%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG042+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 : n001.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 11:47:52 AM UTC 2026
% Result : Theorem 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 24
% Syntax : Number of formulae : 175 ( 43 unt; 19 def)
% Number of atoms : 585 ( 404 equ)
% Maximal formula atoms : 72 ( 3 avg)
% Number of connectives : 551 ( 141 ~; 210 |; 179 &)
% ( 19 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 48 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 21 ( 19 usr; 20 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
( e22 != e23
& e21 != e23
& e21 != e22
& e20 != e23
& e20 != e22
& e20 != e21 ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(f13,plain,
e12 != e13,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
e20 != e23,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f36,plain,
op1(e10,e10) = e10,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f40,plain,
op1(e11,e10) = e11,
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(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(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(f67,plain,
op2(e23,e23) = e20,
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(f71,plain,
( h(e12) = e23
| h(e12) = e22
| h(e12) = e21
| h(e12) = e20 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f72,plain,
( h(e13) = e23
| h(e13) = e22
| h(e13) = e21
| h(e13) = e20 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f77,plain,
h(op1(e10,e10)) = op2(h(e10),h(e10)),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f81,plain,
h(op1(e11,e10)) = op2(h(e11),h(e10)),
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(f86,plain,
h(op1(e12,e11)) = op2(h(e12),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(f93,plain,
j(op2(e20,e20)) = op1(j(e20),j(e20)),
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(f108,plain,
j(op2(e23,e23)) = op1(j(e23),j(e23)),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f109,plain,
h(j(e20)) = e20,
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(f115,plain,
j(h(e12)) = e12,
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f116,plain,
j(h(e13)) = e13,
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(f126,definition,
( sQ3_spl
<=> h(e10) = e23 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f127,plain,
( ~ sQ3_spl
| h(e10) = e23 ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f128,plain,
( sQ3_spl
| h(e10) != e23 ),
inference(component_clause,[status(thm)],[f126]) ).
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(f143,definition,
( sQ8_spl
<=> h(e12) = e20 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( ~ sQ8_spl
| h(e12) = e20 ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,definition,
( sQ9_spl
<=> h(e12) = e21 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( ~ sQ9_spl
| h(e12) = e21 ),
inference(component_clause,[status(thm)],[f146]) ).
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(f152,definition,
( sQ11_spl
<=> h(e12) = e23 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( ~ sQ11_spl
| h(e12) = e23 ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,plain,
( sQ11_spl
| sQ10_spl
| sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f71,f143,f146,f149,f152]) ).
fof(f156,definition,
( sQ12_spl
<=> h(e13) = e20 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( ~ sQ12_spl
| h(e13) = e20 ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f158,plain,
( sQ12_spl
| h(e13) != e20 ),
inference(component_clause,[status(thm)],[f156]) ).
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(f162,definition,
( sQ14_spl
<=> h(e13) = e22 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f163,plain,
( ~ sQ14_spl
| h(e13) = e22 ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f165,definition,
( sQ15_spl
<=> h(e13) = e23 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ15_spl
| h(e13) = e23 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ15_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f72,f156,f159,f162,f165]) ).
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(f171,plain,
( sQ16_spl
| j(e20) != e10 ),
inference(component_clause,[status(thm)],[f169]) ).
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(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(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(f221,plain,
h(e10) = op2(h(e10),h(e10)),
inference(forward_demodulation,[status(thm)],[f36,f77]) ).
fof(f225,plain,
h(e11) = op2(h(e11),h(e10)),
inference(forward_demodulation,[status(thm)],[f40,f81]) ).
fof(f226,plain,
h(e10) = op2(h(e11),h(e11)),
inference(forward_demodulation,[status(thm)],[f41,f82]) ).
fof(f230,plain,
h(e13) = op2(h(e12),h(e11)),
inference(forward_demodulation,[status(thm)],[f45,f86]) ).
fof(f231,plain,
h(e10) = op2(h(e12),h(e12)),
inference(forward_demodulation,[status(thm)],[f46,f87]) ).
