TSTP Solution File: RNG123+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : RNG123+4 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 02:39:21 EST 2010
% Result : Theorem 0.25s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 234 ( 54 equ)
% Maximal formula atoms : 33 ( 7 avg)
% Number of connectives : 293 ( 89 ~; 86 |; 112 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 62 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(28,axiom,
( aSet0(xI)
& ! [X1] :
( aElementOf0(X1,xI)
=> ( ! [X2] :
( aElementOf0(X2,xI)
=> aElementOf0(sdtpldt0(X1,X2),xI) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),xI) ) ) )
& aIdeal0(xI)
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xb))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xb,X2) = X1 ) )
& ! [X1] :
( aElementOf0(X1,xI)
<=> ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/tmp/tmpoTVwrx/sel_RNG123+4.p_1',m__2174) ).
fof(44,axiom,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
file('/tmp/tmpoTVwrx/sel_RNG123+4.p_1',m__2718) ).
fof(48,axiom,
( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = smndt0(sdtasdt0(xq,xu)) )
& aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
file('/tmp/tmpoTVwrx/sel_RNG123+4.p_1',m__2690) ).
fof(54,conjecture,
( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xr )
| aElementOf0(xr,xI) ),
file('/tmp/tmpoTVwrx/sel_RNG123+4.p_1',m__) ).
fof(55,axiom,
( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xb )
& ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xb )
& aElementOf0(xb,xI) ),
file('/tmp/tmpoTVwrx/sel_RNG123+4.p_1',m__2699) ).
fof(56,negated_conjecture,
~ ( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xr )
| aElementOf0(xr,xI) ),
inference(assume_negation,[status(cth)],[54]) ).
fof(58,plain,
( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xb )
& aElementOf0(xb,xI) ),
inference(fof_simplification,[status(thm)],[55,theory(equality)]) ).
fof(238,plain,
( aSet0(xI)
& ! [X1] :
( ~ aElementOf0(X1,xI)
| ( ! [X2] :
( ~ aElementOf0(X2,xI)
| aElementOf0(sdtpldt0(X1,X2),xI) )
& ! [X2] :
( ~ aElement0(X2)
| aElementOf0(sdtasdt0(X2,X1),xI) ) ) )
& aIdeal0(xI)
& ! [X1] :
( ( ~ aElementOf0(X1,slsdtgt0(xa))
| ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) )
& ( ! [X2] :
( ~ aElement0(X2)
| sdtasdt0(xa,X2) != X1 )
| aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X1] :
( ( ~ aElementOf0(X1,slsdtgt0(xb))
| ? [X2] :
( aElement0(X2)
& sdtasdt0(xb,X2) = X1 ) )
& ( ! [X2] :
( ~ aElement0(X2)
| sdtasdt0(xb,X2) != X1 )
| aElementOf0(X1,slsdtgt0(xb)) ) )
& ! [X1] :
( ( ~ aElementOf0(X1,xI)
| ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 ) )
& ( ! [X2,X3] :
( ~ aElementOf0(X2,slsdtgt0(xa))
| ~ aElementOf0(X3,slsdtgt0(xb))
| sdtpldt0(X2,X3) != X1 )
| aElementOf0(X1,xI) ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(239,plain,
( aSet0(xI)
& ! [X4] :
( ~ aElementOf0(X4,xI)
| ( ! [X5] :
( ~ aElementOf0(X5,xI)
| aElementOf0(sdtpldt0(X4,X5),xI) )
& ! [X6] :
( ~ aElement0(X6)
| aElementOf0(sdtasdt0(X6,X4),xI) ) ) )
& aIdeal0(xI)
& ! [X7] :
( ( ~ aElementOf0(X7,slsdtgt0(xa))
| ? [X8] :
( aElement0(X8)
& sdtasdt0(xa,X8) = X7 ) )
& ( ! [X9] :
( ~ aElement0(X9)
| sdtasdt0(xa,X9) != X7 )
| aElementOf0(X7,slsdtgt0(xa)) ) )
& ! [X10] :
( ( ~ aElementOf0(X10,slsdtgt0(xb))
| ? [X11] :
( aElement0(X11)
& sdtasdt0(xb,X11) = X10 ) )
& ( ! [X12] :
( ~ aElement0(X12)
| sdtasdt0(xb,X12) != X10 )
| aElementOf0(X10,slsdtgt0(xb)) ) )
& ! [X13] :
( ( ~ aElementOf0(X13,xI)
| ? [X14,X15] :
( aElementOf0(X14,slsdtgt0(xa))
& aElementOf0(X15,slsdtgt0(xb))
& sdtpldt0(X14,X15) = X13 ) )
& ( ! [X16,X17] :
( ~ aElementOf0(X16,slsdtgt0(xa))
| ~ aElementOf0(X17,slsdtgt0(xb))
| sdtpldt0(X16,X17) != X13 )
| aElementOf0(X13,xI) ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(variable_rename,[status(thm)],[238]) ).
