TSTP Solution File: RNG060+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : RNG060+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 01:56:08 EST 2010
% Result : Theorem 6.37s
% Output : CNFRefutation 6.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 16 unt; 0 def)
% Number of atoms : 142 ( 42 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 148 ( 61 ~; 68 |; 15 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2,X3,X4] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3)
& aScalar0(X4) )
=> sdtasdt0(sdtpldt0(X1,X2),sdtpldt0(X3,X4)) = sdtpldt0(sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X1,X4)),sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,X4))) ),
file('/tmp/tmppmQGsz/sel_RNG060+2.p_1',mDistr2) ).
fof(21,axiom,
! [X1] :
( aScalar0(X1)
=> aScalar0(smndt0(X1)) ),
file('/tmp/tmppmQGsz/sel_RNG060+2.p_1',mNegSc) ).
fof(23,axiom,
( sdtasdt0(xR,smndt0(xS)) = smndt0(xN)
& sdtasdt0(smndt0(xS),xR) = smndt0(xN)
& sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS) ),
file('/tmp/tmppmQGsz/sel_RNG060+2.p_1',m__2144) ).
fof(25,axiom,
( aScalar0(xF)
& xF = sdtasdt0(xA,xA) ),
file('/tmp/tmppmQGsz/sel_RNG060+2.p_1',m__1837) ).
fof(35,axiom,
( aScalar0(xR)
& xR = sdtasdt0(xC,xG) ),
file('/tmp/tmppmQGsz/sel_RNG060+2.p_1',m__1892) ).
fof(37,axiom,
( aScalar0(xS)
& xS = sdtasdt0(xF,xD) ),
file('/tmp/tmppmQGsz/sel_RNG060+2.p_1',m__1930) ).
fof(43,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/tmp/tmppmQGsz/sel_RNG060+2.p_1',mMulSc) ).
fof(44,conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
file('/tmp/tmppmQGsz/sel_RNG060+2.p_1',m__) ).
fof(45,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/tmppmQGsz/sel_RNG060+2.p_1',mMNeg) ).
fof(48,axiom,
( aScalar0(xD)
& xD = sdtasasdt0(xq,xq) ),
file('/tmp/tmppmQGsz/sel_RNG060+2.p_1',m__1800) ).
fof(60,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(assume_negation,[status(cth)],[44]) ).
fof(61,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(fof_simplification,[status(thm)],[60,theory(equality)]) ).
fof(65,plain,
! [X1,X2,X3,X4] :
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ aScalar0(X4)
| sdtasdt0(sdtpldt0(X1,X2),sdtpldt0(X3,X4)) = sdtpldt0(sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X1,X4)),sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,X4))) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(66,plain,
! [X5,X6,X7,X8] :
( ~ aScalar0(X5)
| ~ aScalar0(X6)
| ~ aScalar0(X7)
| ~ aScalar0(X8)
| sdtasdt0(sdtpldt0(X5,X6),sdtpldt0(X7,X8)) = sdtpldt0(sdtpldt0(sdtasdt0(X5,X7),sdtasdt0(X5,X8)),sdtpldt0(sdtasdt0(X6,X7),sdtasdt0(X6,X8))) ),
inference(variable_rename,[status(thm)],[65]) ).
cnf(67,plain,
( sdtasdt0(sdtpldt0(X1,X2),sdtpldt0(X3,X4)) = sdtpldt0(sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X1,X4)),sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,X4)))
| ~ aScalar0(X4)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[66]) ).
fof(126,plain,
! [X1] :
( ~ aScalar0(X1)
| aScalar0(smndt0(X1)) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(127,plain,
! [X2] :
( ~ aScalar0(X2)
| aScalar0(smndt0(X2)) ),
inference(variable_rename,[status(thm)],[126]) ).
cnf(128,plain,
( aScalar0(smndt0(X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[127]) ).
cnf(132,plain,
sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(133,plain,
sdtasdt0(smndt0(xS),xR) = smndt0(xN),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(134,plain,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(138,plain,
aScalar0(xF),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(178,plain,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(182,plain,
xS = sdtasdt0(xF,xD),
inference(split_conjunct,[status(thm)],[37]) ).
fof(200,plain,
! [X1,X2] :
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| aScalar0(sdtasdt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[43]) ).
fof(201,plain,
! [X3,X4] :
( ~ aScalar0(X3)
| ~ aScalar0(X4)
| aScalar0(sdtasdt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[200]) ).
cnf(202,plain,
( aScalar0(sdtasdt0(X1,X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[201]) ).
cnf(203,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(split_conjunct,[status(thm)],[61]) ).
fof(204,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)],[45]) ).
fof(205,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)],[204]) ).
fof(206,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)],[205]) ).
cnf(208,plain,
( sdtasdt0(X2,smndt0(X1)) = smndt0(sdtasdt0(X2,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[206]) ).
