TSTP Solution File: RNG090+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : RNG090+2 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 02:14:43 EST 2010
% Result : Theorem 0.43s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 85 ( 25 unt; 0 def)
% Number of atoms : 255 ( 40 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 279 ( 109 ~; 115 |; 44 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/tmp/tmp5ZAqy8/sel_RNG090+2.p_1',mEOfElem) ).
fof(3,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/tmp/tmp5ZAqy8/sel_RNG090+2.p_1',mAddComm) ).
fof(4,axiom,
( aElementOf0(sdtpldt0(xk,xm),xI)
& aElementOf0(sdtpldt0(xl,xn),xJ) ),
file('/tmp/tmp5ZAqy8/sel_RNG090+2.p_1',m__994) ).
fof(7,axiom,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ)
& xx = sdtpldt0(xk,xl) ),
file('/tmp/tmp5ZAqy8/sel_RNG090+2.p_1',m__934) ).
fof(9,conjecture,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
file('/tmp/tmp5ZAqy8/sel_RNG090+2.p_1',m__) ).
fof(10,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/tmp5ZAqy8/sel_RNG090+2.p_1',m__870) ).
fof(13,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/tmp/tmp5ZAqy8/sel_RNG090+2.p_1',mAddAsso) ).
fof(22,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/tmp/tmp5ZAqy8/sel_RNG090+2.p_1',mSortsB) ).
fof(28,axiom,
( aElementOf0(xm,xI)
& aElementOf0(xn,xJ)
& xy = sdtpldt0(xm,xn) ),
file('/tmp/tmp5ZAqy8/sel_RNG090+2.p_1',m__967) ).
fof(32,negated_conjecture,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(assume_negation,[status(cth)],[9]) ).
fof(33,negated_conjecture,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(fof_simplification,[status(thm)],[32,theory(equality)]) ).
fof(34,plain,
! [X1] :
( ~ aSet0(X1)
| ! [X2] :
( ~ aElementOf0(X2,X1)
| aElement0(X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(35,plain,
! [X3] :
( ~ aSet0(X3)
| ! [X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4) ) ),
inference(variable_rename,[status(thm)],[34]) ).
fof(36,plain,
! [X3,X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4)
| ~ aSet0(X3) ),
inference(shift_quantors,[status(thm)],[35]) ).
cnf(37,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[36]) ).
fof(43,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(44,plain,
! [X3,X4] :
( ~ aElement0(X3)
| ~ aElement0(X4)
| sdtpldt0(X3,X4) = sdtpldt0(X4,X3) ),
inference(variable_rename,[status(thm)],[43]) ).
cnf(45,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(46,plain,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(split_conjunct,[status(thm)],[4]) ).
cnf(61,plain,
xx = sdtpldt0(xk,xl),
inference(split_conjunct,[status(thm)],[7]) ).
cnf(62,plain,
aElementOf0(xl,xJ),
inference(split_conjunct,[status(thm)],[7]) ).
cnf(63,plain,
aElementOf0(xk,xI),
inference(split_conjunct,[status(thm)],[7]) ).
cnf(67,negated_conjecture,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(split_conjunct,[status(thm)],[33]) ).
fof(68,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)],[10]) ).
fof(69,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)],[68]) ).
fof(70,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)],[69]) ).
fof(71,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)],[70]) ).
cnf(73,plain,
aSet0(xJ),
inference(split_conjunct,[status(thm)],[71]) ).
cnf(75,plain,
aSet0(xI),
inference(split_conjunct,[status(thm)],[71]) ).
fof(88,plain,
! [X1,X2,X3] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(89,plain,
! [X4,X5,X6] :
( ~ aElement0(X4)
| ~ aElement0(X5)
| ~ aElement0(X6)
| sdtpldt0(sdtpldt0(X4,X5),X6) = sdtpldt0(X4,sdtpldt0(X5,X6)) ),
inference(variable_rename,[status(thm)],[88]) ).
cnf(90,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[89]) ).
fof(132,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| aElement0(sdtpldt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(133,plain,
! [X3,X4] :
( ~ aElement0(X3)
| ~ aElement0(X4)
| aElement0(sdtpldt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[132]) ).
cnf(134,plain,
( aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[133]) ).
cnf(154,plain,
xy = sdtpldt0(xm,xn),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(155,plain,
aElementOf0(xn,xJ),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(156,plain,
aElementOf0(xm,xI),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(198,plain,
( aElement0(xk)
| ~ aSet0(xI) ),
inference(spm,[status(thm)],[37,63,theory(equality)]) ).
