%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET683+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 : n017.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 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 28
% Syntax : Number of formulae : 155 ( 16 unt; 14 def)
% Number of atoms : 510 ( 12 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 618 ( 263 ~; 246 |; 44 &)
% ( 24 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 15 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 220 ( 210 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( member(B,range_of(C))
=> ? [D] :
( member(D,domain_of(C))
& ilf_type(D,set_type) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,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(f4,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(f6,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(f10,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(f12,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(f14,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(f15,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(f18,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(f20,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(f21,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(f22,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(f24,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,conjecture,
! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ! [E] :
( ilf_type(E,member_type(B))
=> ( member(E,range(C,B,D))
=> ? [F] :
( member(F,domain(C,B,D))
& ilf_type(F,member_type(C)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
~ ! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ! [E] :
( ilf_type(E,member_type(B))
=> ( member(E,range(C,B,D))
=> ? [F] :
( member(F,domain(C,B,D))
& ilf_type(F,member_type(C)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f27,plain,
! [B] :
( ! [C] :
( ? [D] :
( member(D,domain_of(C))
& ilf_type(D,set_type) )
| ~ member(B,range_of(C))
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f28,plain,
! [B] :
( ! [C] :
( ( member(sK0_skl(C,B),domain_of(C))
& ilf_type(sK0_skl(C,B),set_type) )
| ~ member(B,range_of(C))
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f27]) ).
fof(f30,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),domain_of(X1))
| ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f31,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)],[f2]) ).
fof(f33,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)],[f31]) ).
fof(f37,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)],[f4]) ).
fof(f38,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)],[f37]) ).
fof(f39,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)],[f38]) ).
fof(f40,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)],[f38]) ).
fof(f44,plain,
! [B] :
( ( empty(B)
<=> ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) ) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f45,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)],[f44]) ).
fof(f46,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))],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
! [X0] :
( member(sK3_skl(X0),X0)
| empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f56,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)],[f10]) ).
fof(f57,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)],[f56]) ).
fof(f60,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)],[f57]) ).
fof(f63,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)],[f12]) ).
fof(f64,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)],[f63]) ).
fof(f65,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)],[f64]) ).
fof(f70,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)],[f14]) ).
fof(f71,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)],[f70]) ).
fof(f72,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK6_skl(C,B),C)
& member(sK6_skl(C,B),B)
& ilf_type(sK6_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,[sK6_skl]),skolemize(D,sK6_skl(C,B))],[f71]) ).
fof(f73,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)],[f72]) ).
fof(f77,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f78,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f91,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)],[f18]) ).
fof(f92,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)],[f91]) ).
fof(f95,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)],[f20]) ).
fof(f96,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)],[f95]) ).
fof(f97,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)],[f21]) ).
fof(f98,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)],[f97]) ).
fof(f99,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)],[f22]) ).
fof(f100,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)],[f99]) ).
fof(f103,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f104,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ! [F] :
( ~ member(F,domain(C,B,D))
| ~ ilf_type(F,member_type(C)) )
& member(E,range(C,B,D))
& ilf_type(E,member_type(B)) )
& ilf_type(D,relation_type(C,B)) )
& ilf_type(C,set_type)
& ~ empty(C) )
& ilf_type(B,set_type)
& ~ empty(B) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f105,plain,
( ! [F] :
( ~ member(F,domain(sK11_skl,sK10_skl,sK12_skl))
| ~ ilf_type(F,member_type(sK11_skl)) )
& member(sK13_skl,range(sK11_skl,sK10_skl,sK12_skl))
& ilf_type(sK13_skl,member_type(sK10_skl))
& ilf_type(sK12_skl,relation_type(sK11_skl,sK10_skl))
& ilf_type(sK11_skl,set_type)
& ~ empty(sK11_skl)
& ilf_type(sK10_skl,set_type)
& ~ empty(sK10_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl,sK13_skl]),skolemize(B,sK10_skl),skolemize(C,sK11_skl),skolemize(D,sK12_skl),skolemize(E,sK13_skl)],[f104]) ).
fof(f108,plain,
~ empty(sK11_skl),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f110,plain,
ilf_type(sK12_skl,relation_type(sK11_skl,sK10_skl)),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f112,plain,
member(sK13_skl,range(sK11_skl,sK10_skl,sK12_skl)),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f113,plain,
! [X0] :
( ~ member(X0,domain(sK11_skl,sK10_skl,sK12_skl))
| ~ ilf_type(X0,member_type(sK11_skl)) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f114,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f60]) ).
