TSTP Solution File: COM016+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : COM016+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n026.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 : Wed May 31 12:03:55 EDT 2023
% Result : Theorem 0.18s 0.37s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 22
% Syntax : Number of formulae : 88 ( 17 unt; 2 def)
% Number of atoms : 262 ( 16 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 286 ( 112 ~; 127 |; 26 &)
% ( 19 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 16 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 48 (; 43 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,definition,
! [W0,W1,W2] :
( ( aElement0(W0)
& aRewritingSystem0(W1)
& aElement0(W2) )
=> ( sdtmndtplgtdt0(W0,W1,W2)
<=> ( aReductOfIn0(W2,W0,W1)
| ? [W3] :
( aElement0(W3)
& aReductOfIn0(W3,W0,W1)
& sdtmndtplgtdt0(W3,W1,W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,definition,
! [W0,W1,W2] :
( ( aElement0(W0)
& aRewritingSystem0(W1)
& aElement0(W2) )
=> ( sdtmndtasgtdt0(W0,W1,W2)
<=> ( W0 = W2
| sdtmndtplgtdt0(W0,W1,W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
aRewritingSystem0(xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
( isLocallyConfluent0(xR)
& isTerminating0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
( sdtmndtplgtdt0(xa,xR,xb)
& sdtmndtplgtdt0(xa,xR,xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,conjecture,
? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtasgtdt0(W0,xR,xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtasgtdt0(W0,xR,xb) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f34,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W2)
| ( sdtmndtplgtdt0(W0,W1,W2)
<=> ( aReductOfIn0(W2,W0,W1)
| ? [W3] :
( aElement0(W3)
& aReductOfIn0(W3,W0,W1)
& sdtmndtplgtdt0(W3,W1,W2) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f35,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W2)
| ( ( ~ sdtmndtplgtdt0(W0,W1,W2)
| aReductOfIn0(W2,W0,W1)
| ? [W3] :
( aElement0(W3)
& aReductOfIn0(W3,W0,W1)
& sdtmndtplgtdt0(W3,W1,W2) ) )
& ( sdtmndtplgtdt0(W0,W1,W2)
| ( ~ aReductOfIn0(W2,W0,W1)
& ! [W3] :
( ~ aElement0(W3)
| ~ aReductOfIn0(W3,W0,W1)
| ~ sdtmndtplgtdt0(W3,W1,W2) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f34]) ).
fof(f36,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W2)
| ( ( ~ sdtmndtplgtdt0(W0,W1,W2)
| aReductOfIn0(W2,W0,W1)
| ( aElement0(sk0_0(W2,W1,W0))
& aReductOfIn0(sk0_0(W2,W1,W0),W0,W1)
& sdtmndtplgtdt0(sk0_0(W2,W1,W0),W1,W2) ) )
& ( sdtmndtplgtdt0(W0,W1,W2)
| ( ~ aReductOfIn0(W2,W0,W1)
& ! [W3] :
( ~ aElement0(W3)
| ~ aReductOfIn0(W3,W0,W1)
| ~ sdtmndtplgtdt0(W3,W1,W2) ) ) ) ) ),
inference(skolemization,[status(esa)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| aReductOfIn0(X2,X0,X1)
| aElement0(sk0_0(X2,X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| aReductOfIn0(X2,X0,X1)
| aReductOfIn0(sk0_0(X2,X1,X0),X0,X1) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| aReductOfIn0(X2,X0,X1)
| sdtmndtplgtdt0(sk0_0(X2,X1,X0),X1,X2) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f44,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W2)
| ( sdtmndtasgtdt0(W0,W1,W2)
<=> ( W0 = W2
| sdtmndtplgtdt0(W0,W1,W2) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f45,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W2)
| ( ( ~ sdtmndtasgtdt0(W0,W1,W2)
| W0 = W2
| sdtmndtplgtdt0(W0,W1,W2) )
& ( sdtmndtasgtdt0(W0,W1,W2)
| ( W0 != W2
& ~ sdtmndtplgtdt0(W0,W1,W2) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f44]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| sdtmndtasgtdt0(X0,X1,X2)
| X0 != X2 ),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| sdtmndtasgtdt0(X0,X1,X2)
| ~ sdtmndtplgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f96,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f98,plain,
isTerminating0(xR),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f99,plain,
aElement0(xa),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f100,plain,
aElement0(xb),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f101,plain,
aElement0(xc),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f107,plain,
sdtmndtplgtdt0(xa,xR,xb),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f109,plain,
! [W0] :
( ~ aElement0(W0)
| ~ aReductOfIn0(W0,xa,xR)
| ~ sdtmndtasgtdt0(W0,xR,xb) ),
inference(pre_NNF_transformation,[status(esa)],[f21]) ).
