TSTP Solution File: RNG093+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : RNG093+2 : 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 02:15:59 EST 2010
% Result : Theorem 0.31s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 3
% Syntax : Number of formulae : 92 ( 11 unt; 0 def)
% Number of atoms : 474 ( 0 equ)
% Maximal formula atoms : 29 ( 5 avg)
% Number of connectives : 603 ( 221 ~; 247 |; 115 &)
% ( 3 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn 67 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(7,axiom,
( aSet0(xI)
& ! [X1] :
( aElementOf0(X1,xI)
=> ( ! [X2] :
( aElementOf0(X2,xI)
=> aElementOf0(sdtpldt0(X1,X2),xI) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X1] :
( aElementOf0(X1,xJ)
=> ( ! [X2] :
( aElementOf0(X2,xJ)
=> aElementOf0(sdtpldt0(X1,X2),xJ) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),xJ) ) ) )
& aIdeal0(xJ) ),
file('/tmp/tmpB9WeDK/sel_RNG093+2.p_1',m__1150) ).
fof(14,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/tmpB9WeDK/sel_RNG093+2.p_1',mDefIdeal) ).
fof(27,conjecture,
( ( aSet0(sdtasasdt0(xI,xJ))
& ! [X1] :
( aElementOf0(X1,sdtasasdt0(xI,xJ))
<=> ( aElementOf0(X1,xI)
& aElementOf0(X1,xJ) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,sdtasasdt0(xI,xJ))
=> ( ! [X2] :
( aElementOf0(X2,sdtasasdt0(xI,xJ))
=> aElementOf0(sdtpldt0(X1,X2),sdtasasdt0(xI,xJ)) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),sdtasasdt0(xI,xJ)) ) ) )
| aIdeal0(sdtasasdt0(xI,xJ)) ) ),
file('/tmp/tmpB9WeDK/sel_RNG093+2.p_1',m__) ).
fof(28,negated_conjecture,
~ ( ( aSet0(sdtasasdt0(xI,xJ))
& ! [X1] :
( aElementOf0(X1,sdtasasdt0(xI,xJ))
<=> ( aElementOf0(X1,xI)
& aElementOf0(X1,xJ) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,sdtasasdt0(xI,xJ))
=> ( ! [X2] :
( aElementOf0(X2,sdtasasdt0(xI,xJ))
=> aElementOf0(sdtpldt0(X1,X2),sdtasasdt0(xI,xJ)) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),sdtasasdt0(xI,xJ)) ) ) )
| aIdeal0(sdtasasdt0(xI,xJ)) ) ),
inference(assume_negation,[status(cth)],[27]) ).
fof(57,plain,
( aSet0(xI)
& ! [X1] :
( ~ aElementOf0(X1,xI)
| ( ! [X2] :
( ~ aElementOf0(X2,xI)
| aElementOf0(sdtpldt0(X1,X2),xI) )
& ! [X2] :
( ~ aElement0(X2)
| aElementOf0(sdtasdt0(X2,X1),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X1] :
( ~ aElementOf0(X1,xJ)
| ( ! [X2] :
( ~ aElementOf0(X2,xJ)
| aElementOf0(sdtpldt0(X1,X2),xJ) )
& ! [X2] :
( ~ aElement0(X2)
| aElementOf0(sdtasdt0(X2,X1),xJ) ) ) )
& aIdeal0(xJ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(58,plain,
( aSet0(xI)
& ! [X3] :
( ~ aElementOf0(X3,xI)
| ( ! [X4] :
( ~ aElementOf0(X4,xI)
| aElementOf0(sdtpldt0(X3,X4),xI) )
& ! [X5] :
( ~ aElement0(X5)
| aElementOf0(sdtasdt0(X5,X3),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X6] :
( ~ aElementOf0(X6,xJ)
| ( ! [X7] :
( ~ aElementOf0(X7,xJ)
| aElementOf0(sdtpldt0(X6,X7),xJ) )
& ! [X8] :
( ~ aElement0(X8)
| aElementOf0(sdtasdt0(X8,X6),xJ) ) ) )
& aIdeal0(xJ) ),
inference(variable_rename,[status(thm)],[57]) ).
