TSTP Solution File: LAT381+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : LAT381+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 17:17:41 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 68 ( 21 unt; 0 def)
% Number of atoms : 239 ( 13 equ)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 285 ( 114 ~; 138 |; 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,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/tmp/tmpAQ6zmF/sel_LAT381+1.p_1',mASymm) ).
fof(3,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/tmp/tmpAQ6zmF/sel_LAT381+1.p_1',mEOfElem) ).
fof(5,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
=> ! [X3] :
( aSupremumOfIn0(X3,X2,X1)
<=> ( aElementOf0(X3,X1)
& aUpperBoundOfIn0(X3,X2,X1)
& ! [X4] :
( aUpperBoundOfIn0(X4,X2,X1)
=> sdtlseqdt0(X3,X4) ) ) ) ) ),
file('/tmp/tmpAQ6zmF/sel_LAT381+1.p_1',mDefSup) ).
fof(10,axiom,
( aSupremumOfIn0(xu,xS,xT)
& aSupremumOfIn0(xv,xS,xT) ),
file('/tmp/tmpAQ6zmF/sel_LAT381+1.p_1',m__744) ).
fof(11,axiom,
aSet0(xT),
file('/tmp/tmpAQ6zmF/sel_LAT381+1.p_1',m__725) ).
fof(12,conjecture,
xu = xv,
file('/tmp/tmpAQ6zmF/sel_LAT381+1.p_1',m__) ).
fof(15,axiom,
aSubsetOf0(xS,xT),
file('/tmp/tmpAQ6zmF/sel_LAT381+1.p_1',m__725_01) ).
fof(18,negated_conjecture,
xu != xv,
inference(assume_negation,[status(cth)],[12]) ).
fof(19,negated_conjecture,
xu != xv,
inference(fof_simplification,[status(thm)],[18,theory(equality)]) ).
fof(20,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1)
| X1 = X2 ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(21,plain,
! [X3,X4] :
( ~ aElement0(X3)
| ~ aElement0(X4)
| ~ sdtlseqdt0(X3,X4)
| ~ sdtlseqdt0(X4,X3)
| X3 = X4 ),
inference(variable_rename,[status(thm)],[20]) ).
cnf(22,plain,
( X1 = X2
| ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[21]) ).
fof(26,plain,
! [X1] :
( ~ aSet0(X1)
| ! [X2] :
( ~ aElementOf0(X2,X1)
| aElement0(X2) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(27,plain,
! [X3] :
( ~ aSet0(X3)
| ! [X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4) ) ),
inference(variable_rename,[status(thm)],[26]) ).
fof(28,plain,
! [X3,X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4)
| ~ aSet0(X3) ),
inference(shift_quantors,[status(thm)],[27]) ).
cnf(29,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[28]) ).
fof(40,plain,
! [X1] :
( ~ aSet0(X1)
| ! [X2] :
( ~ aSubsetOf0(X2,X1)
| ! [X3] :
( ( ~ aSupremumOfIn0(X3,X2,X1)
| ( aElementOf0(X3,X1)
& aUpperBoundOfIn0(X3,X2,X1)
& ! [X4] :
( ~ aUpperBoundOfIn0(X4,X2,X1)
| sdtlseqdt0(X3,X4) ) ) )
& ( ~ aElementOf0(X3,X1)
| ~ aUpperBoundOfIn0(X3,X2,X1)
| ? [X4] :
( aUpperBoundOfIn0(X4,X2,X1)
& ~ sdtlseqdt0(X3,X4) )
| aSupremumOfIn0(X3,X2,X1) ) ) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(41,plain,
! [X5] :
( ~ aSet0(X5)
| ! [X6] :
( ~ aSubsetOf0(X6,X5)
| ! [X7] :
( ( ~ aSupremumOfIn0(X7,X6,X5)
| ( aElementOf0(X7,X5)
& aUpperBoundOfIn0(X7,X6,X5)
& ! [X8] :
( ~ aUpperBoundOfIn0(X8,X6,X5)
| sdtlseqdt0(X7,X8) ) ) )
& ( ~ aElementOf0(X7,X5)
| ~ aUpperBoundOfIn0(X7,X6,X5)
| ? [X9] :
( aUpperBoundOfIn0(X9,X6,X5)
& ~ sdtlseqdt0(X7,X9) )
| aSupremumOfIn0(X7,X6,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[40]) ).
