TSTP Solution File: RNG119+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : RNG119+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 02:33:17 EST 2010
% Result : Theorem 0.31s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 12
% Syntax : Number of formulae : 75 ( 21 unt; 0 def)
% Number of atoms : 301 ( 58 equ)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 372 ( 146 ~; 145 |; 68 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn 70 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/tmp/tmptXSq2t/sel_RNG119+1.p_1',mEOfElem) ).
fof(5,axiom,
~ doDivides0(xu,xb),
file('/tmp/tmptXSq2t/sel_RNG119+1.p_1',m__2612) ).
fof(9,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X1,X3) = X2 ) ) ),
file('/tmp/tmptXSq2t/sel_RNG119+1.p_1',mDefDiv) ).
fof(12,axiom,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
file('/tmp/tmptXSq2t/sel_RNG119+1.p_1',m__2273) ).
fof(13,axiom,
( aElement0(xq)
& aElement0(xr)
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& ( xr = sz00
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
file('/tmp/tmptXSq2t/sel_RNG119+1.p_1',m__2666) ).
fof(28,axiom,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/tmp/tmptXSq2t/sel_RNG119+1.p_1',m__2174) ).
fof(29,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/tmptXSq2t/sel_RNG119+1.p_1',mDefIdeal) ).
fof(34,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/tmp/tmptXSq2t/sel_RNG119+1.p_1',mSortsB_02) ).
fof(39,axiom,
( aElement0(xa)
& aElement0(xb) ),
file('/tmp/tmptXSq2t/sel_RNG119+1.p_1',m__2091) ).
fof(41,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/tmp/tmptXSq2t/sel_RNG119+1.p_1',mAddZero) ).
fof(42,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/tmp/tmptXSq2t/sel_RNG119+1.p_1',mMulComm) ).
fof(51,conjecture,
xr != sz00,
file('/tmp/tmptXSq2t/sel_RNG119+1.p_1',m__) ).
fof(52,negated_conjecture,
~ ( xr != sz00 ),
inference(assume_negation,[status(cth)],[51]) ).
fof(53,plain,
~ doDivides0(xu,xb),
inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).
fof(54,plain,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).
fof(56,negated_conjecture,
xr = sz00,
inference(fof_simplification,[status(thm)],[52,theory(equality)]) ).
fof(57,plain,
! [X1] :
( ~ aSet0(X1)
| ! [X2] :
( ~ aElementOf0(X2,X1)
| aElement0(X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(58,plain,
! [X3] :
( ~ aSet0(X3)
| ! [X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4) ) ),
inference(variable_rename,[status(thm)],[57]) ).
fof(59,plain,
! [X3,X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4)
| ~ aSet0(X3) ),
inference(shift_quantors,[status(thm)],[58]) ).
cnf(60,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(72,plain,
~ doDivides0(xu,xb),
inference(split_conjunct,[status(thm)],[53]) ).
fof(90,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| ( ( ~ doDivides0(X1,X2)
| ? [X3] :
( aElement0(X3)
& sdtasdt0(X1,X3) = X2 ) )
& ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X1,X3) != X2 )
| doDivides0(X1,X2) ) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(91,plain,
! [X4,X5] :
( ~ aElement0(X4)
| ~ aElement0(X5)
| ( ( ~ doDivides0(X4,X5)
| ? [X6] :
( aElement0(X6)
& sdtasdt0(X4,X6) = X5 ) )
& ( ! [X7] :
( ~ aElement0(X7)
| sdtasdt0(X4,X7) != X5 )
| doDivides0(X4,X5) ) ) ),
inference(variable_rename,[status(thm)],[90]) ).
fof(92,plain,
! [X4,X5] :
( ~ aElement0(X4)
| ~ aElement0(X5)
| ( ( ~ doDivides0(X4,X5)
| ( aElement0(esk3_2(X4,X5))
& sdtasdt0(X4,esk3_2(X4,X5)) = X5 ) )
& ( ! [X7] :
( ~ aElement0(X7)
| sdtasdt0(X4,X7) != X5 )
| doDivides0(X4,X5) ) ) ),
inference(skolemize,[status(esa)],[91]) ).
fof(93,plain,
! [X4,X5,X7] :
( ( ( ~ aElement0(X7)
| sdtasdt0(X4,X7) != X5
| doDivides0(X4,X5) )
& ( ~ doDivides0(X4,X5)
| ( aElement0(esk3_2(X4,X5))
& sdtasdt0(X4,esk3_2(X4,X5)) = X5 ) ) )
| ~ aElement0(X4)
| ~ aElement0(X5) ),
inference(shift_quantors,[status(thm)],[92]) ).