cnf(199,plain,
( aElement0(xm)
| ~ aSet0(xI) ),
inference(spm,[status(thm)],[37,156,theory(equality)]) ).
cnf(200,plain,
( aElement0(xl)
| ~ aSet0(xJ) ),
inference(spm,[status(thm)],[37,62,theory(equality)]) ).
cnf(201,plain,
( aElement0(xn)
| ~ aSet0(xJ) ),
inference(spm,[status(thm)],[37,155,theory(equality)]) ).
cnf(207,plain,
( aElement0(sdtpldt0(xl,xn))
| ~ aSet0(xJ) ),
inference(spm,[status(thm)],[37,46,theory(equality)]) ).
cnf(212,plain,
( aElement0(xk)
| $false ),
inference(rw,[status(thm)],[198,75,theory(equality)]) ).
cnf(213,plain,
aElement0(xk),
inference(cn,[status(thm)],[212,theory(equality)]) ).
cnf(214,plain,
( aElement0(xm)
| $false ),
inference(rw,[status(thm)],[199,75,theory(equality)]) ).
cnf(215,plain,
aElement0(xm),
inference(cn,[status(thm)],[214,theory(equality)]) ).
cnf(216,plain,
( aElement0(xl)
| $false ),
inference(rw,[status(thm)],[200,73,theory(equality)]) ).
cnf(217,plain,
aElement0(xl),
inference(cn,[status(thm)],[216,theory(equality)]) ).
cnf(218,plain,
( aElement0(xn)
| $false ),
inference(rw,[status(thm)],[201,73,theory(equality)]) ).
cnf(219,plain,
aElement0(xn),
inference(cn,[status(thm)],[218,theory(equality)]) ).
cnf(230,plain,
( aElement0(sdtpldt0(xl,xn))
| $false ),
inference(rw,[status(thm)],[207,73,theory(equality)]) ).
cnf(231,plain,
aElement0(sdtpldt0(xl,xn)),
inference(cn,[status(thm)],[230,theory(equality)]) ).
cnf(237,plain,
( aElement0(xy)
| ~ aElement0(xn)
| ~ aElement0(xm) ),
inference(spm,[status(thm)],[134,154,theory(equality)]) ).
cnf(450,plain,
( sdtpldt0(xx,X1) = sdtpldt0(xk,sdtpldt0(xl,X1))
| ~ aElement0(X1)
| ~ aElement0(xl)
| ~ aElement0(xk) ),
inference(spm,[status(thm)],[90,61,theory(equality)]) ).
cnf(451,plain,
( sdtpldt0(xy,X1) = sdtpldt0(xm,sdtpldt0(xn,X1))
| ~ aElement0(X1)
| ~ aElement0(xn)
| ~ aElement0(xm) ),
inference(spm,[status(thm)],[90,154,theory(equality)]) ).
cnf(454,negated_conjecture,
( sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) != sdtpldt0(xx,xy)
| ~ aElement0(sdtpldt0(xl,xn))
| ~ aElement0(xm)
| ~ aElement0(xk) ),
inference(spm,[status(thm)],[67,90,theory(equality)]) ).
cnf(626,negated_conjecture,
( sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) != sdtpldt0(xx,xy)
| ~ aElement0(sdtpldt0(xl,xn))
| ~ aElement0(xm)
| $false ),
inference(rw,[status(thm)],[454,213,theory(equality)]) ).
cnf(627,negated_conjecture,
( sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) != sdtpldt0(xx,xy)
| ~ aElement0(sdtpldt0(xl,xn))
| ~ aElement0(xm) ),
inference(cn,[status(thm)],[626,theory(equality)]) ).
cnf(628,negated_conjecture,
( sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) != sdtpldt0(xx,xy)
| ~ aElement0(sdtpldt0(xl,xn))
| $false ),
inference(rw,[status(thm)],[627,215,theory(equality)]) ).
cnf(629,negated_conjecture,
( sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) != sdtpldt0(xx,xy)
| ~ aElement0(sdtpldt0(xl,xn)) ),
inference(cn,[status(thm)],[628,theory(equality)]) ).
cnf(646,negated_conjecture,
( sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) != sdtpldt0(xx,xy)
| $false ),
inference(rw,[status(thm)],[629,231,theory(equality)]) ).
cnf(647,negated_conjecture,
sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) != sdtpldt0(xx,xy),
inference(cn,[status(thm)],[646,theory(equality)]) ).
