TSTP Solution File: LAT382+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : LAT382+1 : 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 17:18:10 EST 2010
% Result : Theorem 0.24s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 68 ( 21 unt; 0 def)
% Number of atoms : 237 ( 12 equ)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 285 ( 116 ~; 136 |; 25 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 62 ( 0 sgn 38 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
aSubsetOf0(xS,xT),
file('/tmp/tmpgGfJbJ/sel_LAT382+1.p_1',m__773_01) ).
fof(2,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/tmp/tmpgGfJbJ/sel_LAT382+1.p_1',mASymm) ).
fof(4,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/tmp/tmpgGfJbJ/sel_LAT382+1.p_1',mEOfElem) ).
fof(5,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
=> ! [X3] :
( aInfimumOfIn0(X3,X2,X1)
<=> ( aElementOf0(X3,X1)
& aLowerBoundOfIn0(X3,X2,X1)
& ! [X4] :
( aLowerBoundOfIn0(X4,X2,X1)
=> sdtlseqdt0(X4,X3) ) ) ) ) ),
file('/tmp/tmpgGfJbJ/sel_LAT382+1.p_1',mDefInf) ).
fof(12,conjecture,
xu = xv,
file('/tmp/tmpgGfJbJ/sel_LAT382+1.p_1',m__) ).
fof(13,axiom,
aSet0(xT),
file('/tmp/tmpgGfJbJ/sel_LAT382+1.p_1',m__773) ).
fof(14,axiom,
( aInfimumOfIn0(xu,xS,xT)
& aInfimumOfIn0(xv,xS,xT) ),
file('/tmp/tmpgGfJbJ/sel_LAT382+1.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)]) ).
cnf(21,plain,
aSubsetOf0(xS,xT),
inference(split_conjunct,[status(thm)],[1]) ).
fof(22,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1)
| X1 = X2 ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(23,plain,
! [X3,X4] :
( ~ aElement0(X3)
| ~ aElement0(X4)
| ~ sdtlseqdt0(X3,X4)
| ~ sdtlseqdt0(X4,X3)
| X3 = X4 ),
inference(variable_rename,[status(thm)],[22]) ).
cnf(24,plain,
( X1 = X2
| ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[23]) ).
fof(28,plain,
! [X1] :
( ~ aSet0(X1)
| ! [X2] :
( ~ aElementOf0(X2,X1)
| aElement0(X2) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(29,plain,
! [X3] :
( ~ aSet0(X3)
| ! [X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4) ) ),
inference(variable_rename,[status(thm)],[28]) ).
fof(30,plain,
! [X3,X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4)
| ~ aSet0(X3) ),
inference(shift_quantors,[status(thm)],[29]) ).
cnf(31,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[30]) ).
fof(32,plain,
! [X1] :
( ~ aSet0(X1)
| ! [X2] :
( ~ aSubsetOf0(X2,X1)
| ! [X3] :
( ( ~ aInfimumOfIn0(X3,X2,X1)
| ( aElementOf0(X3,X1)
& aLowerBoundOfIn0(X3,X2,X1)
& ! [X4] :
( ~ aLowerBoundOfIn0(X4,X2,X1)
| sdtlseqdt0(X4,X3) ) ) )
& ( ~ aElementOf0(X3,X1)
| ~ aLowerBoundOfIn0(X3,X2,X1)
| ? [X4] :
( aLowerBoundOfIn0(X4,X2,X1)
& ~ sdtlseqdt0(X4,X3) )
| aInfimumOfIn0(X3,X2,X1) ) ) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(33,plain,
! [X5] :
( ~ aSet0(X5)
| ! [X6] :
( ~ aSubsetOf0(X6,X5)
| ! [X7] :
( ( ~ aInfimumOfIn0(X7,X6,X5)
| ( aElementOf0(X7,X5)
& aLowerBoundOfIn0(X7,X6,X5)
& ! [X8] :
( ~ aLowerBoundOfIn0(X8,X6,X5)
| sdtlseqdt0(X8,X7) ) ) )
& ( ~ aElementOf0(X7,X5)
| ~ aLowerBoundOfIn0(X7,X6,X5)
| ? [X9] :
( aLowerBoundOfIn0(X9,X6,X5)
& ~ sdtlseqdt0(X9,X7) )
| aInfimumOfIn0(X7,X6,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[32]) ).