fof(f236,plain,
h(e10) = op2(h(e13),h(e13)),
inference(forward_demodulation,[status(thm)],[f51,f92]) ).
fof(f237,plain,
j(e20) = op1(j(e20),j(e20)),
inference(forward_demodulation,[status(thm)],[f52,f93]) ).
fof(f246,plain,
j(e20) = op1(j(e22),j(e21)),
inference(forward_demodulation,[status(thm)],[f61,f102]) ).
fof(f252,plain,
j(e20) = op1(j(e23),j(e23)),
inference(forward_demodulation,[status(thm)],[f67,f108]) ).
fof(f274,plain,
( ~ sQ26_spl
| ~ sQ27_spl
| e13 = e12 ),
inference(forward_demodulation,[status(thm)],[f205,f202]) ).
fof(f275,plain,
( ~ sQ26_spl
| ~ sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f274,f13]) ).
fof(f276,plain,
( ~ sQ26_spl
| ~ sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f275]) ).
fof(f297,plain,
( ~ sQ15_spl
| j(e23) = e13 ),
inference(backward_demodulation,[status(thm)],[f166,f116]) ).
fof(f314,plain,
( ~ sQ11_spl
| h(e10) = op2(h(e12),e23) ),
inference(backward_demodulation,[status(thm)],[f153,f231]) ).
fof(f323,plain,
( ~ sQ7_spl
| j(e23) = e11 ),
inference(backward_demodulation,[status(thm)],[f140,f114]) ).
fof(f324,plain,
( ~ sQ7_spl
| h(e10) = op2(h(e11),e23) ),
inference(backward_demodulation,[status(thm)],[f140,f226]) ).
fof(f325,plain,
( ~ sQ7_spl
| h(e11) = op2(e23,h(e10)) ),
inference(backward_demodulation,[status(thm)],[f140,f225]) ).
fof(f334,plain,
( ~ sQ3_spl
| h(e10) = op2(h(e10),e23) ),
inference(backward_demodulation,[status(thm)],[f127,f221]) ).
fof(f376,plain,
( ~ sQ12_spl
| j(e20) = e13 ),
inference(backward_demodulation,[status(thm)],[f157,f116]) ).
fof(f385,plain,
( ~ sQ8_spl
| j(e20) = e12 ),
inference(backward_demodulation,[status(thm)],[f144,f115]) ).
fof(f394,plain,
( ~ sQ4_spl
| j(e20) = e11 ),
inference(backward_demodulation,[status(thm)],[f131,f114]) ).
fof(f396,plain,
( ~ sQ3_spl
| e23 = op2(h(e10),e23) ),
inference(forward_demodulation,[status(thm)],[f127,f334]) ).
fof(f397,plain,
( ~ sQ3_spl
| e23 = op2(e23,e23) ),
inference(forward_demodulation,[status(thm)],[f127,f396]) ).
fof(f398,plain,
( ~ sQ3_spl
| e23 = e20 ),
inference(forward_demodulation,[status(thm)],[f67,f397]) ).
fof(f399,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f398,f16]) ).
fof(f400,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f399]) ).
fof(f449,plain,
( ~ sQ12_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f376,f178,f156]) ).
fof(f450,plain,
( ~ sQ8_spl
| ~ sQ16_spl
| e10 = e12 ),
inference(forward_demodulation,[status(thm)],[f170,f385]) ).
fof(f451,plain,
( ~ sQ8_spl
| ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f450,f9]) ).
fof(f452,plain,
( ~ sQ8_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f451]) ).
fof(f509,plain,
( ~ sQ4_spl
| e11 = op1(j(e20),j(e20)) ),
inference(forward_demodulation,[status(thm)],[f394,f237]) ).
fof(f510,plain,
( ~ sQ4_spl
| e11 = op1(e11,j(e20)) ),
inference(forward_demodulation,[status(thm)],[f394,f509]) ).
fof(f511,plain,
( ~ sQ4_spl
| e11 = op1(e11,e11) ),
inference(forward_demodulation,[status(thm)],[f394,f510]) ).
