TSTP Solution File: COM017+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : COM017+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sat Dec 25 05:47:54 EST 2010
% Result : Theorem 0.29s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 8 unt; 0 def)
% Number of atoms : 319 ( 0 equ)
% Maximal formula atoms : 44 ( 6 avg)
% Number of connectives : 473 ( 206 ~; 204 |; 58 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 110 ( 0 sgn 43 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(4,axiom,
aRewritingSystem0(xR),
file('/tmp/tmpvZwfpk/sel_COM017+1.p_1',m__656) ).
fof(5,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aRewritingSystem0(X2) )
=> ! [X3] :
( aReductOfIn0(X3,X1,X2)
=> aElement0(X3) ) ),
file('/tmp/tmpvZwfpk/sel_COM017+1.p_1',mReduct) ).
fof(8,axiom,
! [X1] :
( aRewritingSystem0(X1)
=> ( isLocallyConfluent0(X1)
<=> ! [X2,X3,X4] :
( ( aElement0(X2)
& aElement0(X3)
& aElement0(X4)
& aReductOfIn0(X3,X2,X1)
& aReductOfIn0(X4,X2,X1) )
=> ? [X5] :
( aElement0(X5)
& sdtmndtasgtdt0(X3,X1,X5)
& sdtmndtasgtdt0(X4,X1,X5) ) ) ) ),
file('/tmp/tmpvZwfpk/sel_COM017+1.p_1',mWCRDef) ).
fof(11,conjecture,
? [X1] :
( aElement0(X1)
& sdtmndtasgtdt0(xu,xR,X1)
& sdtmndtasgtdt0(xv,xR,X1) ),
file('/tmp/tmpvZwfpk/sel_COM017+1.p_1',m__) ).
fof(12,axiom,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
file('/tmp/tmpvZwfpk/sel_COM017+1.p_1',m__731) ).
fof(13,axiom,
( aElement0(xu)
& aReductOfIn0(xu,xa,xR)
& sdtmndtasgtdt0(xu,xR,xb) ),
file('/tmp/tmpvZwfpk/sel_COM017+1.p_1',m__755) ).
fof(14,axiom,
( aElement0(xv)
& aReductOfIn0(xv,xa,xR)
& sdtmndtasgtdt0(xv,xR,xc) ),
file('/tmp/tmpvZwfpk/sel_COM017+1.p_1',m__779) ).
fof(20,axiom,
( isLocallyConfluent0(xR)
& isTerminating0(xR) ),
file('/tmp/tmpvZwfpk/sel_COM017+1.p_1',m__656_01) ).
fof(23,negated_conjecture,
~ ? [X1] :
( aElement0(X1)
& sdtmndtasgtdt0(xu,xR,X1)
& sdtmndtasgtdt0(xv,xR,X1) ),
inference(assume_negation,[status(cth)],[11]) ).
cnf(48,plain,
aRewritingSystem0(xR),
inference(split_conjunct,[status(thm)],[4]) ).
fof(49,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ! [X3] :
( ~ aReductOfIn0(X3,X1,X2)
| aElement0(X3) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(50,plain,
! [X4,X5] :
( ~ aElement0(X4)
| ~ aRewritingSystem0(X5)
| ! [X6] :
( ~ aReductOfIn0(X6,X4,X5)
| aElement0(X6) ) ),
inference(variable_rename,[status(thm)],[49]) ).
fof(51,plain,
! [X4,X5,X6] :
( ~ aReductOfIn0(X6,X4,X5)
| aElement0(X6)
| ~ aElement0(X4)
| ~ aRewritingSystem0(X5) ),
inference(shift_quantors,[status(thm)],[50]) ).
cnf(52,plain,
( aElement0(X3)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aReductOfIn0(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[51]) ).