cnf(693,plain,
( aElement0(xy)
| $false
| ~ aElement0(xm) ),
inference(rw,[status(thm)],[237,219,theory(equality)]) ).
cnf(694,plain,
( aElement0(xy)
| $false
| $false ),
inference(rw,[status(thm)],[693,215,theory(equality)]) ).
cnf(695,plain,
aElement0(xy),
inference(cn,[status(thm)],[694,theory(equality)]) ).
cnf(1173,plain,
( sdtpldt0(xk,sdtpldt0(xl,X1)) = sdtpldt0(xx,X1)
| ~ aElement0(X1)
| $false
| ~ aElement0(xk) ),
inference(rw,[status(thm)],[450,217,theory(equality)]) ).
cnf(1174,plain,
( sdtpldt0(xk,sdtpldt0(xl,X1)) = sdtpldt0(xx,X1)
| ~ aElement0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[1173,213,theory(equality)]) ).
cnf(1175,plain,
( sdtpldt0(xk,sdtpldt0(xl,X1)) = sdtpldt0(xx,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[1174,theory(equality)]) ).
cnf(1179,plain,
( sdtpldt0(xk,sdtpldt0(X1,xl)) = sdtpldt0(xx,X1)
| ~ aElement0(X1)
| ~ aElement0(xl) ),
inference(spm,[status(thm)],[1175,45,theory(equality)]) ).
cnf(1194,plain,
( sdtpldt0(xk,sdtpldt0(X1,xl)) = sdtpldt0(xx,X1)
| ~ aElement0(X1)
| $false ),
inference(rw,[status(thm)],[1179,217,theory(equality)]) ).
cnf(1195,plain,
( sdtpldt0(xk,sdtpldt0(X1,xl)) = sdtpldt0(xx,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[1194,theory(equality)]) ).
cnf(8352,plain,
( sdtpldt0(xm,sdtpldt0(xn,X1)) = sdtpldt0(xy,X1)
| ~ aElement0(X1)
| $false
| ~ aElement0(xm) ),
inference(rw,[status(thm)],[451,219,theory(equality)]) ).
cnf(8353,plain,
( sdtpldt0(xm,sdtpldt0(xn,X1)) = sdtpldt0(xy,X1)
| ~ aElement0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[8352,215,theory(equality)]) ).
cnf(8354,plain,
( sdtpldt0(xm,sdtpldt0(xn,X1)) = sdtpldt0(xy,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[8353,theory(equality)]) ).
cnf(8358,plain,
( sdtpldt0(xm,sdtpldt0(X1,xn)) = sdtpldt0(xy,X1)
| ~ aElement0(X1)
| ~ aElement0(xn) ),
inference(spm,[status(thm)],[8354,45,theory(equality)]) ).
cnf(8376,plain,
( sdtpldt0(xm,sdtpldt0(X1,xn)) = sdtpldt0(xy,X1)
| ~ aElement0(X1)
| $false ),
inference(rw,[status(thm)],[8358,219,theory(equality)]) ).
cnf(8377,plain,
( sdtpldt0(xm,sdtpldt0(X1,xn)) = sdtpldt0(xy,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[8376,theory(equality)]) ).
cnf(8524,plain,
( sdtpldt0(xk,sdtpldt0(xy,xl)) != sdtpldt0(xx,xy)
| ~ aElement0(xl) ),
inference(spm,[status(thm)],[647,8377,theory(equality)]) ).
cnf(8542,plain,
( sdtpldt0(xk,sdtpldt0(xy,xl)) != sdtpldt0(xx,xy)
| $false ),
inference(rw,[status(thm)],[8524,217,theory(equality)]) ).
cnf(8543,plain,
sdtpldt0(xk,sdtpldt0(xy,xl)) != sdtpldt0(xx,xy),
inference(cn,[status(thm)],[8542,theory(equality)]) ).
cnf(8678,plain,
~ aElement0(xy),
inference(spm,[status(thm)],[8543,1195,theory(equality)]) ).
cnf(8685,plain,
$false,
inference(rw,[status(thm)],[8678,695,theory(equality)]) ).
cnf(8686,plain,
$false,
inference(cn,[status(thm)],[8685,theory(equality)]) ).
cnf(8687,plain,
$false,
8686,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/RNG/RNG090+2.p
% --creating new selector for []
% -running prover on /tmp/tmp5ZAqy8/sel_RNG090+2.p_1 with time limit 29
% -prover status Theorem
% Problem RNG090+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/RNG/RNG090+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/RNG/RNG090+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
%
%------------------------------------------------------------------------------