TSTP Solution File: LAT381+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : LAT381+3 : 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 17:17:55 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% 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(1,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/tmp/tmp9EJxZW/sel_LAT381+3.p_1',mASymm) ).
fof(3,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/tmp/tmp9EJxZW/sel_LAT381+3.p_1',mEOfElem) ).
fof(10,axiom,
( aElementOf0(xu,xT)
& aElementOf0(xu,xT)
& ! [X1] :
( aElementOf0(X1,xS)
=> sdtlseqdt0(X1,xu) )
& aUpperBoundOfIn0(xu,xS,xT)
& ! [X1] :
( ( ( aElementOf0(X1,xT)
& ! [X2] :
( aElementOf0(X2,xS)
=> sdtlseqdt0(X2,X1) ) )
| aUpperBoundOfIn0(X1,xS,xT) )
=> sdtlseqdt0(xu,X1) )
& aSupremumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& ! [X1] :
( aElementOf0(X1,xS)
=> sdtlseqdt0(X1,xv) )
& aUpperBoundOfIn0(xv,xS,xT)
& ! [X1] :
( ( ( aElementOf0(X1,xT)
& ! [X2] :
( aElementOf0(X2,xS)
=> sdtlseqdt0(X2,X1) ) )
| aUpperBoundOfIn0(X1,xS,xT) )
=> sdtlseqdt0(xv,X1) )
& aSupremumOfIn0(xv,xS,xT) ),
file('/tmp/tmp9EJxZW/sel_LAT381+3.p_1',m__744) ).
fof(11,axiom,
aSet0(xT),
file('/tmp/tmp9EJxZW/sel_LAT381+3.p_1',m__725) ).
fof(12,conjecture,
xu = xv,
file('/tmp/tmp9EJxZW/sel_LAT381+3.p_1',m__) ).
fof(18,negated_conjecture,
xu != xv,
inference(assume_negation,[status(cth)],[12]) ).
fof(19,plain,
( aElementOf0(xu,xT)
& ! [X1] :
( aElementOf0(X1,xS)
=> sdtlseqdt0(X1,xu) )
& aUpperBoundOfIn0(xu,xS,xT)
& ! [X1] :
( ( ( aElementOf0(X1,xT)
& ! [X2] :
( aElementOf0(X2,xS)
=> sdtlseqdt0(X2,X1) ) )
| aUpperBoundOfIn0(X1,xS,xT) )
=> sdtlseqdt0(xu,X1) )
& aSupremumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& ! [X1] :
( aElementOf0(X1,xS)
=> sdtlseqdt0(X1,xv) )
& aUpperBoundOfIn0(xv,xS,xT)
& ! [X1] :
( ( ( aElementOf0(X1,xT)
& ! [X2] :
( aElementOf0(X2,xS)
=> sdtlseqdt0(X2,X1) ) )
| aUpperBoundOfIn0(X1,xS,xT) )
=> sdtlseqdt0(xv,X1) )
& aSupremumOfIn0(xv,xS,xT) ),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
fof(20,negated_conjecture,
xu != xv,
inference(fof_simplification,[status(thm)],[18,theory(equality)]) ).
fof(21,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1)
| X1 = X2 ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(22,plain,
! [X3,X4] :
( ~ aElement0(X3)
| ~ aElement0(X4)
| ~ sdtlseqdt0(X3,X4)
| ~ sdtlseqdt0(X4,X3)
| X3 = X4 ),
inference(variable_rename,[status(thm)],[21]) ).
cnf(23,plain,
( X1 = X2
| ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(27,plain,
! [X1] :
( ~ aSet0(X1)
| ! [X2] :
( ~ aElementOf0(X2,X1)
| aElement0(X2) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(28,plain,
! [X3] :
( ~ aSet0(X3)
| ! [X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4) ) ),
inference(variable_rename,[status(thm)],[27]) ).
fof(29,plain,
! [X3,X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4)
| ~ aSet0(X3) ),
inference(shift_quantors,[status(thm)],[28]) ).
cnf(30,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[29]) ).