fof(64,plain,
! [X1] :
( ~ aRewritingSystem0(X1)
| ( ( ~ isLocallyConfluent0(X1)
| ! [X2,X3,X4] :
( ~ aElement0(X2)
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ aReductOfIn0(X3,X2,X1)
| ~ aReductOfIn0(X4,X2,X1)
| ? [X5] :
( aElement0(X5)
& sdtmndtasgtdt0(X3,X1,X5)
& sdtmndtasgtdt0(X4,X1,X5) ) ) )
& ( ? [X2,X3,X4] :
( aElement0(X2)
& aElement0(X3)
& aElement0(X4)
& aReductOfIn0(X3,X2,X1)
& aReductOfIn0(X4,X2,X1)
& ! [X5] :
( ~ aElement0(X5)
| ~ sdtmndtasgtdt0(X3,X1,X5)
| ~ sdtmndtasgtdt0(X4,X1,X5) ) )
| isLocallyConfluent0(X1) ) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(65,plain,
! [X6] :
( ~ aRewritingSystem0(X6)
| ( ( ~ isLocallyConfluent0(X6)
| ! [X7,X8,X9] :
( ~ aElement0(X7)
| ~ aElement0(X8)
| ~ aElement0(X9)
| ~ aReductOfIn0(X8,X7,X6)
| ~ aReductOfIn0(X9,X7,X6)
| ? [X10] :
( aElement0(X10)
& sdtmndtasgtdt0(X8,X6,X10)
& sdtmndtasgtdt0(X9,X6,X10) ) ) )
& ( ? [X11,X12,X13] :
( aElement0(X11)
& aElement0(X12)
& aElement0(X13)
& aReductOfIn0(X12,X11,X6)
& aReductOfIn0(X13,X11,X6)
& ! [X14] :
( ~ aElement0(X14)
| ~ sdtmndtasgtdt0(X12,X6,X14)
| ~ sdtmndtasgtdt0(X13,X6,X14) ) )
| isLocallyConfluent0(X6) ) ) ),
inference(variable_rename,[status(thm)],[64]) ).
fof(66,plain,
! [X6] :
( ~ aRewritingSystem0(X6)
| ( ( ~ isLocallyConfluent0(X6)
| ! [X7,X8,X9] :
( ~ aElement0(X7)
| ~ aElement0(X8)
| ~ aElement0(X9)
| ~ aReductOfIn0(X8,X7,X6)
| ~ aReductOfIn0(X9,X7,X6)
| ( aElement0(esk7_4(X6,X7,X8,X9))
& sdtmndtasgtdt0(X8,X6,esk7_4(X6,X7,X8,X9))
& sdtmndtasgtdt0(X9,X6,esk7_4(X6,X7,X8,X9)) ) ) )
& ( ( aElement0(esk8_1(X6))
& aElement0(esk9_1(X6))
& aElement0(esk10_1(X6))
& aReductOfIn0(esk9_1(X6),esk8_1(X6),X6)
& aReductOfIn0(esk10_1(X6),esk8_1(X6),X6)
& ! [X14] :
( ~ aElement0(X14)
| ~ sdtmndtasgtdt0(esk9_1(X6),X6,X14)
| ~ sdtmndtasgtdt0(esk10_1(X6),X6,X14) ) )
| isLocallyConfluent0(X6) ) ) ),
inference(skolemize,[status(esa)],[65]) ).
fof(67,plain,
! [X6,X7,X8,X9,X14] :
( ( ( ( ( ~ aElement0(X14)
| ~ sdtmndtasgtdt0(esk9_1(X6),X6,X14)
| ~ sdtmndtasgtdt0(esk10_1(X6),X6,X14) )
& aElement0(esk8_1(X6))
& aElement0(esk9_1(X6))
& aElement0(esk10_1(X6))
& aReductOfIn0(esk9_1(X6),esk8_1(X6),X6)
& aReductOfIn0(esk10_1(X6),esk8_1(X6),X6) )
| isLocallyConfluent0(X6) )
& ( ~ aElement0(X7)
| ~ aElement0(X8)
| ~ aElement0(X9)
| ~ aReductOfIn0(X8,X7,X6)
| ~ aReductOfIn0(X9,X7,X6)
| ( aElement0(esk7_4(X6,X7,X8,X9))
& sdtmndtasgtdt0(X8,X6,esk7_4(X6,X7,X8,X9))
& sdtmndtasgtdt0(X9,X6,esk7_4(X6,X7,X8,X9)) )
| ~ isLocallyConfluent0(X6) ) )
| ~ aRewritingSystem0(X6) ),
inference(shift_quantors,[status(thm)],[66]) ).
