TSTP Solution File: RNG059+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : RNG059+2 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 01:55:52 EST 2010
% Result : Theorem 0.52s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 71 ( 18 unt; 0 def)
% Number of atoms : 232 ( 94 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 254 ( 93 ~; 101 |; 54 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 62 ( 1 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(6,axiom,
! [X1] :
( aScalar0(X1)
=> ( sdtpldt0(X1,sz0z00) = X1
& sdtpldt0(sz0z00,X1) = X1
& sdtasdt0(X1,sz0z00) = sz0z00
& sdtasdt0(sz0z00,X1) = sz0z00
& sdtpldt0(X1,smndt0(X1)) = sz0z00
& sdtpldt0(smndt0(X1),X1) = sz0z00
& smndt0(smndt0(X1)) = X1
& smndt0(sz0z00) = sz0z00 ) ),
file('/tmp/tmpaAKl0W/sel_RNG059+2.p_1',mScZero) ).
fof(16,axiom,
! [X1,X2,X3] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3) )
=> ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
& sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
& sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
& sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ) ),
file('/tmp/tmpaAKl0W/sel_RNG059+2.p_1',mArith) ).
fof(21,axiom,
! [X1] :
( aScalar0(X1)
=> aScalar0(smndt0(X1)) ),
file('/tmp/tmpaAKl0W/sel_RNG059+2.p_1',mNegSc) ).
fof(34,axiom,
( aScalar0(xR)
& xR = sdtasdt0(xC,xG) ),
file('/tmp/tmpaAKl0W/sel_RNG059+2.p_1',m__1892) ).
fof(36,axiom,
( aScalar0(xS)
& xS = sdtasdt0(xF,xD) ),
file('/tmp/tmpaAKl0W/sel_RNG059+2.p_1',m__1930) ).
fof(38,axiom,
( aScalar0(xG)
& xG = sdtasdt0(xB,xB) ),
file('/tmp/tmpaAKl0W/sel_RNG059+2.p_1',m__1854) ).
fof(41,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2) ),
file('/tmp/tmpaAKl0W/sel_RNG059+2.p_1',mMDNeg) ).
fof(42,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/tmp/tmpaAKl0W/sel_RNG059+2.p_1',mMulSc) ).
fof(43,conjecture,
sdtasdt0(smndt0(xS),xR) = smndt0(xN),
file('/tmp/tmpaAKl0W/sel_RNG059+2.p_1',m__) ).
fof(44,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
& sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2)) ) ),
file('/tmp/tmpaAKl0W/sel_RNG059+2.p_1',mMNeg) ).
fof(45,axiom,
( aScalar0(xC)
& xC = sdtasasdt0(xp,xp) ),
file('/tmp/tmpaAKl0W/sel_RNG059+2.p_1',m__1783) ).
fof(53,axiom,
( aScalar0(xN)
& xN = sdtasdt0(xR,xS) ),
file('/tmp/tmpaAKl0W/sel_RNG059+2.p_1',m__1949) ).
fof(59,negated_conjecture,
sdtasdt0(smndt0(xS),xR) != smndt0(xN),
inference(assume_negation,[status(cth)],[43]) ).
fof(60,negated_conjecture,
sdtasdt0(smndt0(xS),xR) != smndt0(xN),
inference(fof_simplification,[status(thm)],[59,theory(equality)]) ).
fof(72,plain,
! [X1] :
( ~ aScalar0(X1)
| ( sdtpldt0(X1,sz0z00) = X1
& sdtpldt0(sz0z00,X1) = X1
& sdtasdt0(X1,sz0z00) = sz0z00
& sdtasdt0(sz0z00,X1) = sz0z00
& sdtpldt0(X1,smndt0(X1)) = sz0z00
& sdtpldt0(smndt0(X1),X1) = sz0z00
& smndt0(smndt0(X1)) = X1
& smndt0(sz0z00) = sz0z00 ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(73,plain,
! [X2] :
( ~ aScalar0(X2)
| ( sdtpldt0(X2,sz0z00) = X2
& sdtpldt0(sz0z00,X2) = X2
& sdtasdt0(X2,sz0z00) = sz0z00
& sdtasdt0(sz0z00,X2) = sz0z00
& sdtpldt0(X2,smndt0(X2)) = sz0z00
& sdtpldt0(smndt0(X2),X2) = sz0z00
& smndt0(smndt0(X2)) = X2
& smndt0(sz0z00) = sz0z00 ) ),
inference(variable_rename,[status(thm)],[72]) ).
