%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET657+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 02:10:22 PM UTC 2026
% Result : Timeout 292.09s 37.41s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 111 ( 17 unt; 0 def)
% Number of atoms : 393 ( 17 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 479 ( 197 ~; 197 |; 30 &)
% ( 10 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 236 ( 231 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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)
=> ( ( subset(D,E)
& subset(B,C) )
=> subset(union(B,D),union(C,E)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> field_of(B) = union(domain_of(B),range_of(B)) ),
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)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,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,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(f21,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,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(f23,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/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(f33,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(f34,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(f35,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(f36,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(f37,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> subset(field_of(D),union(B,C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> subset(field_of(D),union(B,C)) ) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f40,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( subset(union(B,D),union(C,E))
| ~ subset(D,E)
| ~ subset(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)],[f1]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( subset(union(X0,X2),union(X1,X3))
| ~ subset(X2,X3)
| ~ subset(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)],[f40]) ).
fof(f42,plain,
! [B] :
( field_of(B) = union(domain_of(B),range_of(B))
| ~ ilf_type(B,binary_relation_type) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f43,plain,
! [X0] :
( field_of(X0) = union(domain_of(X0),range_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f55,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(f57,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)],[f55]) ).
fof(f61,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)],[f9]) ).
fof(f62,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)],[f61]) ).
fof(f63,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK1_skl(C,B),C)
& member(sK1_skl(C,B),B)
& ilf_type(sK1_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,[sK1_skl]),skolemize(D,sK1_skl(C,B))],[f62]) ).
fof(f66,plain,
! [X0,X1] :
( member(sK1_skl(X1,X0),X0)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f67,plain,
! [X0,X1] :
( ~ member(sK1_skl(X1,X0),X1)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f76,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)],[f14]) ).
fof(f77,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)],[f76]) ).
fof(f80,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)],[f77]) ).
fof(f83,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)],[f16]) ).
fof(f84,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)],[f83]) ).
fof(f85,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)],[f84]) ).
fof(f96,plain,
! [B] :
( ! [C] :
( ( member(B,power_set(C))
<=> ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f97,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)],[f96]) ).
fof(f98,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK4_skl(C,B),C)
& member(sK4_skl(C,B),B)
& ilf_type(sK4_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,[sK4_skl]),skolemize(D,sK4_skl(C,B))],[f97]) ).
fof(f99,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)],[f98]) ).
fof(f103,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f104,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f106,plain,
! [B] :
( ! [C] :
( ( ilf_type(B,member_type(C))
<=> member(B,C) )
| ~ ilf_type(C,set_type)
| empty(C) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f107,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)],[f106]) ).
fof(f108,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)],[f107]) ).
fof(f130,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(f131,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)],[f130]) ).
fof(f146,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)],[f33]) ).
fof(f147,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)],[f146]) ).
fof(f148,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)],[f34]) ).
fof(f149,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)],[f148]) ).
fof(f150,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)],[f35]) ).
fof(f151,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)],[f150]) ).
fof(f152,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)],[f36]) ).
fof(f153,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)],[f152]) ).
fof(f154,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f155,plain,
? [B] :
( ? [C] :
( ? [D] :
( ~ subset(field_of(D),union(B,C))
& ilf_type(D,relation_type(B,C)) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f156,plain,
( ~ subset(field_of(sK13_skl),union(sK11_skl,sK12_skl))
& ilf_type(sK13_skl,relation_type(sK11_skl,sK12_skl))
& ilf_type(sK12_skl,set_type)
& ilf_type(sK11_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl]),skolemize(B,sK11_skl),skolemize(C,sK12_skl),skolemize(D,sK13_skl)],[f155]) ).
fof(f159,plain,
ilf_type(sK13_skl,relation_type(sK11_skl,sK12_skl)),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f160,plain,
~ subset(field_of(sK13_skl),union(sK11_skl,sK12_skl)),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f161,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f80]) ).
fof(f163,plain,
! [X0,X1,X2] :
( ilf_type(range(X0,X2,X1),subset_type(X2))
| ~ ilf_type(X1,relation_type(X0,X2))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f153,f154]) ).
fof(f164,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)],[f151,f154]) ).
fof(f165,plain,
! [X0,X1,X2] :
( ilf_type(domain(X0,X2,X1),subset_type(X0))
| ~ ilf_type(X1,relation_type(X0,X2))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f149,f154]) ).
fof(f166,plain,
! [X0,X1,X2] :
( domain(X0,X2,X1) = domain_of(X1)
| ~ ilf_type(X1,relation_type(X0,X2))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f147,f154]) ).
fof(f172,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)],[f131,f154]) ).
fof(f179,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)],[f108,f154]) ).
fof(f180,plain,
! [X0] : ~ empty(power_set(X0)),
inference(backward_subsumption_resolution,[status(thm)],[f104,f154]) ).
fof(f183,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f99,f154]) ).
fof(f187,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f85,f154]) ).
fof(f188,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f161,f154]) ).
fof(f191,plain,
! [X0,X1] :
( ~ member(sK1_skl(X1,X0),X1)
| subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f67,f154]) ).
fof(f192,plain,
! [X0,X1] :
( member(sK1_skl(X1,X0),X0)
| subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f66,f154]) ).
fof(f195,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)],[f57,f154]) ).
fof(f200,plain,
! [X0,X1,X2,X3] :
( subset(union(X0,X2),union(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f41,f154]) ).