fof(f116,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f47,f103]) ).
fof(f117,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)],[f39,f103]) ).
fof(f118,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)],[f40,f103]) ).
fof(f119,plain,
! [X0] : ~ empty(power_set(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f78,f103]) ).
fof(f121,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f114,f103]) ).
fof(f123,plain,
! [X0] :
( member(sK3_skl(X0),X0)
| empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f49,f103]) ).
fof(f124,plain,
! [X0,X1] :
( member(sK0_skl(X0,X1),domain_of(X0))
| ~ member(X1,range_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f30,f103]) ).
fof(f126,plain,
! [X0] :
( ~ member(X0,sK11_skl)
| ~ ilf_type(sK11_skl,set_type)
| empty(sK11_skl)
| ~ member(X0,domain(sK11_skl,sK10_skl,sK12_skl)) ),
inference(resolution,[status(thm)],[f113,f118]) ).
fof(f127,definition,
! [X0] :
( sQ0_spl
<=> ( ~ member(X0,sK11_skl)
| ~ member(X0,domain(sK11_skl,sK10_skl,sK12_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f128,plain,
! [X0] :
( ~ sQ0_spl
| ~ member(X0,sK11_skl)
| ~ member(X0,domain(sK11_skl,sK10_skl,sK12_skl)) ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,definition,
( sQ1_spl
<=> empty(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( ~ sQ1_spl
| empty(sK11_skl) ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,definition,
( sQ2_spl
<=> ilf_type(sK11_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f135,plain,
( sQ2_spl
| ~ ilf_type(sK11_skl,set_type) ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( ~ sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f126,f127,f130,f133]) ).
fof(f137,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f135,f103]) ).
fof(f138,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f137]) ).
fof(f139,plain,
( ~ sQ0_spl
| empty(domain(sK11_skl,sK10_skl,sK12_skl))
| ~ member(sK3_skl(domain(sK11_skl,sK10_skl,sK12_skl)),sK11_skl) ),
inference(resolution,[status(thm)],[f128,f123]) ).
fof(f141,definition,
( sQ3_spl
<=> member(sK3_skl(domain(sK11_skl,sK10_skl,sK12_skl)),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f143,plain,
( sQ3_spl
| ~ member(sK3_skl(domain(sK11_skl,sK10_skl,sK12_skl)),sK11_skl) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,definition,
( sQ4_spl
<=> empty(domain(sK11_skl,sK10_skl,sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( ~ sQ4_spl
| empty(domain(sK11_skl,sK10_skl,sK12_skl)) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,plain,
( ~ sQ0_spl
| sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f139,f141,f144,f127]) ).
fof(f155,plain,
! [X0] :
( ~ sQ4_spl
| ~ member(X0,domain(sK11_skl,sK10_skl,sK12_skl))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f145,f116]) ).
fof(f156,plain,
! [X0] :
( ~ sQ4_spl
| ~ member(X0,domain(sK11_skl,sK10_skl,sK12_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f103]) ).
fof(f163,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)],[f65,f103]) ).
fof(f165,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)],[f96,f103]) ).
fof(f166,plain,
! [X0,X1,X2] :
( domain(X1,X2,X0) = domain_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f165,f103]) ).
fof(f167,plain,
domain(sK11_skl,sK10_skl,sK12_skl) = domain_of(sK12_skl),
inference(resolution,[status(thm)],[f166,f110]) ).
fof(f170,plain,
! [X0] :
( ~ sQ4_spl
| ~ member(X0,domain_of(sK12_skl)) ),
inference(backward_demodulation,[status(thm)],[f167,f156]) ).
fof(f174,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)],[f98,f103]) ).
fof(f175,plain,
( ilf_type(domain_of(sK12_skl),subset_type(sK11_skl))
| ~ ilf_type(sK12_skl,relation_type(sK11_skl,sK10_skl))
| ~ ilf_type(sK10_skl,set_type) ),
inference(paramodulation,[status(thm)],[f167,f174]) ).
