%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET654+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 : n010.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 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 9 unt; 4 def)
% Number of atoms : 153 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 188 ( 81 ~; 68 |; 13 &)
% ( 4 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 73 ( 69 !; 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(D,B))
=> ( subset(range_of(E),C)
=> ilf_type(E,relation_type(D,C)) ) ) ) ) ),
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(D,B))
=> ( subset(B,C)
=> ilf_type(E,relation_type(D,C)) ) ) ) ) ),
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(D,B))
=> ( subset(B,C)
=> ilf_type(E,relation_type(D,C)) ) ) ) ) ),
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(f29,plain,
! [X0,X1,X2] :
( subset(range_of(X2),X1)
| ~ 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(D,C))
| ~ subset(range_of(E),C)
| ~ ilf_type(E,relation_type(D,B)) )
| ~ 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(X2,X1))
| ~ subset(range_of(X3),X1)
| ~ ilf_type(X3,relation_type(X2,X0))
| ~ 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(D,C))
& subset(B,C)
& ilf_type(E,relation_type(D,B)) )
& 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(sK11_skl,sK10_skl))
& subset(sK9_skl,sK10_skl)
& ilf_type(sK12_skl,relation_type(sK11_skl,sK9_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(f104,plain,
ilf_type(sK12_skl,relation_type(sK11_skl,sK9_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(sK11_skl,sK10_skl)),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f107,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ subset(X0,X1)
| ~ subset(X2,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f26,f98]) ).
fof(f113,plain,
! [X0,X1,X2] :
( subset(range_of(X1),X0)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f29,f98]) ).
fof(f114,plain,
! [X0,X1,X2,X3] :
( ilf_type(X2,relation_type(X1,X0))
| ~ subset(range_of(X2),X0)
| ~ ilf_type(X2,relation_type(X1,X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f31,f98]) ).
fof(f115,plain,
! [X0,X1,X2,X3] :
( ilf_type(X1,relation_type(X2,X0))
| ~ subset(range_of(X1),X0)
| ~ ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f114,f98]) ).
fof(f116,plain,
! [X0,X1,X2,X3] :
( ilf_type(X0,relation_type(X1,X3))
| ~ subset(range_of(X0),X3)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f115,f98]) ).
fof(f122,plain,
! [X0] :
( ~ subset(range_of(sK12_skl),sK10_skl)
| ~ ilf_type(sK12_skl,relation_type(sK11_skl,X0)) ),
inference(resolution,[status(thm)],[f116,f106]) ).
fof(f123,definition,
! [X0] :
( sQ0_spl
<=> ~ ilf_type(sK12_skl,relation_type(sK11_skl,X0)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f124,plain,
! [X0] :
( ~ sQ0_spl
| ~ ilf_type(sK12_skl,relation_type(sK11_skl,X0)) ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,definition,
( sQ1_spl
<=> subset(range_of(sK12_skl),sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( sQ1_spl
| ~ subset(range_of(sK12_skl),sK10_skl) ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f122,f123,f126]) ).
fof(f130,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f104,f124]) ).
fof(f132,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f130]) ).
fof(f134,plain,
! [X0] :
( sQ1_spl
| ~ subset(X0,sK10_skl)
| ~ subset(range_of(sK12_skl),X0)
| ~ ilf_type(sK10_skl,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f128,f107]) ).
fof(f135,definition,
( sQ2_spl
<=> ilf_type(sK10_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( sQ2_spl
| ~ ilf_type(sK10_skl,set_type) ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f142,definition,
! [X0] :
( sQ4_spl
<=> ( ~ subset(X0,sK10_skl)
| ~ subset(range_of(sK12_skl),X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0] :
( ~ sQ4_spl
| ~ subset(X0,sK10_skl)
| ~ subset(range_of(sK12_skl),X0)
| ~ ilf_type(X0,set_type) ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ1_spl
| ~ sQ2_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f134,f142,f135,f126]) ).
fof(f146,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f137,f98]) ).
fof(f147,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f146]) ).
fof(f148,plain,
! [X0] :
( ~ sQ4_spl
| ~ subset(X0,sK10_skl)
| ~ subset(range_of(sK12_skl),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f143,f98]) ).
fof(f154,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ ilf_type(sK12_skl,relation_type(X1,X0))
| ~ ilf_type(X0,set_type)
| ~ subset(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f148,f113]) ).
fof(f157,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ ilf_type(sK12_skl,relation_type(X1,X0))
| ~ subset(X0,sK10_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f154,f98]) ).
fof(f159,plain,
( ~ sQ4_spl
| ~ subset(sK9_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f157,f104]) ).
fof(f161,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f159,f105]) ).
fof(f162,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f163,plain,
$false,
inference(sat_refutation,[status(thm)],[f129,f132,f145,f147,f162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET654+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 05:31:39 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.051969 seconds
% 0.09/0.43 % CPU time: 0.140279 seconds
% 0.09/0.43 % Total memory used: 73.957 MB
% 0.09/0.43 % Net memory used: 73.876 MB
%------------------------------------------------------------------------------