fof(34,plain,
! [X5] :
( ~ aSet0(X5)
| ! [X6] :
( ~ aSubsetOf0(X6,X5)
| ! [X7] :
( ( ~ aInfimumOfIn0(X7,X6,X5)
| ( aElementOf0(X7,X5)
& aLowerBoundOfIn0(X7,X6,X5)
& ! [X8] :
( ~ aLowerBoundOfIn0(X8,X6,X5)
| sdtlseqdt0(X8,X7) ) ) )
& ( ~ aElementOf0(X7,X5)
| ~ aLowerBoundOfIn0(X7,X6,X5)
| ( aLowerBoundOfIn0(esk1_3(X5,X6,X7),X6,X5)
& ~ sdtlseqdt0(esk1_3(X5,X6,X7),X7) )
| aInfimumOfIn0(X7,X6,X5) ) ) ) ),
inference(skolemize,[status(esa)],[33]) ).
fof(35,plain,
! [X5,X6,X7,X8] :
( ( ( ( ( ~ aLowerBoundOfIn0(X8,X6,X5)
| sdtlseqdt0(X8,X7) )
& aElementOf0(X7,X5)
& aLowerBoundOfIn0(X7,X6,X5) )
| ~ aInfimumOfIn0(X7,X6,X5) )
& ( ~ aElementOf0(X7,X5)
| ~ aLowerBoundOfIn0(X7,X6,X5)
| ( aLowerBoundOfIn0(esk1_3(X5,X6,X7),X6,X5)
& ~ sdtlseqdt0(esk1_3(X5,X6,X7),X7) )
| aInfimumOfIn0(X7,X6,X5) ) )
| ~ aSubsetOf0(X6,X5)
| ~ aSet0(X5) ),
inference(shift_quantors,[status(thm)],[34]) ).
fof(36,plain,
! [X5,X6,X7,X8] :
( ( ~ aLowerBoundOfIn0(X8,X6,X5)
| sdtlseqdt0(X8,X7)
| ~ aInfimumOfIn0(X7,X6,X5)
| ~ aSubsetOf0(X6,X5)
| ~ aSet0(X5) )
& ( aElementOf0(X7,X5)
| ~ aInfimumOfIn0(X7,X6,X5)
| ~ aSubsetOf0(X6,X5)
| ~ aSet0(X5) )
& ( aLowerBoundOfIn0(X7,X6,X5)
| ~ aInfimumOfIn0(X7,X6,X5)
| ~ aSubsetOf0(X6,X5)
| ~ aSet0(X5) )
& ( aLowerBoundOfIn0(esk1_3(X5,X6,X7),X6,X5)
| ~ aElementOf0(X7,X5)
| ~ aLowerBoundOfIn0(X7,X6,X5)
| aInfimumOfIn0(X7,X6,X5)
| ~ aSubsetOf0(X6,X5)
| ~ aSet0(X5) )
& ( ~ sdtlseqdt0(esk1_3(X5,X6,X7),X7)
| ~ aElementOf0(X7,X5)
| ~ aLowerBoundOfIn0(X7,X6,X5)
| aInfimumOfIn0(X7,X6,X5)
| ~ aSubsetOf0(X6,X5)
| ~ aSet0(X5) ) ),
inference(distribute,[status(thm)],[35]) ).
