%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU158+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 02:19:27 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 1 unt; 2 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 56 ( 23 ~; 23 |; 4 &)
% ( 5 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 20 ( 16 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f41,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,conjecture,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,negated_conjecture,
~ ! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
inference(negated_conjecture,[status(cth)],[f67]) ).
fof(f213,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(NNF_transformation,[status(thm)],[f41]) ).
fof(f214,plain,
( ! [A,B] :
( ~ in(A,B)
| subset(singleton(A),B) )
& ! [A,B] :
( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(miniscoping,[status(thm)],[f213]) ).
fof(f215,plain,
! [X0,X1] :
( in(X0,X1)
| ~ subset(singleton(X0),X1) ),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f216,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f280,plain,
? [A,B] :
( subset(singleton(A),B)
<~> in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f281,plain,
? [A,B] :
( ( ~ in(A,B)
| ~ subset(singleton(A),B) )
& ( in(A,B)
| subset(singleton(A),B) ) ),
inference(NNF_transformation,[status(thm)],[f280]) ).
fof(f282,plain,
( ( ~ in(sK19_skl,sK20_skl)
| ~ subset(singleton(sK19_skl),sK20_skl) )
& ( in(sK19_skl,sK20_skl)
| subset(singleton(sK19_skl),sK20_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl]),skolemize(A,sK19_skl),skolemize(B,sK20_skl)],[f281]) ).
fof(f283,plain,
( in(sK19_skl,sK20_skl)
| subset(singleton(sK19_skl),sK20_skl) ),
inference(cnf_transformation,[status(thm)],[f282]) ).
fof(f284,plain,
( ~ in(sK19_skl,sK20_skl)
| ~ subset(singleton(sK19_skl),sK20_skl) ),
inference(cnf_transformation,[status(thm)],[f282]) ).
fof(f340,definition,
( sQ0_spl
<=> subset(singleton(sK19_skl),sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f341,plain,
( ~ sQ0_spl
| subset(singleton(sK19_skl),sK20_skl) ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f342,plain,
( sQ0_spl
| ~ subset(singleton(sK19_skl),sK20_skl) ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f343,definition,
( sQ1_spl
<=> in(sK19_skl,sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f344,plain,
( ~ sQ1_spl
| in(sK19_skl,sK20_skl) ),
inference(component_clause,[status(thm)],[f343]) ).
fof(f346,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f283,f340,f343]) ).
fof(f347,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f284,f340,f343]) ).
fof(f381,plain,
( sQ0_spl
| ~ in(sK19_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f216,f342]) ).
fof(f384,plain,
( sQ0_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f381,f344]) ).
fof(f385,plain,
( sQ0_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f384]) ).
fof(f386,plain,
( ~ sQ0_spl
| in(sK19_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f341,f215]) ).
fof(f388,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f386,f343,f340]) ).
fof(f396,plain,
$false,
inference(sat_refutation,[status(thm)],[f346,f347,f385,f388]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU158+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:52:50 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.044897 seconds
% 0.13/0.40 % CPU time: 0.114656 seconds
% 0.13/0.40 % Total memory used: 56.644 MB
% 0.13/0.40 % Net memory used: 56.590 MB
%------------------------------------------------------------------------------