TSTP Solution File: RNG125+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : RNG125+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 02:35:21 EST 2010
% Result : Theorem 0.29s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 17 unt; 0 def)
% Number of atoms : 226 ( 11 equ)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 280 ( 110 ~; 103 |; 57 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 47 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/tmp/tmpQPTtUR/sel_RNG125+1.p_1',mEOfElem) ).
fof(5,axiom,
~ ~ doDivides0(xu,xb),
file('/tmp/tmpQPTtUR/sel_RNG125+1.p_1',m__2612) ).
fof(10,axiom,
~ ( aDivisorOf0(xu,xa)
& aDivisorOf0(xu,xb) ),
file('/tmp/tmpQPTtUR/sel_RNG125+1.p_1',m__2383) ).
fof(12,axiom,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
file('/tmp/tmpQPTtUR/sel_RNG125+1.p_1',m__2273) ).
fof(21,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( aElement0(X2)
& doDivides0(X2,X1) ) ) ),
file('/tmp/tmpQPTtUR/sel_RNG125+1.p_1',mDefDvs) ).
fof(27,axiom,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/tmp/tmpQPTtUR/sel_RNG125+1.p_1',m__2174) ).
fof(28,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/tmpQPTtUR/sel_RNG125+1.p_1',mDefIdeal) ).
fof(38,axiom,
( aElement0(xa)
& aElement0(xb) ),
file('/tmp/tmpQPTtUR/sel_RNG125+1.p_1',m__2091) ).
fof(45,axiom,
~ ~ doDivides0(xu,xa),
file('/tmp/tmpQPTtUR/sel_RNG125+1.p_1',m__2479) ).
fof(52,plain,
doDivides0(xu,xb),
inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).
fof(53,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(54,plain,
doDivides0(xu,xa),
inference(fof_simplification,[status(thm)],[45,theory(equality)]) ).
fof(56,plain,
! [X1] :
( ~ aSet0(X1)
| ! [X2] :
( ~ aElementOf0(X2,X1)
| aElement0(X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(57,plain,
! [X3] :
( ~ aSet0(X3)
| ! [X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4) ) ),
inference(variable_rename,[status(thm)],[56]) ).
fof(58,plain,
! [X3,X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4)
| ~ aSet0(X3) ),
inference(shift_quantors,[status(thm)],[57]) ).
cnf(59,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(71,plain,
doDivides0(xu,xb),
inference(split_conjunct,[status(thm)],[52]) ).
fof(97,plain,
( ~ aDivisorOf0(xu,xa)
| ~ aDivisorOf0(xu,xb) ),
inference(fof_nnf,[status(thm)],[10]) ).
cnf(98,plain,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(split_conjunct,[status(thm)],[97]) ).
fof(107,plain,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ~ aElementOf0(X1,xI)
| X1 = sz00
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
inference(fof_nnf,[status(thm)],[53]) ).
fof(108,plain,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X2] :
( ~ aElementOf0(X2,xI)
| X2 = sz00
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) ) ),
inference(variable_rename,[status(thm)],[107]) ).
fof(109,plain,
! [X2] :
( ( ~ aElementOf0(X2,xI)
| X2 = sz00
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
& aElementOf0(xu,xI)
& xu != sz00 ),
inference(shift_quantors,[status(thm)],[108]) ).
cnf(111,plain,
aElementOf0(xu,xI),
inference(split_conjunct,[status(thm)],[109]) ).
fof(141,plain,
! [X1] :
( ~ aElement0(X1)
| ! [X2] :
( ( ~ aDivisorOf0(X2,X1)
| ( aElement0(X2)
& doDivides0(X2,X1) ) )
& ( ~ aElement0(X2)
| ~ doDivides0(X2,X1)
| aDivisorOf0(X2,X1) ) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(142,plain,
! [X3] :
( ~ aElement0(X3)
| ! [X4] :
( ( ~ aDivisorOf0(X4,X3)
| ( aElement0(X4)
& doDivides0(X4,X3) ) )
& ( ~ aElement0(X4)
| ~ doDivides0(X4,X3)
| aDivisorOf0(X4,X3) ) ) ),
inference(variable_rename,[status(thm)],[141]) ).
fof(143,plain,
! [X3,X4] :
( ( ( ~ aDivisorOf0(X4,X3)
| ( aElement0(X4)
& doDivides0(X4,X3) ) )
& ( ~ aElement0(X4)
| ~ doDivides0(X4,X3)
| aDivisorOf0(X4,X3) ) )
| ~ aElement0(X3) ),
inference(shift_quantors,[status(thm)],[142]) ).