fof(68,plain,
! [X6,X7,X8,X9,X14] :
( ( ~ aElement0(X14)
| ~ sdtmndtasgtdt0(esk9_1(X6),X6,X14)
| ~ sdtmndtasgtdt0(esk10_1(X6),X6,X14)
| isLocallyConfluent0(X6)
| ~ aRewritingSystem0(X6) )
& ( aElement0(esk8_1(X6))
| isLocallyConfluent0(X6)
| ~ aRewritingSystem0(X6) )
& ( aElement0(esk9_1(X6))
| isLocallyConfluent0(X6)
| ~ aRewritingSystem0(X6) )
& ( aElement0(esk10_1(X6))
| isLocallyConfluent0(X6)
| ~ aRewritingSystem0(X6) )
& ( aReductOfIn0(esk9_1(X6),esk8_1(X6),X6)
| isLocallyConfluent0(X6)
| ~ aRewritingSystem0(X6) )
& ( aReductOfIn0(esk10_1(X6),esk8_1(X6),X6)
| isLocallyConfluent0(X6)
| ~ aRewritingSystem0(X6) )
& ( aElement0(esk7_4(X6,X7,X8,X9))
| ~ aElement0(X7)
| ~ aElement0(X8)
| ~ aElement0(X9)
| ~ aReductOfIn0(X8,X7,X6)
| ~ aReductOfIn0(X9,X7,X6)
| ~ isLocallyConfluent0(X6)
| ~ aRewritingSystem0(X6) )
& ( sdtmndtasgtdt0(X8,X6,esk7_4(X6,X7,X8,X9))
| ~ aElement0(X7)
| ~ aElement0(X8)
| ~ aElement0(X9)
| ~ aReductOfIn0(X8,X7,X6)
| ~ aReductOfIn0(X9,X7,X6)
| ~ isLocallyConfluent0(X6)
| ~ aRewritingSystem0(X6) )
& ( sdtmndtasgtdt0(X9,X6,esk7_4(X6,X7,X8,X9))
| ~ aElement0(X7)
| ~ aElement0(X8)
| ~ aElement0(X9)
| ~ aReductOfIn0(X8,X7,X6)
| ~ aReductOfIn0(X9,X7,X6)
| ~ isLocallyConfluent0(X6)
| ~ aRewritingSystem0(X6) ) ),
inference(distribute,[status(thm)],[67]) ).
cnf(69,plain,
( sdtmndtasgtdt0(X2,X1,esk7_4(X1,X3,X4,X2))
| ~ aRewritingSystem0(X1)
| ~ isLocallyConfluent0(X1)
| ~ aReductOfIn0(X2,X3,X1)
| ~ aReductOfIn0(X4,X3,X1)
| ~ aElement0(X2)
| ~ aElement0(X4)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[68]) ).
cnf(70,plain,
( sdtmndtasgtdt0(X4,X1,esk7_4(X1,X3,X4,X2))
| ~ aRewritingSystem0(X1)
| ~ isLocallyConfluent0(X1)
| ~ aReductOfIn0(X2,X3,X1)
| ~ aReductOfIn0(X4,X3,X1)
| ~ aElement0(X2)
| ~ aElement0(X4)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[68]) ).
cnf(71,plain,
( aElement0(esk7_4(X1,X3,X4,X2))
| ~ aRewritingSystem0(X1)
| ~ isLocallyConfluent0(X1)
| ~ aReductOfIn0(X2,X3,X1)
| ~ aReductOfIn0(X4,X3,X1)
| ~ aElement0(X2)
| ~ aElement0(X4)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[68]) ).
fof(83,negated_conjecture,
! [X1] :
( ~ aElement0(X1)
| ~ sdtmndtasgtdt0(xu,xR,X1)
| ~ sdtmndtasgtdt0(xv,xR,X1) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(84,negated_conjecture,
! [X2] :
( ~ aElement0(X2)
| ~ sdtmndtasgtdt0(xu,xR,X2)
| ~ sdtmndtasgtdt0(xv,xR,X2) ),
inference(variable_rename,[status(thm)],[83]) ).
