%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG020+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 : n003.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 0.12s 0.42s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 27
% Syntax : Number of formulae : 226 ( 57 unt; 22 def)
% Number of atoms : 707 ( 446 equ)
% Maximal formula atoms : 72 ( 3 avg)
% Number of connectives : 699 ( 218 ~; 278 |; 179 &)
% ( 22 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 48 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( e12 != e13
& e11 != e13
& e11 != e12
& e10 != e13
& e10 != e12
& e10 != e11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
( e22 != e23
& e21 != e23
& e21 != e22
& e20 != e23
& e20 != e22
& e20 != e21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
( op1(e13,e13) = e10
& op1(e13,e12) = e11
& op1(e13,e11) = e12
& op1(e13,e10) = e13
& op1(e12,e13) = e11
& op1(e12,e12) = e10
& op1(e12,e11) = e13
& op1(e12,e10) = e12
& op1(e11,e13) = e12
& op1(e11,e12) = e13
& op1(e11,e11) = e10
& op1(e11,e10) = e11
& op1(e10,e13) = e13
& op1(e10,e12) = e12
& op1(e10,e11) = e11
& op1(e10,e10) = e10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
( op2(e23,e23) = e20
& op2(e23,e22) = e21
& op2(e23,e21) = e22
& op2(e23,e20) = e23
& op2(e22,e23) = e21
& op2(e22,e22) = e23
& op2(e22,e21) = e20
& op2(e22,e20) = e22
& op2(e21,e23) = e22
& op2(e21,e22) = e20
& op2(e21,e21) = e23
& op2(e21,e20) = e21
& op2(e20,e23) = e23
& op2(e20,e22) = e22
& op2(e20,e21) = e21
& op2(e20,e20) = e20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
( ( ( j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 )
& ( j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 )
& ( j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 )
& ( j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 )
& ( h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 )
& ( h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 )
& ( h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 )
& ( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ) )
=> ~ ( j(h(e13)) = e13
& j(h(e12)) = e12
& j(h(e11)) = e11
& j(h(e10)) = e10
& h(j(e23)) = e23
& h(j(e22)) = e22
& h(j(e21)) = e21
& h(j(e20)) = e20
& j(op2(e23,e23)) = op1(j(e23),j(e23))
& j(op2(e23,e22)) = op1(j(e23),j(e22))
& j(op2(e23,e21)) = op1(j(e23),j(e21))
& j(op2(e23,e20)) = op1(j(e23),j(e20))
& j(op2(e22,e23)) = op1(j(e22),j(e23))
& j(op2(e22,e22)) = op1(j(e22),j(e22))
& j(op2(e22,e21)) = op1(j(e22),j(e21))
& j(op2(e22,e20)) = op1(j(e22),j(e20))
& j(op2(e21,e23)) = op1(j(e21),j(e23))
& j(op2(e21,e22)) = op1(j(e21),j(e22))
& j(op2(e21,e21)) = op1(j(e21),j(e21))
& j(op2(e21,e20)) = op1(j(e21),j(e20))
& j(op2(e20,e23)) = op1(j(e20),j(e23))
& j(op2(e20,e22)) = op1(j(e20),j(e22))
& j(op2(e20,e21)) = op1(j(e20),j(e21))
& j(op2(e20,e20)) = op1(j(e20),j(e20))
& h(op1(e13,e13)) = op2(h(e13),h(e13))
& h(op1(e13,e12)) = op2(h(e13),h(e12))
& h(op1(e13,e11)) = op2(h(e13),h(e11))
& h(op1(e13,e10)) = op2(h(e13),h(e10))
& h(op1(e12,e13)) = op2(h(e12),h(e13))
& h(op1(e12,e12)) = op2(h(e12),h(e12))
& h(op1(e12,e11)) = op2(h(e12),h(e11))
& h(op1(e12,e10)) = op2(h(e12),h(e10))
& h(op1(e11,e13)) = op2(h(e11),h(e13))
& h(op1(e11,e12)) = op2(h(e11),h(e12))
& h(op1(e11,e11)) = op2(h(e11),h(e11))
& h(op1(e11,e10)) = op2(h(e11),h(e10))
& h(op1(e10,e13)) = op2(h(e10),h(e13))
& h(op1(e10,e12)) = op2(h(e10),h(e12))
& h(op1(e10,e11)) = op2(h(e10),h(e11))
& h(op1(e10,e10)) = op2(h(e10),h(e10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ( ( ( j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 )
& ( j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 )
& ( j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 )
& ( j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 )
& ( h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 )
& ( h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 )
& ( h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 )
& ( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ) )
=> ~ ( j(h(e13)) = e13
& j(h(e12)) = e12
& j(h(e11)) = e11
& j(h(e10)) = e10
& h(j(e23)) = e23
& h(j(e22)) = e22
& h(j(e21)) = e21
& h(j(e20)) = e20
& j(op2(e23,e23)) = op1(j(e23),j(e23))
& j(op2(e23,e22)) = op1(j(e23),j(e22))