fof(f512,plain,
( ~ sQ4_spl
| e11 = e10 ),
inference(forward_demodulation,[status(thm)],[f41,f511]) ).
fof(f513,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f512,f8]) ).
fof(f514,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f513]) ).
fof(f530,plain,
( ~ sQ0_spl
| j(e20) = e10 ),
inference(forward_demodulation,[status(thm)],[f118,f113]) ).
fof(f531,plain,
( ~ sQ0_spl
| sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f530,f171]) ).
fof(f532,plain,
( ~ sQ0_spl
| sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f531]) ).
fof(f539,plain,
( ~ sQ29_spl
| j(e20) = op1(e11,j(e23)) ),
inference(forward_demodulation,[status(thm)],[f212,f252]) ).
fof(f540,plain,
( ~ sQ29_spl
| j(e20) = op1(e11,e11) ),
inference(forward_demodulation,[status(thm)],[f212,f539]) ).
fof(f544,plain,
( ~ sQ29_spl
| e10 = op1(j(e22),j(e21)) ),
inference(backward_demodulation,[status(thm)],[f550,f246]) ).
fof(f549,plain,
( ~ sQ29_spl
| h(e10) = e20 ),
inference(backward_demodulation,[status(thm)],[f550,f109]) ).
fof(f550,plain,
( ~ sQ29_spl
| j(e20) = e10 ),
inference(forward_demodulation,[status(thm)],[f41,f540]) ).
fof(f557,plain,
( ~ sQ13_spl
| h(e10) = op2(e21,h(e13)) ),
inference(forward_demodulation,[status(thm)],[f160,f236]) ).
fof(f558,plain,
( ~ sQ13_spl
| h(e10) = op2(e21,e21) ),
inference(forward_demodulation,[status(thm)],[f160,f557]) ).
fof(f559,plain,
( ~ sQ13_spl
| h(e10) = e23 ),
inference(forward_demodulation,[status(thm)],[f57,f558]) ).
fof(f560,plain,
( ~ sQ13_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f559,f128]) ).
fof(f561,plain,
( ~ sQ13_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f560]) ).
fof(f562,plain,
( ~ sQ9_spl
| h(e10) = op2(e21,h(e12)) ),
inference(forward_demodulation,[status(thm)],[f147,f231]) ).
fof(f563,plain,
( ~ sQ9_spl
| h(e10) = op2(e21,e21) ),
inference(forward_demodulation,[status(thm)],[f147,f562]) ).
fof(f564,plain,
( ~ sQ9_spl
| h(e10) = e23 ),
inference(forward_demodulation,[status(thm)],[f57,f563]) ).
fof(f565,plain,
( ~ sQ9_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f564,f128]) ).
fof(f566,plain,
( ~ sQ9_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f565]) ).
fof(f572,plain,
( ~ sQ5_spl
| h(e10) = op2(h(e11),e21) ),
inference(backward_demodulation,[status(thm)],[f134,f226]) ).
fof(f617,plain,
( ~ sQ14_spl
| j(e22) = e13 ),
inference(backward_demodulation,[status(thm)],[f163,f116]) ).
fof(f641,plain,
( ~ sQ5_spl
| h(e10) = op2(e21,e21) ),
inference(forward_demodulation,[status(thm)],[f134,f572]) ).
fof(f646,plain,
( ~ sQ5_spl
| h(e10) = e23 ),
inference(forward_demodulation,[status(thm)],[f57,f641]) ).
fof(f651,plain,
( sQ3_spl
| ~ sQ5_spl
| e23 != e23 ),
inference(forward_demodulation,[status(thm)],[f646,f128]) ).
fof(f652,plain,
( sQ3_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f651]) ).
fof(f653,plain,
( sQ3_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f652]) ).
fof(f706,plain,
( ~ sQ19_spl
| e13 = op1(j(e22),j(e21)) ),
inference(forward_demodulation,[status(thm)],[f179,f246]) ).
