TSTP Solution File: ALG036+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : ALG036+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:09:05 EDT 2024
% Result : Theorem 0.21s 0.36s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 24
% Syntax : Number of formulae : 81 ( 1 unt; 0 def)
% Number of atoms : 430 ( 300 equ)
% Maximal formula atoms : 64 ( 5 avg)
% Number of connectives : 445 ( 96 ~; 199 |; 128 &)
% ( 19 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 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(f1,axiom,
( ( op(e0,e0) = e0
| op(e0,e0) = e1
| op(e0,e0) = e2
| op(e0,e0) = e3 )
& ( op(e0,e1) = e0
| op(e0,e1) = e1
| op(e0,e1) = e2
| op(e0,e1) = e3 )
& ( op(e0,e2) = e0
| op(e0,e2) = e1
| op(e0,e2) = e2
| op(e0,e2) = e3 )
& ( op(e0,e3) = e0
| op(e0,e3) = e1
| op(e0,e3) = e2
| op(e0,e3) = e3 )
& ( op(e1,e0) = e0
| op(e1,e0) = e1
| op(e1,e0) = e2
| op(e1,e0) = e3 )
& ( op(e1,e1) = e0
| op(e1,e1) = e1
| op(e1,e1) = e2
| op(e1,e1) = e3 )
& ( op(e1,e2) = e0
| op(e1,e2) = e1
| op(e1,e2) = e2
| op(e1,e2) = e3 )
& ( op(e1,e3) = e0
| op(e1,e3) = e1
| op(e1,e3) = e2
| op(e1,e3) = e3 )
& ( op(e2,e0) = e0
| op(e2,e0) = e1
| op(e2,e0) = e2
| op(e2,e0) = e3 )
& ( op(e2,e1) = e0
| op(e2,e1) = e1
| op(e2,e1) = e2
| op(e2,e1) = e3 )
& ( op(e2,e2) = e0
| op(e2,e2) = e1
| op(e2,e2) = e2
| op(e2,e2) = e3 )
& ( op(e2,e3) = e0
| op(e2,e3) = e1
| op(e2,e3) = e2
| op(e2,e3) = e3 )
& ( op(e3,e0) = e0
| op(e3,e0) = e1
| op(e3,e0) = e2
| op(e3,e0) = e3 )
& ( op(e3,e1) = e0
| op(e3,e1) = e1
| op(e3,e1) = e2
| op(e3,e1) = e3 )
& ( op(e3,e2) = e0
| op(e3,e2) = e1
| op(e3,e2) = e2
| op(e3,e2) = e3 )
& ( op(e3,e3) = e0
| op(e3,e3) = e1
| op(e3,e3) = e2
| op(e3,e3) = e3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 )
| ~ ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 )
| ~ ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
( op(e0,e0) = e0
| op(e0,e0) = e1
| op(e0,e0) = e2
| op(e0,e0) = e3 ),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f14,plain,
( op(e1,e1) = e0
| op(e1,e1) = e1
| op(e1,e1) = e2
| op(e1,e1) = e3 ),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f19,plain,
( op(e2,e2) = e0
| op(e2,e2) = e1
| op(e2,e2) = e2
| op(e2,e2) = e3 ),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f24,plain,
( op(e3,e3) = e0
| op(e3,e3) = e1
| op(e3,e3) = e2
| op(e3,e3) = e3 ),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f121,plain,
( ( op(e0,e0) != e0
| op(e1,e1) != e0
| op(e2,e2) != e0
| op(e3,e3) != e0 )
& ( op(e0,e0) != e1
| op(e1,e1) != e1
| op(e2,e2) != e1
| op(e3,e3) != e1 )
& ( op(e0,e0) != e2
| op(e1,e1) != e2
| op(e2,e2) != e2
| op(e3,e3) != e2 )
& ( op(e0,e0) != e3
| op(e1,e1) != e3
| op(e2,e2) != e3
| op(e3,e3) != e3 )
& ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f122,plain,
( pd0_0
=> ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 ) ) ),
introduced(predicate_definition,[f121]) ).