& j(op2(e23,e21)) = op1(j(e23),j(e21))
& j(op2(e23,e20)) = op1(j(e23),j(e20))
& j(op2(e22,e23)) = op1(j(e22),j(e23))
& j(op2(e22,e22)) = op1(j(e22),j(e22))
& j(op2(e22,e21)) = op1(j(e22),j(e21))
& j(op2(e22,e20)) = op1(j(e22),j(e20))
& j(op2(e21,e23)) = op1(j(e21),j(e23))
& j(op2(e21,e22)) = op1(j(e21),j(e22))
& j(op2(e21,e21)) = op1(j(e21),j(e21))
& j(op2(e21,e20)) = op1(j(e21),j(e20))
& j(op2(e20,e23)) = op1(j(e20),j(e23))
& j(op2(e20,e22)) = op1(j(e20),j(e22))
& j(op2(e20,e21)) = op1(j(e20),j(e21))
& j(op2(e20,e20)) = op1(j(e20),j(e20))
& h(op1(e13,e13)) = op2(h(e13),h(e13))
& h(op1(e13,e12)) = op2(h(e13),h(e12))
& h(op1(e13,e11)) = op2(h(e13),h(e11))
& h(op1(e13,e10)) = op2(h(e13),h(e10))
& h(op1(e12,e13)) = op2(h(e12),h(e13))
& h(op1(e12,e12)) = op2(h(e12),h(e12))
& h(op1(e12,e11)) = op2(h(e12),h(e11))
& h(op1(e12,e10)) = op2(h(e12),h(e10))
& h(op1(e11,e13)) = op2(h(e11),h(e13))
& h(op1(e11,e12)) = op2(h(e11),h(e12))
& h(op1(e11,e11)) = op2(h(e11),h(e11))
& h(op1(e11,e10)) = op2(h(e11),h(e10))
& h(op1(e10,e13)) = op2(h(e10),h(e13))
& h(op1(e10,e12)) = op2(h(e10),h(e12))
& h(op1(e10,e11)) = op2(h(e10),h(e11))
& h(op1(e10,e10)) = op2(h(e10),h(e10)) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
e10 != e11,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
e10 != e12,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
e10 != e13,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
e11 != e13,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
e20 != e21,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
e20 != e22,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
e20 != e23,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
e21 != e22,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f36,plain,
op1(e10,e10) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f37,plain,
op1(e10,e11) = e11,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
op1(e10,e13) = e13,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f41,plain,
op1(e11,e11) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f45,plain,
op1(e12,e11) = e13,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f46,plain,
op1(e12,e12) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f48,plain,
op1(e13,e10) = e13,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f49,plain,
op1(e13,e11) = e12,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f50,plain,
op1(e13,e12) = e11,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f51,plain,
op1(e13,e13) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f52,plain,
op2(e20,e20) = e20,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f54,plain,
op2(e20,e22) = e22,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f55,plain,
op2(e20,e23) = e23,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f57,plain,
op2(e21,e21) = e23,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f61,plain,
op2(e22,e21) = e20,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f62,plain,
op2(e22,e22) = e23,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f64,plain,
op2(e23,e20) = e23,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f65,plain,
op2(e23,e21) = e22,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f68,plain,
( j(h(e13)) = e13
& j(h(e12)) = e12
& j(h(e11)) = e11
& j(h(e10)) = e10
& h(j(e23)) = e23
& h(j(e22)) = e22
& h(j(e21)) = e21
& h(j(e20)) = e20
& j(op2(e23,e23)) = op1(j(e23),j(e23))
& j(op2(e23,e22)) = op1(j(e23),j(e22))
& j(op2(e23,e21)) = op1(j(e23),j(e21))
& j(op2(e23,e20)) = op1(j(e23),j(e20))
& j(op2(e22,e23)) = op1(j(e22),j(e23))
& j(op2(e22,e22)) = op1(j(e22),j(e22))
& j(op2(e22,e21)) = op1(j(e22),j(e21))
& j(op2(e22,e20)) = op1(j(e22),j(e20))
& j(op2(e21,e23)) = op1(j(e21),j(e23))
& j(op2(e21,e22)) = op1(j(e21),j(e22))
& j(op2(e21,e21)) = op1(j(e21),j(e21))
& j(op2(e21,e20)) = op1(j(e21),j(e20))
& j(op2(e20,e23)) = op1(j(e20),j(e23))
& j(op2(e20,e22)) = op1(j(e20),j(e22))
& j(op2(e20,e21)) = op1(j(e20),j(e21))
& j(op2(e20,e20)) = op1(j(e20),j(e20))
& h(op1(e13,e13)) = op2(h(e13),h(e13))
& h(op1(e13,e12)) = op2(h(e13),h(e12))
& h(op1(e13,e11)) = op2(h(e13),h(e11))
& h(op1(e13,e10)) = op2(h(e13),h(e10))
& h(op1(e12,e13)) = op2(h(e12),h(e13))
& h(op1(e12,e12)) = op2(h(e12),h(e12))
