%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG039+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 0.09s 0.40s
% Output : CNFRefutation 0.09s
% 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 : 379 ( 110 ~; 134 |; 111 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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/sandbox2/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(f122,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(f123,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(f124,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 )
| sP0_prd ) ),
inference(formula_renaming,[status(thm)],[f122,f123]) ).
fof(f125,plain,
( op(e0,e0) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f126,plain,
( op(e1,e1) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f127,plain,
( op(e2,e2) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f128,plain,
( op(e3,e3) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f129,plain,
( op(e3,e3) != e0
| op(e2,e2) != e0
| op(e1,e1) != e0
| op(e0,e0) != e0 ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f130,plain,
( op(e3,e3) != e1
| op(e2,e2) != e1
| op(e1,e1) != e1
| op(e0,e0) != e1 ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f131,plain,
( op(e3,e3) != e2
| op(e2,e2) != e2
| op(e1,e1) != e2
| op(e0,e0) != e2 ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f132,plain,
( op(e3,e3) != e3
| op(e2,e2) != e3
| op(e1,e1) != e3
| op(e0,e0) != e3 ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f133,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(f134,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)],[f123,f133]) ).
fof(f135,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)],[f134]) ).
fof(f136,plain,
( op(e0,e0) = e2
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
( op(e1,e1) = e2
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f138,plain,
( op(e2,e2) = e2
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f139,plain,
( op(e3,e3) = e2
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f142,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(f143,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)],[f133,f142]) ).
fof(f144,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)],[f143]) ).
fof(f145,plain,
( op(e0,e0) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f146,plain,
( op(e1,e1) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f147,plain,
( op(e2,e2) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f148,plain,
( op(e3,e3) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f151,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)],[f142]) ).
fof(f152,plain,
( op(e0,e0) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f153,plain,
( op(e1,e1) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f154,plain,
( op(e2,e2) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f155,plain,
( op(e3,e3) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f157,definition,
( sQ0_spl
<=> op(e0,e0) = e0 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f160,definition,
( sQ1_spl
<=> op(e0,e0) = e1 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f163,definition,
( sQ2_spl
<=> op(e0,e0) = e2 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f166,definition,
( sQ3_spl
<=> op(e0,e0) = e3 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f222,definition,
( sQ20_spl
<=> op(e1,e1) = e0 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f225,definition,
( sQ21_spl
<=> op(e1,e1) = e1 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f228,definition,
( sQ22_spl
<=> op(e1,e1) = e2 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f231,definition,
( sQ23_spl
<=> op(e1,e1) = e3 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f287,definition,
( sQ40_spl
<=> op(e2,e2) = e0 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f290,definition,
( sQ41_spl
<=> op(e2,e2) = e1 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f293,definition,
( sQ42_spl
<=> op(e2,e2) = e2 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f296,definition,
( sQ43_spl
<=> op(e2,e2) = e3 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f352,definition,
( sQ60_spl
<=> op(e3,e3) = e0 ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f355,definition,
( sQ61_spl
<=> op(e3,e3) = e1 ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f358,definition,
( sQ62_spl
<=> op(e3,e3) = e2 ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f361,definition,
( sQ63_spl
<=> op(e3,e3) = e3 ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f410,definition,
( sQ68_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f413,plain,
( sQ3_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f125,f410,f166]) ).
fof(f414,plain,
( sQ23_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f126,f410,f231]) ).
fof(f415,plain,
( sQ43_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f127,f410,f296]) ).
fof(f416,plain,
( sQ63_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f128,f410,f361]) ).
fof(f417,plain,
( ~ sQ60_spl
| ~ sQ40_spl
| ~ sQ20_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f129,f157,f222,f287,f352]) ).
fof(f418,plain,
( ~ sQ61_spl
| ~ sQ41_spl
| ~ sQ21_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f130,f160,f225,f290,f355]) ).
fof(f419,plain,
( ~ sQ62_spl
| ~ sQ42_spl
| ~ sQ22_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f131,f163,f228,f293,f358]) ).
fof(f420,plain,
( ~ sQ63_spl
| ~ sQ43_spl
| ~ sQ23_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f132,f166,f231,f296,f361]) ).
fof(f421,definition,
( sQ69_spl
<=> sP1_prd ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f424,plain,
( sQ2_spl
| sQ69_spl
| ~ sQ68_spl ),
inference(split_clause,[status(thm)],[f136,f410,f421,f163]) ).
fof(f425,plain,
( sQ22_spl
| sQ69_spl
| ~ sQ68_spl ),
inference(split_clause,[status(thm)],[f137,f410,f421,f228]) ).
fof(f426,plain,
( sQ42_spl
| sQ69_spl
| ~ sQ68_spl ),
inference(split_clause,[status(thm)],[f138,f410,f421,f293]) ).
fof(f427,plain,
( sQ62_spl
| sQ69_spl
| ~ sQ68_spl ),
inference(split_clause,[status(thm)],[f139,f410,f421,f358]) ).
fof(f430,definition,
( sQ70_spl
<=> sP2_prd ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f433,plain,
( sQ1_spl
| sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f145,f421,f430,f160]) ).
fof(f434,plain,
( sQ21_spl
| sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f146,f421,f430,f225]) ).
fof(f435,plain,
( sQ41_spl
| sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f147,f421,f430,f290]) ).
fof(f436,plain,
( sQ61_spl
| sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f148,f421,f430,f355]) ).
fof(f439,plain,
( sQ0_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f152,f430,f157]) ).
fof(f440,plain,
( sQ20_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f153,f430,f222]) ).
fof(f441,plain,
( sQ40_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f154,f430,f287]) ).
fof(f442,plain,
( sQ60_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f155,f430,f352]) ).
fof(f444,plain,
$false,
inference(sat_refutation,[status(thm)],[f413,f414,f415,f416,f417,f418,f419,f420,f424,f425,f426,f427,f433,f434,f435,f436,f439,f440,f441,f442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG039+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.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 12:54:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.45 % Elapsed time: 0.065262 seconds
% 0.09/0.45 % CPU time: 0.182029 seconds
% 0.09/0.45 % Total memory used: 108.129 MB
% 0.09/0.45 % Net memory used: 108.075 MB
%------------------------------------------------------------------------------