fof(42,plain,
! [X5] :
( ~ aSet0(X5)
| ! [X6] :
( ~ aSubsetOf0(X6,X5)
| ! [X7] :
( ( ~ aSupremumOfIn0(X7,X6,X5)
| ( aElementOf0(X7,X5)
& aUpperBoundOfIn0(X7,X6,X5)
& ! [X8] :
( ~ aUpperBoundOfIn0(X8,X6,X5)
| sdtlseqdt0(X7,X8) ) ) )
& ( ~ aElementOf0(X7,X5)
| ~ aUpperBoundOfIn0(X7,X6,X5)
| ( aUpperBoundOfIn0(esk2_3(X5,X6,X7),X6,X5)
& ~ sdtlseqdt0(X7,esk2_3(X5,X6,X7)) )
| aSupremumOfIn0(X7,X6,X5) ) ) ) ),
inference(skolemize,[status(esa)],[41]) ).
fof(43,plain,
! [X5,X6,X7,X8] :
( ( ( ( ( ~ aUpperBoundOfIn0(X8,X6,X5)
| sdtlseqdt0(X7,X8) )
& aElementOf0(X7,X5)
& aUpperBoundOfIn0(X7,X6,X5) )
| ~ aSupremumOfIn0(X7,X6,X5) )
& ( ~ aElementOf0(X7,X5)
| ~ aUpperBoundOfIn0(X7,X6,X5)
| ( aUpperBoundOfIn0(esk2_3(X5,X6,X7),X6,X5)
& ~ sdtlseqdt0(X7,esk2_3(X5,X6,X7)) )
| aSupremumOfIn0(X7,X6,X5) ) )
| ~ aSubsetOf0(X6,X5)
| ~ aSet0(X5) ),
inference(shift_quantors,[status(thm)],[42]) ).
fof(44,plain,
! [X5,X6,X7,X8] :
( ( ~ aUpperBoundOfIn0(X8,X6,X5)
| sdtlseqdt0(X7,X8)
| ~ aSupremumOfIn0(X7,X6,X5)
| ~ aSubsetOf0(X6,X5)
| ~ aSet0(X5) )
& ( aElementOf0(X7,X5)
| ~ aSupremumOfIn0(X7,X6,X5)
| ~ aSubsetOf0(X6,X5)
| ~ aSet0(X5) )
& ( aUpperBoundOfIn0(X7,X6,X5)
| ~ aSupremumOfIn0(X7,X6,X5)
| ~ aSubsetOf0(X6,X5)
| ~ aSet0(X5) )
& ( aUpperBoundOfIn0(esk2_3(X5,X6,X7),X6,X5)
| ~ aElementOf0(X7,X5)
| ~ aUpperBoundOfIn0(X7,X6,X5)
| aSupremumOfIn0(X7,X6,X5)
| ~ aSubsetOf0(X6,X5)
| ~ aSet0(X5) )
& ( ~ sdtlseqdt0(X7,esk2_3(X5,X6,X7))
| ~ aElementOf0(X7,X5)
| ~ aUpperBoundOfIn0(X7,X6,X5)
| aSupremumOfIn0(X7,X6,X5)
| ~ aSubsetOf0(X6,X5)
| ~ aSet0(X5) ) ),
inference(distribute,[status(thm)],[43]) ).
cnf(47,plain,
( aUpperBoundOfIn0(X3,X2,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(X2,X1)
| ~ aSupremumOfIn0(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(48,plain,
( aElementOf0(X3,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(X2,X1)
| ~ aSupremumOfIn0(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(49,plain,
( sdtlseqdt0(X3,X4)
| ~ aSet0(X1)
| ~ aSubsetOf0(X2,X1)
| ~ aSupremumOfIn0(X3,X2,X1)
| ~ aUpperBoundOfIn0(X4,X2,X1) ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(72,plain,
aSupremumOfIn0(xv,xS,xT),
inference(split_conjunct,[status(thm)],[10]) ).