fof(74,plain,
! [X2] :
( ( sdtpldt0(X2,sz0z00) = X2
| ~ aScalar0(X2) )
& ( sdtpldt0(sz0z00,X2) = X2
| ~ aScalar0(X2) )
& ( sdtasdt0(X2,sz0z00) = sz0z00
| ~ aScalar0(X2) )
& ( sdtasdt0(sz0z00,X2) = sz0z00
| ~ aScalar0(X2) )
& ( sdtpldt0(X2,smndt0(X2)) = sz0z00
| ~ aScalar0(X2) )
& ( sdtpldt0(smndt0(X2),X2) = sz0z00
| ~ aScalar0(X2) )
& ( smndt0(smndt0(X2)) = X2
| ~ aScalar0(X2) )
& ( smndt0(sz0z00) = sz0z00
| ~ aScalar0(X2) ) ),
inference(distribute,[status(thm)],[73]) ).
cnf(76,plain,
( smndt0(smndt0(X1)) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[74]) ).
fof(107,plain,
! [X1,X2,X3] :
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
& sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
& sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
& sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(108,plain,
! [X4,X5,X6] :
( ~ aScalar0(X4)
| ~ aScalar0(X5)
| ~ aScalar0(X6)
| ( sdtpldt0(sdtpldt0(X4,X5),X6) = sdtpldt0(X4,sdtpldt0(X5,X6))
& sdtpldt0(X4,X5) = sdtpldt0(X5,X4)
& sdtasdt0(sdtasdt0(X4,X5),X6) = sdtasdt0(X4,sdtasdt0(X5,X6))
& sdtasdt0(X4,X5) = sdtasdt0(X5,X4) ) ),
inference(variable_rename,[status(thm)],[107]) ).
fof(109,plain,
! [X4,X5,X6] :
( ( sdtpldt0(sdtpldt0(X4,X5),X6) = sdtpldt0(X4,sdtpldt0(X5,X6))
| ~ aScalar0(X4)
| ~ aScalar0(X5)
| ~ aScalar0(X6) )
& ( sdtpldt0(X4,X5) = sdtpldt0(X5,X4)
| ~ aScalar0(X4)
| ~ aScalar0(X5)
| ~ aScalar0(X6) )
& ( sdtasdt0(sdtasdt0(X4,X5),X6) = sdtasdt0(X4,sdtasdt0(X5,X6))
| ~ aScalar0(X4)
| ~ aScalar0(X5)
| ~ aScalar0(X6) )
& ( sdtasdt0(X4,X5) = sdtasdt0(X5,X4)
| ~ aScalar0(X4)
| ~ aScalar0(X5)
| ~ aScalar0(X6) ) ),
inference(distribute,[status(thm)],[108]) ).
cnf(110,plain,
( sdtasdt0(X3,X2) = sdtasdt0(X2,X3)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[109]) ).
fof(125,plain,
! [X1] :
( ~ aScalar0(X1)
| aScalar0(smndt0(X1)) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(126,plain,
! [X2] :
( ~ aScalar0(X2)
| aScalar0(smndt0(X2)) ),
inference(variable_rename,[status(thm)],[125]) ).
cnf(127,plain,
( aScalar0(smndt0(X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[126]) ).
cnf(173,plain,
xR = sdtasdt0(xC,xG),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(174,plain,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(179,plain,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(184,plain,
aScalar0(xG),
inference(split_conjunct,[status(thm)],[38]) ).