fof(f176,definition,
( sQ8_spl
<=> ilf_type(sK10_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( sQ8_spl
| ~ ilf_type(sK10_skl,set_type) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f179,definition,
( sQ9_spl
<=> ilf_type(sK12_skl,relation_type(sK11_skl,sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( sQ9_spl
| ~ ilf_type(sK12_skl,relation_type(sK11_skl,sK10_skl)) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,definition,
( sQ10_spl
<=> ilf_type(domain_of(sK12_skl),subset_type(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f175,f176,f179,f182]) ).
fof(f186,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)],[f100,f103]) ).
fof(f187,plain,
! [X0,X1,X2] :
( range(X1,X2,X0) = range_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f186,f103]) ).
fof(f188,plain,
! [X0] :
( ~ sQ4_spl
| ~ member(X0,range_of(sK12_skl))
| ~ ilf_type(sK12_skl,binary_relation_type) ),
inference(resolution,[status(thm)],[f170,f124]) ).
fof(f191,definition,
( sQ11_spl
<=> ilf_type(sK12_skl,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( sQ11_spl
| ~ ilf_type(sK12_skl,binary_relation_type) ),
inference(component_clause,[status(thm)],[f191]) ).
fof(f194,definition,
! [X0] :
( sQ12_spl
<=> ~ member(X0,range_of(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f195,plain,
! [X0] :
( ~ sQ12_spl
| ~ member(X0,range_of(sK12_skl)) ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f197,plain,
( ~ sQ4_spl
| sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f188,f191,f194,f144]) ).
fof(f208,plain,
( sQ3_spl
| ~ member(sK3_skl(domain_of(sK12_skl)),sK11_skl) ),
inference(forward_demodulation,[status(thm)],[f167,f143]) ).
fof(f211,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f181,f110]) ).
fof(f212,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f211]) ).
fof(f213,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f178,f103]) ).
fof(f214,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f213]) ).
fof(f224,plain,
( ~ sQ12_spl
| empty(range_of(sK12_skl)) ),
inference(resolution,[status(thm)],[f195,f123]) ).
fof(f226,definition,
( sQ16_spl
<=> empty(range_of(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f227,plain,
( ~ sQ16_spl
| empty(range_of(sK12_skl)) ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f238,plain,
! [X0] :
( ~ sQ16_spl
| ~ member(X0,range_of(sK12_skl))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f227,f116]) ).
fof(f239,plain,
! [X0] :
( ~ sQ16_spl
| ~ member(X0,range_of(sK12_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f238,f103]) ).
fof(f240,plain,
( sQ11_spl
| ~ relation_like(sK12_skl) ),
inference(resolution,[status(thm)],[f193,f121]) ).
fof(f251,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)],[f33,f103]) ).
fof(f258,definition,
! [X0] :
( sQ19_spl
<=> ~ member(X0,domain_of(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f259,plain,
! [X0] :
( ~ sQ19_spl
| ~ member(X0,domain_of(sK12_skl)) ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f262,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f131,f108]) ).
fof(f263,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f262]) ).
fof(f266,plain,
! [X0] :
( ~ sQ19_spl
| ~ member(X0,range_of(sK12_skl))
| ~ ilf_type(sK12_skl,binary_relation_type) ),
inference(resolution,[status(thm)],[f259,f124]) ).
fof(f269,plain,
( ~ sQ19_spl
| sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f266,f191,f194,f258]) ).
fof(f289,plain,
( sQ3_spl
| ~ ilf_type(sK3_skl(domain_of(sK12_skl)),member_type(sK11_skl))
| ~ ilf_type(sK11_skl,set_type)
| empty(sK11_skl) ),
inference(resolution,[status(thm)],[f208,f117]) ).
fof(f290,definition,
( sQ22_spl
<=> ilf_type(sK3_skl(domain_of(sK12_skl)),member_type(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f292,plain,
( sQ22_spl
| ~ ilf_type(sK3_skl(domain_of(sK12_skl)),member_type(sK11_skl)) ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f293,plain,
( sQ3_spl
| ~ sQ22_spl
| ~ sQ2_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f289,f130,f133,f290,f141]) ).
fof(f296,plain,
range(sK11_skl,sK10_skl,sK12_skl) = range_of(sK12_skl),
inference(resolution,[status(thm)],[f187,f110]) ).
