%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : RNG099+1 : 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 02:21:06 EST 2010
% Result : Theorem 0.27s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 75 ( 20 unt; 0 def)
% Number of atoms : 277 ( 3 equ)
% Maximal formula atoms : 29 ( 3 avg)
% Number of connectives : 349 ( 147 ~; 144 |; 48 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn 58 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
( aElement0(xx)
& aElement0(xy) ),
file('/tmp/tmpguXJ2B/sel_RNG099+1.p_1',m__1217) ).
fof(2,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/tmp/tmpguXJ2B/sel_RNG099+1.p_1',mEOfElem) ).
fof(4,axiom,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/tmp/tmpguXJ2B/sel_RNG099+1.p_1',m__1319) ).
fof(7,axiom,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/tmp/tmpguXJ2B/sel_RNG099+1.p_1',m__1332) ).
fof(10,axiom,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
file('/tmp/tmpguXJ2B/sel_RNG099+1.p_1',m__1409) ).
fof(11,axiom,
( aElementOf0(xa,xI)
& aElementOf0(xb,xJ)
& sdtpldt0(xa,xb) = sz10 ),
file('/tmp/tmpguXJ2B/sel_RNG099+1.p_1',m__1294) ).
fof(20,axiom,
! [X1] :
( aIdeal0(X1)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> ( ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(sdtpldt0(X2,X3),X1) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) ),
file('/tmp/tmpguXJ2B/sel_RNG099+1.p_1',mDefIdeal) ).
fof(24,axiom,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/tmp/tmpguXJ2B/sel_RNG099+1.p_1',m__1205) ).
fof(25,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/tmp/tmpguXJ2B/sel_RNG099+1.p_1',mSortsB_02) ).
fof(27,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/tmp/tmpguXJ2B/sel_RNG099+1.p_1',mSortsB) ).
fof(33,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aIdeal0(X3) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aElementOf0(sdtpldt0(X1,smndt0(X2)),X3) ) ),
file('/tmp/tmpguXJ2B/sel_RNG099+1.p_1',mDefMod) ).
fof(35,conjecture,
? [X1] :
( aElement0(X1)
& sdteqdtlpzmzozddtrp0(X1,xx,xI)
& sdteqdtlpzmzozddtrp0(X1,xy,xJ) ),
file('/tmp/tmpguXJ2B/sel_RNG099+1.p_1',m__) ).
fof(36,negated_conjecture,
~ ? [X1] :
( aElement0(X1)
& sdteqdtlpzmzozddtrp0(X1,xx,xI)
& sdteqdtlpzmzozddtrp0(X1,xy,xJ) ),
inference(assume_negation,[status(cth)],[35]) ).
cnf(37,plain,
aElement0(xy),
inference(split_conjunct,[status(thm)],[1]) ).
cnf(38,plain,
aElement0(xx),
inference(split_conjunct,[status(thm)],[1]) ).
fof(39,plain,
! [X1] :
( ~ aSet0(X1)
| ! [X2] :
( ~ aElementOf0(X2,X1)
| aElement0(X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(40,plain,
! [X3] :
( ~ aSet0(X3)
| ! [X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4) ) ),
inference(variable_rename,[status(thm)],[39]) ).
fof(41,plain,
! [X3,X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4)
| ~ aSet0(X3) ),
inference(shift_quantors,[status(thm)],[40]) ).
cnf(42,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[41]) ).
cnf(46,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(split_conjunct,[status(thm)],[4]) ).
cnf(55,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(split_conjunct,[status(thm)],[7]) ).
cnf(69,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(split_conjunct,[status(thm)],[10]) ).
cnf(71,plain,
aElementOf0(xb,xJ),
inference(split_conjunct,[status(thm)],[11]) ).
cnf(72,plain,
aElementOf0(xa,xI),
inference(split_conjunct,[status(thm)],[11]) ).
