%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET669+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 : n005.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 02:10:24 PM UTC 2026
% Result : Theorem 0.13s 5.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 117 ( 14 unt; 6 def)
% Number of atoms : 398 ( 29 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 477 ( 196 ~; 199 |; 30 &)
% ( 14 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 199 ( 194 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ( subset(C,B)
& subset(B,C) )
=> B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,C))
=> ( subset(identity_relation_of(D),E)
=> ( subset(D,range(B,C,E))
& subset(D,domain(B,C,E)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,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(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(f20,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(f21,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(f22,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(f28,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(f30,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> range(B,C,D) = range_of(D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [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(f32,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(identity_relation_of(C),D)
=> ( C = range(B,C,D)
& subset(C,domain(B,C,D)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(identity_relation_of(C),D)
=> ( C = range(B,C,D)
& subset(C,domain(B,C,D)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,plain,
! [B] :
( ! [C] :
( B = C
| ~ subset(C,B)
| ~ subset(B,C)
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f36,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ( subset(D,range(B,C,E))
& subset(D,domain(B,C,E)) )
| ~ subset(identity_relation_of(D),E)
| ~ ilf_type(E,relation_type(B,C)) )
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( subset(X2,domain(X0,X1,X3))
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( subset(X2,range(X0,X1,X3))
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f53,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)],[f7]) ).
fof(f54,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)],[f53]) ).
fof(f55,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))],[f54]) ).
fof(f58,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)],[f55]) ).
fof(f59,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)],[f55]) ).
fof(f88,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(f89,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)],[f88]) ).
fof(f90,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)],[f89]) ).
fof(f99,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)],[f20]) ).
fof(f100,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)],[f99]) ).
fof(f101,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))],[f100]) ).
fof(f102,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)],[f101]) ).
fof(f106,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f107,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f109,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)],[f22]) ).
fof(f110,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)],[f109]) ).
fof(f111,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)],[f110]) ).
fof(f135,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)],[f28]) ).
fof(f136,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)],[f135]) ).
fof(f139,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)],[f30]) ).
fof(f140,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)],[f139]) ).
fof(f141,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)],[f31]) ).
fof(f142,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)],[f141]) ).
fof(f143,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f144,plain,
? [B] :
( ? [C] :
( ? [D] :
( ( C != range(B,C,D)
| ~ subset(C,domain(B,C,D)) )
& subset(identity_relation_of(C),D)
& 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(f145,plain,
( ( sK13_skl != range(sK12_skl,sK13_skl,sK14_skl)
| ~ subset(sK13_skl,domain(sK12_skl,sK13_skl,sK14_skl)) )
& subset(identity_relation_of(sK13_skl),sK14_skl)
& ilf_type(sK14_skl,relation_type(sK12_skl,sK13_skl))
& ilf_type(sK13_skl,set_type)
& ilf_type(sK12_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl,sK14_skl]),skolemize(B,sK12_skl),skolemize(C,sK13_skl),skolemize(D,sK14_skl)],[f144]) ).
fof(f148,plain,
ilf_type(sK14_skl,relation_type(sK12_skl,sK13_skl)),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f149,plain,
subset(identity_relation_of(sK13_skl),sK14_skl),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f150,plain,
( sK13_skl != range(sK12_skl,sK13_skl,sK14_skl)
| ~ subset(sK13_skl,domain(sK12_skl,sK13_skl,sK14_skl)) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f151,definition,
( sQ0_spl
<=> subset(sK13_skl,domain(sK12_skl,sK13_skl,sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( sQ0_spl
| ~ subset(sK13_skl,domain(sK12_skl,sK13_skl,sK14_skl)) ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,definition,
( sQ1_spl
<=> sK13_skl = range(sK12_skl,sK13_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( sQ1_spl
| sK13_skl != range(sK12_skl,sK13_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f150,f151,f154]) ).
fof(f166,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)],[f142,f143]) ).
fof(f167,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)],[f140,f143]) ).
fof(f169,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)],[f136,f143]) ).