fof(f300,plain,
( sQ22_spl
| ~ member(sK3_skl(domain_of(sK12_skl)),sK11_skl)
| ~ ilf_type(sK11_skl,set_type)
| empty(sK11_skl) ),
inference(resolution,[status(thm)],[f292,f118]) ).
fof(f301,definition,
( sQ23_spl
<=> member(sK3_skl(domain_of(sK12_skl)),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f303,plain,
( sQ23_spl
| ~ member(sK3_skl(domain_of(sK12_skl)),sK11_skl) ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f304,plain,
( sQ22_spl
| ~ sQ23_spl
| ~ sQ2_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f300,f130,f133,f301,f290]) ).
fof(f305,plain,
member(sK13_skl,range_of(sK12_skl)),
inference(backward_demodulation,[status(thm)],[f296,f112]) ).
fof(f307,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f305,f239]) ).
fof(f308,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f307]) ).
fof(f315,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)],[f73,f103]) ).
fof(f316,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f315,f103]) ).
fof(f317,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f316,f103]) ).
fof(f344,plain,
! [X0,X1,X2] :
( ~ ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(power_set(X2),set_type)
| empty(power_set(X2))
| member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f317,f117]) ).
fof(f346,plain,
! [X0,X1,X2] :
( ~ ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(power_set(X2),set_type)
| member(X0,X2)
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f344,f119]) ).
fof(f372,plain,
! [X0,X1,X2] :
( ~ ilf_type(X1,member_type(power_set(X2)))
| member(X0,X2)
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f346,f103]) ).
fof(f374,plain,
! [X0,X1,X2] :
( ~ ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,set_type)
| member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f372,f163]) ).
fof(f377,plain,
! [X0,X1,X2] :
( ~ ilf_type(X1,subset_type(X2))
| member(X0,X2)
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f374,f103]) ).
fof(f386,plain,
! [X0,X1] :
( empty(X0)
| ~ ilf_type(X0,subset_type(X1))
| member(sK3_skl(X0),X1) ),
inference(resolution,[status(thm)],[f377,f123]) ).
fof(f401,plain,
( ~ sQ12_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f224,f226,f194]) ).
fof(f458,plain,
! [X0,X1,X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,subset_type(X1))
| member(sK3_skl(X0),X1) ),
inference(resolution,[status(thm)],[f386,f116]) ).
fof(f459,plain,
! [X0,X1,X2] :
( ~ member(X2,X0)
| ~ ilf_type(X0,subset_type(X1))
| member(sK3_skl(X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f458,f103]) ).
fof(f537,plain,
! [X0] :
( sQ23_spl
| ~ member(X0,domain_of(sK12_skl))
| ~ ilf_type(domain_of(sK12_skl),subset_type(sK11_skl)) ),
inference(resolution,[status(thm)],[f303,f459]) ).
fof(f539,plain,
( sQ23_spl
| sQ19_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f537,f182,f258,f301]) ).
fof(f659,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)],[f92,f103]) ).
fof(f660,plain,
! [X0,X1,X2] :
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f659,f103]) ).
fof(f675,plain,
! [X0,X1] :
( sQ11_spl
| ~ ilf_type(sK12_skl,subset_type(cross_product(X0,X1))) ),
inference(resolution,[status(thm)],[f660,f240]) ).
fof(f677,plain,
! [X0,X1] :
( sQ11_spl
| ~ ilf_type(sK12_skl,relation_type(X1,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f675,f251]) ).
fof(f679,plain,
! [X0,X1] :
( sQ11_spl
| ~ ilf_type(sK12_skl,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f677,f103]) ).
fof(f684,plain,
( sQ11_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f110,f679]) ).
fof(f686,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f684]) ).
fof(f687,plain,
$false,
inference(sat_refutation,[status(thm)],[f136,f138,f147,f185,f197,f212,f214,f263,f269,f293,f304,f308,f401,f539,f686]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET683+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n017.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Mon Sep 21 05:27:26 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.19/0.44 % Drodi V4.1.1
% 0.19/0.48 % Refutation found
% 0.19/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.52 % Elapsed time: 0.085627 seconds
% 0.19/0.52 % CPU time: 0.326724 seconds
% 0.19/0.52 % Total memory used: 52.322 MB
% 0.19/0.52 % Net memory used: 52.073 MB
%------------------------------------------------------------------------------