cnf(213,plain,
aScalar0(xD),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(403,plain,
( smndt0(xS) = sdtasdt0(xF,smndt0(xD))
| ~ aScalar0(xF)
| ~ aScalar0(xD) ),
inference(spm,[status(thm)],[208,182,theory(equality)]) ).
cnf(425,plain,
( smndt0(xS) = sdtasdt0(xF,smndt0(xD))
| $false
| ~ aScalar0(xD) ),
inference(rw,[status(thm)],[403,138,theory(equality)]) ).
cnf(426,plain,
( smndt0(xS) = sdtasdt0(xF,smndt0(xD))
| $false
| $false ),
inference(rw,[status(thm)],[425,213,theory(equality)]) ).
cnf(427,plain,
smndt0(xS) = sdtasdt0(xF,smndt0(xD)),
inference(cn,[status(thm)],[426,theory(equality)]) ).
cnf(1070,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xR,X1),smndt0(xN)),sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X2,smndt0(xS)))) = sdtasdt0(sdtpldt0(xR,X2),sdtpldt0(X1,smndt0(xS)))
| ~ aScalar0(smndt0(xS))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(xR) ),
inference(spm,[status(thm)],[67,134,theory(equality)]) ).
cnf(1161,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xR,X1),smndt0(xN)),sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X2,smndt0(xS)))) = sdtasdt0(sdtpldt0(xR,X2),sdtpldt0(X1,smndt0(xS)))
| ~ aScalar0(smndt0(xS))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| $false ),
inference(rw,[status(thm)],[1070,178,theory(equality)]) ).
cnf(1162,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xR,X1),smndt0(xN)),sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X2,smndt0(xS)))) = sdtasdt0(sdtpldt0(xR,X2),sdtpldt0(X1,smndt0(xS)))
| ~ aScalar0(smndt0(xS))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cn,[status(thm)],[1161,theory(equality)]) ).
cnf(1415,plain,
( aScalar0(smndt0(xS))
| ~ aScalar0(smndt0(xD))
| ~ aScalar0(xF) ),
inference(spm,[status(thm)],[202,427,theory(equality)]) ).
cnf(1430,plain,
( aScalar0(smndt0(xS))
| ~ aScalar0(smndt0(xD))
| $false ),
inference(rw,[status(thm)],[1415,138,theory(equality)]) ).
cnf(1431,plain,
( aScalar0(smndt0(xS))
| ~ aScalar0(smndt0(xD)) ),
inference(cn,[status(thm)],[1430,theory(equality)]) ).
cnf(3056,plain,
( aScalar0(smndt0(xS))
| ~ aScalar0(xD) ),
inference(spm,[status(thm)],[1431,128,theory(equality)]) ).
cnf(3057,plain,
( aScalar0(smndt0(xS))
| $false ),
inference(rw,[status(thm)],[3056,213,theory(equality)]) ).
cnf(3058,plain,
aScalar0(smndt0(xS)),
inference(cn,[status(thm)],[3057,theory(equality)]) ).
cnf(196012,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xR,X1),smndt0(xN)),sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X2,smndt0(xS)))) = sdtasdt0(sdtpldt0(xR,X2),sdtpldt0(X1,smndt0(xS)))
| $false
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(rw,[status(thm)],[1162,3058,theory(equality)]) ).
cnf(196013,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xR,X1),smndt0(xN)),sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X2,smndt0(xS)))) = sdtasdt0(sdtpldt0(xR,X2),sdtpldt0(X1,smndt0(xS)))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cn,[status(thm)],[196012,theory(equality)]) ).
cnf(196021,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(smndt0(xS),smndt0(xS)))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))
| ~ aScalar0(xR)
| ~ aScalar0(smndt0(xS)) ),
inference(spm,[status(thm)],[196013,133,theory(equality)]) ).
cnf(196529,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))
| ~ aScalar0(xR)
| ~ aScalar0(smndt0(xS)) ),
inference(rw,[status(thm)],[196021,132,theory(equality)]) ).
cnf(196530,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))
| $false
| ~ aScalar0(smndt0(xS)) ),
inference(rw,[status(thm)],[196529,178,theory(equality)]) ).
cnf(196531,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))
| $false
| $false ),
inference(rw,[status(thm)],[196530,3058,theory(equality)]) ).
cnf(196532,plain,
sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),
inference(cn,[status(thm)],[196531,theory(equality)]) ).
cnf(196533,plain,
$false,
inference(sr,[status(thm)],[196532,203,theory(equality)]) ).
cnf(196534,plain,
$false,
196533,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/RNG/RNG060+2.p
% --creating new selector for []
% -running prover on /tmp/tmppmQGsz/sel_RNG060+2.p_1 with time limit 29
% -prover status Theorem
% Problem RNG060+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/RNG/RNG060+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/RNG/RNG060+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
%
%------------------------------------------------------------------------------