%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET653+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 : Theorem 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 12 unt; 7 def)
% Number of atoms : 174 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 194 ( 77 ~; 75 |; 13 &)
% ( 7 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 59 ( 55 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(range_of(D),C)
& subset(domain_of(D),B) ) ) ) ),
file('/export/starexec/sandbox/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,relation_type(B,D))
=> ( subset(domain_of(E),C)
=> ilf_type(E,relation_type(C,D)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,conjecture,
! [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,D))
=> ( subset(B,C)
=> ilf_type(E,relation_type(C,D)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ ! [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,D))
=> ( subset(B,C)
=> ilf_type(E,relation_type(C,D)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f25,plain,
! [B] :
( ! [C] :
( ! [D] :
( subset(B,D)
| ~ subset(C,D)
| ~ subset(B,C)
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f26,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( subset(range_of(D),C)
& subset(domain_of(D),B) )
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f28,plain,
! [X0,X1,X2] :
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ilf_type(E,relation_type(C,D))
| ~ subset(domain_of(E),C)
| ~ ilf_type(E,relation_type(B,D)) )
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( ilf_type(X3,relation_type(X1,X2))
| ~ subset(domain_of(X3),X1)
| ~ ilf_type(X3,relation_type(X0,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f98,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f99,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ~ ilf_type(E,relation_type(C,D))
& subset(B,C)
& ilf_type(E,relation_type(B,D)) )
& ilf_type(D,set_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f100,plain,
( ~ ilf_type(sK12_skl,relation_type(sK10_skl,sK11_skl))
& subset(sK9_skl,sK10_skl)
& ilf_type(sK12_skl,relation_type(sK9_skl,sK11_skl))
& ilf_type(sK11_skl,set_type)
& ilf_type(sK10_skl,set_type)
& ilf_type(sK9_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl,sK11_skl,sK12_skl]),skolemize(B,sK9_skl),skolemize(C,sK10_skl),skolemize(D,sK11_skl),skolemize(E,sK12_skl)],[f99]) ).
fof(f101,plain,
ilf_type(sK9_skl,set_type),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f102,plain,
ilf_type(sK10_skl,set_type),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f104,plain,
ilf_type(sK12_skl,relation_type(sK9_skl,sK11_skl)),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f105,plain,
subset(sK9_skl,sK10_skl),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f106,plain,
~ ilf_type(sK12_skl,relation_type(sK10_skl,sK11_skl)),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f117,plain,
! [X0] :
( subset(X0,sK10_skl)
| ~ subset(X0,sK9_skl)
| ~ ilf_type(sK10_skl,set_type)
| ~ ilf_type(sK9_skl,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f26,f105]) ).
fof(f140,definition,
( sQ6_spl
<=> ilf_type(sK9_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( sQ6_spl
| ~ ilf_type(sK9_skl,set_type) ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,definition,
( sQ7_spl
<=> ilf_type(sK10_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( sQ7_spl
| ~ ilf_type(sK10_skl,set_type) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f150,definition,
! [X0] :
( sQ9_spl
<=> ( subset(X0,sK10_skl)
| ~ subset(X0,sK9_skl)
| ~ ilf_type(X0,set_type) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f151,plain,
! [X0] :
( ~ sQ9_spl
| subset(X0,sK10_skl)
| ~ subset(X0,sK9_skl)
| ~ ilf_type(X0,set_type) ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f117,f150,f140,f143]) ).
fof(f154,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f145,f102]) ).
fof(f155,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f154]) ).
fof(f156,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f101]) ).
fof(f157,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f156]) ).
fof(f163,plain,
! [X0] :
( ~ sQ9_spl
| subset(X0,sK10_skl)
| ~ subset(X0,sK9_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f98]) ).
fof(f207,plain,
! [X0,X1,X2] :
( subset(domain_of(X1),X2)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f28,f98]) ).
fof(f209,plain,
( subset(domain_of(sK12_skl),sK9_skl)
| ~ ilf_type(sK11_skl,set_type) ),
inference(resolution,[status(thm)],[f207,f104]) ).
fof(f211,definition,
( sQ15_spl
<=> ilf_type(sK11_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( sQ15_spl
| ~ ilf_type(sK11_skl,set_type) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,definition,
( sQ16_spl
<=> subset(domain_of(sK12_skl),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f215,plain,
( ~ sQ16_spl
| subset(domain_of(sK12_skl),sK9_skl) ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f217,plain,
( sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f209,f211,f214]) ).
fof(f218,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f213,f98]) ).
fof(f219,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f218]) ).
fof(f228,plain,
! [X0,X1,X2,X3] :
( ilf_type(X2,relation_type(X0,X1))
| ~ subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X3,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f31,f98]) ).
fof(f230,plain,
! [X0] :
( ilf_type(sK12_skl,relation_type(X0,sK11_skl))
| ~ subset(domain_of(sK12_skl),X0)
| ~ ilf_type(sK11_skl,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f228,f104]) ).
fof(f232,definition,
! [X0] :
( sQ18_spl
<=> ( ilf_type(sK12_skl,relation_type(X0,sK11_skl))
| ~ subset(domain_of(sK12_skl),X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f233,plain,
! [X0] :
( ~ sQ18_spl
| ilf_type(sK12_skl,relation_type(X0,sK11_skl))
| ~ subset(domain_of(sK12_skl),X0)
| ~ ilf_type(X0,set_type) ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f235,plain,
( ~ sQ15_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f230,f232,f211]) ).
fof(f236,plain,
! [X0] :
( ~ sQ18_spl
| ilf_type(sK12_skl,relation_type(X0,sK11_skl))
| ~ subset(domain_of(sK12_skl),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f233,f98]) ).
fof(f237,plain,
( ~ sQ9_spl
| ~ sQ16_spl
| subset(domain_of(sK12_skl),sK10_skl) ),
inference(resolution,[status(thm)],[f215,f163]) ).
fof(f262,definition,
( sQ23_spl
<=> ilf_type(sK8_skl(domain_of(sK12_skl)),set_type) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( sQ23_spl
| ~ ilf_type(sK8_skl(domain_of(sK12_skl)),set_type) ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f266,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f264,f98]) ).
fof(f267,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f266]) ).
fof(f268,plain,
( ~ sQ18_spl
| ~ subset(domain_of(sK12_skl),sK10_skl) ),
inference(resolution,[status(thm)],[f236,f106]) ).
fof(f272,plain,
( ~ sQ18_spl
| ~ sQ9_spl
| ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f268,f237]) ).
fof(f273,plain,
( ~ sQ18_spl
| ~ sQ9_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f272]) ).
fof(f274,plain,
$false,
inference(sat_refutation,[status(thm)],[f153,f155,f157,f217,f219,f235,f267,f273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET653+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:34:01 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.043562 seconds
% 0.13/0.40 % CPU time: 0.123552 seconds
% 0.13/0.40 % Total memory used: 51.171 MB
% 0.13/0.40 % Net memory used: 51.108 MB
%------------------------------------------------------------------------------