%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN392+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 : n004.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 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 1 unt; 4 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 117 ( 43 ~; 51 |; 11 &)
% ( 10 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 7 ( 6 usr; 7 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( p1
<=> p2 )
<=> ( ( p1
| ~ p2 )
& ( ~ p1
| p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ( p1
<=> p2 )
<=> ( ( p1
| ~ p2 )
& ( ~ p1
| p2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( p1
<=> p2 )
<~> ( ( p1
| ~ p2 )
& ( ~ p1
| p2 ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
( sP0_prd
<=> ( p1
<=> p2 ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( sP0_prd
<~> ( ( p1
| ~ p2 )
& ( ~ p1
| p2 ) ) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ( ( ~ p1
& p2 )
| ( p1
& ~ p2 )
| ~ sP0_prd )
& ( ( ( p1
| ~ p2 )
& ( ~ p1
| p2 ) )
| sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
( ~ p1
| p2
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
( p1
| ~ p2
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f10,plain,
( ~ p1
| ~ p2
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f11,plain,
( p2
| p1
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f13,plain,
( ( ( ( p2
| p1 )
& ( ~ p2
| ~ p1 ) )
| sP0_prd )
& ( ( ( ~ p2
| p1 )
& ( p2
| ~ p1 ) )
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
( p2
| ~ p1
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
( ~ p2
| p1
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,plain,
( ~ p2
| ~ p1
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f17,plain,
( p2
| p1
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f18,definition,
( sQ0_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f21,definition,
( sQ1_spl
<=> p2 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f24,definition,
( sQ2_spl
<=> p1 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f27,plain,
( ~ sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f7,f18,f21,f24]) ).
fof(f28,plain,
( sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f8,f18,f21,f24]) ).
fof(f30,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f10,f18,f21,f24]) ).
fof(f31,plain,
( sQ1_spl
| sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f11,f18,f24,f21]) ).
fof(f33,plain,
( sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f14,f18,f24,f21]) ).
fof(f34,plain,
( ~ sQ1_spl
| sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f15,f18,f24,f21]) ).
fof(f35,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f16,f18,f24,f21]) ).
fof(f36,plain,
( sQ1_spl
| sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f17,f18,f24,f21]) ).
fof(f37,plain,
$false,
inference(sat_refutation,[status(thm)],[f27,f28,f30,f31,f33,f34,f35,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN392+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.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 10:53:04 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.39 % Elapsed time: 0.036321 seconds
% 0.13/0.39 % CPU time: 0.097193 seconds
% 0.13/0.39 % Total memory used: 16.553 MB
% 0.13/0.39 % Net memory used: 15.970 MB
%------------------------------------------------------------------------------