fof(59,plain,
! [X3,X4,X5,X6,X7,X8] :
( ( ( ( ~ aElement0(X8)
| aElementOf0(sdtasdt0(X8,X6),xJ) )
& ( ~ aElementOf0(X7,xJ)
| aElementOf0(sdtpldt0(X6,X7),xJ) ) )
| ~ aElementOf0(X6,xJ) )
& ( ( ( ~ aElement0(X5)
| aElementOf0(sdtasdt0(X5,X3),xI) )
& ( ~ aElementOf0(X4,xI)
| aElementOf0(sdtpldt0(X3,X4),xI) ) )
| ~ aElementOf0(X3,xI) )
& aSet0(xI)
& aIdeal0(xI)
& aSet0(xJ)
& aIdeal0(xJ) ),
inference(shift_quantors,[status(thm)],[58]) ).
fof(60,plain,
! [X3,X4,X5,X6,X7,X8] :
( ( ~ aElement0(X8)
| aElementOf0(sdtasdt0(X8,X6),xJ)
| ~ aElementOf0(X6,xJ) )
& ( ~ aElementOf0(X7,xJ)
| aElementOf0(sdtpldt0(X6,X7),xJ)
| ~ aElementOf0(X6,xJ) )
& ( ~ aElement0(X5)
| aElementOf0(sdtasdt0(X5,X3),xI)
| ~ aElementOf0(X3,xI) )
& ( ~ aElementOf0(X4,xI)
| aElementOf0(sdtpldt0(X3,X4),xI)
| ~ aElementOf0(X3,xI) )
& aSet0(xI)
& aIdeal0(xI)
& aSet0(xJ)
& aIdeal0(xJ) ),
inference(distribute,[status(thm)],[59]) ).
cnf(65,plain,
( aElementOf0(sdtpldt0(X1,X2),xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X2,xI) ),
inference(split_conjunct,[status(thm)],[60]) ).
cnf(66,plain,
( aElementOf0(sdtasdt0(X2,X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[60]) ).
cnf(67,plain,
( aElementOf0(sdtpldt0(X1,X2),xJ)
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X2,xJ) ),
inference(split_conjunct,[status(thm)],[60]) ).
cnf(68,plain,
( aElementOf0(sdtasdt0(X2,X1),xJ)
| ~ aElementOf0(X1,xJ)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[60]) ).
fof(85,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)],[14]) ).
fof(86,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)],[85]) ).
fof(87,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)],[86]) ).
fof(88,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)],[87]) ).
fof(89,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)],[88]) ).
cnf(90,plain,
( aIdeal0(X1)
| ~ aSet0(X1)
| ~ aElementOf0(sdtpldt0(esk3_1(X1),esk4_1(X1)),X1)
| ~ aElementOf0(sdtasdt0(esk5_1(X1),esk3_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[89]) ).
cnf(91,plain,
( aIdeal0(X1)
| aElement0(esk5_1(X1))
| ~ aSet0(X1)
| ~ aElementOf0(sdtpldt0(esk3_1(X1),esk4_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[89]) ).
cnf(92,plain,
( aIdeal0(X1)
| aElementOf0(esk4_1(X1),X1)
| ~ aSet0(X1)
| ~ aElementOf0(sdtasdt0(esk5_1(X1),esk3_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[89]) ).
cnf(93,plain,
( aIdeal0(X1)
| aElementOf0(esk4_1(X1),X1)
| aElement0(esk5_1(X1))
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[89]) ).
cnf(94,plain,
( aIdeal0(X1)
| aElementOf0(esk3_1(X1),X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[89]) ).
