TSTP Solution File: LAT382+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : LAT382+3 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 : Sat Dec 25 17:18:27 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 17 unt; 0 def)
% Number of atoms : 232 ( 12 equ)
% Maximal formula atoms : 27 ( 5 avg)
% Number of connectives : 266 ( 77 ~; 76 |; 97 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 56 ( 0 sgn 46 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/tmp/tmpNNnyPF/sel_LAT382+3.p_1',mASymm) ).
fof(4,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/tmp/tmpNNnyPF/sel_LAT382+3.p_1',mEOfElem) ).
fof(12,conjecture,
xu = xv,
file('/tmp/tmpNNnyPF/sel_LAT382+3.p_1',m__) ).
fof(13,axiom,
aSet0(xT),
file('/tmp/tmpNNnyPF/sel_LAT382+3.p_1',m__773) ).
fof(14,axiom,
( aElementOf0(xu,xT)
& aElementOf0(xu,xT)
& ! [X1] :
( aElementOf0(X1,xS)
=> sdtlseqdt0(xu,X1) )
& aLowerBoundOfIn0(xu,xS,xT)
& ! [X1] :
( ( ( aElementOf0(X1,xT)
& ! [X2] :
( aElementOf0(X2,xS)
=> sdtlseqdt0(X1,X2) ) )
| aLowerBoundOfIn0(X1,xS,xT) )
=> sdtlseqdt0(X1,xu) )
& aInfimumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& ! [X1] :
( aElementOf0(X1,xS)
=> sdtlseqdt0(xv,X1) )
& aLowerBoundOfIn0(xv,xS,xT)
& ! [X1] :
( ( ( aElementOf0(X1,xT)
& ! [X2] :
( aElementOf0(X2,xS)
=> sdtlseqdt0(X1,X2) ) )
| aLowerBoundOfIn0(X1,xS,xT) )
=> sdtlseqdt0(X1,xv) )
& aInfimumOfIn0(xv,xS,xT) ),
file('/tmp/tmpNNnyPF/sel_LAT382+3.p_1',m__792) ).
fof(19,negated_conjecture,
xu != xv,
inference(assume_negation,[status(cth)],[12]) ).
fof(20,negated_conjecture,
xu != xv,
inference(fof_simplification,[status(thm)],[19,theory(equality)]) ).
fof(21,plain,
( aElementOf0(xu,xT)
& ! [X1] :
( aElementOf0(X1,xS)
=> sdtlseqdt0(xu,X1) )
& aLowerBoundOfIn0(xu,xS,xT)
& ! [X1] :
( ( ( aElementOf0(X1,xT)
& ! [X2] :
( aElementOf0(X2,xS)
=> sdtlseqdt0(X1,X2) ) )
| aLowerBoundOfIn0(X1,xS,xT) )
=> sdtlseqdt0(X1,xu) )
& aInfimumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& ! [X1] :
( aElementOf0(X1,xS)
=> sdtlseqdt0(xv,X1) )
& aLowerBoundOfIn0(xv,xS,xT)
& ! [X1] :
( ( ( aElementOf0(X1,xT)
& ! [X2] :
( aElementOf0(X2,xS)
=> sdtlseqdt0(X1,X2) ) )
| aLowerBoundOfIn0(X1,xS,xT) )
=> sdtlseqdt0(X1,xv) )
& aInfimumOfIn0(xv,xS,xT) ),
inference(fof_simplification,[status(thm)],[14,theory(equality)]) ).
fof(28,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1)
| X1 = X2 ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(29,plain,
! [X3,X4] :
( ~ aElement0(X3)
| ~ aElement0(X4)
| ~ sdtlseqdt0(X3,X4)
| ~ sdtlseqdt0(X4,X3)
| X3 = X4 ),
inference(variable_rename,[status(thm)],[28]) ).
cnf(30,plain,
( X1 = X2
| ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[29]) ).
fof(34,plain,
! [X1] :
( ~ aSet0(X1)
| ! [X2] :
( ~ aElementOf0(X2,X1)
| aElement0(X2) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
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]) ).
cnf(84,negated_conjecture,
xu != xv,
inference(split_conjunct,[status(thm)],[20]) ).
cnf(85,plain,
aSet0(xT),
inference(split_conjunct,[status(thm)],[13]) ).