& h(op1(e12,e11)) = op2(h(e12),h(e11))
& h(op1(e12,e10)) = op2(h(e12),h(e10))
& h(op1(e11,e13)) = op2(h(e11),h(e13))
& h(op1(e11,e12)) = op2(h(e11),h(e12))
& h(op1(e11,e11)) = op2(h(e11),h(e11))
& h(op1(e11,e10)) = op2(h(e11),h(e10))
& h(op1(e10,e13)) = op2(h(e10),h(e13))
& h(op1(e10,e12)) = op2(h(e10),h(e12))
& h(op1(e10,e11)) = op2(h(e10),h(e11))
& h(op1(e10,e10)) = op2(h(e10),h(e10))
& ( j(e23) = e13
| j(e23) = e12
| j(e23) = e11
| j(e23) = e10 )
& ( j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 )
& ( j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 )
& ( j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 )
& ( h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 )
& ( h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 )
& ( h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 )
& ( h(e10) = e23
| h(e10) = e22
| h(e10) = e21
| h(e10) = e20 ) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f70,plain,
( h(e11) = e23
| h(e11) = e22
| h(e11) = e21
| h(e11) = e20 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f73,plain,
( j(e20) = e13
| j(e20) = e12
| j(e20) = e11
| j(e20) = e10 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f74,plain,
( j(e21) = e13
| j(e21) = e12
| j(e21) = e11
| j(e21) = e10 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f75,plain,
( j(e22) = e13
| j(e22) = e12
| j(e22) = e11
| j(e22) = e10 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f78,plain,
h(op1(e10,e11)) = op2(h(e10),h(e11)),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f80,plain,
h(op1(e10,e13)) = op2(h(e10),h(e13)),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f82,plain,
h(op1(e11,e11)) = op2(h(e11),h(e11)),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f87,plain,
h(op1(e12,e12)) = op2(h(e12),h(e12)),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f92,plain,
h(op1(e13,e13)) = op2(h(e13),h(e13)),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f95,plain,
j(op2(e20,e22)) = op1(j(e20),j(e22)),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f96,plain,
j(op2(e20,e23)) = op1(j(e20),j(e23)),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f98,plain,
j(op2(e21,e21)) = op1(j(e21),j(e21)),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f102,plain,
j(op2(e22,e21)) = op1(j(e22),j(e21)),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f103,plain,
j(op2(e22,e22)) = op1(j(e22),j(e22)),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f105,plain,
j(op2(e23,e20)) = op1(j(e23),j(e20)),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f109,plain,
h(j(e20)) = e20,
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f110,plain,
h(j(e21)) = e21,
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f111,plain,
h(j(e22)) = e22,
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f112,plain,
h(j(e23)) = e23,
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f113,plain,
j(h(e10)) = e10,
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f114,plain,
j(h(e11)) = e11,
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f117,definition,
( sQ0_spl
<=> h(e10) = e20 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ0_spl
| h(e10) = e20 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f119,plain,
( sQ0_spl
| h(e10) != e20 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,definition,
( sQ1_spl
<=> h(e10) = e21 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f121,plain,
( ~ sQ1_spl
| h(e10) = e21 ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f130,definition,
( sQ4_spl
<=> h(e11) = e20 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( ~ sQ4_spl
| h(e11) = e20 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,definition,
( sQ5_spl
<=> h(e11) = e21 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ5_spl
| h(e11) = e21 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
( sQ6_spl
<=> h(e11) = e22 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ6_spl
| h(e11) = e22 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
( sQ7_spl
<=> h(e11) = e23 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( ~ sQ7_spl
| h(e11) = e23 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( sQ7_spl
| sQ6_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f70,f130,f133,f136,f139]) ).
