%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG036+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 11:47:51 AM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 23
% Syntax : Number of formulae : 72 ( 1 unt; 22 def)
% Number of atoms : 341 ( 220 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 377 ( 108 ~; 136 |; 109 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,conjecture,
( ~ ( ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) )
| ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ( ~ ( ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) )
| ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f121,plain,
( ( ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) )
& ( op(e3,e3) != e3
| op(e2,e2) != e3
| op(e1,e1) != e3
| op(e0,e0) != e3 )
& ( op(e3,e3) != e2
| op(e2,e2) != e2
| op(e1,e1) != e2
| op(e0,e0) != e2 )
& ( op(e3,e3) != e1
| op(e2,e2) != e1
| op(e1,e1) != e1
| op(e0,e0) != e1 )
& ( op(e3,e3) != e0
| op(e2,e2) != e0
| op(e1,e1) != e0
| op(e0,e0) != e0 ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f122,definition,
( sP0_prd
<=> ( ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f123,plain,
( ( ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| sP0_prd )
& ( op(e3,e3) != e3
| op(e2,e2) != e3
| op(e1,e1) != e3
| op(e0,e0) != e3 )
& ( op(e3,e3) != e2
| op(e2,e2) != e2
| op(e1,e1) != e2
| op(e0,e0) != e2 )
& ( op(e3,e3) != e1
| op(e2,e2) != e1
| op(e1,e1) != e1
| op(e0,e0) != e1 )
& ( op(e3,e3) != e0
| op(e2,e2) != e0
| op(e1,e1) != e0
| op(e0,e0) != e0 ) ),
inference(formula_renaming,[status(thm)],[f121,f122]) ).
fof(f124,plain,
( op(e3,e3) != e0
| op(e2,e2) != e0
| op(e1,e1) != e0
| op(e0,e0) != e0 ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f125,plain,
( op(e3,e3) != e1
| op(e2,e2) != e1
| op(e1,e1) != e1
| op(e0,e0) != e1 ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f126,plain,
( op(e3,e3) != e2
| op(e2,e2) != e2
| op(e1,e1) != e2
| op(e0,e0) != e2 ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f127,plain,
( op(e3,e3) != e3
| op(e2,e2) != e3
| op(e1,e1) != e3
| op(e0,e0) != e3 ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f128,plain,
( op(e0,e0) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f129,plain,
( op(e1,e1) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f130,plain,
( op(e2,e2) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f131,plain,
( op(e3,e3) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f132,definition,
( sP1_prd
<=> ( ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f133,plain,
( sP0_prd
<=> ( ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| sP1_prd ) ),
inference(formula_renaming,[status(thm)],[f122,f132]) ).
fof(f134,plain,
( ( ( ( op(e3,e3) != e2
| op(e2,e2) != e2
| op(e1,e1) != e2
| op(e0,e0) != e2 )
& ~ sP1_prd )
| sP0_prd )
& ( ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| sP1_prd
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
( op(e0,e0) = e2
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f134]) ).
fof(f136,plain,
( op(e1,e1) = e2
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f134]) ).
fof(f137,plain,
( op(e2,e2) = e2
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f134]) ).
fof(f138,plain,
( op(e3,e3) = e2
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f134]) ).
fof(f141,definition,
( sP2_prd
<=> ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f142,plain,
( sP1_prd
<=> ( ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| sP2_prd ) ),
inference(formula_renaming,[status(thm)],[f132,f141]) ).
fof(f143,plain,
( ( ( ( op(e3,e3) != e1
| op(e2,e2) != e1
| op(e1,e1) != e1
| op(e0,e0) != e1 )
& ~ sP2_prd )
| sP1_prd )
& ( ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| sP2_prd
| ~ sP1_prd ) ),
inference(NNF_transformation,[status(thm)],[f142]) ).
fof(f144,plain,
( op(e0,e0) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f145,plain,
( op(e1,e1) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f146,plain,
( op(e2,e2) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f147,plain,
( op(e3,e3) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f150,plain,
( ( op(e3,e3) != e0
| op(e2,e2) != e0
| op(e1,e1) != e0
| op(e0,e0) != e0
| sP2_prd )
& ( ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 )
| ~ sP2_prd ) ),
inference(NNF_transformation,[status(thm)],[f141]) ).
