plain,
! [X0,X1] :
( ~ sQ11_spl
| member(sK0_skl(sK13_skl,sK14_skl),X0)
| ~ ilf_type(sK13_skl,relation_type(X1,X0))
| ~ ilf_type(sK0_skl(sK13_skl,sK14_skl),set_type)
| ~ ilf_type(sK14_skl,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f254,f178]) ).
fof(f330,definition,
( sQ21_spl
<=> ilf_type(sK0_skl(sK13_skl,sK14_skl),set_type) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f332,plain,
( sQ21_spl
| ~ ilf_type(sK0_skl(sK13_skl,sK14_skl),set_type) ),
inference(component_clause,[status(thm)],[f330]) ).
fof(f338,definition,
! [X0,X1] :
( sQ23_spl
<=> ( member(sK0_skl(sK13_skl,sK14_skl),X0)
| ~ ilf_type(sK13_skl,relation_type(X1,X0))
| ~ ilf_type(X0,set_type) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f339,plain,
! [X0,X1] :
( ~ sQ23_spl
| member(sK0_skl(sK13_skl,sK14_skl),X0)
| ~ ilf_type(sK13_skl,relation_type(X1,X0))
| ~ ilf_type(X0,set_type) ),
inference(component_clause,[status(thm)],[f338]) ).
fof(f341,plain,
( ~ sQ11_spl
| ~ sQ21_spl
| ~ sQ19_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f328,f338,f291,f330,f253]) ).
fof(f343,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f332,f137]) ).
fof(f344,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f343]) ).
fof(f345,plain,
! [X0,X1] :
( ~ sQ23_spl
| member(sK0_skl(sK13_skl,sK14_skl),X1)
| ~ ilf_type(sK13_skl,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f339,f137]) ).
fof(f350,plain,
( ilf_type(domain_of(sK13_skl),member_type(power_set(sK11_skl)))
| ~ ilf_type(domain_of(sK13_skl),set_type) ),
inference(resolution,[status(thm)],[f315,f203]) ).
fof(f351,definition,
( sQ24_spl
<=> ilf_type(domain_of(sK13_skl),set_type) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( sQ24_spl
| ~ ilf_type(domain_of(sK13_skl),set_type) ),
inference(component_clause,[status(thm)],[f351]) ).
fof(f354,definition,
( sQ25_spl
<=> ilf_type(domain_of(sK13_skl),member_type(power_set(sK11_skl))) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f355,plain,
( ~ sQ25_spl
| ilf_type(domain_of(sK13_skl),member_type(power_set(sK11_skl))) ),
inference(component_clause,[status(thm)],[f354]) ).
fof(f357,plain,
( sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f350,f351,f354]) ).
fof(f358,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f353,f137]) ).
fof(f359,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f358]) ).
fof(f371,plain,
( ~ sQ25_spl
| ilf_type(domain_of(sK13_skl),subset_type(sK11_skl))
| ~ ilf_type(domain_of(sK13_skl),set_type) ),
inference(resolution,[status(thm)],[f355,f204]) ).
fof(f372,plain,
( ~ sQ25_spl
| member(domain_of(sK13_skl),power_set(sK11_skl))
| ~ ilf_type(power_set(sK11_skl),set_type)
| empty(power_set(sK11_skl)) ),
inference(resolution,[status(thm)],[f355,f179]) ).
fof(f373,definition,
( sQ26_spl
<=> ilf_type(domain_of(sK13_skl),subset_type(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f376,plain,
( ~ sQ25_spl
| sQ26_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f371,f351,f373,f354]) ).
fof(f377,definition,
( sQ27_spl
<=> empty(power_set(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f378,plain,
( ~ sQ27_spl
| empty(power_set(sK11_skl)) ),
inference(component_clause,[status(thm)],[f377]) ).
fof(f380,definition,
( sQ28_spl
<=> ilf_type(power_set(sK11_skl),set_type) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f382,plain,
( sQ28_spl
| ~ ilf_type(power_set(sK11_skl),set_type) ),
inference(component_clause,[status(thm)],[f380]) ).
fof(f383,definition,
( sQ29_spl
<=> member(domain_of(sK13_skl),power_set(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f384,plain,
( ~ sQ29_spl
| member(domain_of(sK13_skl),power_set(sK11_skl)) ),
inference(component_clause,[status(thm)],[f383]) ).
fof(f386,plain,
( ~ sQ25_spl
| sQ29_spl
| ~ sQ28_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f372,f377,f380,f383,f354]) ).
fof(f387,plain,
( sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f382,f137]) ).
fof(f388,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f387]) ).
fof(f389,plain,
( ~ sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f378,f205]) ).
fof(f390,plain,
~ sQ27_spl,
inference(contradiction_clause,[status(thm)],[f389]) ).
fof(f398,plain,
( ~ sQ23_spl
| member(sK0_skl(sK13_skl,sK14_skl),sK12_skl) ),
inference(resolution,[status(thm)],[f345,f145]) ).
fof(f402,plain,
! [X0] :
( ~ sQ29_spl
| member(X0,sK11_skl)
| ~ member(X0,domain_of(sK13_skl)) ),
inference(resolution,[status(thm)],[f321,f384]) ).
fof(f428,plain,
( ~ sQ29_spl
| empty(domain_of(sK13_skl))
| member(sK2_skl(domain_of(sK13_skl)),sK11_skl) ),
inference(resolution,[status(thm)],[f402,f214]) ).
fof(f429,plain,
( ~ sQ29_spl
| empty(domain_of(sK13_skl))
| member(sK3_skl(domain_of(sK13_skl)),sK11_skl) ),
inference(resolution,[status(thm)],[f402,f215]) ).
