TSTP Solution File: RNG120+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : RNG120+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 02:33:52 EST 2010
% Result : Theorem 0.31s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 63 ( 14 unt; 0 def)
% Number of atoms : 244 ( 22 equ)
% Maximal formula atoms : 29 ( 3 avg)
% Number of connectives : 305 ( 124 ~; 116 |; 54 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 50 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/tmp/tmpq3n1mp/sel_RNG120+1.p_1',mEOfElem) ).
fof(12,axiom,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
file('/tmp/tmpq3n1mp/sel_RNG120+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/tmpq3n1mp/sel_RNG120+1.p_1',m__2666) ).
fof(27,axiom,
aElement0(sz10),
file('/tmp/tmpq3n1mp/sel_RNG120+1.p_1',mSortsC_01) ).
fof(28,axiom,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/tmp/tmpq3n1mp/sel_RNG120+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/tmpq3n1mp/sel_RNG120+1.p_1',mDefIdeal) ).
fof(34,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/tmp/tmpq3n1mp/sel_RNG120+1.p_1',mSortsB_02) ).
fof(48,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('/tmp/tmpq3n1mp/sel_RNG120+1.p_1',mMulMnOne) ).
fof(49,axiom,
! [X1] :
( aElement0(X1)
=> aElement0(smndt0(X1)) ),
file('/tmp/tmpq3n1mp/sel_RNG120+1.p_1',mSortsU) ).
fof(52,conjecture,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
file('/tmp/tmpq3n1mp/sel_RNG120+1.p_1',m__) ).
fof(53,negated_conjecture,
~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(assume_negation,[status(cth)],[52]) ).
fof(55,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(57,negated_conjecture,
~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(fof_simplification,[status(thm)],[53,theory(equality)]) ).
fof(58,plain,
! [X1] :
( ~ aSet0(X1)
| ! [X2] :
( ~ aElementOf0(X2,X1)
| aElement0(X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(59,plain,
! [X3] :
( ~ aSet0(X3)
| ! [X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4) ) ),
inference(variable_rename,[status(thm)],[58]) ).
fof(60,plain,
! [X3,X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4)
| ~ aSet0(X3) ),
inference(shift_quantors,[status(thm)],[59]) ).
cnf(61,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[60]) ).
fof(109,plain,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ~ aElementOf0(X1,xI)
| X1 = sz00
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
inference(fof_nnf,[status(thm)],[55]) ).
fof(110,plain,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X2] :
( ~ aElementOf0(X2,xI)
| X2 = sz00
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) ) ),
inference(variable_rename,[status(thm)],[109]) ).
fof(111,plain,
! [X2] :
( ( ~ aElementOf0(X2,xI)
| X2 = sz00
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
& aElementOf0(xu,xI)
& xu != sz00 ),
inference(shift_quantors,[status(thm)],[110]) ).
cnf(113,plain,
aElementOf0(xu,xI),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(118,plain,
aElement0(xq),
inference(split_conjunct,[status(thm)],[13]) ).
cnf(173,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(175,plain,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[28]) ).
fof(176,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(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)
| ? [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)],[176]) ).
fof(178,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)],[177]) ).
fof(179,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)],[178]) ).
fof(180,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)],[179]) ).
cnf(186,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[180]) ).
cnf(188,plain,
( aElementOf0(sdtasdt0(X3,X2),X1)
| ~ aIdeal0(X1)
| ~ aElementOf0(X2,X1)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[180]) ).
fof(215,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| aElement0(sdtasdt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(216,plain,
! [X3,X4] :
( ~ aElement0(X3)
| ~ aElement0(X4)
| aElement0(sdtasdt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[215]) ).
cnf(217,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[216]) ).
fof(266,plain,
! [X1] :
( ~ aElement0(X1)
| ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
inference(fof_nnf,[status(thm)],[48]) ).
fof(267,plain,
! [X2] :
( ~ aElement0(X2)
| ( sdtasdt0(smndt0(sz10),X2) = smndt0(X2)
& smndt0(X2) = sdtasdt0(X2,smndt0(sz10)) ) ),
inference(variable_rename,[status(thm)],[266]) ).
fof(268,plain,
! [X2] :
( ( sdtasdt0(smndt0(sz10),X2) = smndt0(X2)
| ~ aElement0(X2) )
& ( smndt0(X2) = sdtasdt0(X2,smndt0(sz10))
| ~ aElement0(X2) ) ),
inference(distribute,[status(thm)],[267]) ).
cnf(270,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[268]) ).
fof(271,plain,
! [X1] :
( ~ aElement0(X1)
| aElement0(smndt0(X1)) ),
inference(fof_nnf,[status(thm)],[49]) ).