fof(f716,plain,
( ~ sQ29_spl
| ~ sQ19_spl
| e10 = e13 ),
inference(forward_demodulation,[status(thm)],[f706,f544]) ).
fof(f717,plain,
( ~ sQ29_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f716,f10]) ).
fof(f718,plain,
( ~ sQ29_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f717]) ).
fof(f719,plain,
( ~ sQ7_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f323,f211,f139]) ).
fof(f721,plain,
( ~ sQ7_spl
| e23 = op2(e23,h(e10)) ),
inference(backward_demodulation,[status(thm)],[f140,f325]) ).
fof(f722,plain,
( ~ sQ7_spl
| h(e10) = op2(e23,e23) ),
inference(backward_demodulation,[status(thm)],[f140,f324]) ).
fof(f725,plain,
( ~ sQ7_spl
| h(e11) = op2(e23,h(e10)) ),
inference(backward_demodulation,[status(thm)],[f140,f225]) ).
fof(f772,plain,
( ~ sQ10_spl
| j(e22) = e12 ),
inference(backward_demodulation,[status(thm)],[f150,f115]) ).
fof(f821,plain,
( ~ sQ14_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f617,f204,f162]) ).
fof(f884,plain,
( ~ sQ6_spl
| h(e10) = op2(e22,h(e11)) ),
inference(forward_demodulation,[status(thm)],[f137,f226]) ).
fof(f885,plain,
( ~ sQ6_spl
| h(e10) = op2(e22,e22) ),
inference(forward_demodulation,[status(thm)],[f137,f884]) ).
fof(f888,plain,
( ~ sQ6_spl
| h(e10) = e23 ),
inference(forward_demodulation,[status(thm)],[f62,f885]) ).
fof(f893,plain,
( sQ3_spl
| ~ sQ6_spl
| e23 != e23 ),
inference(forward_demodulation,[status(thm)],[f888,f128]) ).
fof(f894,plain,
( sQ3_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f893]) ).
fof(f895,plain,
( sQ3_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f894]) ).
fof(f896,plain,
( ~ sQ10_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f772,f201,f149]) ).
fof(f926,plain,
( ~ sQ29_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f549,f117,f211]) ).
fof(f965,plain,
( ~ sQ7_spl
| h(e10) = e20 ),
inference(forward_demodulation,[status(thm)],[f67,f722]) ).
fof(f972,plain,
( ~ sQ7_spl
| h(e11) = e23 ),
inference(forward_demodulation,[status(thm)],[f721,f725]) ).
fof(f1008,plain,
( ~ sQ7_spl
| h(e13) = op2(h(e12),e23) ),
inference(forward_demodulation,[status(thm)],[f972,f230]) ).
fof(f1012,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| e20 = op2(h(e12),e23) ),
inference(forward_demodulation,[status(thm)],[f965,f314]) ).
fof(f1013,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| e20 = h(e13) ),
inference(forward_demodulation,[status(thm)],[f1008,f1012]) ).
fof(f1014,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1013,f158]) ).
fof(f1015,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1014]) ).
fof(f1054,plain,
( ~ sQ15_spl
| ~ sQ29_spl
| e11 = e13 ),
inference(forward_demodulation,[status(thm)],[f212,f297]) ).
fof(f1055,plain,
( ~ sQ15_spl
| ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1054,f12]) ).
fof(f1056,plain,
( ~ sQ15_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f1055]) ).
fof(f1057,plain,
$false,
inference(sat_refutation,[status(thm)],[f142,f155,f168,f276,f400,f449,f452,f514,f532,f561,f566,f653,f718,f719,f821,f895,f896,f926,f1015,f1056]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG042+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 13:00:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.45 % Elapsed time: 0.073882 seconds
% 0.10/0.45 % CPU time: 0.228915 seconds
% 0.10/0.45 % Total memory used: 107.412 MB
% 0.10/0.45 % Net memory used: 107.326 MB
%------------------------------------------------------------------------------