%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG017+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 : 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 11:47:46 AM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : CNFRefutation 0.17s
% 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(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/sandbox2/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(f199,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(f200,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(f201,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)],[f199,f200]) ).
fof(f202,plain,
( op(e0,e0) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f203,plain,
( op(e1,e1) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f204,plain,
( op(e2,e2) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f205,plain,
( op(e3,e3) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f206,plain,
( op(e3,e3) != e0
| op(e2,e2) != e0
| op(e1,e1) != e0
| op(e0,e0) != e0 ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f207,plain,
( op(e3,e3) != e1
| op(e2,e2) != e1
| op(e1,e1) != e1
| op(e0,e0) != e1 ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f208,plain,
( op(e3,e3) != e2
| op(e2,e2) != e2
| op(e1,e1) != e2
| op(e0,e0) != e2 ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f209,plain,
( op(e3,e3) != e3
| op(e2,e2) != e3
| op(e1,e1) != e3
| op(e0,e0) != e3 ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f210,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(f211,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)],[f200,f210]) ).
fof(f212,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)],[f211]) ).
fof(f213,plain,
( op(e0,e0) = e2
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f212]) ).
fof(f214,plain,
( op(e1,e1) = e2
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f212]) ).
fof(f215,plain,
( op(e2,e2) = e2
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f212]) ).
fof(f216,plain,
( op(e3,e3) = e2
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f212]) ).
fof(f219,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(f220,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)],[f210,f219]) ).
fof(f221,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)],[f220]) ).
fof(f222,plain,
( op(e0,e0) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f223,plain,
( op(e1,e1) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f224,plain,
( op(e2,e2) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f225,plain,
( op(e3,e3) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f228,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)],[f219]) ).
fof(f229,plain,
( op(e0,e0) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f228]) ).
fof(f230,plain,
( op(e1,e1) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f228]) ).
fof(f231,plain,
( op(e2,e2) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f228]) ).
fof(f232,plain,
( op(e3,e3) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f228]) ).
fof(f234,definition,
( sQ0_spl
<=> op(e0,e0) = e0 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f237,definition,
( sQ1_spl
<=> op(e0,e0) = e1 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f240,definition,
( sQ2_spl
<=> op(e0,e0) = e2 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f243,definition,
( sQ3_spl
<=> op(e0,e0) = e3 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f299,definition,
( sQ20_spl
<=> op(e1,e1) = e0 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f302,definition,
( sQ21_spl
<=> op(e1,e1) = e1 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f305,definition,
( sQ22_spl
<=> op(e1,e1) = e2 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f308,definition,
( sQ23_spl
<=> op(e1,e1) = e3 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f364,definition,
( sQ40_spl
<=> op(e2,e2) = e0 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f367,definition,
( sQ41_spl
<=> op(e2,e2) = e1 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f370,definition,
( sQ42_spl
<=> op(e2,e2) = e2 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f373,definition,
( sQ43_spl
<=> op(e2,e2) = e3 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f429,definition,
( sQ60_spl
<=> op(e3,e3) = e0 ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f432,definition,
( sQ61_spl
<=> op(e3,e3) = e1 ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f435,definition,
( sQ62_spl
<=> op(e3,e3) = e2 ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f438,definition,
( sQ63_spl
<=> op(e3,e3) = e3 ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f523,definition,
( sQ84_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f526,plain,
( sQ3_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f202,f523,f243]) ).
fof(f527,plain,
( sQ23_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f203,f523,f308]) ).
fof(f528,plain,
( sQ43_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f204,f523,f373]) ).
fof(f529,plain,
( sQ63_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f205,f523,f438]) ).
fof(f530,plain,
( ~ sQ60_spl
| ~ sQ40_spl
| ~ sQ20_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f206,f234,f299,f364,f429]) ).
fof(f531,plain,
( ~ sQ61_spl
| ~ sQ41_spl
| ~ sQ21_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f207,f237,f302,f367,f432]) ).
fof(f532,plain,
( ~ sQ62_spl
| ~ sQ42_spl
| ~ sQ22_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f208,f240,f305,f370,f435]) ).
fof(f533,plain,
( ~ sQ63_spl
| ~ sQ43_spl
| ~ sQ23_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f209,f243,f308,f373,f438]) ).
fof(f534,definition,
( sQ85_spl
<=> sP1_prd ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f537,plain,
( sQ2_spl
| sQ85_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f213,f523,f534,f240]) ).
fof(f538,plain,
( sQ22_spl
| sQ85_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f214,f523,f534,f305]) ).
fof(f539,plain,
( sQ42_spl
| sQ85_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f215,f523,f534,f370]) ).
fof(f540,plain,
( sQ62_spl
| sQ85_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f216,f523,f534,f435]) ).
fof(f543,definition,
( sQ86_spl
<=> sP2_prd ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( sQ1_spl
| sQ86_spl
| ~ sQ85_spl ),
inference(split_clause,[status(thm)],[f222,f534,f543,f237]) ).
fof(f547,plain,
( sQ21_spl
| sQ86_spl
| ~ sQ85_spl ),
inference(split_clause,[status(thm)],[f223,f534,f543,f302]) ).
fof(f548,plain,
( sQ41_spl
| sQ86_spl
| ~ sQ85_spl ),
inference(split_clause,[status(thm)],[f224,f534,f543,f367]) ).
fof(f549,plain,
( sQ61_spl
| sQ86_spl
| ~ sQ85_spl ),
inference(split_clause,[status(thm)],[f225,f534,f543,f432]) ).
fof(f552,plain,
( sQ0_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f229,f543,f234]) ).
fof(f553,plain,
( sQ20_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f230,f543,f299]) ).
fof(f554,plain,
( sQ40_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f231,f543,f364]) ).
fof(f555,plain,
( sQ60_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f232,f543,f429]) ).
fof(f557,plain,
$false,
inference(sat_refutation,[status(thm)],[f526,f527,f528,f529,f530,f531,f532,f533,f537,f538,f539,f540,f546,f547,f548,f549,f552,f553,f554,f555]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG017+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n017.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 12:48:43 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.46 % Refutation found
% 0.17/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.50 % Elapsed time: 0.064508 seconds
% 0.17/0.50 % CPU time: 0.155187 seconds
% 0.17/0.50 % Total memory used: 52.049 MB
% 0.17/0.50 % Net memory used: 52.020 MB
%------------------------------------------------------------------------------