%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN045+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 : n014.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 03:15:00 PM UTC 2026
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 1 unt; 5 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 97 ( 28 ~; 45 |; 15 &)
% ( 7 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 9 ( 8 usr; 9 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ( r
& q )
| p )
<=> ( ( r
| p )
& ( q
| p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ( ( r
& q )
| p )
<=> ( ( r
| p )
& ( q
| p ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( ( r
& q )
| p )
<~> ( ( r
| p )
& ( q
| p ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
( sP0_prd
<=> ( q
| p ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( ( ( r
& q )
| p )
<~> ( ( r
| p )
& sP0_prd ) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ( ( ~ r
& ~ p )
| ~ sP0_prd
| ( ( ~ r
| ~ q )
& ~ p ) )
& ( ( ( r
| p )
& sP0_prd )
| ( r
& q )
| p ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
( sP0_prd
| q
| p ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f10,plain,
( r
| p
| r
| p ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f11,plain,
( ~ p
| ~ sP0_prd
| ~ p ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f14,plain,
( ~ r
| ~ sP0_prd
| ~ r
| ~ q ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f15,plain,
( ( ( ~ q
& ~ p )
| sP0_prd )
& ( q
| p
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f16,plain,
( q
| p
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
( ~ p
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f18,plain,
( ~ q
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f19,definition,
( sQ0_spl
<=> p ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f22,definition,
( sQ1_spl
<=> q ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f25,definition,
( sQ2_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f28,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f7,f19,f22,f25]) ).
fof(f29,definition,
( sQ3_spl
<=> r ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f34,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f10,f19,f29]) ).
fof(f35,plain,
( ~ sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f11,f19,f25]) ).
fof(f38,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f14,f22,f29,f25]) ).
fof(f39,plain,
( sQ1_spl
| sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f16,f25,f19,f22]) ).
fof(f40,plain,
( ~ sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f17,f25,f19]) ).
fof(f41,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f18,f25,f22]) ).
fof(f42,plain,
$false,
inference(sat_refutation,[status(thm)],[f28,f34,f35,f38,f39,f40,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN045+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.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 10:39:49 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % 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
% 0.13/0.40 % Elapsed time: 0.028169 seconds
% 0.13/0.40 % CPU time: 0.029167 seconds
% 0.13/0.40 % Total memory used: 517.136 KB
% 0.13/0.40 % Net memory used: 500.240 KB
%------------------------------------------------------------------------------