fof(f149,definition,
( sQ10_spl
<=> h(e12) = e22 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ10_spl
| h(e12) = e22 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f159,definition,
( sQ13_spl
<=> h(e13) = e21 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( ~ sQ13_spl
| h(e13) = e21 ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f169,definition,
( sQ16_spl
<=> j(e20) = e10 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( ~ sQ16_spl
| j(e20) = e10 ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,definition,
( sQ17_spl
<=> j(e20) = e11 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( ~ sQ17_spl
| j(e20) = e11 ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,definition,
( sQ18_spl
<=> j(e20) = e12 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( ~ sQ18_spl
| j(e20) = e12 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,definition,
( sQ19_spl
<=> j(e20) = e13 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f179,plain,
( ~ sQ19_spl
| j(e20) = e13 ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,plain,
( sQ19_spl
| sQ18_spl
| sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f73,f169,f172,f175,f178]) ).
fof(f182,definition,
( sQ20_spl
<=> j(e21) = e10 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( ~ sQ20_spl
| j(e21) = e10 ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,definition,
( sQ21_spl
<=> j(e21) = e11 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( ~ sQ21_spl
| j(e21) = e11 ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,definition,
( sQ22_spl
<=> j(e21) = e12 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f189,plain,
( ~ sQ22_spl
| j(e21) = e12 ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f191,definition,
( sQ23_spl
<=> j(e21) = e13 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( ~ sQ23_spl
| j(e21) = e13 ),
inference(component_clause,[status(thm)],[f191]) ).
fof(f194,plain,
( sQ23_spl
| sQ22_spl
| sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f74,f182,f185,f188,f191]) ).
fof(f195,definition,
( sQ24_spl
<=> j(e22) = e10 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( ~ sQ24_spl
| j(e22) = e10 ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f198,definition,
( sQ25_spl
<=> j(e22) = e11 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f199,plain,
( ~ sQ25_spl
| j(e22) = e11 ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f201,definition,
( sQ26_spl
<=> j(e22) = e12 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f202,plain,
( ~ sQ26_spl
| j(e22) = e12 ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f204,definition,
( sQ27_spl
<=> j(e22) = e13 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( ~ sQ27_spl
| j(e22) = e13 ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,plain,
( sQ27_spl
| sQ26_spl
| sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f75,f195,f198,f201,f204]) ).
fof(f208,definition,
( sQ28_spl
<=> j(e23) = e10 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( ~ sQ28_spl
| j(e23) = e10 ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f210,plain,
( sQ28_spl
| j(e23) != e10 ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,definition,
( sQ29_spl
<=> j(e23) = e11 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( ~ sQ29_spl
| j(e23) = e11 ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f284,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| e21 = e20 ),
inference(forward_demodulation,[status(thm)],[f121,f118]) ).
fof(f285,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f284,f14]) ).
fof(f286,plain,
( ~ sQ0_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f285]) ).
fof(f309,plain,
( ~ sQ16_spl
| h(e10) = e20 ),
inference(forward_demodulation,[status(thm)],[f170,f109]) ).
fof(f310,plain,
( ~ sQ20_spl
| h(e10) = e21 ),
inference(forward_demodulation,[status(thm)],[f183,f110]) ).
fof(f314,plain,
( ~ sQ16_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f309,f117,f169]) ).
fof(f315,plain,
h(e13) = op2(h(e10),h(e13)),
inference(forward_demodulation,[status(thm)],[f39,f80]) ).