fof(f178,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)],[f111,f143]) ).
fof(f179,plain,
! [X0] : ~ empty(power_set(X0)),
inference(backward_subsumption_resolution,[status(thm)],[f107,f143]) ).
fof(f182,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)],[f102,f143]) ).
fof(f185,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)],[f90,f143]) ).
fof(f190,plain,
! [X0,X1] :
( ~ member(sK1_skl(X1,X0),X1)
| subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f59,f143]) ).
fof(f191,plain,
! [X0,X1] :
( member(sK1_skl(X1,X0),X0)
| subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f58,f143]) ).
fof(f200,plain,
! [X0,X1,X2,X3] :
( subset(X3,range(X0,X1,X2))
| ~ subset(identity_relation_of(X3),X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f39,f143]) ).
fof(f201,plain,
! [X0,X1,X2,X3] :
( subset(X3,domain(X0,X1,X2))
| ~ subset(identity_relation_of(X3),X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f38,f143]) ).
fof(f202,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f36,f143]) ).
fof(f204,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)],[f166,f143]) ).
fof(f205,plain,
! [X0,X1,X2] :
( range(X1,X2,X0) = range_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f167,f143]) ).
fof(f207,plain,
! [X0,X1,X2] :
( domain(X1,X2,X0) = domain_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f169,f143]) ).
fof(f212,plain,
! [X0,X1] :
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f178,f143]) ).
fof(f215,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)],[f182,f143]) ).
fof(f217,plain,
! [X0,X1] :
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f185,f143]) ).
fof(f219,plain,
! [X0,X1] :
( ~ member(sK1_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f143]) ).
fof(f220,plain,
! [X0,X1] :
( member(sK1_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f143]) ).
fof(f228,plain,
! [X0,X1,X2,X3] :
( subset(X3,range(X2,X0,X1))
| ~ subset(identity_relation_of(X3),X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f200,f143]) ).
fof(f229,plain,
! [X0,X1,X2,X3] :
( subset(X3,domain(X2,X0,X1))
| ~ subset(identity_relation_of(X3),X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f201,f143]) ).
fof(f230,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f202,f143]) ).
fof(f233,plain,
range(sK12_skl,sK13_skl,sK14_skl) = range_of(sK14_skl),
inference(resolution,[status(thm)],[f205,f148]) ).
fof(f234,plain,
( ilf_type(range_of(sK14_skl),subset_type(sK13_skl))
| ~ ilf_type(sK14_skl,relation_type(sK12_skl,sK13_skl)) ),
inference(paramodulation,[status(thm)],[f233,f204]) ).
fof(f235,definition,
( sQ2_spl
<=> ilf_type(sK14_skl,relation_type(sK12_skl,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f237,plain,
( sQ2_spl
| ~ ilf_type(sK14_skl,relation_type(sK12_skl,sK13_skl)) ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f238,definition,
( sQ3_spl
<=> ilf_type(range_of(sK14_skl),subset_type(sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( ~ sQ3_spl
| ilf_type(range_of(sK14_skl),subset_type(sK13_skl)) ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f234,f235,f238]) ).
fof(f242,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f237,f148]) ).
fof(f243,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f242]) ).
fof(f255,plain,
domain(sK12_skl,sK13_skl,sK14_skl) = domain_of(sK14_skl),
inference(resolution,[status(thm)],[f207,f148]) ).
fof(f256,plain,
( sQ0_spl
| ~ subset(sK13_skl,domain_of(sK14_skl)) ),
inference(backward_demodulation,[status(thm)],[f255,f153]) ).
fof(f269,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(resolution,[status(thm)],[f212,f179]) ).
fof(f273,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f215,f143]) ).
fof(f281,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f269,f217]) ).
fof(f307,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ member(sK1_skl(X1,X2),X0)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f273,f219]) ).
fof(f311,plain,
! [X0,X1,X2,X3] :
( subset(X3,range(X1,X2,X0))
| ~ subset(identity_relation_of(X3),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f228,f143]) ).