fof(f123,plain,
( ( op(e0,e0) != e0
| op(e1,e1) != e0
| op(e2,e2) != e0
| op(e3,e3) != e0 )
& ( op(e0,e0) != e1
| op(e1,e1) != e1
| op(e2,e2) != e1
| op(e3,e3) != e1 )
& ( op(e0,e0) != e2
| op(e1,e1) != e2
| op(e2,e2) != e2
| op(e3,e3) != e2 )
& ( op(e0,e0) != e3
| op(e1,e1) != e3
| op(e2,e2) != e3
| op(e3,e3) != e3 )
& ( pd0_0
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) ) ),
inference(formula_renaming,[status(thm)],[f121,f122]) ).
fof(f124,plain,
( op(e0,e0) != e0
| op(e1,e1) != e0
| op(e2,e2) != e0
| op(e3,e3) != e0 ),
inference(cnf_transformation,[status(esa)],[f123]) ).
fof(f125,plain,
( op(e0,e0) != e1
| op(e1,e1) != e1
| op(e2,e2) != e1
| op(e3,e3) != e1 ),
inference(cnf_transformation,[status(esa)],[f123]) ).
fof(f126,plain,
( op(e0,e0) != e2
| op(e1,e1) != e2
| op(e2,e2) != e2
| op(e3,e3) != e2 ),
inference(cnf_transformation,[status(esa)],[f123]) ).
fof(f127,plain,
( op(e0,e0) != e3
| op(e1,e1) != e3
| op(e2,e2) != e3
| op(e3,e3) != e3 ),
inference(cnf_transformation,[status(esa)],[f123]) ).
fof(f128,plain,
( pd0_0
| op(e0,e0) = e3 ),
inference(cnf_transformation,[status(esa)],[f123]) ).
fof(f129,plain,
( pd0_0
| op(e1,e1) = e3 ),
inference(cnf_transformation,[status(esa)],[f123]) ).
fof(f130,plain,
( pd0_0
| op(e2,e2) = e3 ),
inference(cnf_transformation,[status(esa)],[f123]) ).
fof(f131,plain,
( pd0_0
| op(e3,e3) = e3 ),
inference(cnf_transformation,[status(esa)],[f123]) ).
fof(f132,plain,
( ~ pd0_0
| ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 ) ),
inference(pre_NNF_transformation,[status(esa)],[f122]) ).
fof(f133,plain,
( pd0_1
=> ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 ) ) ),
introduced(predicate_definition,[f132]) ).
fof(f134,plain,
( ~ pd0_0
| pd0_1
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 ) ),
inference(formula_renaming,[status(thm)],[f132,f133]) ).
fof(f135,plain,
( ~ pd0_0
| pd0_1
| op(e0,e0) = e2 ),
inference(cnf_transformation,[status(esa)],[f134]) ).
fof(f136,plain,
( ~ pd0_0
| pd0_1
| op(e1,e1) = e2 ),
inference(cnf_transformation,[status(esa)],[f134]) ).
fof(f137,plain,
( ~ pd0_0
| pd0_1
| op(e2,e2) = e2 ),
inference(cnf_transformation,[status(esa)],[f134]) ).
fof(f138,plain,
( ~ pd0_0
| pd0_1
| op(e3,e3) = e2 ),
inference(cnf_transformation,[status(esa)],[f134]) ).
fof(f139,plain,
( ~ pd0_1
| ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 ) ),
inference(pre_NNF_transformation,[status(esa)],[f133]) ).
fof(f140,plain,
( pd0_2
=> ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 ) ),
introduced(predicate_definition,[f139]) ).
fof(f141,plain,
( ~ pd0_1
| pd0_2
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 ) ),
inference(formula_renaming,[status(thm)],[f139,f140]) ).
fof(f142,plain,
( ~ pd0_1
| pd0_2
| op(e0,e0) = e1 ),
inference(cnf_transformation,[status(esa)],[f141]) ).
fof(f143,plain,
( ~ pd0_1
| pd0_2
| op(e1,e1) = e1 ),
inference(cnf_transformation,[status(esa)],[f141]) ).
fof(f144,plain,
( ~ pd0_1
| pd0_2
| op(e2,e2) = e1 ),
inference(cnf_transformation,[status(esa)],[f141]) ).