fof(f329,plain,
h(e10) = op2(h(e11),h(e11)),
inference(forward_demodulation,[status(thm)],[f41,f82]) ).
fof(f337,plain,
( ~ sQ24_spl
| h(e10) = e22 ),
inference(forward_demodulation,[status(thm)],[f196,f111]) ).
fof(f338,plain,
( ~ sQ24_spl
| ~ sQ0_spl
| e20 = e22 ),
inference(forward_demodulation,[status(thm)],[f118,f337]) ).
fof(f339,plain,
( ~ sQ24_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f338,f15]) ).
fof(f340,plain,
( ~ sQ24_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f339]) ).
fof(f341,plain,
( ~ sQ4_spl
| h(e10) = op2(e20,h(e11)) ),
inference(forward_demodulation,[status(thm)],[f131,f329]) ).
fof(f342,plain,
( ~ sQ4_spl
| h(e10) = op2(e20,e20) ),
inference(forward_demodulation,[status(thm)],[f131,f341]) ).
fof(f343,plain,
( ~ sQ4_spl
| h(e10) = e20 ),
inference(forward_demodulation,[status(thm)],[f52,f342]) ).
fof(f345,plain,
( sQ0_spl
| ~ sQ4_spl
| e20 != e20 ),
inference(forward_demodulation,[status(thm)],[f343,f119]) ).
fof(f346,plain,
( sQ0_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f345]) ).
fof(f347,plain,
( sQ0_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f346]) ).
fof(f388,plain,
h(e10) = op2(h(e12),h(e12)),
inference(forward_demodulation,[status(thm)],[f46,f87]) ).
fof(f414,plain,
( ~ sQ0_spl
| j(e20) = e10 ),
inference(forward_demodulation,[status(thm)],[f118,f113]) ).
fof(f420,plain,
( ~ sQ10_spl
| h(e10) = op2(e22,h(e12)) ),
inference(forward_demodulation,[status(thm)],[f150,f388]) ).
fof(f421,plain,
( ~ sQ10_spl
| h(e10) = op2(e22,e22) ),
inference(forward_demodulation,[status(thm)],[f150,f420]) ).
fof(f422,plain,
( ~ sQ10_spl
| h(e10) = e23 ),
inference(forward_demodulation,[status(thm)],[f62,f421]) ).
fof(f435,plain,
h(e10) = op2(h(e13),h(e13)),
inference(forward_demodulation,[status(thm)],[f51,f92]) ).
fof(f447,plain,
( ~ sQ6_spl
| j(e22) = e11 ),
inference(forward_demodulation,[status(thm)],[f137,f114]) ).
fof(f457,plain,
( ~ sQ13_spl
| h(e10) = op2(e21,h(e13)) ),
inference(forward_demodulation,[status(thm)],[f160,f435]) ).
fof(f458,plain,
( ~ sQ13_spl
| h(e10) = op2(e21,e21) ),
inference(forward_demodulation,[status(thm)],[f160,f457]) ).
fof(f459,plain,
( ~ sQ13_spl
| h(e10) = e23 ),
inference(forward_demodulation,[status(thm)],[f57,f458]) ).
fof(f470,plain,
j(e22) = op1(j(e20),j(e22)),
inference(forward_demodulation,[status(thm)],[f54,f95]) ).
fof(f482,plain,
j(e23) = op1(j(e20),j(e23)),
inference(forward_demodulation,[status(thm)],[f55,f96]) ).
fof(f483,plain,
( ~ sQ29_spl
| e11 = op1(j(e20),j(e23)) ),
inference(forward_demodulation,[status(thm)],[f212,f482]) ).
fof(f484,plain,
( ~ sQ29_spl
| e11 = op1(j(e20),e11) ),
inference(forward_demodulation,[status(thm)],[f212,f483]) ).
fof(f498,plain,
j(e23) = op1(j(e21),j(e21)),
inference(forward_demodulation,[status(thm)],[f57,f98]) ).
fof(f499,plain,
( ~ sQ29_spl
| e11 = op1(j(e21),j(e21)) ),
inference(forward_demodulation,[status(thm)],[f212,f498]) ).
fof(f500,plain,
( ~ sQ29_spl
| ~ sQ21_spl
| e11 = op1(e11,j(e21)) ),
inference(forward_demodulation,[status(thm)],[f186,f499]) ).