fof(73,plain,
( aElementOf0(xu,xT)
& ! [X1] :
( ~ aElementOf0(X1,xS)
| sdtlseqdt0(X1,xu) )
& aUpperBoundOfIn0(xu,xS,xT)
& ! [X1] :
( ( ( ~ aElementOf0(X1,xT)
| ? [X2] :
( aElementOf0(X2,xS)
& ~ sdtlseqdt0(X2,X1) ) )
& ~ aUpperBoundOfIn0(X1,xS,xT) )
| sdtlseqdt0(xu,X1) )
& aSupremumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& ! [X1] :
( ~ aElementOf0(X1,xS)
| sdtlseqdt0(X1,xv) )
& aUpperBoundOfIn0(xv,xS,xT)
& ! [X1] :
( ( ( ~ aElementOf0(X1,xT)
| ? [X2] :
( aElementOf0(X2,xS)
& ~ sdtlseqdt0(X2,X1) ) )
& ~ aUpperBoundOfIn0(X1,xS,xT) )
| sdtlseqdt0(xv,X1) )
& aSupremumOfIn0(xv,xS,xT) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(74,plain,
( aElementOf0(xu,xT)
& ! [X3] :
( ~ aElementOf0(X3,xS)
| sdtlseqdt0(X3,xu) )
& aUpperBoundOfIn0(xu,xS,xT)
& ! [X4] :
( ( ( ~ aElementOf0(X4,xT)
| ? [X5] :
( aElementOf0(X5,xS)
& ~ sdtlseqdt0(X5,X4) ) )
& ~ aUpperBoundOfIn0(X4,xS,xT) )
| sdtlseqdt0(xu,X4) )
& aSupremumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& ! [X6] :
( ~ aElementOf0(X6,xS)
| sdtlseqdt0(X6,xv) )
& aUpperBoundOfIn0(xv,xS,xT)
& ! [X7] :
( ( ( ~ aElementOf0(X7,xT)
| ? [X8] :
( aElementOf0(X8,xS)
& ~ sdtlseqdt0(X8,X7) ) )
& ~ aUpperBoundOfIn0(X7,xS,xT) )
| sdtlseqdt0(xv,X7) )
& aSupremumOfIn0(xv,xS,xT) ),
inference(variable_rename,[status(thm)],[73]) ).
fof(75,plain,
( aElementOf0(xu,xT)
& ! [X3] :
( ~ aElementOf0(X3,xS)
| sdtlseqdt0(X3,xu) )
& aUpperBoundOfIn0(xu,xS,xT)
& ! [X4] :
( ( ( ~ aElementOf0(X4,xT)
| ( aElementOf0(esk5_1(X4),xS)
& ~ sdtlseqdt0(esk5_1(X4),X4) ) )
& ~ aUpperBoundOfIn0(X4,xS,xT) )
| sdtlseqdt0(xu,X4) )
& aSupremumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& ! [X6] :
( ~ aElementOf0(X6,xS)
| sdtlseqdt0(X6,xv) )
& aUpperBoundOfIn0(xv,xS,xT)
& ! [X7] :
( ( ( ~ aElementOf0(X7,xT)
| ( aElementOf0(esk6_1(X7),xS)
& ~ sdtlseqdt0(esk6_1(X7),X7) ) )
& ~ aUpperBoundOfIn0(X7,xS,xT) )
| sdtlseqdt0(xv,X7) )
& aSupremumOfIn0(xv,xS,xT) ),
inference(skolemize,[status(esa)],[74]) ).
fof(76,plain,
! [X3,X4,X6,X7] :
( ( ( ( ~ aElementOf0(X7,xT)
| ( aElementOf0(esk6_1(X7),xS)
& ~ sdtlseqdt0(esk6_1(X7),X7) ) )
& ~ aUpperBoundOfIn0(X7,xS,xT) )
| sdtlseqdt0(xv,X7) )
& ( ~ aElementOf0(X6,xS)
| sdtlseqdt0(X6,xv) )
& ( ( ( ~ aElementOf0(X4,xT)
| ( aElementOf0(esk5_1(X4),xS)
& ~ sdtlseqdt0(esk5_1(X4),X4) ) )
& ~ aUpperBoundOfIn0(X4,xS,xT) )
| sdtlseqdt0(xu,X4) )
& ( ~ aElementOf0(X3,xS)
| sdtlseqdt0(X3,xu) )
& aElementOf0(xu,xT)
& aUpperBoundOfIn0(xu,xS,xT)
& aSupremumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& aUpperBoundOfIn0(xv,xS,xT)
& aSupremumOfIn0(xv,xS,xT) ),
inference(shift_quantors,[status(thm)],[75]) ).