cnf(85,negated_conjecture,
( ~ sdtmndtasgtdt0(xv,xR,X1)
| ~ sdtmndtasgtdt0(xu,xR,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[84]) ).
cnf(88,plain,
aElement0(xa),
inference(split_conjunct,[status(thm)],[12]) ).
cnf(90,plain,
aReductOfIn0(xu,xa,xR),
inference(split_conjunct,[status(thm)],[13]) ).
cnf(93,plain,
aReductOfIn0(xv,xa,xR),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(131,plain,
isLocallyConfluent0(xR),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(248,plain,
( aElement0(esk7_4(X1,X3,X4,X2))
| ~ isLocallyConfluent0(X1)
| ~ aReductOfIn0(X4,X3,X1)
| ~ aReductOfIn0(X2,X3,X1)
| ~ aElement0(X4)
| ~ aElement0(X3)
| ~ aRewritingSystem0(X1) ),
inference(csr,[status(thm)],[71,52]) ).
cnf(249,plain,
( aElement0(esk7_4(X1,X3,X4,X2))
| ~ isLocallyConfluent0(X1)
| ~ aReductOfIn0(X4,X3,X1)
| ~ aReductOfIn0(X2,X3,X1)
| ~ aElement0(X3)
| ~ aRewritingSystem0(X1) ),
inference(csr,[status(thm)],[248,52]) ).
cnf(271,plain,
( sdtmndtasgtdt0(X4,X1,esk7_4(X1,X3,X4,X2))
| ~ isLocallyConfluent0(X1)
| ~ aReductOfIn0(X4,X3,X1)
| ~ aReductOfIn0(X2,X3,X1)
| ~ aElement0(X4)
| ~ aElement0(X3)
| ~ aRewritingSystem0(X1) ),
inference(csr,[status(thm)],[70,52]) ).
cnf(272,plain,
( sdtmndtasgtdt0(X4,X1,esk7_4(X1,X3,X4,X2))
| ~ isLocallyConfluent0(X1)
| ~ aReductOfIn0(X4,X3,X1)
| ~ aReductOfIn0(X2,X3,X1)
| ~ aElement0(X3)
| ~ aRewritingSystem0(X1) ),
inference(csr,[status(thm)],[271,52]) ).
cnf(273,negated_conjecture,
( ~ sdtmndtasgtdt0(xu,xR,esk7_4(xR,X1,xv,X2))
| ~ aElement0(esk7_4(xR,X1,xv,X2))
| ~ isLocallyConfluent0(xR)
| ~ aReductOfIn0(xv,X1,xR)
| ~ aReductOfIn0(X2,X1,xR)
| ~ aElement0(X1)
| ~ aRewritingSystem0(xR) ),
inference(spm,[status(thm)],[85,272,theory(equality)]) ).
cnf(277,negated_conjecture,
( ~ sdtmndtasgtdt0(xu,xR,esk7_4(xR,X1,xv,X2))
| ~ aElement0(esk7_4(xR,X1,xv,X2))
| $false
| ~ aReductOfIn0(xv,X1,xR)
| ~ aReductOfIn0(X2,X1,xR)
| ~ aElement0(X1)
| ~ aRewritingSystem0(xR) ),
inference(rw,[status(thm)],[273,131,theory(equality)]) ).
cnf(278,negated_conjecture,
( ~ sdtmndtasgtdt0(xu,xR,esk7_4(xR,X1,xv,X2))
| ~ aElement0(esk7_4(xR,X1,xv,X2))
| $false
| ~ aReductOfIn0(xv,X1,xR)
| ~ aReductOfIn0(X2,X1,xR)
| ~ aElement0(X1)
| $false ),
inference(rw,[status(thm)],[277,48,theory(equality)]) ).
cnf(279,negated_conjecture,
( ~ sdtmndtasgtdt0(xu,xR,esk7_4(xR,X1,xv,X2))
| ~ aElement0(esk7_4(xR,X1,xv,X2))
| ~ aReductOfIn0(xv,X1,xR)
| ~ aReductOfIn0(X2,X1,xR)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[278,theory(equality)]) ).