fof(f110,plain,
! [X0] :
( ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR)
| ~ sdtmndtasgtdt0(X0,xR,xb) ),
inference(cnf_transformation,[status(esa)],[f109]) ).
fof(f111,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X0)
| ~ aElement0(X1)
| sdtmndtasgtdt0(xb,X0,X1)
| xb != X1 ),
inference(resolution,[status(thm)],[f47,f100]) ).
fof(f113,plain,
! [X0] :
( ~ aElement0(X0)
| sdtmndtasgtdt0(xb,xR,X0)
| xb != X0 ),
inference(resolution,[status(thm)],[f111,f96]) ).
fof(f115,plain,
( spl0_0
<=> sdtmndtasgtdt0(xb,xR,xb) ),
introduced(split_symbol_definition) ).
fof(f116,plain,
( sdtmndtasgtdt0(xb,xR,xb)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,plain,
( spl0_1
<=> xb = xb ),
introduced(split_symbol_definition) ).
fof(f120,plain,
( xb != xb
| spl0_1 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,plain,
( sdtmndtasgtdt0(xb,xR,xb)
| xb != xb ),
inference(resolution,[status(thm)],[f113,f100]) ).
fof(f122,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f121,f115,f118]) ).
fof(f131,plain,
( $false
| spl0_1 ),
inference(equality_resolution,[status(esa)],[f120]) ).
fof(f132,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f131]) ).
fof(f133,plain,
( spl0_4
<=> aElement0(xb) ),
introduced(split_symbol_definition) ).
fof(f135,plain,
( ~ aElement0(xb)
| spl0_4 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( spl0_5
<=> aReductOfIn0(xb,xa,xR) ),
introduced(split_symbol_definition) ).
fof(f139,plain,
( ~ aElement0(xb)
| ~ aReductOfIn0(xb,xa,xR)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f116,f110]) ).
fof(f140,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f139,f133,f136,f115]) ).
fof(f141,plain,
( spl0_6
<=> aRewritingSystem0(xR) ),
introduced(split_symbol_definition) ).
fof(f143,plain,
( ~ aRewritingSystem0(xR)
| spl0_6 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f149,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f143,f96]) ).
fof(f150,plain,
spl0_6,
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f151,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f135,f100]) ).
fof(f152,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f151]) ).
fof(f168,plain,
( spl0_11
<=> aElement0(xa) ),
introduced(split_symbol_definition) ).
fof(f170,plain,
( ~ aElement0(xa)
| spl0_11 ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f176,plain,
( $false
| spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f99]) ).
fof(f177,plain,
spl0_11,
inference(contradiction_clause,[status(thm)],[f176]) ).
fof(f199,plain,
( spl0_18
<=> xc = xc ),
introduced(split_symbol_definition) ).
fof(f201,plain,
( xc != xc
| spl0_18 ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f214,plain,
( $false
| spl0_18 ),
inference(equality_resolution,[status(esa)],[f201]) ).
fof(f215,plain,
spl0_18,
inference(contradiction_clause,[status(thm)],[f214]) ).
fof(f216,plain,
( spl0_21
<=> aElement0(xc) ),
introduced(split_symbol_definition) ).
fof(f218,plain,
( ~ aElement0(xc)
| spl0_21 ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f224,plain,
( $false
| spl0_21 ),
inference(forward_subsumption_resolution,[status(thm)],[f218,f101]) ).
fof(f225,plain,
spl0_21,
inference(contradiction_clause,[status(thm)],[f224]) ).
fof(f226,plain,
( spl0_23
<=> isTerminating0(xR) ),
introduced(split_symbol_definition) ).
fof(f228,plain,
( ~ isTerminating0(xR)
| spl0_23 ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f316,plain,
( $false
| spl0_23 ),
inference(forward_subsumption_resolution,[status(thm)],[f228,f98]) ).
fof(f317,plain,
spl0_23,
inference(contradiction_clause,[status(thm)],[f316]) ).
fof(f324,plain,
( spl0_39
<=> sdtmndtplgtdt0(sk0_0(xb,xR,xa),xR,xb) ),
introduced(split_symbol_definition) ).
fof(f325,plain,
( sdtmndtplgtdt0(sk0_0(xb,xR,xa),xR,xb)
| ~ spl0_39 ),
inference(component_clause,[status(thm)],[f324]) ).
fof(f327,plain,
( ~ aElement0(xa)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xb)
| aReductOfIn0(xb,xa,xR)
| sdtmndtplgtdt0(sk0_0(xb,xR,xa),xR,xb) ),
inference(resolution,[status(thm)],[f39,f107]) ).