fof(193,plain,
! [X1,X2] :
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2) ),
inference(fof_nnf,[status(thm)],[41]) ).
fof(194,plain,
! [X3,X4] :
( ~ aScalar0(X3)
| ~ aScalar0(X4)
| sdtasdt0(smndt0(X3),smndt0(X4)) = sdtasdt0(X3,X4) ),
inference(variable_rename,[status(thm)],[193]) ).
cnf(195,plain,
( sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[194]) ).
fof(196,plain,
! [X1,X2] :
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| aScalar0(sdtasdt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[42]) ).
fof(197,plain,
! [X3,X4] :
( ~ aScalar0(X3)
| ~ aScalar0(X4)
| aScalar0(sdtasdt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[196]) ).
cnf(198,plain,
( aScalar0(sdtasdt0(X1,X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[197]) ).
cnf(199,negated_conjecture,
sdtasdt0(smndt0(xS),xR) != smndt0(xN),
inference(split_conjunct,[status(thm)],[60]) ).
fof(200,plain,
! [X1,X2] :
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| ( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
& sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[44]) ).
fof(201,plain,
! [X3,X4] :
( ~ aScalar0(X3)
| ~ aScalar0(X4)
| ( sdtasdt0(X3,smndt0(X4)) = smndt0(sdtasdt0(X3,X4))
& sdtasdt0(smndt0(X3),X4) = smndt0(sdtasdt0(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[200]) ).
fof(202,plain,
! [X3,X4] :
( ( sdtasdt0(X3,smndt0(X4)) = smndt0(sdtasdt0(X3,X4))
| ~ aScalar0(X3)
| ~ aScalar0(X4) )
& ( sdtasdt0(smndt0(X3),X4) = smndt0(sdtasdt0(X3,X4))
| ~ aScalar0(X3)
| ~ aScalar0(X4) ) ),
inference(distribute,[status(thm)],[201]) ).
cnf(203,plain,
( sdtasdt0(smndt0(X2),X1) = smndt0(sdtasdt0(X2,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[202]) ).
cnf(204,plain,
( sdtasdt0(X2,smndt0(X1)) = smndt0(sdtasdt0(X2,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[202]) ).
cnf(206,plain,
aScalar0(xC),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(231,plain,
xN = sdtasdt0(xR,xS),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(232,plain,
aScalar0(xN),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(301,plain,
( sdtasdt0(X1,smndt0(X2)) = sdtasdt0(smndt0(X1),X2)
| ~ aScalar0(X2)
| ~ aScalar0(smndt0(X1))
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[195,76,theory(equality)]) ).
cnf(306,plain,
( smndt0(xR) = sdtasdt0(xC,smndt0(xG))
| ~ aScalar0(xC)
| ~ aScalar0(xG) ),
inference(spm,[status(thm)],[204,173,theory(equality)]) ).
cnf(311,plain,
( aScalar0(sdtasdt0(X1,smndt0(X2)))
| ~ aScalar0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(spm,[status(thm)],[127,204,theory(equality)]) ).
cnf(326,plain,
( smndt0(xR) = sdtasdt0(xC,smndt0(xG))
| $false
| ~ aScalar0(xG) ),
inference(rw,[status(thm)],[306,206,theory(equality)]) ).
cnf(327,plain,
( smndt0(xR) = sdtasdt0(xC,smndt0(xG))
| $false
| $false ),
inference(rw,[status(thm)],[326,184,theory(equality)]) ).
cnf(328,plain,
smndt0(xR) = sdtasdt0(xC,smndt0(xG)),
inference(cn,[status(thm)],[327,theory(equality)]) ).
cnf(429,plain,
( smndt0(xN) = sdtasdt0(smndt0(xR),xS)
| ~ aScalar0(xR)
| ~ aScalar0(xS) ),
inference(spm,[status(thm)],[203,231,theory(equality)]) ).