fof(158,negated_conjecture,
( aSet0(sdtasasdt0(xI,xJ))
& ! [X1] :
( ( ~ aElementOf0(X1,sdtasasdt0(xI,xJ))
| ( aElementOf0(X1,xI)
& aElementOf0(X1,xJ) ) )
& ( ~ aElementOf0(X1,xI)
| ~ aElementOf0(X1,xJ)
| aElementOf0(X1,sdtasasdt0(xI,xJ)) ) )
& ? [X1] :
( aElementOf0(X1,sdtasasdt0(xI,xJ))
& ( ? [X2] :
( aElementOf0(X2,sdtasasdt0(xI,xJ))
& ~ aElementOf0(sdtpldt0(X1,X2),sdtasasdt0(xI,xJ)) )
| ? [X2] :
( aElement0(X2)
& ~ aElementOf0(sdtasdt0(X2,X1),sdtasasdt0(xI,xJ)) ) ) )
& ~ aIdeal0(sdtasasdt0(xI,xJ)) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(159,negated_conjecture,
( aSet0(sdtasasdt0(xI,xJ))
& ! [X3] :
( ( ~ aElementOf0(X3,sdtasasdt0(xI,xJ))
| ( aElementOf0(X3,xI)
& aElementOf0(X3,xJ) ) )
& ( ~ aElementOf0(X3,xI)
| ~ aElementOf0(X3,xJ)
| aElementOf0(X3,sdtasasdt0(xI,xJ)) ) )
& ? [X4] :
( aElementOf0(X4,sdtasasdt0(xI,xJ))
& ( ? [X5] :
( aElementOf0(X5,sdtasasdt0(xI,xJ))
& ~ aElementOf0(sdtpldt0(X4,X5),sdtasasdt0(xI,xJ)) )
| ? [X6] :
( aElement0(X6)
& ~ aElementOf0(sdtasdt0(X6,X4),sdtasasdt0(xI,xJ)) ) ) )
& ~ aIdeal0(sdtasasdt0(xI,xJ)) ),
inference(variable_rename,[status(thm)],[158]) ).
fof(160,negated_conjecture,
( aSet0(sdtasasdt0(xI,xJ))
& ! [X3] :
( ( ~ aElementOf0(X3,sdtasasdt0(xI,xJ))
| ( aElementOf0(X3,xI)
& aElementOf0(X3,xJ) ) )
& ( ~ aElementOf0(X3,xI)
| ~ aElementOf0(X3,xJ)
| aElementOf0(X3,sdtasasdt0(xI,xJ)) ) )
& aElementOf0(esk12_0,sdtasasdt0(xI,xJ))
& ( ( aElementOf0(esk13_0,sdtasasdt0(xI,xJ))
& ~ aElementOf0(sdtpldt0(esk12_0,esk13_0),sdtasasdt0(xI,xJ)) )
| ( aElement0(esk14_0)
& ~ aElementOf0(sdtasdt0(esk14_0,esk12_0),sdtasasdt0(xI,xJ)) ) )
& ~ aIdeal0(sdtasasdt0(xI,xJ)) ),
inference(skolemize,[status(esa)],[159]) ).
fof(161,negated_conjecture,
! [X3] :
( ( ~ aElementOf0(X3,sdtasasdt0(xI,xJ))
| ( aElementOf0(X3,xI)
& aElementOf0(X3,xJ) ) )
& ( ~ aElementOf0(X3,xI)
| ~ aElementOf0(X3,xJ)
| aElementOf0(X3,sdtasasdt0(xI,xJ)) )
& aSet0(sdtasasdt0(xI,xJ))
& aElementOf0(esk12_0,sdtasasdt0(xI,xJ))
& ( ( aElementOf0(esk13_0,sdtasasdt0(xI,xJ))
& ~ aElementOf0(sdtpldt0(esk12_0,esk13_0),sdtasasdt0(xI,xJ)) )
| ( aElement0(esk14_0)
& ~ aElementOf0(sdtasdt0(esk14_0,esk12_0),sdtasasdt0(xI,xJ)) ) )
& ~ aIdeal0(sdtasasdt0(xI,xJ)) ),
inference(shift_quantors,[status(thm)],[160]) ).
fof(162,negated_conjecture,
! [X3] :
( ( aElementOf0(X3,xI)
| ~ aElementOf0(X3,sdtasasdt0(xI,xJ)) )
& ( aElementOf0(X3,xJ)
| ~ aElementOf0(X3,sdtasasdt0(xI,xJ)) )
& ( ~ aElementOf0(X3,xI)
| ~ aElementOf0(X3,xJ)
| aElementOf0(X3,sdtasasdt0(xI,xJ)) )
& aSet0(sdtasasdt0(xI,xJ))
& aElementOf0(esk12_0,sdtasasdt0(xI,xJ))
& ( aElement0(esk14_0)
| aElementOf0(esk13_0,sdtasasdt0(xI,xJ)) )
& ( ~ aElementOf0(sdtasdt0(esk14_0,esk12_0),sdtasasdt0(xI,xJ))
| aElementOf0(esk13_0,sdtasasdt0(xI,xJ)) )
& ( aElement0(esk14_0)
| ~ aElementOf0(sdtpldt0(esk12_0,esk13_0),sdtasasdt0(xI,xJ)) )
& ( ~ aElementOf0(sdtasdt0(esk14_0,esk12_0),sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtpldt0(esk12_0,esk13_0),sdtasasdt0(xI,xJ)) )
& ~ aIdeal0(sdtasasdt0(xI,xJ)) ),
inference(distribute,[status(thm)],[161]) ).