fof(144,plain,
! [X3,X4] :
( ( aElement0(X4)
| ~ aDivisorOf0(X4,X3)
| ~ aElement0(X3) )
& ( doDivides0(X4,X3)
| ~ aDivisorOf0(X4,X3)
| ~ aElement0(X3) )
& ( ~ aElement0(X4)
| ~ doDivides0(X4,X3)
| aDivisorOf0(X4,X3)
| ~ aElement0(X3) ) ),
inference(distribute,[status(thm)],[143]) ).
cnf(145,plain,
( aDivisorOf0(X2,X1)
| ~ aElement0(X1)
| ~ doDivides0(X2,X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[144]) ).
cnf(169,plain,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[27]) ).
fof(170,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)],[28]) ).
fof(171,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)],[170]) ).
fof(172,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)],[171]) ).
fof(173,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)],[172]) ).
fof(174,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)],[173]) ).
cnf(180,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[174]) ).
cnf(230,plain,
aElement0(xb),
inference(split_conjunct,[status(thm)],[38]) ).
cnf(231,plain,
aElement0(xa),
inference(split_conjunct,[status(thm)],[38]) ).
cnf(258,plain,
doDivides0(xu,xa),
inference(split_conjunct,[status(thm)],[54]) ).
cnf(285,plain,
aSet0(xI),
inference(spm,[status(thm)],[180,169,theory(equality)]) ).
cnf(300,plain,
( aElement0(xu)
| ~ aSet0(xI) ),
inference(spm,[status(thm)],[59,111,theory(equality)]) ).
cnf(404,plain,
( aDivisorOf0(xu,xb)
| ~ aElement0(xu)
| ~ aElement0(xb) ),
inference(spm,[status(thm)],[145,71,theory(equality)]) ).
cnf(405,plain,
( aDivisorOf0(xu,xa)
| ~ aElement0(xu)
| ~ aElement0(xa) ),
inference(spm,[status(thm)],[145,258,theory(equality)]) ).
cnf(407,plain,
( aDivisorOf0(xu,xb)
| ~ aElement0(xu)
| $false ),
inference(rw,[status(thm)],[404,230,theory(equality)]) ).
cnf(408,plain,
( aDivisorOf0(xu,xb)
| ~ aElement0(xu) ),
inference(cn,[status(thm)],[407,theory(equality)]) ).
cnf(409,plain,
( aDivisorOf0(xu,xa)
| ~ aElement0(xu)
| $false ),
inference(rw,[status(thm)],[405,231,theory(equality)]) ).
cnf(410,plain,
( aDivisorOf0(xu,xa)
| ~ aElement0(xu) ),
inference(cn,[status(thm)],[409,theory(equality)]) ).
cnf(750,plain,
( aElement0(xu)
| $false ),
inference(rw,[status(thm)],[300,285,theory(equality)]) ).
cnf(751,plain,
aElement0(xu),
inference(cn,[status(thm)],[750,theory(equality)]) ).
cnf(859,plain,
( aDivisorOf0(xu,xb)
| $false ),
inference(rw,[status(thm)],[408,751,theory(equality)]) ).
cnf(860,plain,
aDivisorOf0(xu,xb),
inference(cn,[status(thm)],[859,theory(equality)]) ).
cnf(862,plain,
( $false
| ~ aDivisorOf0(xu,xa) ),
inference(rw,[status(thm)],[98,860,theory(equality)]) ).
cnf(863,plain,
~ aDivisorOf0(xu,xa),
inference(cn,[status(thm)],[862,theory(equality)]) ).
cnf(888,plain,
( aDivisorOf0(xu,xa)
| $false ),
inference(rw,[status(thm)],[410,751,theory(equality)]) ).
cnf(889,plain,
aDivisorOf0(xu,xa),
inference(cn,[status(thm)],[888,theory(equality)]) ).
cnf(890,plain,
$false,
inference(sr,[status(thm)],[889,863,theory(equality)]) ).
cnf(891,plain,
$false,
890,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/RNG/RNG125+1.p
% --creating new selector for []
% -running prover on /tmp/tmpQPTtUR/sel_RNG125+1.p_1 with time limit 29
% -prover status Theorem
% Problem RNG125+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/RNG/RNG125+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/RNG/RNG125+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
%
%------------------------------------------------------------------------------