fof(94,plain,
! [X4,X5,X7] :
( ( ~ aElement0(X7)
| sdtasdt0(X4,X7) != X5
| doDivides0(X4,X5)
| ~ aElement0(X4)
| ~ aElement0(X5) )
& ( aElement0(esk3_2(X4,X5))
| ~ doDivides0(X4,X5)
| ~ aElement0(X4)
| ~ aElement0(X5) )
& ( sdtasdt0(X4,esk3_2(X4,X5)) = X5
| ~ doDivides0(X4,X5)
| ~ aElement0(X4)
| ~ aElement0(X5) ) ),
inference(distribute,[status(thm)],[93]) ).
cnf(97,plain,
( doDivides0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2)
| sdtasdt0(X2,X3) != X1
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[94]) ).
fof(108,plain,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ~ aElementOf0(X1,xI)
| X1 = sz00
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
inference(fof_nnf,[status(thm)],[54]) ).
fof(109,plain,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X2] :
( ~ aElementOf0(X2,xI)
| X2 = sz00
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) ) ),
inference(variable_rename,[status(thm)],[108]) ).
fof(110,plain,
! [X2] :
( ( ~ aElementOf0(X2,xI)
| X2 = sz00
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
& aElementOf0(xu,xI)
& xu != sz00 ),
inference(shift_quantors,[status(thm)],[109]) ).
cnf(112,plain,
aElementOf0(xu,xI),
inference(split_conjunct,[status(thm)],[110]) ).
cnf(115,plain,
xb = sdtpldt0(sdtasdt0(xq,xu),xr),
inference(split_conjunct,[status(thm)],[13]) ).
cnf(117,plain,
aElement0(xq),
inference(split_conjunct,[status(thm)],[13]) ).
cnf(174,plain,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[28]) ).
fof(175,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)],[29]) ).
fof(176,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)],[175]) ).
fof(177,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(esk11_1(X4),X4)
& ( ( aElementOf0(esk12_1(X4),X4)
& ~ aElementOf0(sdtpldt0(esk11_1(X4),esk12_1(X4)),X4) )
| ( aElement0(esk13_1(X4))
& ~ aElementOf0(sdtasdt0(esk13_1(X4),esk11_1(X4)),X4) ) ) )
| aIdeal0(X4) ) ),
inference(skolemize,[status(esa)],[176]) ).
fof(178,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(esk11_1(X4),X4)
& ( ( aElementOf0(esk12_1(X4),X4)
& ~ aElementOf0(sdtpldt0(esk11_1(X4),esk12_1(X4)),X4) )
| ( aElement0(esk13_1(X4))
& ~ aElementOf0(sdtasdt0(esk13_1(X4),esk11_1(X4)),X4) ) ) )
| aIdeal0(X4) ) ),
inference(shift_quantors,[status(thm)],[177]) ).
fof(179,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(esk11_1(X4),X4)
| ~ aSet0(X4)
| aIdeal0(X4) )
& ( aElement0(esk13_1(X4))
| aElementOf0(esk12_1(X4),X4)
| ~ aSet0(X4)
| aIdeal0(X4) )
& ( ~ aElementOf0(sdtasdt0(esk13_1(X4),esk11_1(X4)),X4)
| aElementOf0(esk12_1(X4),X4)
| ~ aSet0(X4)
| aIdeal0(X4) )
& ( aElement0(esk13_1(X4))
| ~ aElementOf0(sdtpldt0(esk11_1(X4),esk12_1(X4)),X4)
| ~ aSet0(X4)
| aIdeal0(X4) )
& ( ~ aElementOf0(sdtasdt0(esk13_1(X4),esk11_1(X4)),X4)
| ~ aElementOf0(sdtpldt0(esk11_1(X4),esk12_1(X4)),X4)
| ~ aSet0(X4)
| aIdeal0(X4) ) ),
inference(distribute,[status(thm)],[178]) ).
cnf(185,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[179]) ).
fof(214,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| aElement0(sdtasdt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(215,plain,
! [X3,X4] :
( ~ aElement0(X3)
| ~ aElement0(X4)
| aElement0(sdtasdt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[214]) ).
cnf(216,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[215]) ).
cnf(235,plain,
aElement0(xb),
inference(split_conjunct,[status(thm)],[39]) ).
fof(245,plain,
! [X1] :
( ~ aElement0(X1)
| ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
inference(fof_nnf,[status(thm)],[41]) ).
fof(246,plain,
! [X2] :
( ~ aElement0(X2)
| ( sdtpldt0(X2,sz00) = X2
& X2 = sdtpldt0(sz00,X2) ) ),
inference(variable_rename,[status(thm)],[245]) ).