fof(f501,plain,
( ~ sQ29_spl
| ~ sQ21_spl
| e11 = op1(e11,e11) ),
inference(forward_demodulation,[status(thm)],[f186,f500]) ).
fof(f502,plain,
( ~ sQ29_spl
| ~ sQ21_spl
| e11 = e10 ),
inference(forward_demodulation,[status(thm)],[f41,f501]) ).
fof(f503,plain,
( ~ sQ29_spl
| ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f502,f8]) ).
fof(f504,plain,
( ~ sQ29_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f503]) ).
fof(f555,plain,
j(e20) = op1(j(e22),j(e21)),
inference(forward_demodulation,[status(thm)],[f61,f102]) ).
fof(f556,plain,
( ~ sQ0_spl
| e10 = op1(j(e22),j(e21)) ),
inference(forward_demodulation,[status(thm)],[f414,f555]) ).
fof(f557,plain,
( ~ sQ0_spl
| ~ sQ27_spl
| e10 = op1(e13,j(e21)) ),
inference(forward_demodulation,[status(thm)],[f205,f556]) ).
fof(f558,plain,
( ~ sQ0_spl
| ~ sQ27_spl
| ~ sQ22_spl
| e10 = op1(e13,e12) ),
inference(forward_demodulation,[status(thm)],[f189,f557]) ).
fof(f559,plain,
( ~ sQ0_spl
| ~ sQ27_spl
| ~ sQ22_spl
| e10 = e11 ),
inference(forward_demodulation,[status(thm)],[f50,f558]) ).
fof(f560,plain,
( ~ sQ0_spl
| ~ sQ27_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f559,f8]) ).
fof(f561,plain,
( ~ sQ0_spl
| ~ sQ27_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f560]) ).
fof(f569,plain,
j(e23) = op1(j(e22),j(e22)),
inference(forward_demodulation,[status(thm)],[f62,f103]) ).
fof(f577,plain,
( ~ sQ0_spl
| h(e10) = e20 ),
inference(forward_demodulation,[status(thm)],[f414,f109]) ).
fof(f578,plain,
( ~ sQ26_spl
| h(e12) = e22 ),
inference(forward_demodulation,[status(thm)],[f202,f111]) ).
fof(f582,plain,
( ~ sQ26_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f578,f149,f201]) ).
fof(f586,plain,
( ~ sQ28_spl
| e10 = op1(j(e20),j(e23)) ),
inference(forward_demodulation,[status(thm)],[f209,f482]) ).
fof(f587,plain,
( ~ sQ28_spl
| e10 = op1(j(e20),e10) ),
inference(forward_demodulation,[status(thm)],[f209,f586]) ).
fof(f600,plain,
j(e23) = op1(j(e23),j(e20)),
inference(forward_demodulation,[status(thm)],[f64,f105]) ).
fof(f601,plain,
( ~ sQ28_spl
| e10 = op1(j(e23),j(e20)) ),
inference(forward_demodulation,[status(thm)],[f209,f600]) ).
fof(f602,plain,
( ~ sQ28_spl
| e10 = op1(e10,j(e20)) ),
inference(forward_demodulation,[status(thm)],[f209,f601]) ).
fof(f612,plain,
( ~ sQ28_spl
| ~ sQ17_spl
| e10 = op1(e10,e11) ),
inference(backward_demodulation,[status(thm)],[f173,f602]) ).
fof(f615,plain,
( ~ sQ28_spl
| ~ sQ17_spl
| e10 = e11 ),
inference(forward_demodulation,[status(thm)],[f37,f612]) ).
fof(f616,plain,
( ~ sQ28_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f615,f8]) ).
fof(f617,plain,
( ~ sQ28_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f616]) ).
fof(f635,plain,
h(e11) = op2(h(e10),h(e11)),
inference(forward_demodulation,[status(thm)],[f37,f78]) ).
fof(f636,plain,
( ~ sQ5_spl
| e21 = op2(h(e10),h(e11)) ),
inference(forward_demodulation,[status(thm)],[f134,f635]) ).
fof(f637,plain,
( ~ sQ5_spl
| e21 = op2(h(e10),e21) ),
inference(forward_demodulation,[status(thm)],[f134,f636]) ).
