%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG014+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 : n017.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 11:47:45 AM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% 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(f12,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(f13,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)],[f12]) ).
fof(f198,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)],[f13]) ).
fof(f199,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(f200,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)],[f198,f199]) ).
fof(f201,plain,
( op(e3,e3) != e0
| op(e2,e2) != e0
| op(e1,e1) != e0
| op(e0,e0) != e0 ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f202,plain,
( op(e3,e3) != e1
| op(e2,e2) != e1
| op(e1,e1) != e1
| op(e0,e0) != e1 ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f203,plain,
( op(e3,e3) != e2
| op(e2,e2) != e2
| op(e1,e1) != e2
| op(e0,e0) != e2 ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f204,plain,
( op(e3,e3) != e3
| op(e2,e2) != e3
| op(e1,e1) != e3
| op(e0,e0) != e3 ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f205,plain,
( op(e0,e0) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f206,plain,
( op(e1,e1) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f207,plain,
( op(e2,e2) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f208,plain,
( op(e3,e3) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f209,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(f210,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)],[f199,f209]) ).
fof(f211,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)],[f210]) ).
fof(f212,plain,
( op(e0,e0) = e2
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f213,plain,
( op(e1,e1) = e2
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f214,plain,
( op(e2,e2) = e2
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f215,plain,
( op(e3,e3) = e2
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f218,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(f219,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)],[f209,f218]) ).
fof(f220,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)],[f219]) ).
fof(f221,plain,
( op(e0,e0) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f220]) ).
fof(f222,plain,
( op(e1,e1) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f220]) ).
fof(f223,plain,
( op(e2,e2) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f220]) ).
fof(f224,plain,
( op(e3,e3) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f220]) ).
fof(f227,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)],[f218]) ).
fof(f228,plain,
( op(e0,e0) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f227]) ).
fof(f229,plain,
( op(e1,e1) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f227]) ).
fof(f230,plain,
( op(e2,e2) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f227]) ).
fof(f231,plain,
( op(e3,e3) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f227]) ).
fof(f233,definition,
( sQ0_spl
<=> op(e0,e0) = e0 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f236,definition,
( sQ1_spl
<=> op(e0,e0) = e1 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f239,definition,
( sQ2_spl
<=> op(e0,e0) = e2 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f242,definition,
( sQ3_spl
<=> op(e0,e0) = e3 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f298,definition,
( sQ20_spl
<=> op(e1,e1) = e0 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f301,definition,
( sQ21_spl
<=> op(e1,e1) = e1 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f304,definition,
( sQ22_spl
<=> op(e1,e1) = e2 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f307,definition,
( sQ23_spl
<=> op(e1,e1) = e3 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f363,definition,
( sQ40_spl
<=> op(e2,e2) = e0 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f366,definition,
( sQ41_spl
<=> op(e2,e2) = e1 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f369,definition,
( sQ42_spl
<=> op(e2,e2) = e2 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f372,definition,
( sQ43_spl
<=> op(e2,e2) = e3 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f428,definition,
( sQ60_spl
<=> op(e3,e3) = e0 ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f431,definition,
( sQ61_spl
<=> op(e3,e3) = e1 ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f434,definition,
( sQ62_spl
<=> op(e3,e3) = e2 ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f437,definition,
( sQ63_spl
<=> op(e3,e3) = e3 ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f522,plain,
( ~ sQ60_spl
| ~ sQ40_spl
| ~ sQ20_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f201,f233,f298,f363,f428]) ).
fof(f523,plain,
( ~ sQ61_spl
| ~ sQ41_spl
| ~ sQ21_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f202,f236,f301,f366,f431]) ).
fof(f524,plain,
( ~ sQ62_spl
| ~ sQ42_spl
| ~ sQ22_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f203,f239,f304,f369,f434]) ).
fof(f525,plain,
( ~ sQ63_spl
| ~ sQ43_spl
| ~ sQ23_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f204,f242,f307,f372,f437]) ).
fof(f526,definition,
( sQ84_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f529,plain,
( sQ3_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f205,f526,f242]) ).
fof(f530,plain,
( sQ23_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f206,f526,f307]) ).
fof(f531,plain,
( sQ43_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f207,f526,f372]) ).
fof(f532,plain,
( sQ63_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f208,f526,f437]) ).
fof(f533,definition,
( sQ85_spl
<=> sP1_prd ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f536,plain,
( sQ2_spl
| sQ85_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f212,f526,f533,f239]) ).
fof(f537,plain,
( sQ22_spl
| sQ85_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f213,f526,f533,f304]) ).
fof(f538,plain,
( sQ42_spl
| sQ85_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f214,f526,f533,f369]) ).
fof(f539,plain,
( sQ62_spl
| sQ85_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f215,f526,f533,f434]) ).
fof(f542,definition,
( sQ86_spl
<=> sP2_prd ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f545,plain,
( sQ1_spl
| sQ86_spl
| ~ sQ85_spl ),
inference(split_clause,[status(thm)],[f221,f533,f542,f236]) ).
fof(f546,plain,
( sQ21_spl
| sQ86_spl
| ~ sQ85_spl ),
inference(split_clause,[status(thm)],[f222,f533,f542,f301]) ).
fof(f547,plain,
( sQ41_spl
| sQ86_spl
| ~ sQ85_spl ),
inference(split_clause,[status(thm)],[f223,f533,f542,f366]) ).
fof(f548,plain,
( sQ61_spl
| sQ86_spl
| ~ sQ85_spl ),
inference(split_clause,[status(thm)],[f224,f533,f542,f431]) ).
fof(f551,plain,
( sQ0_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f228,f542,f233]) ).
fof(f552,plain,
( sQ20_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f229,f542,f298]) ).
fof(f553,plain,
( sQ40_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f230,f542,f363]) ).
fof(f554,plain,
( sQ60_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f231,f542,f428]) ).
fof(f556,plain,
$false,
inference(sat_refutation,[status(thm)],[f522,f523,f524,f525,f529,f530,f531,f532,f536,f537,f538,f539,f545,f546,f547,f548,f551,f552,f553,f554]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG014+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 12:47:57 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.057067 seconds
% 0.14/0.42 % CPU time: 0.150109 seconds
% 0.14/0.42 % Total memory used: 110.965 MB
% 0.14/0.42 % Net memory used: 110.897 MB
%------------------------------------------------------------------------------