TSTP Solution File: SET802+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET802+4 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 03:40:23 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 58 ( 6 unt; 0 def)
% Number of atoms : 276 ( 0 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 340 ( 122 ~; 134 |; 72 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 153 ( 5 sgn 86 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X4,X5,X6] :
( lower_bound(X6,X4,X5)
<=> ! [X3] :
( member(X3,X5)
=> apply(X4,X6,X3) ) ),
file('/tmp/tmpzbGe7m/sel_SET802+4.p_1',lower_bound) ).
fof(3,axiom,
! [X1,X3,X4,X5] :
( greatest_lower_bound(X1,X3,X4,X5)
<=> ( member(X1,X3)
& lower_bound(X1,X4,X3)
& ! [X6] :
( ( member(X6,X5)
& lower_bound(X6,X4,X3) )
=> apply(X4,X6,X1) ) ) ),
file('/tmp/tmpzbGe7m/sel_SET802+4.p_1',greatest_lower_bound) ).
fof(5,axiom,
! [X4,X5,X6] :
( least(X6,X4,X5)
<=> ( member(X6,X5)
& ! [X3] :
( member(X3,X5)
=> apply(X4,X6,X3) ) ) ),
file('/tmp/tmpzbGe7m/sel_SET802+4.p_1',least) ).
fof(6,conjecture,
! [X4,X5] :
( order(X4,X5)
=> ! [X3] :
( subset(X3,X5)
=> ! [X6] :
( least(X6,X4,X3)
<=> ( member(X6,X3)
& greatest_lower_bound(X6,X3,X4,X5) ) ) ) ),
file('/tmp/tmpzbGe7m/sel_SET802+4.p_1',thIV14) ).
fof(7,negated_conjecture,
~ ! [X4,X5] :
( order(X4,X5)
=> ! [X3] :
( subset(X3,X5)
=> ! [X6] :
( least(X6,X4,X3)
<=> ( member(X6,X3)
& greatest_lower_bound(X6,X3,X4,X5) ) ) ) ),
inference(assume_negation,[status(cth)],[6]) ).
fof(18,plain,
! [X4,X5,X6] :
( ( ~ lower_bound(X6,X4,X5)
| ! [X3] :
( ~ member(X3,X5)
| apply(X4,X6,X3) ) )
& ( ? [X3] :
( member(X3,X5)
& ~ apply(X4,X6,X3) )
| lower_bound(X6,X4,X5) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(19,plain,
! [X7,X8,X9] :
( ( ~ lower_bound(X9,X7,X8)
| ! [X10] :
( ~ member(X10,X8)
| apply(X7,X9,X10) ) )
& ( ? [X11] :
( member(X11,X8)
& ~ apply(X7,X9,X11) )
| lower_bound(X9,X7,X8) ) ),
inference(variable_rename,[status(thm)],[18]) ).
fof(20,plain,
! [X7,X8,X9] :
( ( ~ lower_bound(X9,X7,X8)
| ! [X10] :
( ~ member(X10,X8)
| apply(X7,X9,X10) ) )
& ( ( member(esk2_3(X7,X8,X9),X8)
& ~ apply(X7,X9,esk2_3(X7,X8,X9)) )
| lower_bound(X9,X7,X8) ) ),
inference(skolemize,[status(esa)],[19]) ).
fof(21,plain,
! [X7,X8,X9,X10] :
( ( ~ member(X10,X8)
| apply(X7,X9,X10)
| ~ lower_bound(X9,X7,X8) )
& ( ( member(esk2_3(X7,X8,X9),X8)
& ~ apply(X7,X9,esk2_3(X7,X8,X9)) )
| lower_bound(X9,X7,X8) ) ),
inference(shift_quantors,[status(thm)],[20]) ).
fof(22,plain,
! [X7,X8,X9,X10] :
( ( ~ member(X10,X8)
| apply(X7,X9,X10)
| ~ lower_bound(X9,X7,X8) )
& ( member(esk2_3(X7,X8,X9),X8)
| lower_bound(X9,X7,X8) )
& ( ~ apply(X7,X9,esk2_3(X7,X8,X9))
| lower_bound(X9,X7,X8) ) ),
inference(distribute,[status(thm)],[21]) ).