fof(77,plain,
! [X3,X4,X6,X7] :
( ( aElementOf0(esk6_1(X7),xS)
| ~ aElementOf0(X7,xT)
| sdtlseqdt0(xv,X7) )
& ( ~ sdtlseqdt0(esk6_1(X7),X7)
| ~ aElementOf0(X7,xT)
| sdtlseqdt0(xv,X7) )
& ( ~ aUpperBoundOfIn0(X7,xS,xT)
| sdtlseqdt0(xv,X7) )
& ( ~ aElementOf0(X6,xS)
| sdtlseqdt0(X6,xv) )
& ( aElementOf0(esk5_1(X4),xS)
| ~ aElementOf0(X4,xT)
| sdtlseqdt0(xu,X4) )
& ( ~ sdtlseqdt0(esk5_1(X4),X4)
| ~ aElementOf0(X4,xT)
| sdtlseqdt0(xu,X4) )
& ( ~ aUpperBoundOfIn0(X4,xS,xT)
| sdtlseqdt0(xu,X4) )
& ( ~ aElementOf0(X3,xS)
| sdtlseqdt0(X3,xu) )
& aElementOf0(xu,xT)
& aUpperBoundOfIn0(xu,xS,xT)
& aSupremumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& aUpperBoundOfIn0(xv,xS,xT)
& aSupremumOfIn0(xv,xS,xT) ),
inference(distribute,[status(thm)],[76]) ).
cnf(79,plain,
aUpperBoundOfIn0(xv,xS,xT),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(80,plain,
aElementOf0(xv,xT),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(83,plain,
aUpperBoundOfIn0(xu,xS,xT),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(84,plain,
aElementOf0(xu,xT),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(86,plain,
( sdtlseqdt0(xu,X1)
| ~ aUpperBoundOfIn0(X1,xS,xT) ),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(90,plain,
( sdtlseqdt0(xv,X1)
| ~ aUpperBoundOfIn0(X1,xS,xT) ),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(93,plain,
aSet0(xT),
inference(split_conjunct,[status(thm)],[11]) ).
cnf(94,negated_conjecture,
xu != xv,
inference(split_conjunct,[status(thm)],[20]) ).
cnf(127,plain,
sdtlseqdt0(xu,xv),
inference(spm,[status(thm)],[86,79,theory(equality)]) ).
cnf(128,plain,
( aElement0(xu)
| ~ aSet0(xT) ),
inference(spm,[status(thm)],[30,84,theory(equality)]) ).
cnf(129,plain,
( aElement0(xv)
| ~ aSet0(xT) ),
inference(spm,[status(thm)],[30,80,theory(equality)]) ).
cnf(130,plain,
( aElement0(xu)
| $false ),
inference(rw,[status(thm)],[128,93,theory(equality)]) ).
cnf(131,plain,
aElement0(xu),
inference(cn,[status(thm)],[130,theory(equality)]) ).
cnf(132,plain,
( aElement0(xv)
| $false ),
inference(rw,[status(thm)],[129,93,theory(equality)]) ).
cnf(133,plain,
aElement0(xv),
inference(cn,[status(thm)],[132,theory(equality)]) ).
cnf(138,plain,
sdtlseqdt0(xv,xu),
inference(spm,[status(thm)],[90,83,theory(equality)]) ).
cnf(269,plain,
( xv = xu
| ~ sdtlseqdt0(xv,xu)
| ~ aElement0(xu)
| ~ aElement0(xv) ),
inference(spm,[status(thm)],[23,127,theory(equality)]) ).
cnf(271,plain,
( xv = xu
| ~ sdtlseqdt0(xv,xu)
| $false
| ~ aElement0(xv) ),
inference(rw,[status(thm)],[269,131,theory(equality)]) ).
cnf(272,plain,
( xv = xu
| ~ sdtlseqdt0(xv,xu)
| $false
| $false ),
inference(rw,[status(thm)],[271,133,theory(equality)]) ).
cnf(273,plain,
( xv = xu
| ~ sdtlseqdt0(xv,xu) ),
inference(cn,[status(thm)],[272,theory(equality)]) ).
cnf(274,plain,
~ sdtlseqdt0(xv,xu),
inference(sr,[status(thm)],[273,94,theory(equality)]) ).
cnf(279,plain,
$false,
inference(sr,[status(thm)],[138,274,theory(equality)]) ).
cnf(280,plain,
$false,
279,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/LAT/LAT381+3.p
% --creating new selector for []
% -running prover on /tmp/tmp9EJxZW/sel_LAT381+3.p_1 with time limit 29
% -prover status Theorem
% Problem LAT381+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/LAT/LAT381+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/LAT/LAT381+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
%
%------------------------------------------------------------------------------