%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN393+1.003 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 0.15s 0.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 1 unt; 9 def)
% Number of atoms : 187 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 204 ( 69 ~; 88 |; 12 &)
% ( 32 <=>; 0 =>; 0 <=; 3 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 13 ( 12 usr; 13 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 )
<=> p3 )
<=> ( p1
<=> ( p2
<=> p3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ( ( p1
<=> p2 )
<=> p3 )
<=> ( p1
<=> ( p2
<=> p3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( ( p1
<=> p2 )
<=> p3 )
<~> ( p1
<=> ( p2
<=> p3 ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
( sP0_prd
<=> ( ( p1
<=> p2 )
<=> p3 ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( sP0_prd
<~> ( p1
<=> ( p2
<=> p3 ) ) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,definition,
( sP1_prd
<=> ( p2
<=> p3 ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f7,plain,
( sP0_prd
<~> ( p1
<=> sP1_prd ) ),
inference(formula_renaming,[status(thm)],[f5,f6]) ).
fof(f8,plain,
( ( ( ( sP1_prd
| p1 )
& ( ~ sP1_prd
| ~ p1 ) )
| ~ sP0_prd )
& ( ( ( ~ sP1_prd
| p1 )
& ( sP1_prd
| ~ p1 ) )
| sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
( sP1_prd
| ~ p1
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
( ~ sP1_prd
| p1
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f11,plain,
( ~ sP1_prd
| ~ p1
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f12,plain,
( sP1_prd
| p1
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f13,definition,
( sP2_prd
<=> ( p1
<=> p2 ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f14,plain,
( sP0_prd
<=> ( sP2_prd
<=> p3 ) ),
inference(formula_renaming,[status(thm)],[f4,f13]) ).
fof(f15,plain,
( ( ( ( p3
| sP2_prd )
& ( ~ p3
| ~ sP2_prd ) )
| sP0_prd )
& ( ( ( ~ p3
| sP2_prd )
& ( p3
| ~ sP2_prd ) )
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
( p3
| ~ sP2_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
( ~ p3
| sP2_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f18,plain,
( ~ p3
| ~ sP2_prd
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f19,plain,
( p3
| sP2_prd
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f20,plain,
( ( ( ( p3
| p2 )
& ( ~ p3
| ~ p2 ) )
| sP1_prd )
& ( ( ( ~ p3
| p2 )
& ( p3
| ~ p2 ) )
| ~ sP1_prd ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
( p3
| ~ p2
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
( ~ p3
| p2
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f23,plain,
( ~ p3
| ~ p2
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f24,plain,
( p3
| p2
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f25,plain,
( ( ( ( p2
| p1 )
& ( ~ p2
| ~ p1 ) )
| sP2_prd )
& ( ( ( ~ p2
| p1 )
& ( p2
| ~ p1 ) )
| ~ sP2_prd ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f26,plain,
( p2
| ~ p1
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
( ~ p2
| p1
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,plain,
( ~ p2
| ~ p1
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f29,plain,
( p2
| p1
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f30,definition,
( sQ0_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f33,definition,
( sQ1_spl
<=> p1 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f36,definition,
( sQ2_spl
<=> sP1_prd ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f39,plain,
( sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f9,f30,f33,f36]) ).
fof(f40,plain,
( ~ sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f10,f30,f33,f36]) ).
fof(f41,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f11,f30,f33,f36]) ).
fof(f42,plain,
( sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f12,f30,f33,f36]) ).
fof(f43,definition,
( sQ3_spl
<=> sP2_prd ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f46,definition,
( sQ4_spl
<=> p3 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f49,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f16,f30,f43,f46]) ).
fof(f50,plain,
( ~ sQ4_spl
| sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f17,f30,f43,f46]) ).
fof(f51,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f18,f30,f43,f46]) ).
fof(f52,plain,
( sQ4_spl
| sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f19,f30,f43,f46]) ).
fof(f53,definition,
( sQ5_spl
<=> p2 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f21,f36,f53,f46]) ).
fof(f57,plain,
( ~ sQ4_spl
| sQ5_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f22,f36,f53,f46]) ).
fof(f58,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f23,f36,f53,f46]) ).
fof(f59,plain,
( sQ4_spl
| sQ5_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f24,f36,f53,f46]) ).
fof(f60,plain,
( sQ5_spl
| ~ sQ1_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f26,f43,f33,f53]) ).
fof(f61,plain,
( ~ sQ5_spl
| sQ1_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f27,f43,f33,f53]) ).
fof(f62,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f28,f43,f33,f53]) ).
fof(f63,plain,
( sQ5_spl
| sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f29,f43,f33,f53]) ).
fof(f64,plain,
$false,
inference(sat_refutation,[status(thm)],[f39,f40,f41,f42,f49,f50,f51,f52,f56,f57,f58,f59,f60,f61,f62,f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN393+1.003 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 10:57:53 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.15/0.40 % Refutation found
% 0.15/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.42 % Elapsed time: 0.045732 seconds
% 0.15/0.42 % CPU time: 0.113163 seconds
% 0.15/0.42 % Total memory used: 16.667 MB
% 0.15/0.42 % Net memory used: 16.182 MB
%------------------------------------------------------------------------------