TSTP Solution File: RNG047+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : RNG047+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 : Sun Dec 26 01:46:57 EST 2010
% Result : Theorem 0.29s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 59 ( 12 unt; 0 def)
% Number of atoms : 226 ( 121 equ)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 266 ( 99 ~; 123 |; 35 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 36 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(17,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( szszuzczcdt0(X1) = szszuzczcdt0(X2)
=> X1 = X2 ) ),
file('/tmp/tmp-pFL8o/sel_RNG047+1.p_1',mSuccEqu) ).
fof(19,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( aNaturalNumber0(szszuzczcdt0(X1))
& szszuzczcdt0(X1) != sz00 ) ),
file('/tmp/tmp-pFL8o/sel_RNG047+1.p_1',mSuccNat) ).
fof(20,axiom,
! [X1] :
( aVector0(X1)
=> ( aDimensionOf0(X1) != sz00
=> ! [X2] :
( X2 = sziznziztdt0(X1)
<=> ( aVector0(X2)
& szszuzczcdt0(aDimensionOf0(X2)) = aDimensionOf0(X1)
& ! [X3] :
( aNaturalNumber0(X3)
=> sdtlbdtrb0(X2,X3) = sdtlbdtrb0(X1,X3) ) ) ) ) ),
file('/tmp/tmp-pFL8o/sel_RNG047+1.p_1',mDefInit) ).
fof(21,axiom,
! [X1] :
( aVector0(X1)
=> aNaturalNumber0(aDimensionOf0(X1)) ),
file('/tmp/tmp-pFL8o/sel_RNG047+1.p_1',mDimNat) ).
fof(22,axiom,
( aDimensionOf0(xs) = aDimensionOf0(xt)
& aDimensionOf0(xt) != sz00 ),
file('/tmp/tmp-pFL8o/sel_RNG047+1.p_1',m__1329_01) ).
fof(23,axiom,
( aVector0(xs)
& aVector0(xt) ),
file('/tmp/tmp-pFL8o/sel_RNG047+1.p_1',m__1329) ).
fof(24,axiom,
! [X1] :
( ( aNaturalNumber0(X1)
& X1 != sz00 )
=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = szszuzczcdt0(X2) ) ),
file('/tmp/tmp-pFL8o/sel_RNG047+1.p_1',mNatExtr) ).
fof(27,conjecture,
aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)),
file('/tmp/tmp-pFL8o/sel_RNG047+1.p_1',m__) ).
fof(36,negated_conjecture,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(assume_negation,[status(cth)],[27]) ).
fof(37,negated_conjecture,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(fof_simplification,[status(thm)],[36,theory(equality)]) ).
fof(96,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| szszuzczcdt0(X1) != szszuzczcdt0(X2)
| X1 = X2 ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(97,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| szszuzczcdt0(X3) != szszuzczcdt0(X4)
| X3 = X4 ),
inference(variable_rename,[status(thm)],[96]) ).
cnf(98,plain,
( X1 = X2
| szszuzczcdt0(X1) != szszuzczcdt0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[97]) ).
fof(102,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| ( aNaturalNumber0(szszuzczcdt0(X1))
& szszuzczcdt0(X1) != sz00 ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(103,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| ( aNaturalNumber0(szszuzczcdt0(X2))
& szszuzczcdt0(X2) != sz00 ) ),
inference(variable_rename,[status(thm)],[102]) ).
fof(104,plain,
! [X2] :
( ( aNaturalNumber0(szszuzczcdt0(X2))
| ~ aNaturalNumber0(X2) )
& ( szszuzczcdt0(X2) != sz00
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[103]) ).
cnf(105,plain,
( ~ aNaturalNumber0(X1)
| szszuzczcdt0(X1) != sz00 ),
inference(split_conjunct,[status(thm)],[104]) ).
cnf(106,plain,
( aNaturalNumber0(szszuzczcdt0(X1))
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[104]) ).
