TSTP Solution File: COM016+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% 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 : n012.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 20:14:02 EDT 2024
% Result : Theorem 0.17s 0.33s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 73 ( 14 unt; 2 def)
% Number of atoms : 233 ( 5 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 267 ( 107 ~; 115 |; 27 &)
% ( 14 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 11 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 56 ( 51 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aRewritingSystem0(W1) )
=> ! [W2] :
( aReductOfIn0(W2,W0,W1)
=> aElement0(W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f28,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aRewritingSystem0(W1)
| ! [W2] :
( ~ aReductOfIn0(W2,W0,W1)
| aElement0(W2) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
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(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,
! [X2,X1] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| sdtmndtasgtdt0(X2,X1,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f47]) ).
fof(f112,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| sdtmndtasgtdt0(X0,X1,X0) ),
inference(duplicate_literals_removal,[status(esa)],[f111]) ).
fof(f113,plain,
! [X0] :
( ~ aRewritingSystem0(X0)
| sdtmndtasgtdt0(xb,X0,xb) ),
inference(resolution,[status(thm)],[f112,f100]) ).
fof(f115,plain,
sdtmndtasgtdt0(xb,xR,xb),
inference(resolution,[status(thm)],[f113,f96]) ).
fof(f116,plain,
( spl0_0
<=> aElement0(xb) ),
introduced(split_symbol_definition) ).
fof(f118,plain,
( ~ aElement0(xb)
| spl0_0 ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f119,plain,
( spl0_1
<=> aReductOfIn0(xb,xa,xR) ),
introduced(split_symbol_definition) ).
fof(f122,plain,
( ~ aElement0(xb)
| ~ aReductOfIn0(xb,xa,xR) ),
inference(resolution,[status(thm)],[f115,f110]) ).
fof(f123,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f122,f116,f119]) ).
fof(f127,plain,
( spl0_3
<=> aRewritingSystem0(xR) ),
introduced(split_symbol_definition) ).
fof(f129,plain,
( ~ aRewritingSystem0(xR)
| spl0_3 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f132,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f129,f96]) ).
fof(f133,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f132]) ).
fof(f134,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f118,f100]) ).
fof(f135,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f134]) ).
fof(f140,plain,
( spl0_5
<=> aElement0(xa) ),
introduced(split_symbol_definition) ).
fof(f142,plain,
( ~ aElement0(xa)
| spl0_5 ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f145,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f99]) ).
fof(f146,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f145]) ).
fof(f152,plain,
( spl0_7
<=> aElement0(xc) ),
introduced(split_symbol_definition) ).
fof(f154,plain,
( ~ aElement0(xc)
| spl0_7 ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f157,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f154,f101]) ).
fof(f158,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f157]) ).
fof(f237,plain,
( spl0_19
<=> isTerminating0(xR) ),
introduced(split_symbol_definition) ).
fof(f239,plain,
( ~ isTerminating0(xR)
| spl0_19 ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f245,plain,
( $false
| spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f239,f98]) ).
fof(f246,plain,
spl0_19,
inference(contradiction_clause,[status(thm)],[f245]) ).
fof(f258,plain,
( spl0_23
<=> aReductOfIn0(sk0_0(xb,xR,xa),xa,xR) ),
introduced(split_symbol_definition) ).
fof(f259,plain,
( aReductOfIn0(sk0_0(xb,xR,xa),xa,xR)
| ~ spl0_23 ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,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(f262,plain,
( ~ spl0_5
| ~ spl0_3
| ~ spl0_0
| spl0_1
| spl0_23 ),
inference(split_clause,[status(thm)],[f261,f140,f127,f116,f119,f258]) ).
fof(f268,plain,
( spl0_25
<=> aElement0(sk0_0(xb,xR,xa)) ),
introduced(split_symbol_definition) ).
fof(f271,plain,
( ~ aElement0(xa)
| ~ aRewritingSystem0(xR)
| aElement0(sk0_0(xb,xR,xa))
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f259,f29]) ).
fof(f272,plain,
( ~ spl0_5
| ~ spl0_3
| spl0_25
| ~ spl0_23 ),
inference(split_clause,[status(thm)],[f271,f140,f127,f268,f258]) ).
fof(f337,plain,
( spl0_38
<=> sdtmndtplgtdt0(sk0_0(xb,xR,xa),xR,xb) ),
introduced(split_symbol_definition) ).
fof(f338,plain,
( sdtmndtplgtdt0(sk0_0(xb,xR,xa),xR,xb)
| ~ spl0_38 ),
inference(component_clause,[status(thm)],[f337]) ).
fof(f340,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(f341,plain,
( ~ spl0_5
| ~ spl0_3
| ~ spl0_0
| spl0_1
| spl0_38 ),
inference(split_clause,[status(thm)],[f340,f140,f127,f116,f119,f337]) ).
fof(f375,plain,
( spl0_46
<=> sdtmndtasgtdt0(sk0_0(xb,xR,xa),xR,xb) ),
introduced(split_symbol_definition) ).
fof(f376,plain,
( sdtmndtasgtdt0(sk0_0(xb,xR,xa),xR,xb)
| ~ spl0_46 ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f378,plain,
( ~ aElement0(sk0_0(xb,xR,xa))
| ~ aRewritingSystem0(xR)
| ~ aElement0(xb)
| sdtmndtasgtdt0(sk0_0(xb,xR,xa),xR,xb)
| ~ spl0_38 ),
inference(resolution,[status(thm)],[f338,f48]) ).
fof(f379,plain,
( ~ spl0_25
| ~ spl0_3
| ~ spl0_0
| spl0_46
| ~ spl0_38 ),
inference(split_clause,[status(thm)],[f378,f268,f127,f116,f375,f337]) ).
fof(f384,plain,
( ~ aElement0(sk0_0(xb,xR,xa))
| ~ aReductOfIn0(sk0_0(xb,xR,xa),xa,xR)
| ~ spl0_46 ),
inference(resolution,[status(thm)],[f376,f110]) ).
fof(f385,plain,
( ~ spl0_25
| ~ spl0_23
| ~ spl0_46 ),
inference(split_clause,[status(thm)],[f384,f268,f258,f375]) ).
fof(f396,plain,
$false,
inference(sat_refutation,[status(thm)],[f123,f133,f135,f146,f158,f246,f262,f272,f341,f379,f385]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : COM016+1 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n012.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Apr 30 00:57:41 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.17/0.32 % Drodi V3.6.0
% 0.17/0.33 % Refutation found
% 0.17/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.34 % Elapsed time: 0.022282 seconds
% 0.17/0.34 % CPU time: 0.067414 seconds
% 0.17/0.34 % Total memory used: 13.669 MB
% 0.17/0.34 % Net memory used: 13.638 MB
%------------------------------------------------------------------------------