fof(247,plain,
! [X2] :
( ( sdtpldt0(X2,sz00) = X2
| ~ aElement0(X2) )
& ( X2 = sdtpldt0(sz00,X2)
| ~ aElement0(X2) ) ),
inference(distribute,[status(thm)],[246]) ).
cnf(249,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[247]) ).
fof(250,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(fof_nnf,[status(thm)],[42]) ).
fof(251,plain,
! [X3,X4] :
( ~ aElement0(X3)
| ~ aElement0(X4)
| sdtasdt0(X3,X4) = sdtasdt0(X4,X3) ),
inference(variable_rename,[status(thm)],[250]) ).
cnf(252,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[251]) ).
cnf(289,negated_conjecture,
xr = sz00,
inference(split_conjunct,[status(thm)],[56]) ).
cnf(291,plain,
aSet0(xI),
inference(spm,[status(thm)],[185,174,theory(equality)]) ).
cnf(292,plain,
sdtpldt0(sdtasdt0(xq,xu),sz00) = xb,
inference(rw,[status(thm)],[115,289,theory(equality)]) ).
cnf(293,plain,
( xb = sdtasdt0(xq,xu)
| ~ aElement0(sdtasdt0(xq,xu)) ),
inference(spm,[status(thm)],[249,292,theory(equality)]) ).
cnf(311,plain,
( aElement0(xu)
| ~ aSet0(xI) ),
inference(spm,[status(thm)],[60,112,theory(equality)]) ).
cnf(775,plain,
( sdtasdt0(xq,xu) = xb
| ~ aElement0(xu)
| ~ aElement0(xq) ),
inference(spm,[status(thm)],[293,216,theory(equality)]) ).
cnf(780,plain,
( sdtasdt0(xq,xu) = xb
| ~ aElement0(xu)
| $false ),
inference(rw,[status(thm)],[775,117,theory(equality)]) ).
cnf(781,plain,
( sdtasdt0(xq,xu) = xb
| ~ aElement0(xu) ),
inference(cn,[status(thm)],[780,theory(equality)]) ).
cnf(832,plain,
( aElement0(xu)
| $false ),
inference(rw,[status(thm)],[311,291,theory(equality)]) ).
cnf(833,plain,
aElement0(xu),
inference(cn,[status(thm)],[832,theory(equality)]) ).
cnf(969,plain,
( sdtasdt0(xq,xu) = xb
| $false ),
inference(rw,[status(thm)],[781,833,theory(equality)]) ).
cnf(970,plain,
sdtasdt0(xq,xu) = xb,
inference(cn,[status(thm)],[969,theory(equality)]) ).
cnf(971,plain,
( xb = sdtasdt0(xu,xq)
| ~ aElement0(xu)
| ~ aElement0(xq) ),
inference(spm,[status(thm)],[252,970,theory(equality)]) ).
cnf(987,plain,
( xb = sdtasdt0(xu,xq)
| $false
| ~ aElement0(xq) ),
inference(rw,[status(thm)],[971,833,theory(equality)]) ).
cnf(988,plain,
( xb = sdtasdt0(xu,xq)
| $false
| $false ),
inference(rw,[status(thm)],[987,117,theory(equality)]) ).
cnf(989,plain,
xb = sdtasdt0(xu,xq),
inference(cn,[status(thm)],[988,theory(equality)]) ).
cnf(1153,plain,
( doDivides0(xu,X1)
| xb != X1
| ~ aElement0(xq)
| ~ aElement0(xu)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[97,989,theory(equality)]) ).
cnf(1170,plain,
( doDivides0(xu,X1)
| xb != X1
| $false
| ~ aElement0(xu)
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[1153,117,theory(equality)]) ).
cnf(1171,plain,
( doDivides0(xu,X1)
| xb != X1
| $false
| $false
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[1170,833,theory(equality)]) ).
cnf(1172,plain,
( doDivides0(xu,X1)
| xb != X1
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[1171,theory(equality)]) ).
cnf(1248,plain,
~ aElement0(xb),
inference(spm,[status(thm)],[72,1172,theory(equality)]) ).
cnf(1250,plain,
$false,
inference(rw,[status(thm)],[1248,235,theory(equality)]) ).
cnf(1251,plain,
$false,
inference(cn,[status(thm)],[1250,theory(equality)]) ).
cnf(1252,plain,
$false,
1251,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/RNG/RNG119+1.p
% --creating new selector for []
% -running prover on /tmp/tmptXSq2t/sel_RNG119+1.p_1 with time limit 29
% -prover status Theorem
% Problem RNG119+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/RNG/RNG119+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/RNG/RNG119+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
%
%------------------------------------------------------------------------------