cnf(163,negated_conjecture,
~ aIdeal0(sdtasasdt0(xI,xJ)),
inference(split_conjunct,[status(thm)],[162]) ).
cnf(169,negated_conjecture,
aSet0(sdtasasdt0(xI,xJ)),
inference(split_conjunct,[status(thm)],[162]) ).
cnf(170,negated_conjecture,
( aElementOf0(X1,sdtasasdt0(xI,xJ))
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X1,xI) ),
inference(split_conjunct,[status(thm)],[162]) ).
cnf(171,negated_conjecture,
( aElementOf0(X1,xJ)
| ~ aElementOf0(X1,sdtasasdt0(xI,xJ)) ),
inference(split_conjunct,[status(thm)],[162]) ).
cnf(172,negated_conjecture,
( aElementOf0(X1,xI)
| ~ aElementOf0(X1,sdtasasdt0(xI,xJ)) ),
inference(split_conjunct,[status(thm)],[162]) ).
cnf(221,negated_conjecture,
( aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xI)
| aIdeal0(sdtasasdt0(xI,xJ))
| ~ aSet0(sdtasasdt0(xI,xJ)) ),
inference(spm,[status(thm)],[172,94,theory(equality)]) ).
cnf(222,negated_conjecture,
( aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xJ)
| aIdeal0(sdtasasdt0(xI,xJ))
| ~ aSet0(sdtasasdt0(xI,xJ)) ),
inference(spm,[status(thm)],[171,94,theory(equality)]) ).
cnf(224,negated_conjecture,
( aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xI)
| aIdeal0(sdtasasdt0(xI,xJ))
| $false ),
inference(rw,[status(thm)],[221,169,theory(equality)]) ).
cnf(225,negated_conjecture,
( aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xI)
| aIdeal0(sdtasasdt0(xI,xJ)) ),
inference(cn,[status(thm)],[224,theory(equality)]) ).
cnf(226,negated_conjecture,
aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xI),
inference(sr,[status(thm)],[225,163,theory(equality)]) ).
cnf(227,negated_conjecture,
( aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xJ)
| aIdeal0(sdtasasdt0(xI,xJ))
| $false ),
inference(rw,[status(thm)],[222,169,theory(equality)]) ).
cnf(228,negated_conjecture,
( aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xJ)
| aIdeal0(sdtasasdt0(xI,xJ)) ),
inference(cn,[status(thm)],[227,theory(equality)]) ).
cnf(229,negated_conjecture,
aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xJ),
inference(sr,[status(thm)],[228,163,theory(equality)]) ).
cnf(352,negated_conjecture,
( aIdeal0(sdtasasdt0(xI,xJ))
| aElement0(esk5_1(sdtasasdt0(xI,xJ)))
| aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ)) ),
inference(spm,[status(thm)],[93,169,theory(equality)]) ).
cnf(355,negated_conjecture,
( aElement0(esk5_1(sdtasasdt0(xI,xJ)))
| aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ)) ),
inference(sr,[status(thm)],[352,163,theory(equality)]) ).
cnf(395,negated_conjecture,
( aIdeal0(sdtasasdt0(xI,xJ))
| aElement0(esk5_1(sdtasasdt0(xI,xJ)))
| ~ aSet0(sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xJ) ),
inference(spm,[status(thm)],[91,170,theory(equality)]) ).
cnf(398,negated_conjecture,
( aIdeal0(sdtasasdt0(xI,xJ))
| aElement0(esk5_1(sdtasasdt0(xI,xJ)))
| $false
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xJ) ),
inference(rw,[status(thm)],[395,169,theory(equality)]) ).
cnf(399,negated_conjecture,
( aIdeal0(sdtasasdt0(xI,xJ))
| aElement0(esk5_1(sdtasasdt0(xI,xJ)))
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xJ) ),
inference(cn,[status(thm)],[398,theory(equality)]) ).