fof(f650,plain,
( ~ sQ29_spl
| ~ sQ22_spl
| e11 = op1(e12,j(e21)) ),
inference(forward_demodulation,[status(thm)],[f189,f499]) ).
fof(f651,plain,
( ~ sQ29_spl
| ~ sQ22_spl
| e11 = op1(e12,e12) ),
inference(forward_demodulation,[status(thm)],[f189,f650]) ).
fof(f652,plain,
( ~ sQ29_spl
| ~ sQ22_spl
| e11 = e10 ),
inference(forward_demodulation,[status(thm)],[f46,f651]) ).
fof(f653,plain,
( ~ sQ29_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f652,f8]) ).
fof(f654,plain,
( ~ sQ29_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f653]) ).
fof(f655,plain,
( ~ sQ29_spl
| ~ sQ18_spl
| e11 = op1(e12,e11) ),
inference(forward_demodulation,[status(thm)],[f176,f484]) ).
fof(f656,plain,
( ~ sQ29_spl
| ~ sQ18_spl
| e11 = e13 ),
inference(forward_demodulation,[status(thm)],[f45,f655]) ).
fof(f657,plain,
( ~ sQ29_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f656,f12]) ).
fof(f658,plain,
( ~ sQ29_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f657]) ).
fof(f665,plain,
( ~ sQ5_spl
| h(e10) = op2(e21,h(e11)) ),
inference(forward_demodulation,[status(thm)],[f134,f329]) ).
fof(f666,plain,
( ~ sQ5_spl
| h(e10) = op2(e21,e21) ),
inference(forward_demodulation,[status(thm)],[f134,f665]) ).
fof(f667,plain,
( ~ sQ5_spl
| e21 = op2(e23,e21) ),
inference(backward_demodulation,[status(thm)],[f669,f637]) ).
fof(f669,plain,
( ~ sQ5_spl
| h(e10) = e23 ),
inference(forward_demodulation,[status(thm)],[f57,f666]) ).
fof(f670,plain,
( ~ sQ5_spl
| e21 = e22 ),
inference(forward_demodulation,[status(thm)],[f65,f667]) ).
fof(f671,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f670,f17]) ).
fof(f672,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f671]) ).
fof(f673,plain,
( ~ sQ6_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f447,f198,f136]) ).
fof(f698,plain,
( ~ sQ28_spl
| h(e10) = e23 ),
inference(backward_demodulation,[status(thm)],[f209,f112]) ).
fof(f699,plain,
( ~ sQ28_spl
| ~ sQ0_spl
| e20 = e23 ),
inference(forward_demodulation,[status(thm)],[f577,f698]) ).
fof(f700,plain,
( ~ sQ28_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f699,f16]) ).
fof(f701,plain,
( ~ sQ28_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f700]) ).
fof(f704,plain,
( ~ sQ13_spl
| e21 = op2(h(e10),h(e13)) ),
inference(forward_demodulation,[status(thm)],[f160,f315]) ).
fof(f705,plain,
( ~ sQ13_spl
| e21 = op2(e23,h(e13)) ),
inference(forward_demodulation,[status(thm)],[f459,f704]) ).
fof(f706,plain,
( ~ sQ13_spl
| e21 = op2(e23,e21) ),
inference(forward_demodulation,[status(thm)],[f160,f705]) ).
fof(f707,plain,
( ~ sQ13_spl
| e21 = e22 ),
inference(forward_demodulation,[status(thm)],[f65,f706]) ).
fof(f708,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f707,f17]) ).
fof(f709,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f708]) ).
fof(f752,plain,
( ~ sQ20_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f310,f120,f182]) ).
fof(f787,plain,
( ~ sQ23_spl
| h(e13) = e21 ),
inference(backward_demodulation,[status(thm)],[f192,f110]) ).
fof(f792,plain,
( ~ sQ25_spl
| e11 = op1(j(e20),j(e22)) ),
inference(forward_demodulation,[status(thm)],[f199,f470]) ).
fof(f793,plain,
( ~ sQ25_spl
| e11 = op1(j(e20),e11) ),
inference(forward_demodulation,[status(thm)],[f199,f792]) ).
fof(f800,plain,
( ~ sQ25_spl
| ~ sQ18_spl
| e11 = op1(e12,e11) ),
inference(backward_demodulation,[status(thm)],[f176,f793]) ).