fof(107,plain,
! [X1] :
( ~ aVector0(X1)
| aDimensionOf0(X1) = sz00
| ! [X2] :
( ( X2 != sziznziztdt0(X1)
| ( aVector0(X2)
& szszuzczcdt0(aDimensionOf0(X2)) = aDimensionOf0(X1)
& ! [X3] :
( ~ aNaturalNumber0(X3)
| sdtlbdtrb0(X2,X3) = sdtlbdtrb0(X1,X3) ) ) )
& ( ~ aVector0(X2)
| szszuzczcdt0(aDimensionOf0(X2)) != aDimensionOf0(X1)
| ? [X3] :
( aNaturalNumber0(X3)
& sdtlbdtrb0(X2,X3) != sdtlbdtrb0(X1,X3) )
| X2 = sziznziztdt0(X1) ) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(108,plain,
! [X4] :
( ~ aVector0(X4)
| aDimensionOf0(X4) = sz00
| ! [X5] :
( ( X5 != sziznziztdt0(X4)
| ( aVector0(X5)
& szszuzczcdt0(aDimensionOf0(X5)) = aDimensionOf0(X4)
& ! [X6] :
( ~ aNaturalNumber0(X6)
| sdtlbdtrb0(X5,X6) = sdtlbdtrb0(X4,X6) ) ) )
& ( ~ aVector0(X5)
| szszuzczcdt0(aDimensionOf0(X5)) != aDimensionOf0(X4)
| ? [X7] :
( aNaturalNumber0(X7)
& sdtlbdtrb0(X5,X7) != sdtlbdtrb0(X4,X7) )
| X5 = sziznziztdt0(X4) ) ) ),
inference(variable_rename,[status(thm)],[107]) ).
fof(109,plain,
! [X4] :
( ~ aVector0(X4)
| aDimensionOf0(X4) = sz00
| ! [X5] :
( ( X5 != sziznziztdt0(X4)
| ( aVector0(X5)
& szszuzczcdt0(aDimensionOf0(X5)) = aDimensionOf0(X4)
& ! [X6] :
( ~ aNaturalNumber0(X6)
| sdtlbdtrb0(X5,X6) = sdtlbdtrb0(X4,X6) ) ) )
& ( ~ aVector0(X5)
| szszuzczcdt0(aDimensionOf0(X5)) != aDimensionOf0(X4)
| ( aNaturalNumber0(esk1_2(X4,X5))
& sdtlbdtrb0(X5,esk1_2(X4,X5)) != sdtlbdtrb0(X4,esk1_2(X4,X5)) )
| X5 = sziznziztdt0(X4) ) ) ),
inference(skolemize,[status(esa)],[108]) ).
fof(110,plain,
! [X4,X5,X6] :
( ( ( ( ( ~ aNaturalNumber0(X6)
| sdtlbdtrb0(X5,X6) = sdtlbdtrb0(X4,X6) )
& aVector0(X5)
& szszuzczcdt0(aDimensionOf0(X5)) = aDimensionOf0(X4) )
| X5 != sziznziztdt0(X4) )
& ( ~ aVector0(X5)
| szszuzczcdt0(aDimensionOf0(X5)) != aDimensionOf0(X4)
| ( aNaturalNumber0(esk1_2(X4,X5))
& sdtlbdtrb0(X5,esk1_2(X4,X5)) != sdtlbdtrb0(X4,esk1_2(X4,X5)) )
| X5 = sziznziztdt0(X4) ) )
| aDimensionOf0(X4) = sz00
| ~ aVector0(X4) ),
inference(shift_quantors,[status(thm)],[109]) ).