fof(272,plain,
! [X2] :
( ~ aElement0(X2)
| aElement0(smndt0(X2)) ),
inference(variable_rename,[status(thm)],[271]) ).
cnf(273,plain,
( aElement0(smndt0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[272]) ).
cnf(291,negated_conjecture,
~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(split_conjunct,[status(thm)],[57]) ).
cnf(292,plain,
aSet0(xI),
inference(spm,[status(thm)],[186,175,theory(equality)]) ).
cnf(301,plain,
( aElement0(xu)
| ~ aSet0(xI) ),
inference(spm,[status(thm)],[61,113,theory(equality)]) ).
cnf(449,plain,
( aElementOf0(smndt0(X1),X2)
| ~ aIdeal0(X2)
| ~ aElement0(smndt0(sz10))
| ~ aElementOf0(X1,X2)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[188,270,theory(equality)]) ).
cnf(791,plain,
( aElement0(xu)
| $false ),
inference(rw,[status(thm)],[301,292,theory(equality)]) ).
cnf(792,plain,
aElement0(xu),
inference(cn,[status(thm)],[791,theory(equality)]) ).
cnf(1751,negated_conjecture,
( ~ aIdeal0(xI)
| ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtasdt0(xq,xu))
| ~ aElementOf0(sdtasdt0(xq,xu),xI) ),
inference(spm,[status(thm)],[291,449,theory(equality)]) ).
cnf(1759,negated_conjecture,
( $false
| ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtasdt0(xq,xu))
| ~ aElementOf0(sdtasdt0(xq,xu),xI) ),
inference(rw,[status(thm)],[1751,175,theory(equality)]) ).
cnf(1760,negated_conjecture,
( ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtasdt0(xq,xu))
| ~ aElementOf0(sdtasdt0(xq,xu),xI) ),
inference(cn,[status(thm)],[1759,theory(equality)]) ).
cnf(2023,negated_conjecture,
( ~ aElement0(sdtasdt0(xq,xu))
| ~ aElementOf0(sdtasdt0(xq,xu),xI)
| ~ aElement0(sz10) ),
inference(spm,[status(thm)],[1760,273,theory(equality)]) ).
cnf(2025,negated_conjecture,
( ~ aElement0(sdtasdt0(xq,xu))
| ~ aElementOf0(sdtasdt0(xq,xu),xI)
| $false ),
inference(rw,[status(thm)],[2023,173,theory(equality)]) ).
cnf(2026,negated_conjecture,
( ~ aElement0(sdtasdt0(xq,xu))
| ~ aElementOf0(sdtasdt0(xq,xu),xI) ),
inference(cn,[status(thm)],[2025,theory(equality)]) ).
cnf(2029,negated_conjecture,
( ~ aElement0(sdtasdt0(xq,xu))
| ~ aIdeal0(xI)
| ~ aElement0(xq)
| ~ aElementOf0(xu,xI) ),
inference(spm,[status(thm)],[2026,188,theory(equality)]) ).
cnf(2037,negated_conjecture,
( ~ aElement0(sdtasdt0(xq,xu))
| $false
| ~ aElement0(xq)
| ~ aElementOf0(xu,xI) ),
inference(rw,[status(thm)],[2029,175,theory(equality)]) ).
cnf(2038,negated_conjecture,
( ~ aElement0(sdtasdt0(xq,xu))
| $false
| $false
| ~ aElementOf0(xu,xI) ),
inference(rw,[status(thm)],[2037,118,theory(equality)]) ).
cnf(2039,negated_conjecture,
( ~ aElement0(sdtasdt0(xq,xu))
| $false
| $false
| $false ),
inference(rw,[status(thm)],[2038,113,theory(equality)]) ).
cnf(2040,negated_conjecture,
~ aElement0(sdtasdt0(xq,xu)),
inference(cn,[status(thm)],[2039,theory(equality)]) ).
cnf(2075,negated_conjecture,
( ~ aElement0(xu)
| ~ aElement0(xq) ),
inference(spm,[status(thm)],[2040,217,theory(equality)]) ).
cnf(2080,negated_conjecture,
( $false
| ~ aElement0(xq) ),
inference(rw,[status(thm)],[2075,792,theory(equality)]) ).
cnf(2081,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[2080,118,theory(equality)]) ).
cnf(2082,negated_conjecture,
$false,
inference(cn,[status(thm)],[2081,theory(equality)]) ).
cnf(2083,negated_conjecture,
$false,
2082,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/RNG/RNG120+1.p
% --creating new selector for []
% -running prover on /tmp/tmpq3n1mp/sel_RNG120+1.p_1 with time limit 29
% -prover status Theorem
% Problem RNG120+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/RNG/RNG120+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/RNG/RNG120+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
%
%------------------------------------------------------------------------------