fof(f145,plain,
( ~ pd0_1
| pd0_2
| op(e3,e3) = e1 ),
inference(cnf_transformation,[status(esa)],[f141]) ).
fof(f146,plain,
( ~ pd0_2
| ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 ) ),
inference(pre_NNF_transformation,[status(esa)],[f140]) ).
fof(f147,plain,
( ~ pd0_2
| op(e0,e0) = e0 ),
inference(cnf_transformation,[status(esa)],[f146]) ).
fof(f148,plain,
( ~ pd0_2
| op(e1,e1) = e0 ),
inference(cnf_transformation,[status(esa)],[f146]) ).
fof(f149,plain,
( ~ pd0_2
| op(e2,e2) = e0 ),
inference(cnf_transformation,[status(esa)],[f146]) ).
fof(f150,plain,
( ~ pd0_2
| op(e3,e3) = e0 ),
inference(cnf_transformation,[status(esa)],[f146]) ).
fof(f151,plain,
( spl0_0
<=> op(e0,e0) = e0 ),
introduced(split_symbol_definition) ).
fof(f154,plain,
( spl0_1
<=> op(e0,e0) = e1 ),
introduced(split_symbol_definition) ).
fof(f157,plain,
( spl0_2
<=> op(e0,e0) = e2 ),
introduced(split_symbol_definition) ).
fof(f160,plain,
( spl0_3
<=> op(e0,e0) = e3 ),
introduced(split_symbol_definition) ).
fof(f163,plain,
( spl0_0
| spl0_1
| spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f9,f151,f154,f157,f160]) ).
fof(f216,plain,
( spl0_20
<=> op(e1,e1) = e0 ),
introduced(split_symbol_definition) ).
fof(f219,plain,
( spl0_21
<=> op(e1,e1) = e1 ),
introduced(split_symbol_definition) ).
fof(f222,plain,
( spl0_22
<=> op(e1,e1) = e2 ),
introduced(split_symbol_definition) ).
fof(f225,plain,
( spl0_23
<=> op(e1,e1) = e3 ),
introduced(split_symbol_definition) ).
fof(f228,plain,
( spl0_20
| spl0_21
| spl0_22
| spl0_23 ),
inference(split_clause,[status(thm)],[f14,f216,f219,f222,f225]) ).
fof(f281,plain,
( spl0_40
<=> op(e2,e2) = e0 ),
introduced(split_symbol_definition) ).
fof(f284,plain,
( spl0_41
<=> op(e2,e2) = e1 ),
introduced(split_symbol_definition) ).
fof(f287,plain,
( spl0_42
<=> op(e2,e2) = e2 ),
introduced(split_symbol_definition) ).
fof(f290,plain,
( spl0_43
<=> op(e2,e2) = e3 ),
introduced(split_symbol_definition) ).
fof(f293,plain,
( spl0_40
| spl0_41
| spl0_42
| spl0_43 ),
inference(split_clause,[status(thm)],[f19,f281,f284,f287,f290]) ).
fof(f346,plain,
( spl0_60
<=> op(e3,e3) = e0 ),
introduced(split_symbol_definition) ).
fof(f349,plain,
( spl0_61
<=> op(e3,e3) = e1 ),
introduced(split_symbol_definition) ).
fof(f352,plain,
( spl0_62
<=> op(e3,e3) = e2 ),
introduced(split_symbol_definition) ).
fof(f355,plain,
( spl0_63
<=> op(e3,e3) = e3 ),
introduced(split_symbol_definition) ).
fof(f358,plain,
( spl0_60
| spl0_61
| spl0_62
| spl0_63 ),
inference(split_clause,[status(thm)],[f24,f346,f349,f352,f355]) ).
fof(f404,plain,
( ~ spl0_0
| ~ spl0_20
| ~ spl0_40
| ~ spl0_60 ),
inference(split_clause,[status(thm)],[f124,f151,f216,f281,f346]) ).
fof(f405,plain,
( ~ spl0_1
| ~ spl0_21
| ~ spl0_41
| ~ spl0_61 ),
inference(split_clause,[status(thm)],[f125,f154,f219,f284,f349]) ).