cnf(73,plain,
aSupremumOfIn0(xu,xS,xT),
inference(split_conjunct,[status(thm)],[10]) ).
cnf(74,plain,
aSet0(xT),
inference(split_conjunct,[status(thm)],[11]) ).
cnf(75,negated_conjecture,
xu != xv,
inference(split_conjunct,[status(thm)],[19]) ).
cnf(94,plain,
aSubsetOf0(xS,xT),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(109,plain,
( aElementOf0(xu,xT)
| ~ aSubsetOf0(xS,xT)
| ~ aSet0(xT) ),
inference(spm,[status(thm)],[48,73,theory(equality)]) ).
cnf(110,plain,
( aElementOf0(xv,xT)
| ~ aSubsetOf0(xS,xT)
| ~ aSet0(xT) ),
inference(spm,[status(thm)],[48,72,theory(equality)]) ).
cnf(111,plain,
( aElementOf0(xu,xT)
| $false
| ~ aSet0(xT) ),
inference(rw,[status(thm)],[109,94,theory(equality)]) ).
cnf(112,plain,
( aElementOf0(xu,xT)
| $false
| $false ),
inference(rw,[status(thm)],[111,74,theory(equality)]) ).
cnf(113,plain,
aElementOf0(xu,xT),
inference(cn,[status(thm)],[112,theory(equality)]) ).
cnf(114,plain,
( aElementOf0(xv,xT)
| $false
| ~ aSet0(xT) ),
inference(rw,[status(thm)],[110,94,theory(equality)]) ).
cnf(115,plain,
( aElementOf0(xv,xT)
| $false
| $false ),
inference(rw,[status(thm)],[114,74,theory(equality)]) ).
cnf(116,plain,
aElementOf0(xv,xT),
inference(cn,[status(thm)],[115,theory(equality)]) ).
cnf(120,plain,
( aUpperBoundOfIn0(xu,xS,xT)
| ~ aSubsetOf0(xS,xT)
| ~ aSet0(xT) ),
inference(spm,[status(thm)],[47,73,theory(equality)]) ).
cnf(121,plain,
( aUpperBoundOfIn0(xv,xS,xT)
| ~ aSubsetOf0(xS,xT)
| ~ aSet0(xT) ),
inference(spm,[status(thm)],[47,72,theory(equality)]) ).
cnf(122,plain,
( aUpperBoundOfIn0(xu,xS,xT)
| $false
| ~ aSet0(xT) ),
inference(rw,[status(thm)],[120,94,theory(equality)]) ).
cnf(123,plain,
( aUpperBoundOfIn0(xu,xS,xT)
| $false
| $false ),
inference(rw,[status(thm)],[122,74,theory(equality)]) ).
cnf(124,plain,
aUpperBoundOfIn0(xu,xS,xT),
inference(cn,[status(thm)],[123,theory(equality)]) ).
cnf(125,plain,
( aUpperBoundOfIn0(xv,xS,xT)
| $false
| ~ aSet0(xT) ),
inference(rw,[status(thm)],[121,94,theory(equality)]) ).
cnf(126,plain,
( aUpperBoundOfIn0(xv,xS,xT)
| $false
| $false ),
inference(rw,[status(thm)],[125,74,theory(equality)]) ).
cnf(127,plain,
aUpperBoundOfIn0(xv,xS,xT),
inference(cn,[status(thm)],[126,theory(equality)]) ).
cnf(142,plain,
( aElement0(xu)
| ~ aSet0(xT) ),
inference(spm,[status(thm)],[29,113,theory(equality)]) ).
cnf(144,plain,
( aElement0(xu)
| $false ),
inference(rw,[status(thm)],[142,74,theory(equality)]) ).
cnf(145,plain,
aElement0(xu),
inference(cn,[status(thm)],[144,theory(equality)]) ).