cnf(23,plain,
( lower_bound(X1,X2,X3)
| ~ apply(X2,X1,esk2_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(24,plain,
( lower_bound(X1,X2,X3)
| member(esk2_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(25,plain,
( apply(X2,X1,X4)
| ~ lower_bound(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(26,plain,
! [X1,X3,X4,X5] :
( ( ~ greatest_lower_bound(X1,X3,X4,X5)
| ( member(X1,X3)
& lower_bound(X1,X4,X3)
& ! [X6] :
( ~ member(X6,X5)
| ~ lower_bound(X6,X4,X3)
| apply(X4,X6,X1) ) ) )
& ( ~ member(X1,X3)
| ~ lower_bound(X1,X4,X3)
| ? [X6] :
( member(X6,X5)
& lower_bound(X6,X4,X3)
& ~ apply(X4,X6,X1) )
| greatest_lower_bound(X1,X3,X4,X5) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(27,plain,
! [X7,X8,X9,X10] :
( ( ~ greatest_lower_bound(X7,X8,X9,X10)
| ( member(X7,X8)
& lower_bound(X7,X9,X8)
& ! [X11] :
( ~ member(X11,X10)
| ~ lower_bound(X11,X9,X8)
| apply(X9,X11,X7) ) ) )
& ( ~ member(X7,X8)
| ~ lower_bound(X7,X9,X8)
| ? [X12] :
( member(X12,X10)
& lower_bound(X12,X9,X8)
& ~ apply(X9,X12,X7) )
| greatest_lower_bound(X7,X8,X9,X10) ) ),
inference(variable_rename,[status(thm)],[26]) ).
fof(28,plain,
! [X7,X8,X9,X10] :
( ( ~ greatest_lower_bound(X7,X8,X9,X10)
| ( member(X7,X8)
& lower_bound(X7,X9,X8)
& ! [X11] :
( ~ member(X11,X10)
| ~ lower_bound(X11,X9,X8)
| apply(X9,X11,X7) ) ) )
& ( ~ member(X7,X8)
| ~ lower_bound(X7,X9,X8)
| ( member(esk3_4(X7,X8,X9,X10),X10)
& lower_bound(esk3_4(X7,X8,X9,X10),X9,X8)
& ~ apply(X9,esk3_4(X7,X8,X9,X10),X7) )
| greatest_lower_bound(X7,X8,X9,X10) ) ),
inference(skolemize,[status(esa)],[27]) ).
fof(29,plain,
! [X7,X8,X9,X10,X11] :
( ( ( ( ~ member(X11,X10)
| ~ lower_bound(X11,X9,X8)
| apply(X9,X11,X7) )
& member(X7,X8)
& lower_bound(X7,X9,X8) )
| ~ greatest_lower_bound(X7,X8,X9,X10) )
& ( ~ member(X7,X8)
| ~ lower_bound(X7,X9,X8)
| ( member(esk3_4(X7,X8,X9,X10),X10)
& lower_bound(esk3_4(X7,X8,X9,X10),X9,X8)
& ~ apply(X9,esk3_4(X7,X8,X9,X10),X7) )
| greatest_lower_bound(X7,X8,X9,X10) ) ),
inference(shift_quantors,[status(thm)],[28]) ).
fof(30,plain,
! [X7,X8,X9,X10,X11] :
( ( ~ member(X11,X10)
| ~ lower_bound(X11,X9,X8)
| apply(X9,X11,X7)
| ~ greatest_lower_bound(X7,X8,X9,X10) )
& ( member(X7,X8)
| ~ greatest_lower_bound(X7,X8,X9,X10) )
& ( lower_bound(X7,X9,X8)
| ~ greatest_lower_bound(X7,X8,X9,X10) )
& ( member(esk3_4(X7,X8,X9,X10),X10)
| ~ member(X7,X8)
| ~ lower_bound(X7,X9,X8)
| greatest_lower_bound(X7,X8,X9,X10) )
& ( lower_bound(esk3_4(X7,X8,X9,X10),X9,X8)
| ~ member(X7,X8)
| ~ lower_bound(X7,X9,X8)
| greatest_lower_bound(X7,X8,X9,X10) )
& ( ~ apply(X9,esk3_4(X7,X8,X9,X10),X7)
| ~ member(X7,X8)
| ~ lower_bound(X7,X9,X8)
| greatest_lower_bound(X7,X8,X9,X10) ) ),
inference(distribute,[status(thm)],[29]) ).
cnf(31,plain,
( greatest_lower_bound(X1,X2,X3,X4)
| ~ lower_bound(X1,X3,X2)
| ~ member(X1,X2)
| ~ apply(X3,esk3_4(X1,X2,X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[30]) ).
cnf(32,plain,
( greatest_lower_bound(X1,X2,X3,X4)
| lower_bound(esk3_4(X1,X2,X3,X4),X3,X2)
| ~ lower_bound(X1,X3,X2)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[30]) ).
cnf(34,plain,
( lower_bound(X1,X3,X2)
| ~ greatest_lower_bound(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[30]) ).
cnf(35,plain,
( member(X1,X2)
| ~ greatest_lower_bound(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[30]) ).