fof(f328,plain,
( ~ spl0_11
| ~ spl0_6
| ~ spl0_4
| spl0_5
| spl0_39 ),
inference(split_clause,[status(thm)],[f327,f168,f141,f133,f136,f324]) ).
fof(f329,plain,
( spl0_40
<=> aElement0(sk0_0(xb,xR,xa)) ),
introduced(split_symbol_definition) ).
fof(f350,plain,
( spl0_45
<=> sdtmndtasgtdt0(sk0_0(xb,xR,xa),xR,xb) ),
introduced(split_symbol_definition) ).
fof(f351,plain,
( sdtmndtasgtdt0(sk0_0(xb,xR,xa),xR,xb)
| ~ spl0_45 ),
inference(component_clause,[status(thm)],[f350]) ).
fof(f353,plain,
( ~ aElement0(sk0_0(xb,xR,xa))
| ~ aRewritingSystem0(xR)
| ~ aElement0(xb)
| sdtmndtasgtdt0(sk0_0(xb,xR,xa),xR,xb)
| ~ spl0_39 ),
inference(resolution,[status(thm)],[f325,f48]) ).
fof(f354,plain,
( ~ spl0_40
| ~ spl0_6
| ~ spl0_4
| spl0_45
| ~ spl0_39 ),
inference(split_clause,[status(thm)],[f353,f329,f141,f133,f350,f324]) ).
fof(f360,plain,
( ~ aElement0(xa)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xb)
| aReductOfIn0(xb,xa,xR)
| aElement0(sk0_0(xb,xR,xa)) ),
inference(resolution,[status(thm)],[f37,f107]) ).
fof(f361,plain,
( ~ spl0_11
| ~ spl0_6
| ~ spl0_4
| spl0_5
| spl0_40 ),
inference(split_clause,[status(thm)],[f360,f168,f141,f133,f136,f329]) ).
fof(f393,plain,
( spl0_53
<=> aReductOfIn0(sk0_0(xb,xR,xa),xa,xR) ),
introduced(split_symbol_definition) ).
fof(f396,plain,
( ~ aElement0(sk0_0(xb,xR,xa))
| ~ aReductOfIn0(sk0_0(xb,xR,xa),xa,xR)
| ~ spl0_45 ),
inference(resolution,[status(thm)],[f351,f110]) ).
fof(f397,plain,
( ~ spl0_40
| ~ spl0_53
| ~ spl0_45 ),
inference(split_clause,[status(thm)],[f396,f329,f393,f350]) ).
fof(f423,plain,
( spl0_58
<=> sk0_0(xb,xR,xa) = sk0_0(xb,xR,xa) ),
introduced(split_symbol_definition) ).
fof(f425,plain,
( sk0_0(xb,xR,xa) != sk0_0(xb,xR,xa)
| spl0_58 ),
inference(component_clause,[status(thm)],[f423]) ).
fof(f440,plain,
( $false
| spl0_58 ),
inference(equality_resolution,[status(esa)],[f425]) ).
fof(f441,plain,
spl0_58,
inference(contradiction_clause,[status(thm)],[f440]) ).
fof(f533,plain,
( spl0_82
<=> sk0_13(xb,xb,xb) = sk0_13(xb,xb,xb) ),
introduced(split_symbol_definition) ).
fof(f535,plain,
( sk0_13(xb,xb,xb) != sk0_13(xb,xb,xb)
| spl0_82 ),
inference(component_clause,[status(thm)],[f533]) ).
fof(f558,plain,
( $false
| spl0_82 ),
inference(equality_resolution,[status(esa)],[f535]) ).
fof(f559,plain,
spl0_82,
inference(contradiction_clause,[status(thm)],[f558]) ).
fof(f1296,plain,
( ~ aElement0(xa)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xb)
| aReductOfIn0(xb,xa,xR)
| aReductOfIn0(sk0_0(xb,xR,xa),xa,xR) ),
inference(resolution,[status(thm)],[f38,f107]) ).
fof(f1297,plain,
( ~ spl0_11
| ~ spl0_6
| ~ spl0_4
| spl0_5
| spl0_53 ),
inference(split_clause,[status(thm)],[f1296,f168,f141,f133,f136,f393]) ).
fof(f1298,plain,
$false,
inference(sat_refutation,[status(thm)],[f122,f132,f140,f150,f152,f177,f215,f225,f317,f328,f354,f361,f397,f441,f559,f1297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM016+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue May 30 12:05:28 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % Drodi V3.5.1
% 0.18/0.37 % Refutation found
% 0.18/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.39 % Elapsed time: 0.050777 seconds
% 0.18/0.39 % CPU time: 0.247438 seconds
% 0.18/0.39 % Memory used: 21.881 MB
%------------------------------------------------------------------------------