%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET658+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 : n015.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 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 9 unt; 3 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 21 ~; 18 |; 2 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(domain_of(C),B)
=> ilf_type(C,relation_type(B,range_of(C))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [B] :
( ilf_type(B,set_type)
=> subset(B,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [B] :
( ilf_type(B,binary_relation_type)
=> ilf_type(B,relation_type(domain_of(B),range_of(B))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [B] :
( ilf_type(B,binary_relation_type)
=> ilf_type(B,relation_type(domain_of(B),range_of(B))) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [B] :
( ! [C] :
( ilf_type(C,relation_type(B,range_of(C)))
| ~ subset(domain_of(C),B)
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f32,plain,
! [X0,X1] :
( ilf_type(X1,relation_type(X0,range_of(X1)))
| ~ subset(domain_of(X1),X0)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f80,plain,
! [B] :
( subset(B,B)
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f81,plain,
! [X0] :
( subset(X0,X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f126,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f127,plain,
? [B] :
( ~ ilf_type(B,relation_type(domain_of(B),range_of(B)))
& ilf_type(B,binary_relation_type) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f128,plain,
( ~ ilf_type(sK12_skl,relation_type(domain_of(sK12_skl),range_of(sK12_skl)))
& ilf_type(sK12_skl,binary_relation_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(B,sK12_skl)],[f127]) ).
fof(f129,plain,
ilf_type(sK12_skl,binary_relation_type),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
~ ilf_type(sK12_skl,relation_type(domain_of(sK12_skl),range_of(sK12_skl))),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f132,plain,
( ~ subset(domain_of(sK12_skl),domain_of(sK12_skl))
| ~ ilf_type(sK12_skl,binary_relation_type)
| ~ ilf_type(domain_of(sK12_skl),set_type) ),
inference(resolution,[status(thm)],[f32,f130]) ).
fof(f133,definition,
( sQ0_spl
<=> ilf_type(domain_of(sK12_skl),set_type) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f135,plain,
( sQ0_spl
| ~ ilf_type(domain_of(sK12_skl),set_type) ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
( sQ1_spl
<=> ilf_type(sK12_skl,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( sQ1_spl
| ~ ilf_type(sK12_skl,binary_relation_type) ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
( sQ2_spl
<=> subset(domain_of(sK12_skl),domain_of(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f141,plain,
( sQ2_spl
| ~ subset(domain_of(sK12_skl),domain_of(sK12_skl)) ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f132,f133,f136,f139]) ).
fof(f148,plain,
( sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f141,f149]) ).
fof(f149,plain,
! [X0] : subset(X0,X0),
inference(forward_subsumption_resolution,[status(thm)],[f81,f126]) ).
fof(f150,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f148]) ).
fof(f151,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f135,f126]) ).
fof(f152,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f151]) ).
fof(f153,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f138,f129]) ).
fof(f154,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f153]) ).
fof(f155,plain,
$false,
inference(sat_refutation,[status(thm)],[f142,f150,f152,f154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET658+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n015.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 05:34:21 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.11/0.38 % Refutation found
% 0.11/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.40 % Elapsed time: 0.050702 seconds
% 0.11/0.40 % CPU time: 0.140689 seconds
% 0.11/0.40 % Total memory used: 82.103 MB
% 0.11/0.40 % Net memory used: 82.048 MB
%------------------------------------------------------------------------------