fof(86,plain,
( aElementOf0(xu,xT)
& ! [X1] :
( ~ aElementOf0(X1,xS)
| sdtlseqdt0(xu,X1) )
& aLowerBoundOfIn0(xu,xS,xT)
& ! [X1] :
( ( ( ~ aElementOf0(X1,xT)
| ? [X2] :
( aElementOf0(X2,xS)
& ~ sdtlseqdt0(X1,X2) ) )
& ~ aLowerBoundOfIn0(X1,xS,xT) )
| sdtlseqdt0(X1,xu) )
& aInfimumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& ! [X1] :
( ~ aElementOf0(X1,xS)
| sdtlseqdt0(xv,X1) )
& aLowerBoundOfIn0(xv,xS,xT)
& ! [X1] :
( ( ( ~ aElementOf0(X1,xT)
| ? [X2] :
( aElementOf0(X2,xS)
& ~ sdtlseqdt0(X1,X2) ) )
& ~ aLowerBoundOfIn0(X1,xS,xT) )
| sdtlseqdt0(X1,xv) )
& aInfimumOfIn0(xv,xS,xT) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(87,plain,
( aElementOf0(xu,xT)
& ! [X3] :
( ~ aElementOf0(X3,xS)
| sdtlseqdt0(xu,X3) )
& aLowerBoundOfIn0(xu,xS,xT)
& ! [X4] :
( ( ( ~ aElementOf0(X4,xT)
| ? [X5] :
( aElementOf0(X5,xS)
& ~ sdtlseqdt0(X4,X5) ) )
& ~ aLowerBoundOfIn0(X4,xS,xT) )
| sdtlseqdt0(X4,xu) )
& aInfimumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& ! [X6] :
( ~ aElementOf0(X6,xS)
| sdtlseqdt0(xv,X6) )
& aLowerBoundOfIn0(xv,xS,xT)
& ! [X7] :
( ( ( ~ aElementOf0(X7,xT)
| ? [X8] :
( aElementOf0(X8,xS)
& ~ sdtlseqdt0(X7,X8) ) )
& ~ aLowerBoundOfIn0(X7,xS,xT) )
| sdtlseqdt0(X7,xv) )
& aInfimumOfIn0(xv,xS,xT) ),
inference(variable_rename,[status(thm)],[86]) ).
fof(88,plain,
( aElementOf0(xu,xT)
& ! [X3] :
( ~ aElementOf0(X3,xS)
| sdtlseqdt0(xu,X3) )
& aLowerBoundOfIn0(xu,xS,xT)
& ! [X4] :
( ( ( ~ aElementOf0(X4,xT)
| ( aElementOf0(esk5_1(X4),xS)
& ~ sdtlseqdt0(X4,esk5_1(X4)) ) )
& ~ aLowerBoundOfIn0(X4,xS,xT) )
| sdtlseqdt0(X4,xu) )
& aInfimumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& ! [X6] :
( ~ aElementOf0(X6,xS)
| sdtlseqdt0(xv,X6) )
& aLowerBoundOfIn0(xv,xS,xT)
& ! [X7] :
( ( ( ~ aElementOf0(X7,xT)
| ( aElementOf0(esk6_1(X7),xS)
& ~ sdtlseqdt0(X7,esk6_1(X7)) ) )
& ~ aLowerBoundOfIn0(X7,xS,xT) )
| sdtlseqdt0(X7,xv) )
& aInfimumOfIn0(xv,xS,xT) ),
inference(skolemize,[status(esa)],[87]) ).
fof(89,plain,
! [X3,X4,X6,X7] :
( ( ( ( ~ aElementOf0(X7,xT)
| ( aElementOf0(esk6_1(X7),xS)
& ~ sdtlseqdt0(X7,esk6_1(X7)) ) )
& ~ aLowerBoundOfIn0(X7,xS,xT) )
| sdtlseqdt0(X7,xv) )
& ( ~ aElementOf0(X6,xS)
| sdtlseqdt0(xv,X6) )
& ( ( ( ~ aElementOf0(X4,xT)
| ( aElementOf0(esk5_1(X4),xS)
& ~ sdtlseqdt0(X4,esk5_1(X4)) ) )
& ~ aLowerBoundOfIn0(X4,xS,xT) )
| sdtlseqdt0(X4,xu) )
& ( ~ aElementOf0(X3,xS)
| sdtlseqdt0(xu,X3) )
& aElementOf0(xu,xT)
& aLowerBoundOfIn0(xu,xS,xT)
& aInfimumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& aLowerBoundOfIn0(xv,xS,xT)
& aInfimumOfIn0(xv,xS,xT) ),
inference(shift_quantors,[status(thm)],[88]) ).