fof(f151,plain,
( op(e0,e0) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f152,plain,
( op(e1,e1) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f153,plain,
( op(e2,e2) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f154,plain,
( op(e3,e3) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f156,definition,
( sQ0_spl
<=> op(e0,e0) = e0 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f159,definition,
( sQ1_spl
<=> op(e0,e0) = e1 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f162,definition,
( sQ2_spl
<=> op(e0,e0) = e2 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f165,definition,
( sQ3_spl
<=> op(e0,e0) = e3 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f221,definition,
( sQ20_spl
<=> op(e1,e1) = e0 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f224,definition,
( sQ21_spl
<=> op(e1,e1) = e1 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f227,definition,
( sQ22_spl
<=> op(e1,e1) = e2 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f230,definition,
( sQ23_spl
<=> op(e1,e1) = e3 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f286,definition,
( sQ40_spl
<=> op(e2,e2) = e0 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f289,definition,
( sQ41_spl
<=> op(e2,e2) = e1 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f292,definition,
( sQ42_spl
<=> op(e2,e2) = e2 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f295,definition,
( sQ43_spl
<=> op(e2,e2) = e3 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f351,definition,
( sQ60_spl
<=> op(e3,e3) = e0 ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f354,definition,
( sQ61_spl
<=> op(e3,e3) = e1 ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f357,definition,
( sQ62_spl
<=> op(e3,e3) = e2 ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f360,definition,
( sQ63_spl
<=> op(e3,e3) = e3 ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f409,plain,
( ~ sQ60_spl
| ~ sQ40_spl
| ~ sQ20_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f124,f156,f221,f286,f351]) ).
fof(f410,plain,
( ~ sQ61_spl
| ~ sQ41_spl
| ~ sQ21_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f125,f159,f224,f289,f354]) ).
fof(f411,plain,
( ~ sQ62_spl
| ~ sQ42_spl
| ~ sQ22_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f126,f162,f227,f292,f357]) ).
fof(f412,plain,
( ~ sQ63_spl
| ~ sQ43_spl
| ~ sQ23_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f127,f165,f230,f295,f360]) ).
fof(f413,definition,
( sQ68_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f416,plain,
( sQ3_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f128,f413,f165]) ).
fof(f417,plain,
( sQ23_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f129,f413,f230]) ).
fof(f418,plain,
( sQ43_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f130,f413,f295]) ).
fof(f419,plain,
( sQ63_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f131,f413,f360]) ).
fof(f420,definition,
( sQ69_spl
<=> sP1_prd ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f423,plain,
( sQ2_spl
| sQ69_spl
| ~ sQ68_spl ),
inference(split_clause,[status(thm)],[f135,f413,f420,f162]) ).
fof(f424,plain,
( sQ22_spl
| sQ69_spl
| ~ sQ68_spl ),
inference(split_clause,[status(thm)],[f136,f413,f420,f227]) ).
fof(f425,plain,
( sQ42_spl
| sQ69_spl
| ~ sQ68_spl ),
inference(split_clause,[status(thm)],[f137,f413,f420,f292]) ).
fof(f426,plain,
( sQ62_spl
| sQ69_spl
| ~ sQ68_spl ),
inference(split_clause,[status(thm)],[f138,f413,f420,f357]) ).
fof(f429,definition,
( sQ70_spl
<=> sP2_prd ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f432,plain,
( sQ1_spl
| sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f144,f420,f429,f159]) ).
fof(f433,plain,
( sQ21_spl
| sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f145,f420,f429,f224]) ).
fof(f434,plain,
( sQ41_spl
| sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f146,f420,f429,f289]) ).
fof(f435,plain,
( sQ61_spl
| sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f147,f420,f429,f354]) ).
fof(f438,plain,
( sQ0_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f151,f429,f156]) ).
fof(f439,plain,
( sQ20_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f152,f429,f221]) ).
fof(f440,plain,
( sQ40_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f153,f429,f286]) ).
fof(f441,plain,
( sQ60_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f154,f429,f351]) ).
fof(f443,plain,
$false,
inference(sat_refutation,[status(thm)],[f409,f410,f411,f412,f416,f417,f418,f419,f423,f424,f425,f426,f432,f433,f434,f435,f438,f439,f440,f441]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG036+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 % Computer : n018.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 12:55:59 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 0.18/0.47 % Refutation found
% 0.18/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.51 % Elapsed time: 0.075980 seconds
% 0.21/0.51 % CPU time: 0.173548 seconds
% 0.21/0.51 % Total memory used: 70.976 MB
% 0.21/0.51 % Net memory used: 70.941 MB
%------------------------------------------------------------------------------