fof(95,plain,
! [X1] :
( ( ~ aIdeal0(X1)
| ( aSet0(X1)
& ! [X2] :
( ~ aElementOf0(X2,X1)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(sdtpldt0(X2,X3),X1) )
& ! [X3] :
( ~ aElement0(X3)
| aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) )
& ( ~ aSet0(X1)
| ? [X2] :
( aElementOf0(X2,X1)
& ( ? [X3] :
( aElementOf0(X3,X1)
& ~ aElementOf0(sdtpldt0(X2,X3),X1) )
| ? [X3] :
( aElement0(X3)
& ~ aElementOf0(sdtasdt0(X3,X2),X1) ) ) )
| aIdeal0(X1) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(96,plain,
! [X4] :
( ( ~ aIdeal0(X4)
| ( aSet0(X4)
& ! [X5] :
( ~ aElementOf0(X5,X4)
| ( ! [X6] :
( ~ aElementOf0(X6,X4)
| aElementOf0(sdtpldt0(X5,X6),X4) )
& ! [X7] :
( ~ aElement0(X7)
| aElementOf0(sdtasdt0(X7,X5),X4) ) ) ) ) )
& ( ~ aSet0(X4)
| ? [X8] :
( aElementOf0(X8,X4)
& ( ? [X9] :
( aElementOf0(X9,X4)
& ~ aElementOf0(sdtpldt0(X8,X9),X4) )
| ? [X10] :
( aElement0(X10)
& ~ aElementOf0(sdtasdt0(X10,X8),X4) ) ) )
| aIdeal0(X4) ) ),
inference(variable_rename,[status(thm)],[95]) ).
fof(97,plain,
! [X4] :
( ( ~ aIdeal0(X4)
| ( aSet0(X4)
& ! [X5] :
( ~ aElementOf0(X5,X4)
| ( ! [X6] :
( ~ aElementOf0(X6,X4)
| aElementOf0(sdtpldt0(X5,X6),X4) )
& ! [X7] :
( ~ aElement0(X7)
| aElementOf0(sdtasdt0(X7,X5),X4) ) ) ) ) )
& ( ~ aSet0(X4)
| ( aElementOf0(esk3_1(X4),X4)
& ( ( aElementOf0(esk4_1(X4),X4)
& ~ aElementOf0(sdtpldt0(esk3_1(X4),esk4_1(X4)),X4) )
| ( aElement0(esk5_1(X4))
& ~ aElementOf0(sdtasdt0(esk5_1(X4),esk3_1(X4)),X4) ) ) )
| aIdeal0(X4) ) ),
inference(skolemize,[status(esa)],[96]) ).
fof(98,plain,
! [X4,X5,X6,X7] :
( ( ( ( ( ( ~ aElement0(X7)
| aElementOf0(sdtasdt0(X7,X5),X4) )
& ( ~ aElementOf0(X6,X4)
| aElementOf0(sdtpldt0(X5,X6),X4) ) )
| ~ aElementOf0(X5,X4) )
& aSet0(X4) )
| ~ aIdeal0(X4) )
& ( ~ aSet0(X4)
| ( aElementOf0(esk3_1(X4),X4)
& ( ( aElementOf0(esk4_1(X4),X4)
& ~ aElementOf0(sdtpldt0(esk3_1(X4),esk4_1(X4)),X4) )
| ( aElement0(esk5_1(X4))
& ~ aElementOf0(sdtasdt0(esk5_1(X4),esk3_1(X4)),X4) ) ) )
| aIdeal0(X4) ) ),
inference(shift_quantors,[status(thm)],[97]) ).
fof(99,plain,
! [X4,X5,X6,X7] :
( ( ~ aElement0(X7)
| aElementOf0(sdtasdt0(X7,X5),X4)
| ~ aElementOf0(X5,X4)
| ~ aIdeal0(X4) )
& ( ~ aElementOf0(X6,X4)
| aElementOf0(sdtpldt0(X5,X6),X4)
| ~ aElementOf0(X5,X4)
| ~ aIdeal0(X4) )
& ( aSet0(X4)
| ~ aIdeal0(X4) )
& ( aElementOf0(esk3_1(X4),X4)
| ~ aSet0(X4)
| aIdeal0(X4) )
& ( aElement0(esk5_1(X4))
| aElementOf0(esk4_1(X4),X4)
| ~ aSet0(X4)
| aIdeal0(X4) )
& ( ~ aElementOf0(sdtasdt0(esk5_1(X4),esk3_1(X4)),X4)
| aElementOf0(esk4_1(X4),X4)
| ~ aSet0(X4)
| aIdeal0(X4) )
& ( aElement0(esk5_1(X4))
| ~ aElementOf0(sdtpldt0(esk3_1(X4),esk4_1(X4)),X4)
| ~ aSet0(X4)
| aIdeal0(X4) )
& ( ~ aElementOf0(sdtasdt0(esk5_1(X4),esk3_1(X4)),X4)
| ~ aElementOf0(sdtpldt0(esk3_1(X4),esk4_1(X4)),X4)
| ~ aSet0(X4)
| aIdeal0(X4) ) ),
inference(distribute,[status(thm)],[98]) ).