fof(111,plain,
! [X4,X5,X6] :
( ( ~ aNaturalNumber0(X6)
| sdtlbdtrb0(X5,X6) = sdtlbdtrb0(X4,X6)
| X5 != sziznziztdt0(X4)
| aDimensionOf0(X4) = sz00
| ~ aVector0(X4) )
& ( aVector0(X5)
| X5 != sziznziztdt0(X4)
| aDimensionOf0(X4) = sz00
| ~ aVector0(X4) )
& ( szszuzczcdt0(aDimensionOf0(X5)) = aDimensionOf0(X4)
| X5 != sziznziztdt0(X4)
| aDimensionOf0(X4) = sz00
| ~ aVector0(X4) )
& ( aNaturalNumber0(esk1_2(X4,X5))
| ~ aVector0(X5)
| szszuzczcdt0(aDimensionOf0(X5)) != aDimensionOf0(X4)
| X5 = sziznziztdt0(X4)
| aDimensionOf0(X4) = sz00
| ~ aVector0(X4) )
& ( sdtlbdtrb0(X5,esk1_2(X4,X5)) != sdtlbdtrb0(X4,esk1_2(X4,X5))
| ~ aVector0(X5)
| szszuzczcdt0(aDimensionOf0(X5)) != aDimensionOf0(X4)
| X5 = sziznziztdt0(X4)
| aDimensionOf0(X4) = sz00
| ~ aVector0(X4) ) ),
inference(distribute,[status(thm)],[110]) ).
cnf(114,plain,
( aDimensionOf0(X1) = sz00
| szszuzczcdt0(aDimensionOf0(X2)) = aDimensionOf0(X1)
| ~ aVector0(X1)
| X2 != sziznziztdt0(X1) ),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(115,plain,
( aDimensionOf0(X1) = sz00
| aVector0(X2)
| ~ aVector0(X1)
| X2 != sziznziztdt0(X1) ),
inference(split_conjunct,[status(thm)],[111]) ).
fof(117,plain,
! [X1] :
( ~ aVector0(X1)
| aNaturalNumber0(aDimensionOf0(X1)) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(118,plain,
! [X2] :
( ~ aVector0(X2)
| aNaturalNumber0(aDimensionOf0(X2)) ),
inference(variable_rename,[status(thm)],[117]) ).
cnf(119,plain,
( aNaturalNumber0(aDimensionOf0(X1))
| ~ aVector0(X1) ),
inference(split_conjunct,[status(thm)],[118]) ).
cnf(120,plain,
aDimensionOf0(xt) != sz00,
inference(split_conjunct,[status(thm)],[22]) ).
cnf(121,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(122,plain,
aVector0(xt),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(123,plain,
aVector0(xs),
inference(split_conjunct,[status(thm)],[23]) ).
fof(124,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| X1 = sz00
| ? [X2] :
( aNaturalNumber0(X2)
& X1 = szszuzczcdt0(X2) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(125,plain,
! [X3] :
( ~ aNaturalNumber0(X3)
| X3 = sz00
| ? [X4] :
( aNaturalNumber0(X4)
& X3 = szszuzczcdt0(X4) ) ),
inference(variable_rename,[status(thm)],[124]) ).
fof(126,plain,
! [X3] :
( ~ aNaturalNumber0(X3)
| X3 = sz00
| ( aNaturalNumber0(esk2_1(X3))
& X3 = szszuzczcdt0(esk2_1(X3)) ) ),
inference(skolemize,[status(esa)],[125]) ).
fof(127,plain,
! [X3] :
( ( aNaturalNumber0(esk2_1(X3))
| ~ aNaturalNumber0(X3)
| X3 = sz00 )
& ( X3 = szszuzczcdt0(esk2_1(X3))
| ~ aNaturalNumber0(X3)
| X3 = sz00 ) ),
inference(distribute,[status(thm)],[126]) ).
cnf(128,plain,
( X1 = sz00
| X1 = szszuzczcdt0(esk2_1(X1))
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[127]) ).
cnf(129,plain,
( X1 = sz00
| aNaturalNumber0(esk2_1(X1))
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[127]) ).
cnf(138,negated_conjecture,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(200,plain,
( aDimensionOf0(X1) = sz00
| aVector0(sziznziztdt0(X1))
| ~ aVector0(X1) ),
inference(er,[status(thm)],[115,theory(equality)]) ).
cnf(213,plain,
( esk2_1(X1) = X2
| sz00 = X1
| X1 != szszuzczcdt0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(esk2_1(X1))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[98,128,theory(equality)]) ).