fof(90,plain,
! [X3,X4,X6,X7] :
( ( aElementOf0(esk6_1(X7),xS)
| ~ aElementOf0(X7,xT)
| sdtlseqdt0(X7,xv) )
& ( ~ sdtlseqdt0(X7,esk6_1(X7))
| ~ aElementOf0(X7,xT)
| sdtlseqdt0(X7,xv) )
& ( ~ aLowerBoundOfIn0(X7,xS,xT)
| sdtlseqdt0(X7,xv) )
& ( ~ aElementOf0(X6,xS)
| sdtlseqdt0(xv,X6) )
& ( aElementOf0(esk5_1(X4),xS)
| ~ aElementOf0(X4,xT)
| sdtlseqdt0(X4,xu) )
& ( ~ sdtlseqdt0(X4,esk5_1(X4))
| ~ aElementOf0(X4,xT)
| sdtlseqdt0(X4,xu) )
& ( ~ aLowerBoundOfIn0(X4,xS,xT)
| sdtlseqdt0(X4,xu) )
& ( ~ aElementOf0(X3,xS)
| sdtlseqdt0(xu,X3) )
& aElementOf0(xu,xT)
& aLowerBoundOfIn0(xu,xS,xT)
& aInfimumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& aLowerBoundOfIn0(xv,xS,xT)
& aInfimumOfIn0(xv,xS,xT) ),
inference(distribute,[status(thm)],[89]) ).
cnf(92,plain,
aLowerBoundOfIn0(xv,xS,xT),
inference(split_conjunct,[status(thm)],[90]) ).
cnf(93,plain,
aElementOf0(xv,xT),
inference(split_conjunct,[status(thm)],[90]) ).
cnf(96,plain,
aLowerBoundOfIn0(xu,xS,xT),
inference(split_conjunct,[status(thm)],[90]) ).
cnf(97,plain,
aElementOf0(xu,xT),
inference(split_conjunct,[status(thm)],[90]) ).
cnf(99,plain,
( sdtlseqdt0(X1,xu)
| ~ aLowerBoundOfIn0(X1,xS,xT) ),
inference(split_conjunct,[status(thm)],[90]) ).
cnf(103,plain,
( sdtlseqdt0(X1,xv)
| ~ aLowerBoundOfIn0(X1,xS,xT) ),
inference(split_conjunct,[status(thm)],[90]) ).
cnf(132,plain,
sdtlseqdt0(xv,xu),
inference(spm,[status(thm)],[99,92,theory(equality)]) ).
cnf(140,plain,
sdtlseqdt0(xu,xv),
inference(spm,[status(thm)],[103,96,theory(equality)]) ).
cnf(142,plain,
( aElement0(xu)
| ~ aSet0(xT) ),
inference(spm,[status(thm)],[37,97,theory(equality)]) ).
cnf(143,plain,
( aElement0(xv)
| ~ aSet0(xT) ),
inference(spm,[status(thm)],[37,93,theory(equality)]) ).
cnf(145,plain,
( aElement0(xu)
| $false ),
inference(rw,[status(thm)],[142,85,theory(equality)]) ).
cnf(146,plain,
aElement0(xu),
inference(cn,[status(thm)],[145,theory(equality)]) ).
cnf(147,plain,
( aElement0(xv)
| $false ),
inference(rw,[status(thm)],[143,85,theory(equality)]) ).
cnf(148,plain,
aElement0(xv),
inference(cn,[status(thm)],[147,theory(equality)]) ).
cnf(274,plain,
( xu = xv
| ~ sdtlseqdt0(xu,xv)
| ~ aElement0(xv)
| ~ aElement0(xu) ),
inference(spm,[status(thm)],[30,132,theory(equality)]) ).
cnf(276,plain,
( xu = xv
| ~ sdtlseqdt0(xu,xv)
| $false
| ~ aElement0(xu) ),
inference(rw,[status(thm)],[274,148,theory(equality)]) ).
cnf(277,plain,
( xu = xv
| ~ sdtlseqdt0(xu,xv)
| $false
| $false ),
inference(rw,[status(thm)],[276,146,theory(equality)]) ).
cnf(278,plain,
( xu = xv
| ~ sdtlseqdt0(xu,xv) ),
inference(cn,[status(thm)],[277,theory(equality)]) ).
cnf(279,plain,
~ sdtlseqdt0(xu,xv),
inference(sr,[status(thm)],[278,84,theory(equality)]) ).
cnf(284,plain,
$false,
inference(sr,[status(thm)],[140,279,theory(equality)]) ).
cnf(285,plain,
$false,
284,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/LAT/LAT382+3.p
% --creating new selector for []
% -running prover on /tmp/tmpNNnyPF/sel_LAT382+3.p_1 with time limit 29
% -prover status Theorem
% Problem LAT382+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/LAT/LAT382+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/LAT/LAT382+3.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
%
%------------------------------------------------------------------------------