fof(f342,plain,
! [X0,X1,X2,X3] :
( subset(X3,domain(X1,X2,X0))
| ~ subset(identity_relation_of(X3),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f229,f143]) ).
fof(f383,plain,
! [X0,X1] :
( subset(X0,X1)
| subset(X0,X1)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f307,f220]) ).
fof(f388,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(X0,power_set(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f383]) ).
fof(f396,plain,
! [X0,X1] :
( subset(sK13_skl,range(X0,X1,sK14_skl))
| ~ ilf_type(sK14_skl,relation_type(X0,X1)) ),
inference(resolution,[status(thm)],[f311,f149]) ).
fof(f399,plain,
! [X0,X1] :
( subset(sK13_skl,domain(X0,X1,sK14_skl))
| ~ ilf_type(sK14_skl,relation_type(X0,X1)) ),
inference(resolution,[status(thm)],[f342,f149]) ).
fof(f411,plain,
subset(sK13_skl,range(sK12_skl,sK13_skl,sK14_skl)),
inference(resolution,[status(thm)],[f396,f148]) ).
fof(f413,plain,
subset(sK13_skl,range_of(sK14_skl)),
inference(forward_demodulation,[status(thm)],[f233,f411]) ).
fof(f416,plain,
( range_of(sK14_skl) = sK13_skl
| ~ subset(range_of(sK14_skl),sK13_skl) ),
inference(resolution,[status(thm)],[f413,f230]) ).
fof(f427,definition,
( sQ15_spl
<=> subset(range_of(sK14_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f429,plain,
( sQ15_spl
| ~ subset(range_of(sK14_skl),sK13_skl) ),
inference(component_clause,[status(thm)],[f427]) ).
fof(f430,definition,
( sQ16_spl
<=> range_of(sK14_skl) = sK13_skl ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( ~ sQ16_spl
| range_of(sK14_skl) = sK13_skl ),
inference(component_clause,[status(thm)],[f430]) ).
fof(f433,plain,
( sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f416,f427,f430]) ).
fof(f438,plain,
( ~ sQ16_spl
| range(sK12_skl,sK13_skl,sK14_skl) = sK13_skl ),
inference(backward_demodulation,[status(thm)],[f431,f233]) ).
fof(f451,plain,
( sQ15_spl
| ~ member(range_of(sK14_skl),power_set(sK13_skl)) ),
inference(resolution,[status(thm)],[f429,f388]) ).
fof(f460,plain,
( sQ15_spl
| ~ ilf_type(range_of(sK14_skl),subset_type(sK13_skl)) ),
inference(resolution,[status(thm)],[f451,f281]) ).
fof(f462,plain,
( sQ15_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f460,f239]) ).
fof(f463,plain,
( sQ15_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f462]) ).
fof(f499,plain,
subset(sK13_skl,domain(sK12_skl,sK13_skl,sK14_skl)),
inference(resolution,[status(thm)],[f399,f148]) ).
fof(f501,plain,
subset(sK13_skl,domain_of(sK14_skl)),
inference(forward_demodulation,[status(thm)],[f255,f499]) ).
fof(f502,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f501,f256]) ).
fof(f503,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f502]) ).
fof(f504,plain,
( sQ1_spl
| ~ sQ16_spl
| sK13_skl != sK13_skl ),
inference(forward_demodulation,[status(thm)],[f438,f156]) ).
fof(f505,plain,
( sQ1_spl
| ~ sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f504]) ).
fof(f506,plain,
( sQ1_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f505]) ).
fof(f507,plain,
$false,
inference(sat_refutation,[status(thm)],[f157,f241,f243,f433,f463,f503,f506]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET669+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n005.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Mon Sep 21 05:31:38 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 0.13/5.43 % Refutation found
% 0.13/5.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.45 % Elapsed time: 0.083029 seconds
% 0.13/5.45 % CPU time: 0.413789 seconds
% 0.13/5.45 % Total memory used: 90.915 MB
% 0.13/5.45 % Net memory used: 90.352 MB
%------------------------------------------------------------------------------