fof(f804,plain,
( ~ sQ25_spl
| ~ sQ18_spl
| e11 = e13 ),
inference(forward_demodulation,[status(thm)],[f45,f800]) ).
fof(f805,plain,
( ~ sQ25_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f804,f12]) ).
fof(f806,plain,
( ~ sQ25_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f805]) ).
fof(f811,plain,
( ~ sQ0_spl
| ~ sQ27_spl
| ~ sQ21_spl
| e10 = op1(e13,e11) ),
inference(forward_demodulation,[status(thm)],[f186,f557]) ).
fof(f812,plain,
( ~ sQ0_spl
| ~ sQ27_spl
| ~ sQ21_spl
| e10 = e12 ),
inference(forward_demodulation,[status(thm)],[f49,f811]) ).
fof(f813,plain,
( ~ sQ0_spl
| ~ sQ27_spl
| ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f812,f9]) ).
fof(f814,plain,
( ~ sQ0_spl
| ~ sQ27_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f813]) ).
fof(f815,plain,
( ~ sQ23_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f787,f159,f191]) ).
fof(f845,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| e20 = e23 ),
inference(forward_demodulation,[status(thm)],[f577,f422]) ).
fof(f846,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f845,f16]) ).
fof(f847,plain,
( ~ sQ10_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f846]) ).
fof(f887,plain,
( ~ sQ7_spl
| j(e23) = e11 ),
inference(forward_demodulation,[status(thm)],[f140,f114]) ).
fof(f891,plain,
( ~ sQ7_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f887,f211,f139]) ).
fof(f897,plain,
( ~ sQ29_spl
| ~ sQ20_spl
| e11 = op1(e10,j(e21)) ),
inference(forward_demodulation,[status(thm)],[f183,f499]) ).
fof(f898,plain,
( ~ sQ29_spl
| ~ sQ20_spl
| e11 = op1(e10,e10) ),
inference(forward_demodulation,[status(thm)],[f183,f897]) ).
fof(f899,plain,
( ~ sQ29_spl
| ~ sQ20_spl
| e11 = e10 ),
inference(forward_demodulation,[status(thm)],[f36,f898]) ).
fof(f900,plain,
( ~ sQ29_spl
| ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f899,f8]) ).
fof(f901,plain,
( ~ sQ29_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f900]) ).
fof(f909,plain,
( ~ sQ25_spl
| j(e23) = op1(e11,j(e22)) ),
inference(forward_demodulation,[status(thm)],[f199,f569]) ).
fof(f910,plain,
( ~ sQ25_spl
| j(e23) = op1(e11,e11) ),
inference(forward_demodulation,[status(thm)],[f199,f909]) ).
fof(f911,plain,
( ~ sQ25_spl
| j(e23) = e10 ),
inference(forward_demodulation,[status(thm)],[f41,f910]) ).
fof(f912,plain,
( ~ sQ25_spl
| sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f911,f210]) ).
fof(f913,plain,
( ~ sQ25_spl
| sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f912]) ).
fof(f914,plain,
( ~ sQ28_spl
| ~ sQ19_spl
| e10 = op1(e13,e10) ),
inference(forward_demodulation,[status(thm)],[f179,f587]) ).
fof(f915,plain,
( ~ sQ28_spl
| ~ sQ19_spl
| e10 = e13 ),
inference(forward_demodulation,[status(thm)],[f48,f914]) ).
fof(f916,plain,
( ~ sQ28_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f915,f10]) ).
fof(f917,plain,
( ~ sQ28_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f916]) ).
fof(f918,plain,
$false,
inference(sat_refutation,[status(thm)],[f142,f181,f194,f207,f286,f314,f340,f347,f504,f561,f582,f617,f654,f658,f672,f673,f701,f709,f752,f806,f814,f815,f847,f891,f901,f913,f917]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG020+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n003.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 12:54:46 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 0.12/0.42 % Refutation found
% 0.12/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.47 % Elapsed time: 0.079155 seconds
% 0.12/0.47 % CPU time: 0.244431 seconds
% 0.12/0.47 % Total memory used: 108.030 MB
% 0.12/0.47 % Net memory used: 107.882 MB
%------------------------------------------------------------------------------