fof(f406,plain,
( ~ spl0_2
| ~ spl0_22
| ~ spl0_42
| ~ spl0_62 ),
inference(split_clause,[status(thm)],[f126,f157,f222,f287,f352]) ).
fof(f407,plain,
( ~ spl0_3
| ~ spl0_23
| ~ spl0_43
| ~ spl0_63 ),
inference(split_clause,[status(thm)],[f127,f160,f225,f290,f355]) ).
fof(f408,plain,
( spl0_68
<=> pd0_0 ),
introduced(split_symbol_definition) ).
fof(f411,plain,
( spl0_68
| spl0_3 ),
inference(split_clause,[status(thm)],[f128,f408,f160]) ).
fof(f412,plain,
( spl0_68
| spl0_23 ),
inference(split_clause,[status(thm)],[f129,f408,f225]) ).
fof(f413,plain,
( spl0_68
| spl0_43 ),
inference(split_clause,[status(thm)],[f130,f408,f290]) ).
fof(f414,plain,
( spl0_68
| spl0_63 ),
inference(split_clause,[status(thm)],[f131,f408,f355]) ).
fof(f415,plain,
( spl0_69
<=> pd0_1 ),
introduced(split_symbol_definition) ).
fof(f418,plain,
( ~ spl0_68
| spl0_69
| spl0_2 ),
inference(split_clause,[status(thm)],[f135,f408,f415,f157]) ).
fof(f419,plain,
( ~ spl0_68
| spl0_69
| spl0_22 ),
inference(split_clause,[status(thm)],[f136,f408,f415,f222]) ).
fof(f420,plain,
( ~ spl0_68
| spl0_69
| spl0_42 ),
inference(split_clause,[status(thm)],[f137,f408,f415,f287]) ).
fof(f421,plain,
( ~ spl0_68
| spl0_69
| spl0_62 ),
inference(split_clause,[status(thm)],[f138,f408,f415,f352]) ).
fof(f422,plain,
( spl0_70
<=> pd0_2 ),
introduced(split_symbol_definition) ).
fof(f425,plain,
( ~ spl0_69
| spl0_70
| spl0_1 ),
inference(split_clause,[status(thm)],[f142,f415,f422,f154]) ).
fof(f426,plain,
( ~ spl0_69
| spl0_70
| spl0_21 ),
inference(split_clause,[status(thm)],[f143,f415,f422,f219]) ).
fof(f427,plain,
( ~ spl0_69
| spl0_70
| spl0_41 ),
inference(split_clause,[status(thm)],[f144,f415,f422,f284]) ).
fof(f428,plain,
( ~ spl0_69
| spl0_70
| spl0_61 ),
inference(split_clause,[status(thm)],[f145,f415,f422,f349]) ).
fof(f429,plain,
( ~ spl0_70
| spl0_0 ),
inference(split_clause,[status(thm)],[f147,f422,f151]) ).
fof(f430,plain,
( ~ spl0_70
| spl0_20 ),
inference(split_clause,[status(thm)],[f148,f422,f216]) ).
fof(f431,plain,
( ~ spl0_70
| spl0_40 ),
inference(split_clause,[status(thm)],[f149,f422,f281]) ).
fof(f432,plain,
( ~ spl0_70
| spl0_60 ),
inference(split_clause,[status(thm)],[f150,f422,f346]) ).
fof(f433,plain,
$false,
inference(sat_refutation,[status(thm)],[f163,f228,f293,f358,f404,f405,f406,f407,f411,f412,f413,f414,f418,f419,f420,f421,f425,f426,f427,f428,f429,f430,f431,f432]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ALG036+1 : TPTP v8.1.2. Released v2.7.0.
% 0.13/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 30 00:03:47 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.21/0.36 % Drodi V3.6.0
% 0.21/0.36 % Refutation found
% 0.21/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.38 % Elapsed time: 0.018574 seconds
% 0.21/0.38 % CPU time: 0.030098 seconds
% 0.21/0.38 % Total memory used: 2.205 MB
% 0.21/0.38 % Net memory used: 2.188 MB
%------------------------------------------------------------------------------