cnf(446,plain,
( smndt0(xN) = sdtasdt0(smndt0(xR),xS)
| $false
| ~ aScalar0(xS) ),
inference(rw,[status(thm)],[429,174,theory(equality)]) ).
cnf(447,plain,
( smndt0(xN) = sdtasdt0(smndt0(xR),xS)
| $false
| $false ),
inference(rw,[status(thm)],[446,179,theory(equality)]) ).
cnf(448,plain,
smndt0(xN) = sdtasdt0(smndt0(xR),xS),
inference(cn,[status(thm)],[447,theory(equality)]) ).
cnf(469,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[110,232,theory(equality)]) ).
cnf(2649,plain,
( sdtasdt0(smndt0(X1),X2) = sdtasdt0(X1,smndt0(X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(csr,[status(thm)],[301,127]) ).
cnf(2658,negated_conjecture,
( sdtasdt0(xS,smndt0(xR)) != smndt0(xN)
| ~ aScalar0(xR)
| ~ aScalar0(xS) ),
inference(spm,[status(thm)],[199,2649,theory(equality)]) ).
cnf(2716,negated_conjecture,
( sdtasdt0(xS,smndt0(xR)) != smndt0(xN)
| $false
| ~ aScalar0(xS) ),
inference(rw,[status(thm)],[2658,174,theory(equality)]) ).
cnf(2717,negated_conjecture,
( sdtasdt0(xS,smndt0(xR)) != smndt0(xN)
| $false
| $false ),
inference(rw,[status(thm)],[2716,179,theory(equality)]) ).
cnf(2718,negated_conjecture,
sdtasdt0(xS,smndt0(xR)) != smndt0(xN),
inference(cn,[status(thm)],[2717,theory(equality)]) ).
cnf(2937,plain,
( aScalar0(sdtasdt0(X1,smndt0(X2)))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(csr,[status(thm)],[311,198]) ).
cnf(2941,plain,
( aScalar0(smndt0(xR))
| ~ aScalar0(xC)
| ~ aScalar0(xG) ),
inference(spm,[status(thm)],[2937,328,theory(equality)]) ).
cnf(2977,plain,
( aScalar0(smndt0(xR))
| $false
| ~ aScalar0(xG) ),
inference(rw,[status(thm)],[2941,206,theory(equality)]) ).
cnf(2978,plain,
( aScalar0(smndt0(xR))
| $false
| $false ),
inference(rw,[status(thm)],[2977,184,theory(equality)]) ).
cnf(2979,plain,
aScalar0(smndt0(xR)),
inference(cn,[status(thm)],[2978,theory(equality)]) ).
cnf(11174,plain,
( sdtasdt0(xS,smndt0(xR)) = smndt0(xN)
| ~ aScalar0(xS)
| ~ aScalar0(smndt0(xR)) ),
inference(spm,[status(thm)],[448,469,theory(equality)]) ).
cnf(11368,plain,
( sdtasdt0(xS,smndt0(xR)) = smndt0(xN)
| $false
| ~ aScalar0(smndt0(xR)) ),
inference(rw,[status(thm)],[11174,179,theory(equality)]) ).
cnf(11369,plain,
( sdtasdt0(xS,smndt0(xR)) = smndt0(xN)
| $false
| $false ),
inference(rw,[status(thm)],[11368,2979,theory(equality)]) ).
cnf(11370,plain,
sdtasdt0(xS,smndt0(xR)) = smndt0(xN),
inference(cn,[status(thm)],[11369,theory(equality)]) ).
cnf(11371,plain,
$false,
inference(sr,[status(thm)],[11370,2718,theory(equality)]) ).
cnf(11372,plain,
$false,
11371,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/RNG/RNG059+2.p
% --creating new selector for []
% -running prover on /tmp/tmpaAKl0W/sel_RNG059+2.p_1 with time limit 29
% -prover status Theorem
% Problem RNG059+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/RNG/RNG059+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/RNG/RNG059+2.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
%
%------------------------------------------------------------------------------