%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN391+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 03:15:58 PM UTC 2026
% Result : Theorem 0.09s 0.60s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 1 unt; 2 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 54 ( 23 ~; 20 |; 7 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 5 ( 4 usr; 5 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ( ~ p2
| p1 )
& ( p2
| ~ p1 )
& ( p2
| p1 ) )
=> ~ ( ~ p2
| ~ p1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ( ( ~ p2
| p1 )
& ( p2
| ~ p1 )
& ( p2
| p1 ) )
=> ~ ( ~ p2
| ~ p1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( ~ p2
| ~ p1 )
& ( ~ p2
| p1 )
& ( p2
| ~ p1 )
& ( p2
| p1 ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
( p2
| p1 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
( p2
| ~ p1 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f6,plain,
( ~ p2
| p1 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f7,plain,
( ~ p2
| ~ p1 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,definition,
( sQ0_spl
<=> p1 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f11,definition,
( sQ1_spl
<=> p2 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f14,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f4,f8,f11]) ).
fof(f15,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f5,f8,f11]) ).
fof(f16,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f6,f8,f11]) ).
fof(f17,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f7,f8,f11]) ).
fof(f18,plain,
$false,
inference(sat_refutation,[status(thm)],[f14,f15,f16,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN391+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n020.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Mon Sep 21 10:53:50 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 % Drodi V4.1.1
% 0.09/0.60 % Refutation found
% 0.09/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.61 % Elapsed time: 0.041940 seconds
% 0.09/0.61 % CPU time: 0.109553 seconds
% 0.09/0.61 % Total memory used: 16.435 MB
% 0.09/0.61 % Net memory used: 15.793 MB
%------------------------------------------------------------------------------