cnf(155,plain,
( aElement0(xv)
| ~ aSet0(xT) ),
inference(spm,[status(thm)],[29,116,theory(equality)]) ).
cnf(157,plain,
( aElement0(xv)
| $false ),
inference(rw,[status(thm)],[155,74,theory(equality)]) ).
cnf(158,plain,
aElement0(xv),
inference(cn,[status(thm)],[157,theory(equality)]) ).
cnf(175,plain,
( sdtlseqdt0(X1,xu)
| ~ aSupremumOfIn0(X1,xS,xT)
| ~ aSubsetOf0(xS,xT)
| ~ aSet0(xT) ),
inference(spm,[status(thm)],[49,124,theory(equality)]) ).
cnf(183,plain,
( sdtlseqdt0(X1,xu)
| ~ aSupremumOfIn0(X1,xS,xT)
| $false
| ~ aSet0(xT) ),
inference(rw,[status(thm)],[175,94,theory(equality)]) ).
cnf(184,plain,
( sdtlseqdt0(X1,xu)
| ~ aSupremumOfIn0(X1,xS,xT)
| $false
| $false ),
inference(rw,[status(thm)],[183,74,theory(equality)]) ).
cnf(185,plain,
( sdtlseqdt0(X1,xu)
| ~ aSupremumOfIn0(X1,xS,xT) ),
inference(cn,[status(thm)],[184,theory(equality)]) ).
cnf(188,plain,
( sdtlseqdt0(X1,xv)
| ~ aSupremumOfIn0(X1,xS,xT)
| ~ aSubsetOf0(xS,xT)
| ~ aSet0(xT) ),
inference(spm,[status(thm)],[49,127,theory(equality)]) ).
cnf(196,plain,
( sdtlseqdt0(X1,xv)
| ~ aSupremumOfIn0(X1,xS,xT)
| $false
| ~ aSet0(xT) ),
inference(rw,[status(thm)],[188,94,theory(equality)]) ).
cnf(197,plain,
( sdtlseqdt0(X1,xv)
| ~ aSupremumOfIn0(X1,xS,xT)
| $false
| $false ),
inference(rw,[status(thm)],[196,74,theory(equality)]) ).
cnf(198,plain,
( sdtlseqdt0(X1,xv)
| ~ aSupremumOfIn0(X1,xS,xT) ),
inference(cn,[status(thm)],[197,theory(equality)]) ).
cnf(227,plain,
sdtlseqdt0(xv,xu),
inference(spm,[status(thm)],[185,72,theory(equality)]) ).
cnf(238,plain,
sdtlseqdt0(xu,xv),
inference(spm,[status(thm)],[198,73,theory(equality)]) ).
cnf(241,plain,
( xv = xu
| ~ sdtlseqdt0(xv,xu)
| ~ aElement0(xu)
| ~ aElement0(xv) ),
inference(spm,[status(thm)],[22,238,theory(equality)]) ).
cnf(243,plain,
( xv = xu
| $false
| ~ aElement0(xu)
| ~ aElement0(xv) ),
inference(rw,[status(thm)],[241,227,theory(equality)]) ).
cnf(244,plain,
( xv = xu
| $false
| $false
| ~ aElement0(xv) ),
inference(rw,[status(thm)],[243,145,theory(equality)]) ).
cnf(245,plain,
( xv = xu
| $false
| $false
| $false ),
inference(rw,[status(thm)],[244,158,theory(equality)]) ).
cnf(246,plain,
xv = xu,
inference(cn,[status(thm)],[245,theory(equality)]) ).
cnf(247,plain,
$false,
inference(sr,[status(thm)],[246,75,theory(equality)]) ).
cnf(248,plain,
$false,
247,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/LAT/LAT381+1.p
% --creating new selector for []
% -running prover on /tmp/tmpAQ6zmF/sel_LAT381+1.p_1 with time limit 29
% -prover status Theorem
% Problem LAT381+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/LAT/LAT381+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/LAT/LAT381+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
%
%------------------------------------------------------------------------------