fof(240,plain,
( aSet0(xI)
& ! [X4] :
( ~ aElementOf0(X4,xI)
| ( ! [X5] :
( ~ aElementOf0(X5,xI)
| aElementOf0(sdtpldt0(X4,X5),xI) )
& ! [X6] :
( ~ aElement0(X6)
| aElementOf0(sdtasdt0(X6,X4),xI) ) ) )
& aIdeal0(xI)
& ! [X7] :
( ( ~ aElementOf0(X7,slsdtgt0(xa))
| ( aElement0(esk16_1(X7))
& sdtasdt0(xa,esk16_1(X7)) = X7 ) )
& ( ! [X9] :
( ~ aElement0(X9)
| sdtasdt0(xa,X9) != X7 )
| aElementOf0(X7,slsdtgt0(xa)) ) )
& ! [X10] :
( ( ~ aElementOf0(X10,slsdtgt0(xb))
| ( aElement0(esk17_1(X10))
& sdtasdt0(xb,esk17_1(X10)) = X10 ) )
& ( ! [X12] :
( ~ aElement0(X12)
| sdtasdt0(xb,X12) != X10 )
| aElementOf0(X10,slsdtgt0(xb)) ) )
& ! [X13] :
( ( ~ aElementOf0(X13,xI)
| ( aElementOf0(esk18_1(X13),slsdtgt0(xa))
& aElementOf0(esk19_1(X13),slsdtgt0(xb))
& sdtpldt0(esk18_1(X13),esk19_1(X13)) = X13 ) )
& ( ! [X16,X17] :
( ~ aElementOf0(X16,slsdtgt0(xa))
| ~ aElementOf0(X17,slsdtgt0(xb))
| sdtpldt0(X16,X17) != X13 )
| aElementOf0(X13,xI) ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(skolemize,[status(esa)],[239]) ).
fof(241,plain,
! [X4,X5,X6,X7,X9,X10,X12,X13,X16,X17] :
( ( ~ aElementOf0(X16,slsdtgt0(xa))
| ~ aElementOf0(X17,slsdtgt0(xb))
| sdtpldt0(X16,X17) != X13
| aElementOf0(X13,xI) )
& ( ~ aElementOf0(X13,xI)
| ( aElementOf0(esk18_1(X13),slsdtgt0(xa))
& aElementOf0(esk19_1(X13),slsdtgt0(xb))
& sdtpldt0(esk18_1(X13),esk19_1(X13)) = X13 ) )
& ( ~ aElement0(X12)
| sdtasdt0(xb,X12) != X10
| aElementOf0(X10,slsdtgt0(xb)) )
& ( ~ aElementOf0(X10,slsdtgt0(xb))
| ( aElement0(esk17_1(X10))
& sdtasdt0(xb,esk17_1(X10)) = X10 ) )
& ( ~ aElement0(X9)
| sdtasdt0(xa,X9) != X7
| aElementOf0(X7,slsdtgt0(xa)) )
& ( ~ aElementOf0(X7,slsdtgt0(xa))
| ( aElement0(esk16_1(X7))
& sdtasdt0(xa,esk16_1(X7)) = X7 ) )
& ( ( ( ~ aElement0(X6)
| aElementOf0(sdtasdt0(X6,X4),xI) )
& ( ~ aElementOf0(X5,xI)
| aElementOf0(sdtpldt0(X4,X5),xI) ) )
| ~ aElementOf0(X4,xI) )
& aSet0(xI)
& aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(shift_quantors,[status(thm)],[240]) ).
fof(242,plain,
! [X4,X5,X6,X7,X9,X10,X12,X13,X16,X17] :
( ( ~ aElementOf0(X16,slsdtgt0(xa))
| ~ aElementOf0(X17,slsdtgt0(xb))
| sdtpldt0(X16,X17) != X13
| aElementOf0(X13,xI) )
& ( aElementOf0(esk18_1(X13),slsdtgt0(xa))
| ~ aElementOf0(X13,xI) )
& ( aElementOf0(esk19_1(X13),slsdtgt0(xb))
| ~ aElementOf0(X13,xI) )
& ( sdtpldt0(esk18_1(X13),esk19_1(X13)) = X13
| ~ aElementOf0(X13,xI) )
& ( ~ aElement0(X12)
| sdtasdt0(xb,X12) != X10
| aElementOf0(X10,slsdtgt0(xb)) )
& ( aElement0(esk17_1(X10))
| ~ aElementOf0(X10,slsdtgt0(xb)) )
& ( sdtasdt0(xb,esk17_1(X10)) = X10
| ~ aElementOf0(X10,slsdtgt0(xb)) )
& ( ~ aElement0(X9)
| sdtasdt0(xa,X9) != X7
| aElementOf0(X7,slsdtgt0(xa)) )
& ( aElement0(esk16_1(X7))
| ~ aElementOf0(X7,slsdtgt0(xa)) )
& ( sdtasdt0(xa,esk16_1(X7)) = X7
| ~ aElementOf0(X7,slsdtgt0(xa)) )
& ( ~ aElement0(X6)
| aElementOf0(sdtasdt0(X6,X4),xI)
| ~ aElementOf0(X4,xI) )
& ( ~ aElementOf0(X5,xI)
| aElementOf0(sdtpldt0(X4,X5),xI)
| ~ aElementOf0(X4,xI) )
& aSet0(xI)
& aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
inference(distribute,[status(thm)],[241]) ).