cnf(280,plain,
( sdtmndtasgtdt0(X2,X1,esk7_4(X1,X3,X4,X2))
| ~ isLocallyConfluent0(X1)
| ~ aReductOfIn0(X4,X3,X1)
| ~ aReductOfIn0(X2,X3,X1)
| ~ aElement0(X4)
| ~ aElement0(X3)
| ~ aRewritingSystem0(X1) ),
inference(csr,[status(thm)],[69,52]) ).
cnf(281,plain,
( sdtmndtasgtdt0(X2,X1,esk7_4(X1,X3,X4,X2))
| ~ isLocallyConfluent0(X1)
| ~ aReductOfIn0(X4,X3,X1)
| ~ aReductOfIn0(X2,X3,X1)
| ~ aElement0(X3)
| ~ aRewritingSystem0(X1) ),
inference(csr,[status(thm)],[280,52]) ).
cnf(989,negated_conjecture,
( ~ aReductOfIn0(xv,X1,xR)
| ~ aReductOfIn0(xu,X1,xR)
| ~ aElement0(esk7_4(xR,X1,xv,xu))
| ~ aElement0(X1)
| ~ isLocallyConfluent0(xR)
| ~ aRewritingSystem0(xR) ),
inference(spm,[status(thm)],[279,281,theory(equality)]) ).
cnf(990,negated_conjecture,
( ~ aReductOfIn0(xv,X1,xR)
| ~ aReductOfIn0(xu,X1,xR)
| ~ aElement0(esk7_4(xR,X1,xv,xu))
| ~ aElement0(X1)
| $false
| ~ aRewritingSystem0(xR) ),
inference(rw,[status(thm)],[989,131,theory(equality)]) ).
cnf(991,negated_conjecture,
( ~ aReductOfIn0(xv,X1,xR)
| ~ aReductOfIn0(xu,X1,xR)
| ~ aElement0(esk7_4(xR,X1,xv,xu))
| ~ aElement0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[990,48,theory(equality)]) ).
cnf(992,negated_conjecture,
( ~ aReductOfIn0(xv,X1,xR)
| ~ aReductOfIn0(xu,X1,xR)
| ~ aElement0(esk7_4(xR,X1,xv,xu))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[991,theory(equality)]) ).
cnf(993,negated_conjecture,
( ~ aReductOfIn0(xv,X1,xR)
| ~ aReductOfIn0(xu,X1,xR)
| ~ aElement0(X1)
| ~ isLocallyConfluent0(xR)
| ~ aRewritingSystem0(xR) ),
inference(spm,[status(thm)],[992,249,theory(equality)]) ).
cnf(994,negated_conjecture,
( ~ aReductOfIn0(xv,X1,xR)
| ~ aReductOfIn0(xu,X1,xR)
| ~ aElement0(X1)
| $false
| ~ aRewritingSystem0(xR) ),
inference(rw,[status(thm)],[993,131,theory(equality)]) ).
cnf(995,negated_conjecture,
( ~ aReductOfIn0(xv,X1,xR)
| ~ aReductOfIn0(xu,X1,xR)
| ~ aElement0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[994,48,theory(equality)]) ).
cnf(996,negated_conjecture,
( ~ aReductOfIn0(xv,X1,xR)
| ~ aReductOfIn0(xu,X1,xR)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[995,theory(equality)]) ).
cnf(997,plain,
( ~ aReductOfIn0(xu,xa,xR)
| ~ aElement0(xa) ),
inference(spm,[status(thm)],[996,93,theory(equality)]) ).
cnf(998,plain,
( $false
| ~ aElement0(xa) ),
inference(rw,[status(thm)],[997,90,theory(equality)]) ).
cnf(999,plain,
( $false
| $false ),
inference(rw,[status(thm)],[998,88,theory(equality)]) ).
cnf(1000,plain,
$false,
inference(cn,[status(thm)],[999,theory(equality)]) ).
cnf(1001,plain,
$false,
1000,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/COM/COM017+1.p
% --creating new selector for []
% -running prover on /tmp/tmpvZwfpk/sel_COM017+1.p_1 with time limit 29
% -prover status Theorem
% Problem COM017+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/COM/COM017+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/COM/COM017+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------