cnf(215,plain,
( szszuzczcdt0(aDimensionOf0(sziznziztdt0(X1))) = aDimensionOf0(X1)
| aDimensionOf0(X1) = sz00
| ~ aVector0(X1) ),
inference(er,[status(thm)],[114,theory(equality)]) ).
cnf(905,plain,
( esk2_1(X1) = X2
| sz00 = X1
| X1 != szszuzczcdt0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[213,129]) ).
cnf(906,plain,
( esk2_1(szszuzczcdt0(X1)) = X1
| sz00 = szszuzczcdt0(X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(szszuzczcdt0(X1)) ),
inference(er,[status(thm)],[905,theory(equality)]) ).
cnf(3697,plain,
( esk2_1(szszuzczcdt0(X1)) = X1
| szszuzczcdt0(X1) = sz00
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[906,106]) ).
cnf(3698,plain,
( esk2_1(szszuzczcdt0(X1)) = X1
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[3697,105]) ).
cnf(3700,plain,
( esk2_1(aDimensionOf0(X1)) = aDimensionOf0(sziznziztdt0(X1))
| aDimensionOf0(X1) = sz00
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(X1)))
| ~ aVector0(X1) ),
inference(spm,[status(thm)],[3698,215,theory(equality)]) ).
cnf(3702,plain,
( esk2_1(aDimensionOf0(X1)) = aDimensionOf0(sziznziztdt0(X1))
| aDimensionOf0(X1) = sz00
| ~ aVector0(X1)
| ~ aVector0(sziznziztdt0(X1)) ),
inference(spm,[status(thm)],[3700,119,theory(equality)]) ).
cnf(3703,plain,
( esk2_1(aDimensionOf0(X1)) = aDimensionOf0(sziznziztdt0(X1))
| aDimensionOf0(X1) = sz00
| ~ aVector0(X1) ),
inference(csr,[status(thm)],[3702,200]) ).
cnf(3704,plain,
( esk2_1(aDimensionOf0(xt)) = aDimensionOf0(sziznziztdt0(xs))
| aDimensionOf0(xt) = sz00
| ~ aVector0(xs) ),
inference(spm,[status(thm)],[3703,121,theory(equality)]) ).
cnf(3708,plain,
( esk2_1(aDimensionOf0(xt)) = aDimensionOf0(sziznziztdt0(xs))
| aDimensionOf0(xt) = sz00
| $false ),
inference(rw,[status(thm)],[3704,123,theory(equality)]) ).
cnf(3709,plain,
( esk2_1(aDimensionOf0(xt)) = aDimensionOf0(sziznziztdt0(xs))
| aDimensionOf0(xt) = sz00 ),
inference(cn,[status(thm)],[3708,theory(equality)]) ).
cnf(3710,plain,
esk2_1(aDimensionOf0(xt)) = aDimensionOf0(sziznziztdt0(xs)),
inference(sr,[status(thm)],[3709,120,theory(equality)]) ).
cnf(3714,plain,
( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt))
| aDimensionOf0(xt) = sz00
| ~ aVector0(xt) ),
inference(spm,[status(thm)],[3703,3710,theory(equality)]) ).
cnf(3724,plain,
( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt))
| aDimensionOf0(xt) = sz00
| $false ),
inference(rw,[status(thm)],[3714,122,theory(equality)]) ).
cnf(3725,plain,
( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt))
| aDimensionOf0(xt) = sz00 ),
inference(cn,[status(thm)],[3724,theory(equality)]) ).
cnf(3726,plain,
aDimensionOf0(xt) = sz00,
inference(sr,[status(thm)],[3725,138,theory(equality)]) ).
cnf(3727,plain,
$false,
inference(sr,[status(thm)],[3726,120,theory(equality)]) ).
cnf(3728,plain,
$false,
3727,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/RNG/RNG047+1.p
% --creating new selector for []
% -running prover on /tmp/tmp-pFL8o/sel_RNG047+1.p_1 with time limit 29
% -prover status Theorem
% Problem RNG047+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/RNG/RNG047+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/RNG/RNG047+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
%
%------------------------------------------------------------------------------