cnf(400,negated_conjecture,
( aElement0(esk5_1(sdtasasdt0(xI,xJ)))
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xJ) ),
inference(sr,[status(thm)],[399,163,theory(equality)]) ).
cnf(411,negated_conjecture,
( aIdeal0(sdtasasdt0(xI,xJ))
| aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ))
| ~ aSet0(sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ) ),
inference(spm,[status(thm)],[92,170,theory(equality)]) ).
cnf(418,negated_conjecture,
( aIdeal0(sdtasasdt0(xI,xJ))
| aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ))
| $false
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ) ),
inference(rw,[status(thm)],[411,169,theory(equality)]) ).
cnf(419,negated_conjecture,
( aIdeal0(sdtasasdt0(xI,xJ))
| aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ) ),
inference(cn,[status(thm)],[418,theory(equality)]) ).
cnf(420,negated_conjecture,
( aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ) ),
inference(sr,[status(thm)],[419,163,theory(equality)]) ).
cnf(541,negated_conjecture,
( aIdeal0(sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),sdtasasdt0(xI,xJ))
| ~ aSet0(sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xJ) ),
inference(spm,[status(thm)],[90,170,theory(equality)]) ).
cnf(544,negated_conjecture,
( aIdeal0(sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),sdtasasdt0(xI,xJ))
| $false
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xJ) ),
inference(rw,[status(thm)],[541,169,theory(equality)]) ).
cnf(545,negated_conjecture,
( aIdeal0(sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xJ) ),
inference(cn,[status(thm)],[544,theory(equality)]) ).
cnf(546,negated_conjecture,
( ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xJ) ),
inference(sr,[status(thm)],[545,163,theory(equality)]) ).
cnf(609,negated_conjecture,
( aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),xI)
| aElement0(esk5_1(sdtasasdt0(xI,xJ))) ),
inference(spm,[status(thm)],[172,355,theory(equality)]) ).
cnf(610,negated_conjecture,
( aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),xJ)
| aElement0(esk5_1(sdtasasdt0(xI,xJ))) ),
inference(spm,[status(thm)],[171,355,theory(equality)]) ).
cnf(862,plain,
( aElement0(esk5_1(sdtasasdt0(xI,xJ)))
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xJ)
| ~ aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),xI)
| ~ aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xI) ),
inference(spm,[status(thm)],[400,65,theory(equality)]) ).
cnf(863,plain,
( aElement0(esk5_1(sdtasasdt0(xI,xJ)))
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xJ)
| ~ aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),xI)
| $false ),
inference(rw,[status(thm)],[862,226,theory(equality)]) ).
cnf(864,plain,
( aElement0(esk5_1(sdtasasdt0(xI,xJ)))
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xJ)
| ~ aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),xI) ),
inference(cn,[status(thm)],[863,theory(equality)]) ).
cnf(865,plain,
( aElement0(esk5_1(sdtasasdt0(xI,xJ)))
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xJ) ),
inference(csr,[status(thm)],[864,609]) ).
cnf(866,plain,
( aElement0(esk5_1(sdtasasdt0(xI,xJ)))
| ~ aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),xJ)
| ~ aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xJ) ),
inference(spm,[status(thm)],[865,67,theory(equality)]) ).
cnf(867,plain,
( aElement0(esk5_1(sdtasasdt0(xI,xJ)))
| ~ aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),xJ)
| $false ),
inference(rw,[status(thm)],[866,229,theory(equality)]) ).
cnf(868,plain,
( aElement0(esk5_1(sdtasasdt0(xI,xJ)))
| ~ aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),xJ) ),
inference(cn,[status(thm)],[867,theory(equality)]) ).
cnf(869,plain,
aElement0(esk5_1(sdtasasdt0(xI,xJ))),
inference(csr,[status(thm)],[868,610]) ).
cnf(946,plain,
( aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ)
| ~ aElement0(esk5_1(sdtasasdt0(xI,xJ)))
| ~ aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xI) ),
inference(spm,[status(thm)],[420,66,theory(equality)]) ).
cnf(953,plain,
( aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ)
| $false
| ~ aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xI) ),
inference(rw,[status(thm)],[946,869,theory(equality)]) ).
cnf(954,plain,
( aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ)
| $false
| $false ),
inference(rw,[status(thm)],[953,226,theory(equality)]) ).
cnf(955,plain,
( aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ) ),
inference(cn,[status(thm)],[954,theory(equality)]) ).
