%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU165+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 : n026.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 02:19:29 PM UTC 2026
% Result : Theorem 0.06s 0.38s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 1 unt; 3 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 91 ( 35 ~; 37 |; 12 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 36 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f46,lemma,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,conjecture,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f238,plain,
! [A,B,C,D] :
( ( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(NNF_transformation,[status(thm)],[f46]) ).
fof(f239,plain,
( ! [A,B,C,D] :
( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ! [A,B,C,D] :
( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(miniscoping,[status(thm)],[f238]) ).
fof(f240,plain,
! [X0,X1,X2,X3] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f239]) ).
fof(f241,plain,
! [X0,X1,X2,X3] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f239]) ).
fof(f242,plain,
! [X0,X1,X2,X3] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f239]) ).
fof(f251,plain,
? [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<~> ( in(B,D)
& in(A,C) ) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f252,plain,
? [A,B,C,D] :
( ( ~ in(B,D)
| ~ in(A,C)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( ( in(B,D)
& in(A,C) )
| in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(NNF_transformation,[status(thm)],[f251]) ).
fof(f253,plain,
( ( ~ in(sK19_skl,sK21_skl)
| ~ in(sK18_skl,sK20_skl)
| ~ in(ordered_pair(sK18_skl,sK19_skl),cartesian_product2(sK20_skl,sK21_skl)) )
& ( ( in(sK19_skl,sK21_skl)
& in(sK18_skl,sK20_skl) )
| in(ordered_pair(sK18_skl,sK19_skl),cartesian_product2(sK20_skl,sK21_skl)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl,sK19_skl,sK20_skl,sK21_skl]),skolemize(A,sK18_skl),skolemize(B,sK19_skl),skolemize(C,sK20_skl),skolemize(D,sK21_skl)],[f252]) ).
fof(f254,plain,
( in(sK18_skl,sK20_skl)
| in(ordered_pair(sK18_skl,sK19_skl),cartesian_product2(sK20_skl,sK21_skl)) ),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f255,plain,
( in(sK19_skl,sK21_skl)
| in(ordered_pair(sK18_skl,sK19_skl),cartesian_product2(sK20_skl,sK21_skl)) ),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f256,plain,
( ~ in(sK19_skl,sK21_skl)
| ~ in(sK18_skl,sK20_skl)
| ~ in(ordered_pair(sK18_skl,sK19_skl),cartesian_product2(sK20_skl,sK21_skl)) ),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f371,definition,
( sQ0_spl
<=> in(ordered_pair(sK18_skl,sK19_skl),cartesian_product2(sK20_skl,sK21_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f372,plain,
( ~ sQ0_spl
| in(ordered_pair(sK18_skl,sK19_skl),cartesian_product2(sK20_skl,sK21_skl)) ),
inference(component_clause,[status(thm)],[f371]) ).
fof(f373,plain,
( sQ0_spl
| ~ in(ordered_pair(sK18_skl,sK19_skl),cartesian_product2(sK20_skl,sK21_skl)) ),
inference(component_clause,[status(thm)],[f371]) ).
fof(f374,definition,
( sQ1_spl
<=> in(sK18_skl,sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f376,plain,
( sQ1_spl
| ~ in(sK18_skl,sK20_skl) ),
inference(component_clause,[status(thm)],[f374]) ).
fof(f377,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f254,f371,f374]) ).
fof(f378,definition,
( sQ2_spl
<=> in(sK19_skl,sK21_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f381,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f255,f371,f378]) ).
fof(f382,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f256,f371,f374,f378]) ).
fof(f417,plain,
( ~ sQ0_spl
| in(sK18_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f240,f372]) ).
fof(f418,plain,
( ~ sQ0_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f417,f376]) ).
fof(f419,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f418]) ).
fof(f422,plain,
( sQ0_spl
| ~ in(sK19_skl,sK21_skl)
| ~ in(sK18_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f242,f373]) ).
fof(f426,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f422,f374,f378,f371]) ).
fof(f484,plain,
( ~ sQ0_spl
| in(sK19_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f241,f372]) ).
fof(f486,plain,
( ~ sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f484,f378,f371]) ).
fof(f488,plain,
$false,
inference(sat_refutation,[status(thm)],[f377,f381,f382,f419,f426,f486]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU165+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.34 % Computer : n026.cluster.edu
% 0.06/0.34 % Model : x86_64 x86_64
% 0.06/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.34 % Memory : 8046.5625MB
% 0.06/0.34 % OS : Linux 6.8.0-71-generic
% 0.06/0.34 % CPULimit : 300
% 0.06/0.34 % WCLimit : 300
% 0.06/0.34 % DateTime : Mon Sep 21 05:56:37 UTC 2026
% 0.06/0.35 % CPUTime :
% 0.06/0.36 % Drodi V4.1.1
% 0.06/0.38 % Refutation found
% 0.06/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.06/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.42 % Elapsed time: 0.063213 seconds
% 0.15/0.42 % CPU time: 0.175413 seconds
% 0.15/0.42 % Total memory used: 100.363 MB
% 0.15/0.42 % Net memory used: 100.255 MB
%------------------------------------------------------------------------------