cnf(105,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[99]) ).
cnf(130,plain,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[24]) ).
cnf(131,plain,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[24]) ).
fof(132,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| aElement0(sdtasdt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(133,plain,
! [X3,X4] :
( ~ aElement0(X3)
| ~ aElement0(X4)
| aElement0(sdtasdt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[132]) ).
cnf(134,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[133]) ).
fof(136,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| aElement0(sdtpldt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(137,plain,
! [X3,X4] :
( ~ aElement0(X3)
| ~ aElement0(X4)
| aElement0(sdtpldt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[136]) ).
cnf(138,plain,
( aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[137]) ).
fof(158,plain,
! [X1,X2,X3] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aIdeal0(X3)
| ( ( ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| aElementOf0(sdtpldt0(X1,smndt0(X2)),X3) )
& ( ~ aElementOf0(sdtpldt0(X1,smndt0(X2)),X3)
| sdteqdtlpzmzozddtrp0(X1,X2,X3) ) ) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(159,plain,
! [X4,X5,X6] :
( ~ aElement0(X4)
| ~ aElement0(X5)
| ~ aIdeal0(X6)
| ( ( ~ sdteqdtlpzmzozddtrp0(X4,X5,X6)
| aElementOf0(sdtpldt0(X4,smndt0(X5)),X6) )
& ( ~ aElementOf0(sdtpldt0(X4,smndt0(X5)),X6)
| sdteqdtlpzmzozddtrp0(X4,X5,X6) ) ) ),
inference(variable_rename,[status(thm)],[158]) ).
fof(160,plain,
! [X4,X5,X6] :
( ( ~ sdteqdtlpzmzozddtrp0(X4,X5,X6)
| aElementOf0(sdtpldt0(X4,smndt0(X5)),X6)
| ~ aElement0(X4)
| ~ aElement0(X5)
| ~ aIdeal0(X6) )
& ( ~ aElementOf0(sdtpldt0(X4,smndt0(X5)),X6)
| sdteqdtlpzmzozddtrp0(X4,X5,X6)
| ~ aElement0(X4)
| ~ aElement0(X5)
| ~ aIdeal0(X6) ) ),
inference(distribute,[status(thm)],[159]) ).
cnf(161,plain,
( sdteqdtlpzmzozddtrp0(X3,X2,X1)
| ~ aIdeal0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ aElementOf0(sdtpldt0(X3,smndt0(X2)),X1) ),
inference(split_conjunct,[status(thm)],[160]) ).
fof(175,negated_conjecture,
! [X1] :
( ~ aElement0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(X1,xy,xJ) ),
inference(fof_nnf,[status(thm)],[36]) ).
fof(176,negated_conjecture,
! [X2] :
( ~ aElement0(X2)
| ~ sdteqdtlpzmzozddtrp0(X2,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(X2,xy,xJ) ),
inference(variable_rename,[status(thm)],[175]) ).
cnf(177,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(X1,xy,xJ)
| ~ sdteqdtlpzmzozddtrp0(X1,xx,xI)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[176]) ).
cnf(178,plain,
aSet0(xI),
inference(spm,[status(thm)],[105,131,theory(equality)]) ).
cnf(179,plain,
aSet0(xJ),
inference(spm,[status(thm)],[105,130,theory(equality)]) ).
cnf(180,plain,
( aElement0(xa)
| ~ aSet0(xI) ),
inference(spm,[status(thm)],[42,72,theory(equality)]) ).
cnf(181,plain,
( aElement0(xb)
| ~ aSet0(xJ) ),
inference(spm,[status(thm)],[42,71,theory(equality)]) ).
cnf(225,plain,
( aElement0(xw)
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(spm,[status(thm)],[138,46,theory(equality)]) ).
cnf(366,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(X1,xy,xJ)
| ~ aElement0(X1)
| ~ aIdeal0(xI)
| ~ aElementOf0(sdtpldt0(X1,smndt0(xx)),xI)
| ~ aElement0(xx) ),
inference(spm,[status(thm)],[177,161,theory(equality)]) ).
cnf(367,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(X1,xy,xJ)
| ~ aElement0(X1)
| $false
| ~ aElementOf0(sdtpldt0(X1,smndt0(xx)),xI)
| ~ aElement0(xx) ),
inference(rw,[status(thm)],[366,131,theory(equality)]) ).
cnf(368,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(X1,xy,xJ)
| ~ aElement0(X1)
| $false
| ~ aElementOf0(sdtpldt0(X1,smndt0(xx)),xI)
| $false ),
inference(rw,[status(thm)],[367,38,theory(equality)]) ).