fof(41,plain,
! [X4,X5,X6] :
( ( ~ least(X6,X4,X5)
| ( member(X6,X5)
& ! [X3] :
( ~ member(X3,X5)
| apply(X4,X6,X3) ) ) )
& ( ~ member(X6,X5)
| ? [X3] :
( member(X3,X5)
& ~ apply(X4,X6,X3) )
| least(X6,X4,X5) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(42,plain,
! [X7,X8,X9] :
( ( ~ least(X9,X7,X8)
| ( member(X9,X8)
& ! [X10] :
( ~ member(X10,X8)
| apply(X7,X9,X10) ) ) )
& ( ~ member(X9,X8)
| ? [X11] :
( member(X11,X8)
& ~ apply(X7,X9,X11) )
| least(X9,X7,X8) ) ),
inference(variable_rename,[status(thm)],[41]) ).
fof(43,plain,
! [X7,X8,X9] :
( ( ~ least(X9,X7,X8)
| ( member(X9,X8)
& ! [X10] :
( ~ member(X10,X8)
| apply(X7,X9,X10) ) ) )
& ( ~ member(X9,X8)
| ( member(esk4_3(X7,X8,X9),X8)
& ~ apply(X7,X9,esk4_3(X7,X8,X9)) )
| least(X9,X7,X8) ) ),
inference(skolemize,[status(esa)],[42]) ).
fof(44,plain,
! [X7,X8,X9,X10] :
( ( ( ( ~ member(X10,X8)
| apply(X7,X9,X10) )
& member(X9,X8) )
| ~ least(X9,X7,X8) )
& ( ~ member(X9,X8)
| ( member(esk4_3(X7,X8,X9),X8)
& ~ apply(X7,X9,esk4_3(X7,X8,X9)) )
| least(X9,X7,X8) ) ),
inference(shift_quantors,[status(thm)],[43]) ).
fof(45,plain,
! [X7,X8,X9,X10] :
( ( ~ member(X10,X8)
| apply(X7,X9,X10)
| ~ least(X9,X7,X8) )
& ( member(X9,X8)
| ~ least(X9,X7,X8) )
& ( member(esk4_3(X7,X8,X9),X8)
| ~ member(X9,X8)
| least(X9,X7,X8) )
& ( ~ apply(X7,X9,esk4_3(X7,X8,X9))
| ~ member(X9,X8)
| least(X9,X7,X8) ) ),
inference(distribute,[status(thm)],[44]) ).
cnf(46,plain,
( least(X1,X2,X3)
| ~ member(X1,X3)
| ~ apply(X2,X1,esk4_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(47,plain,
( least(X1,X2,X3)
| member(esk4_3(X2,X3,X1),X3)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(48,plain,
( member(X1,X3)
| ~ least(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(49,plain,
( apply(X2,X1,X4)
| ~ least(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[45]) ).
fof(50,negated_conjecture,
? [X4,X5] :
( order(X4,X5)
& ? [X3] :
( subset(X3,X5)
& ? [X6] :
( ( ~ least(X6,X4,X3)
| ~ member(X6,X3)
| ~ greatest_lower_bound(X6,X3,X4,X5) )
& ( least(X6,X4,X3)
| ( member(X6,X3)
& greatest_lower_bound(X6,X3,X4,X5) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(51,negated_conjecture,
? [X7,X8] :
( order(X7,X8)
& ? [X9] :
( subset(X9,X8)
& ? [X10] :
( ( ~ least(X10,X7,X9)
| ~ member(X10,X9)
| ~ greatest_lower_bound(X10,X9,X7,X8) )
& ( least(X10,X7,X9)
| ( member(X10,X9)
& greatest_lower_bound(X10,X9,X7,X8) ) ) ) ) ),
inference(variable_rename,[status(thm)],[50]) ).
fof(52,negated_conjecture,
( order(esk5_0,esk6_0)
& subset(esk7_0,esk6_0)
& ( ~ least(esk8_0,esk5_0,esk7_0)
| ~ member(esk8_0,esk7_0)
| ~ greatest_lower_bound(esk8_0,esk7_0,esk5_0,esk6_0) )
& ( least(esk8_0,esk5_0,esk7_0)
| ( member(esk8_0,esk7_0)
& greatest_lower_bound(esk8_0,esk7_0,esk5_0,esk6_0) ) ) ),
inference(skolemize,[status(esa)],[51]) ).
fof(53,negated_conjecture,
( order(esk5_0,esk6_0)
& subset(esk7_0,esk6_0)
& ( ~ least(esk8_0,esk5_0,esk7_0)
| ~ member(esk8_0,esk7_0)
| ~ greatest_lower_bound(esk8_0,esk7_0,esk5_0,esk6_0) )
& ( member(esk8_0,esk7_0)
| least(esk8_0,esk5_0,esk7_0) )
& ( greatest_lower_bound(esk8_0,esk7_0,esk5_0,esk6_0)
| least(esk8_0,esk5_0,esk7_0) ) ),
inference(distribute,[status(thm)],[52]) ).