fof(f202,plain,
! [X0,X1,X2] :
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f163,f154]) ).
fof(f203,plain,
! [X0,X1,X2] :
( range(X1,X2,X0) = range_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f164,f154]) ).
fof(f204,plain,
! [X0,X1,X2] :
( ilf_type(domain(X1,X2,X0),subset_type(X1))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f165,f154]) ).
fof(f205,plain,
! [X0,X1,X2] :
( domain(X1,X2,X0) = domain_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f166,f154]) ).
fof(f209,plain,
! [X0,X1,X2] :
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f172,f154]) ).
fof(f214,plain,
! [X0,X1] :
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f179,f154]) ).
fof(f217,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f183,f154]) ).
fof(f219,plain,
! [X0,X1] :
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f187,f154]) ).
fof(f221,plain,
! [X0,X1] :
( ~ member(sK1_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f154]) ).
fof(f222,plain,
! [X0,X1] :
( member(sK1_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f192,f154]) ).
fof(f225,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)],[f195,f154]) ).
fof(f230,plain,
! [X0,X1,X2,X3] :
( subset(union(X2,X1),union(X0,X3))
| ~ subset(X1,X3)
| ~ subset(X2,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f200,f154]) ).
fof(f231,plain,
! [X0] :
( field_of(X0) = union(domain_of(X0),range_of(X0))
| ~ relation_like(X0) ),
inference(resolution,[status(thm)],[f188,f43]) ).
fof(f249,plain,
range(sK11_skl,sK12_skl,sK13_skl) = range_of(sK13_skl),
inference(resolution,[status(thm)],[f203,f159]) ).
fof(f252,plain,
domain(sK11_skl,sK12_skl,sK13_skl) = domain_of(sK13_skl),
inference(resolution,[status(thm)],[f205,f159]) ).
fof(f253,plain,
( ilf_type(range_of(sK13_skl),subset_type(sK12_skl))
| ~ ilf_type(sK13_skl,relation_type(sK11_skl,sK12_skl)) ),
inference(paramodulation,[status(thm)],[f249,f202]) ).
fof(f254,plain,
ilf_type(range_of(sK13_skl),subset_type(sK12_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f253,f159]) ).
fof(f255,plain,
( ilf_type(domain_of(sK13_skl),subset_type(sK11_skl))
| ~ ilf_type(sK13_skl,relation_type(sK11_skl,sK12_skl)) ),
inference(paramodulation,[status(thm)],[f252,f204]) ).
fof(f256,plain,
ilf_type(domain_of(sK13_skl),subset_type(sK11_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f255,f159]) ).
fof(f278,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| empty(power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(resolution,[status(thm)],[f219,f214]) ).
fof(f279,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f278,f180]) ).
fof(f280,plain,
member(domain_of(sK13_skl),power_set(sK11_skl)),
inference(resolution,[status(thm)],[f279,f256]) ).
fof(f281,plain,
member(range_of(sK13_skl),power_set(sK12_skl)),
inference(resolution,[status(thm)],[f279,f254]) ).
fof(f346,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f217,f154]) ).
fof(f352,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ member(sK1_skl(X1,X2),X0)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f346,f221]) ).
fof(f354,plain,
! [X0,X1,X2] :
( relation_like(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f225,f209]) ).
fof(f359,plain,
relation_like(sK13_skl),
inference(resolution,[status(thm)],[f354,f159]) ).
fof(f361,plain,
field_of(sK13_skl) = union(domain_of(sK13_skl),range_of(sK13_skl)),
inference(resolution,[status(thm)],[f359,f231]) ).
fof(f438,plain,
! [X0,X1,X2,X3] :
( subset(union(X1,X2),union(X0,X3))
| ~ subset(X2,X3)
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f230,f154]) ).
fof(f439,plain,
! [X0,X1,X2,X3] :
( subset(union(X0,X2),union(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f438,f154]) ).
fof(f788,plain,
! [X0,X1] :
( subset(X0,X1)
| subset(X0,X1)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f352,f222]) ).
fof(f798,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(X0,power_set(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f788]) ).
fof(f809,plain,
subset(range_of(sK13_skl),sK12_skl),
inference(resolution,[status(thm)],[f798,f281]) ).
fof(f814,plain,
subset(domain_of(sK13_skl),sK11_skl),
inference(resolution,[status(thm)],[f798,f280]) ).
fof(f832,plain,
! [X0,X1] :
( subset(union(X0,range_of(sK13_skl)),union(X1,sK12_skl))
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f439,f809]) ).
fof(f1569,plain,
! [X0] :
( subset(field_of(sK13_skl),union(X0,sK12_skl))
| ~ subset(domain_of(sK13_skl),X0) ),
inference(paramodulation,[status(thm)],[f361,f832]) ).
fof(f5605,plain,
~ subset(domain_of(sK13_skl),sK11_skl),
inference(resolution,[status(thm)],[f1569,f160]) ).
fof(f5611,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5605,f814]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET657+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n007.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 05:29:06 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 292.09/37.41 % Refutation found
% 292.09/37.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 292.09/37.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 19.65/38.44 % Elapsed time: 38.057070 seconds
% 19.65/38.44 % CPU time: 295.285814 seconds
% 19.65/38.44 % Total memory used: 845.524 MB
% 19.65/38.44 % Net memory used: 745.607 MB
%------------------------------------------------------------------------------