cnf(39,plain,
( aLowerBoundOfIn0(X3,X2,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(X2,X1)
| ~ aInfimumOfIn0(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(40,plain,
( aElementOf0(X3,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(X2,X1)
| ~ aInfimumOfIn0(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(41,plain,
( sdtlseqdt0(X4,X3)
| ~ aSet0(X1)
| ~ aSubsetOf0(X2,X1)
| ~ aInfimumOfIn0(X3,X2,X1)
| ~ aLowerBoundOfIn0(X4,X2,X1) ),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(78,negated_conjecture,
xu != xv,
inference(split_conjunct,[status(thm)],[20]) ).
cnf(79,plain,
aSet0(xT),
inference(split_conjunct,[status(thm)],[13]) ).
cnf(80,plain,
aInfimumOfIn0(xv,xS,xT),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(81,plain,
aInfimumOfIn0(xu,xS,xT),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(114,plain,
( aElementOf0(xu,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT) ),
inference(spm,[status(thm)],[40,81,theory(equality)]) ).
cnf(115,plain,
( aElementOf0(xv,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT) ),
inference(spm,[status(thm)],[40,80,theory(equality)]) ).
cnf(116,plain,
( aElementOf0(xu,xT)
| $false
| ~ aSubsetOf0(xS,xT) ),
inference(rw,[status(thm)],[114,79,theory(equality)]) ).
cnf(117,plain,
( aElementOf0(xu,xT)
| $false
| $false ),
inference(rw,[status(thm)],[116,21,theory(equality)]) ).
cnf(118,plain,
aElementOf0(xu,xT),
inference(cn,[status(thm)],[117,theory(equality)]) ).
cnf(119,plain,
( aElementOf0(xv,xT)
| $false
| ~ aSubsetOf0(xS,xT) ),
inference(rw,[status(thm)],[115,79,theory(equality)]) ).
cnf(120,plain,
( aElementOf0(xv,xT)
| $false
| $false ),
inference(rw,[status(thm)],[119,21,theory(equality)]) ).
cnf(121,plain,
aElementOf0(xv,xT),
inference(cn,[status(thm)],[120,theory(equality)]) ).
cnf(125,plain,
( aLowerBoundOfIn0(xu,xS,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT) ),
inference(spm,[status(thm)],[39,81,theory(equality)]) ).
cnf(126,plain,
( aLowerBoundOfIn0(xv,xS,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT) ),
inference(spm,[status(thm)],[39,80,theory(equality)]) ).
cnf(127,plain,
( aLowerBoundOfIn0(xu,xS,xT)
| $false
| ~ aSubsetOf0(xS,xT) ),
inference(rw,[status(thm)],[125,79,theory(equality)]) ).
cnf(128,plain,
( aLowerBoundOfIn0(xu,xS,xT)
| $false
| $false ),
inference(rw,[status(thm)],[127,21,theory(equality)]) ).
cnf(129,plain,
aLowerBoundOfIn0(xu,xS,xT),
inference(cn,[status(thm)],[128,theory(equality)]) ).
cnf(130,plain,
( aLowerBoundOfIn0(xv,xS,xT)
| $false
| ~ aSubsetOf0(xS,xT) ),
inference(rw,[status(thm)],[126,79,theory(equality)]) ).
cnf(131,plain,
( aLowerBoundOfIn0(xv,xS,xT)
| $false
| $false ),
inference(rw,[status(thm)],[130,21,theory(equality)]) ).
cnf(132,plain,
aLowerBoundOfIn0(xv,xS,xT),
inference(cn,[status(thm)],[131,theory(equality)]) ).
cnf(150,plain,
( aElement0(xu)
| ~ aSet0(xT) ),
inference(spm,[status(thm)],[31,118,theory(equality)]) ).
cnf(152,plain,
( aElement0(xu)
| $false ),
inference(rw,[status(thm)],[150,79,theory(equality)]) ).
cnf(153,plain,
aElement0(xu),
inference(cn,[status(thm)],[152,theory(equality)]) ).
cnf(160,plain,
( aElement0(xv)
| ~ aSet0(xT) ),
inference(spm,[status(thm)],[31,121,theory(equality)]) ).