cnf(369,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(X1,xy,xJ)
| ~ aElement0(X1)
| ~ aElementOf0(sdtpldt0(X1,smndt0(xx)),xI) ),
inference(cn,[status(thm)],[368,theory(equality)]) ).
cnf(472,negated_conjecture,
( ~ aElementOf0(sdtpldt0(X1,smndt0(xx)),xI)
| ~ aElement0(X1)
| ~ aIdeal0(xJ)
| ~ aElementOf0(sdtpldt0(X1,smndt0(xy)),xJ)
| ~ aElement0(xy) ),
inference(spm,[status(thm)],[369,161,theory(equality)]) ).
cnf(473,negated_conjecture,
( ~ aElementOf0(sdtpldt0(X1,smndt0(xx)),xI)
| ~ aElement0(X1)
| $false
| ~ aElementOf0(sdtpldt0(X1,smndt0(xy)),xJ)
| ~ aElement0(xy) ),
inference(rw,[status(thm)],[472,130,theory(equality)]) ).
cnf(474,negated_conjecture,
( ~ aElementOf0(sdtpldt0(X1,smndt0(xx)),xI)
| ~ aElement0(X1)
| $false
| ~ aElementOf0(sdtpldt0(X1,smndt0(xy)),xJ)
| $false ),
inference(rw,[status(thm)],[473,37,theory(equality)]) ).
cnf(475,negated_conjecture,
( ~ aElementOf0(sdtpldt0(X1,smndt0(xx)),xI)
| ~ aElement0(X1)
| ~ aElementOf0(sdtpldt0(X1,smndt0(xy)),xJ) ),
inference(cn,[status(thm)],[474,theory(equality)]) ).
cnf(476,plain,
( ~ aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ)
| ~ aElement0(xw) ),
inference(spm,[status(thm)],[475,55,theory(equality)]) ).
cnf(484,plain,
( $false
| ~ aElement0(xw) ),
inference(rw,[status(thm)],[476,69,theory(equality)]) ).
cnf(485,plain,
~ aElement0(xw),
inference(cn,[status(thm)],[484,theory(equality)]) ).
cnf(506,plain,
( aElement0(xa)
| $false ),
inference(rw,[status(thm)],[180,178,theory(equality)]) ).
cnf(507,plain,
aElement0(xa),
inference(cn,[status(thm)],[506,theory(equality)]) ).
cnf(508,plain,
( aElement0(xb)
| $false ),
inference(rw,[status(thm)],[181,179,theory(equality)]) ).
cnf(509,plain,
aElement0(xb),
inference(cn,[status(thm)],[508,theory(equality)]) ).
cnf(607,plain,
( ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(sr,[status(thm)],[225,485,theory(equality)]) ).
cnf(608,plain,
( ~ aElement0(sdtasdt0(xy,xa))
| ~ aElement0(xb)
| ~ aElement0(xx) ),
inference(spm,[status(thm)],[607,134,theory(equality)]) ).
cnf(609,plain,
( ~ aElement0(sdtasdt0(xy,xa))
| $false
| ~ aElement0(xx) ),
inference(rw,[status(thm)],[608,509,theory(equality)]) ).
cnf(610,plain,
( ~ aElement0(sdtasdt0(xy,xa))
| $false
| $false ),
inference(rw,[status(thm)],[609,38,theory(equality)]) ).
cnf(611,plain,
~ aElement0(sdtasdt0(xy,xa)),
inference(cn,[status(thm)],[610,theory(equality)]) ).
cnf(612,plain,
( ~ aElement0(xa)
| ~ aElement0(xy) ),
inference(spm,[status(thm)],[611,134,theory(equality)]) ).
cnf(613,plain,
( $false
| ~ aElement0(xy) ),
inference(rw,[status(thm)],[612,507,theory(equality)]) ).
cnf(614,plain,
( $false
| $false ),
inference(rw,[status(thm)],[613,37,theory(equality)]) ).
cnf(615,plain,
$false,
inference(cn,[status(thm)],[614,theory(equality)]) ).
cnf(616,plain,
$false,
615,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/RNG/RNG099+1.p
% --creating new selector for []
% -running prover on /tmp/tmpguXJ2B/sel_RNG099+1.p_1 with time limit 29
% -prover status Theorem
% Problem RNG099+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/RNG/RNG099+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/RNG/RNG099+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
%
%------------------------------------------------------------------------------