cnf(246,plain,
( aElementOf0(sdtpldt0(X1,X2),xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X2,xI) ),
inference(split_conjunct,[status(thm)],[242]) ).
cnf(349,plain,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(split_conjunct,[status(thm)],[44]) ).
fof(370,plain,
( ? [X3,X4] :
( aElementOf0(X3,slsdtgt0(xa))
& aElementOf0(X4,slsdtgt0(xb))
& sdtpldt0(X3,X4) = smndt0(sdtasdt0(xq,xu)) )
& aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
inference(variable_rename,[status(thm)],[48]) ).
fof(371,plain,
( aElementOf0(esk40_0,slsdtgt0(xa))
& aElementOf0(esk41_0,slsdtgt0(xb))
& sdtpldt0(esk40_0,esk41_0) = smndt0(sdtasdt0(xq,xu))
& aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
inference(skolemize,[status(esa)],[370]) ).
cnf(372,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(split_conjunct,[status(thm)],[371]) ).
fof(407,negated_conjecture,
( ! [X1,X2] :
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) != xr )
& ~ aElementOf0(xr,xI) ),
inference(fof_nnf,[status(thm)],[56]) ).
fof(408,negated_conjecture,
( ! [X3,X4] :
( ~ aElementOf0(X3,slsdtgt0(xa))
| ~ aElementOf0(X4,slsdtgt0(xb))
| sdtpldt0(X3,X4) != xr )
& ~ aElementOf0(xr,xI) ),
inference(variable_rename,[status(thm)],[407]) ).
fof(409,negated_conjecture,
! [X3,X4] :
( ( ~ aElementOf0(X3,slsdtgt0(xa))
| ~ aElementOf0(X4,slsdtgt0(xb))
| sdtpldt0(X3,X4) != xr )
& ~ aElementOf0(xr,xI) ),
inference(shift_quantors,[status(thm)],[408]) ).
cnf(410,negated_conjecture,
~ aElementOf0(xr,xI),
inference(split_conjunct,[status(thm)],[409]) ).
fof(412,plain,
( ? [X3,X4] :
( aElementOf0(X3,slsdtgt0(xa))
& aElementOf0(X4,slsdtgt0(xb))
& sdtpldt0(X3,X4) = xb )
& aElementOf0(xb,xI) ),
inference(variable_rename,[status(thm)],[58]) ).
fof(413,plain,
( aElementOf0(esk44_0,slsdtgt0(xa))
& aElementOf0(esk45_0,slsdtgt0(xb))
& sdtpldt0(esk44_0,esk45_0) = xb
& aElementOf0(xb,xI) ),
inference(skolemize,[status(esa)],[412]) ).
cnf(414,plain,
aElementOf0(xb,xI),
inference(split_conjunct,[status(thm)],[413]) ).
cnf(496,plain,
( aElementOf0(xr,xI)
| ~ aElementOf0(xb,xI)
| ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
inference(spm,[status(thm)],[246,349,theory(equality)]) ).
cnf(504,plain,
( aElementOf0(xr,xI)
| $false
| ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
inference(rw,[status(thm)],[496,414,theory(equality)]) ).
cnf(505,plain,
( aElementOf0(xr,xI)
| $false
| $false ),
inference(rw,[status(thm)],[504,372,theory(equality)]) ).
cnf(506,plain,
aElementOf0(xr,xI),
inference(cn,[status(thm)],[505,theory(equality)]) ).
cnf(507,plain,
$false,
inference(sr,[status(thm)],[506,410,theory(equality)]) ).
cnf(508,plain,
$false,
507,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/RNG/RNG123+4.p
% --creating new selector for []
% -running prover on /tmp/tmpoTVwrx/sel_RNG123+4.p_1 with time limit 29
% -prover status Theorem
% Problem RNG123+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/RNG/RNG123+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/RNG/RNG123+4.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
%
%------------------------------------------------------------------------------