cnf(162,plain,
( aElement0(xv)
| $false ),
inference(rw,[status(thm)],[160,79,theory(equality)]) ).
cnf(163,plain,
aElement0(xv),
inference(cn,[status(thm)],[162,theory(equality)]) ).
cnf(180,plain,
( sdtlseqdt0(xu,X1)
| ~ aInfimumOfIn0(X1,xS,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT) ),
inference(spm,[status(thm)],[41,129,theory(equality)]) ).
cnf(188,plain,
( sdtlseqdt0(xu,X1)
| ~ aInfimumOfIn0(X1,xS,xT)
| $false
| ~ aSubsetOf0(xS,xT) ),
inference(rw,[status(thm)],[180,79,theory(equality)]) ).
cnf(189,plain,
( sdtlseqdt0(xu,X1)
| ~ aInfimumOfIn0(X1,xS,xT)
| $false
| $false ),
inference(rw,[status(thm)],[188,21,theory(equality)]) ).
cnf(190,plain,
( sdtlseqdt0(xu,X1)
| ~ aInfimumOfIn0(X1,xS,xT) ),
inference(cn,[status(thm)],[189,theory(equality)]) ).
cnf(193,plain,
( sdtlseqdt0(xv,X1)
| ~ aInfimumOfIn0(X1,xS,xT)
| ~ aSet0(xT)
| ~ aSubsetOf0(xS,xT) ),
inference(spm,[status(thm)],[41,132,theory(equality)]) ).
cnf(201,plain,
( sdtlseqdt0(xv,X1)
| ~ aInfimumOfIn0(X1,xS,xT)
| $false
| ~ aSubsetOf0(xS,xT) ),
inference(rw,[status(thm)],[193,79,theory(equality)]) ).
cnf(202,plain,
( sdtlseqdt0(xv,X1)
| ~ aInfimumOfIn0(X1,xS,xT)
| $false
| $false ),
inference(rw,[status(thm)],[201,21,theory(equality)]) ).
cnf(203,plain,
( sdtlseqdt0(xv,X1)
| ~ aInfimumOfIn0(X1,xS,xT) ),
inference(cn,[status(thm)],[202,theory(equality)]) ).
cnf(232,plain,
sdtlseqdt0(xu,xv),
inference(spm,[status(thm)],[190,80,theory(equality)]) ).
cnf(234,plain,
( xv = xu
| ~ sdtlseqdt0(xv,xu)
| ~ aElement0(xu)
| ~ aElement0(xv) ),
inference(spm,[status(thm)],[24,232,theory(equality)]) ).
cnf(236,plain,
( xv = xu
| ~ sdtlseqdt0(xv,xu)
| $false
| ~ aElement0(xv) ),
inference(rw,[status(thm)],[234,153,theory(equality)]) ).
cnf(237,plain,
( xv = xu
| ~ sdtlseqdt0(xv,xu)
| $false
| $false ),
inference(rw,[status(thm)],[236,163,theory(equality)]) ).
cnf(238,plain,
( xv = xu
| ~ sdtlseqdt0(xv,xu) ),
inference(cn,[status(thm)],[237,theory(equality)]) ).
cnf(239,plain,
~ sdtlseqdt0(xv,xu),
inference(sr,[status(thm)],[238,78,theory(equality)]) ).
cnf(243,plain,
sdtlseqdt0(xv,xu),
inference(spm,[status(thm)],[203,81,theory(equality)]) ).
cnf(249,plain,
$false,
inference(sr,[status(thm)],[243,239,theory(equality)]) ).
cnf(250,plain,
$false,
249,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/LAT/LAT382+1.p
% --creating new selector for []
% -running prover on /tmp/tmpgGfJbJ/sel_LAT382+1.p_1 with time limit 29
% -prover status Theorem
% Problem LAT382+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/LAT/LAT382+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/LAT/LAT382+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
%
%------------------------------------------------------------------------------