cnf(958,plain,
( aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ))
| ~ aElement0(esk5_1(sdtasasdt0(xI,xJ)))
| ~ aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xJ) ),
inference(spm,[status(thm)],[955,68,theory(equality)]) ).
cnf(965,plain,
( aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ))
| $false
| ~ aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xJ) ),
inference(rw,[status(thm)],[958,869,theory(equality)]) ).
cnf(966,plain,
( aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ))
| $false
| $false ),
inference(rw,[status(thm)],[965,229,theory(equality)]) ).
cnf(967,plain,
aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ)),
inference(cn,[status(thm)],[966,theory(equality)]) ).
cnf(968,plain,
aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),xI),
inference(spm,[status(thm)],[172,967,theory(equality)]) ).
cnf(969,plain,
aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),xJ),
inference(spm,[status(thm)],[171,967,theory(equality)]) ).
cnf(997,negated_conjecture,
( ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xJ)
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ) ),
inference(spm,[status(thm)],[546,170,theory(equality)]) ).
cnf(1005,plain,
( ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xJ)
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ)
| ~ aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),xI)
| ~ aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xI) ),
inference(spm,[status(thm)],[997,65,theory(equality)]) ).
cnf(1006,plain,
( ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xJ)
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ)
| $false
| ~ aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xI) ),
inference(rw,[status(thm)],[1005,968,theory(equality)]) ).
cnf(1007,plain,
( ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xJ)
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ)
| $false
| $false ),
inference(rw,[status(thm)],[1006,226,theory(equality)]) ).
cnf(1008,plain,
( ~ aElementOf0(sdtpldt0(esk3_1(sdtasasdt0(xI,xJ)),esk4_1(sdtasasdt0(xI,xJ))),xJ)
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ) ),
inference(cn,[status(thm)],[1007,theory(equality)]) ).
cnf(1069,plain,
( ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ)
| ~ aElementOf0(esk4_1(sdtasasdt0(xI,xJ)),xJ)
| ~ aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xJ) ),
inference(spm,[status(thm)],[1008,67,theory(equality)]) ).
cnf(1070,plain,
( ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ)
| $false
| ~ aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xJ) ),
inference(rw,[status(thm)],[1069,969,theory(equality)]) ).
cnf(1071,plain,
( ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ)
| $false
| $false ),
inference(rw,[status(thm)],[1070,229,theory(equality)]) ).
cnf(1072,plain,
( ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xI)
| ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ) ),
inference(cn,[status(thm)],[1071,theory(equality)]) ).
cnf(1075,plain,
( ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ)
| ~ aElement0(esk5_1(sdtasasdt0(xI,xJ)))
| ~ aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xI) ),
inference(spm,[status(thm)],[1072,66,theory(equality)]) ).
cnf(1082,plain,
( ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ)
| $false
| ~ aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xI) ),
inference(rw,[status(thm)],[1075,869,theory(equality)]) ).
cnf(1083,plain,
( ~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ)
| $false
| $false ),
inference(rw,[status(thm)],[1082,226,theory(equality)]) ).
cnf(1084,plain,
~ aElementOf0(sdtasdt0(esk5_1(sdtasasdt0(xI,xJ)),esk3_1(sdtasasdt0(xI,xJ))),xJ),
inference(cn,[status(thm)],[1083,theory(equality)]) ).
cnf(1087,plain,
( ~ aElement0(esk5_1(sdtasasdt0(xI,xJ)))
| ~ aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xJ) ),
inference(spm,[status(thm)],[1084,68,theory(equality)]) ).
cnf(1094,plain,
( $false
| ~ aElementOf0(esk3_1(sdtasasdt0(xI,xJ)),xJ) ),
inference(rw,[status(thm)],[1087,869,theory(equality)]) ).
cnf(1095,plain,
( $false
| $false ),
inference(rw,[status(thm)],[1094,229,theory(equality)]) ).
cnf(1096,plain,
$false,
inference(cn,[status(thm)],[1095,theory(equality)]) ).
cnf(1097,plain,
$false,
1096,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/RNG/RNG093+2.p
% --creating new selector for []
% -running prover on /tmp/tmpB9WeDK/sel_RNG093+2.p_1 with time limit 29
% -prover status Theorem
% Problem RNG093+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/RNG/RNG093+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/RNG/RNG093+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
%
%------------------------------------------------------------------------------