fof(f431,definition,
( sQ30_spl
<=> member(sK2_skl(domain_of(sK13_skl)),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f434,definition,
( sQ31_spl
<=> empty(domain_of(sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( ~ sQ31_spl
| empty(domain_of(sK13_skl)) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f436,plain,
( sQ31_spl
| ~ empty(domain_of(sK13_skl)) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,plain,
( ~ sQ29_spl
| sQ31_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f428,f431,f434,f383]) ).
fof(f438,definition,
( sQ32_spl
<=> member(sK3_skl(domain_of(sK13_skl)),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( ~ sQ29_spl
| sQ31_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f429,f438,f434,f383]) ).
fof(f442,plain,
! [X0] :
( ~ sQ31_spl
| ~ member(X0,domain_of(sK13_skl))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f435,f202]) ).
fof(f443,plain,
! [X0] :
( ~ sQ31_spl
| ~ member(X0,domain_of(sK13_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f442,f137]) ).
fof(f444,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)],[f128,f137]) ).
fof(f445,plain,
! [X0,X1,X2] :
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f444,f137]) ).
fof(f450,plain,
! [X0,X1] :
( sQ10_spl
| ~ ilf_type(sK13_skl,subset_type(cross_product(X0,X1))) ),
inference(resolution,[status(thm)],[f445,f305]) ).
fof(f456,plain,
( ~ sQ3_spl
| ~ sQ31_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f240,f443]) ).
fof(f461,plain,
( ~ sQ3_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f456]) ).
fof(f465,plain,
( sQ31_spl
| member(ordered_pair(sK3_skl(domain_of(sK13_skl)),sK0_skl(sK13_skl,sK3_skl(domain_of(sK13_skl)))),sK13_skl)
| ~ ilf_type(sK13_skl,binary_relation_type) ),
inference(resolution,[status(thm)],[f436,f216]) ).
fof(f466,definition,
( sQ33_spl
<=> member(ordered_pair(sK3_skl(domain_of(sK13_skl)),sK0_skl(sK13_skl,sK3_skl(domain_of(sK13_skl)))),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f469,plain,
( sQ31_spl
| sQ33_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f465,f250,f466,f434]) ).
fof(f470,plain,
( sQ3_spl
| ~ member(sK14_skl,domain_of(sK13_skl)) ),
inference(forward_demodulation,[status(thm)],[f226,f163]) ).
fof(f501,plain,
( sQ31_spl
| member(ordered_pair(sK2_skl(domain_of(sK13_skl)),sK0_skl(sK13_skl,sK2_skl(domain_of(sK13_skl)))),sK13_skl)
| ~ ilf_type(sK13_skl,binary_relation_type) ),
inference(resolution,[status(thm)],[f436,f217]) ).
fof(f503,definition,
( sQ34_spl
<=> member(ordered_pair(sK2_skl(domain_of(sK13_skl)),sK0_skl(sK13_skl,sK2_skl(domain_of(sK13_skl)))),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f506,plain,
( sQ31_spl
| sQ34_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f501,f250,f503,f434]) ).
fof(f556,plain,
! [X0,X1] :
( sQ10_spl
| ~ ilf_type(sK13_skl,relation_type(X0,X1)) ),
inference(resolution,[status(thm)],[f450,f207]) ).
fof(f558,plain,
( sQ10_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f145,f556]) ).
fof(f559,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f558]) ).
fof(f638,plain,
! [X0] :
( ~ sQ29_spl
| member(X0,power_set(sK11_skl))
| ~ ilf_type(sK11_skl,set_type)
| ~ member(sK7_skl(sK11_skl,X0),domain_of(sK13_skl)) ),
inference(resolution,[status(thm)],[f402,f324]) ).
fof(f644,definition,
! [X0] :
( sQ38_spl
<=> ( member(X0,power_set(sK11_skl))
| ~ member(sK7_skl(sK11_skl,X0),domain_of(sK13_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f647,plain,
( ~ sQ29_spl
| ~ sQ8_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f638,f644,f188,f383]) ).
fof(f662,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f137]) ).
fof(f663,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f662]) ).
fof(f664,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f186,f141]) ).
fof(f665,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f664]) ).
fof(f666,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ member(sK0_skl(sK13_skl,sK14_skl),sK12_skl)
| empty(sK12_skl) ),
inference(resolution,[status(thm)],[f325,f201]) ).
fof(f667,definition,
( sQ42_spl
<=> member(sK0_skl(sK13_skl,sK14_skl),sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f669,plain,
( sQ42_spl
| ~ member(sK0_skl(sK13_skl,sK14_skl),sK12_skl) ),
inference(component_clause,[status(thm)],[f667]) ).
fof(f670,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ42_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f666,f258,f667,f253,f172]) ).
fof(f671,plain,
( sQ42_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f669,f398]) ).
fof(f672,plain,
( sQ42_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f671]) ).
fof(f673,plain,
( sQ3_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f470,f284,f161]) ).
fof(f674,plain,
$false,
inference(sat_refutation,[status(thm)],[f156,f160,f171,f175,f181,f194,f256,f269,f271,f287,f300,f302,f341,f344,f357,f359,f376,f386,f388,f390,f437,f441,f461,f469,f506,f559,f647,f663,f665,f670,f672,f673]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET680+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:32:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.44 % Elapsed time: 0.065008 seconds
% 0.14/0.44 % CPU time: 0.257673 seconds
% 0.14/0.44 % Total memory used: 86.540 MB
% 0.14/0.44 % Net memory used: 86.190 MB
%------------------------------------------------------------------------------