cnf(54,negated_conjecture,
( least(esk8_0,esk5_0,esk7_0)
| greatest_lower_bound(esk8_0,esk7_0,esk5_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(55,negated_conjecture,
( least(esk8_0,esk5_0,esk7_0)
| member(esk8_0,esk7_0) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(56,negated_conjecture,
( ~ greatest_lower_bound(esk8_0,esk7_0,esk5_0,esk6_0)
| ~ member(esk8_0,esk7_0)
| ~ least(esk8_0,esk5_0,esk7_0) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(127,negated_conjecture,
member(esk8_0,esk7_0),
inference(spm,[status(thm)],[48,55,theory(equality)]) ).
cnf(133,negated_conjecture,
( ~ least(esk8_0,esk5_0,esk7_0)
| ~ greatest_lower_bound(esk8_0,esk7_0,esk5_0,esk6_0) ),
inference(csr,[status(thm)],[56,35]) ).
cnf(137,negated_conjecture,
( apply(esk5_0,esk8_0,X1)
| greatest_lower_bound(esk8_0,esk7_0,esk5_0,esk6_0)
| ~ member(X1,esk7_0) ),
inference(spm,[status(thm)],[49,54,theory(equality)]) ).
cnf(138,plain,
( apply(X1,esk3_4(X2,X3,X1,X4),X5)
| greatest_lower_bound(X2,X3,X1,X4)
| ~ member(X5,X3)
| ~ lower_bound(X2,X1,X3)
| ~ member(X2,X3) ),
inference(spm,[status(thm)],[25,32,theory(equality)]) ).
cnf(222,negated_conjecture,
( greatest_lower_bound(esk8_0,esk7_0,esk5_0,esk6_0)
| apply(esk5_0,esk8_0,esk2_3(X1,esk7_0,X2))
| lower_bound(X2,X1,esk7_0) ),
inference(spm,[status(thm)],[137,24,theory(equality)]) ).
cnf(258,plain,
( greatest_lower_bound(X1,X2,X3,X4)
| ~ lower_bound(X1,X3,X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[31,138,theory(equality)]) ).
cnf(267,negated_conjecture,
( lower_bound(esk8_0,esk5_0,esk7_0)
| greatest_lower_bound(esk8_0,esk7_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[23,222,theory(equality)]) ).
cnf(270,negated_conjecture,
lower_bound(esk8_0,esk5_0,esk7_0),
inference(csr,[status(thm)],[267,34]) ).
cnf(271,negated_conjecture,
( apply(esk5_0,esk8_0,X1)
| ~ member(X1,esk7_0) ),
inference(spm,[status(thm)],[25,270,theory(equality)]) ).
cnf(273,negated_conjecture,
( least(esk8_0,esk5_0,X1)
| ~ member(esk8_0,X1)
| ~ member(esk4_3(esk5_0,X1,esk8_0),esk7_0) ),
inference(spm,[status(thm)],[46,271,theory(equality)]) ).
cnf(276,negated_conjecture,
( least(esk8_0,esk5_0,esk7_0)
| ~ member(esk8_0,esk7_0) ),
inference(spm,[status(thm)],[273,47,theory(equality)]) ).
cnf(277,negated_conjecture,
( least(esk8_0,esk5_0,esk7_0)
| $false ),
inference(rw,[status(thm)],[276,127,theory(equality)]) ).
cnf(278,negated_conjecture,
least(esk8_0,esk5_0,esk7_0),
inference(cn,[status(thm)],[277,theory(equality)]) ).
cnf(281,negated_conjecture,
( $false
| ~ greatest_lower_bound(esk8_0,esk7_0,esk5_0,esk6_0) ),
inference(rw,[status(thm)],[133,278,theory(equality)]) ).
cnf(282,negated_conjecture,
~ greatest_lower_bound(esk8_0,esk7_0,esk5_0,esk6_0),
inference(cn,[status(thm)],[281,theory(equality)]) ).
cnf(285,negated_conjecture,
( ~ lower_bound(esk8_0,esk5_0,esk7_0)
| ~ member(esk8_0,esk7_0) ),
inference(spm,[status(thm)],[282,258,theory(equality)]) ).
cnf(288,negated_conjecture,
( $false
| ~ member(esk8_0,esk7_0) ),
inference(rw,[status(thm)],[285,270,theory(equality)]) ).
cnf(289,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[288,127,theory(equality)]) ).
cnf(290,negated_conjecture,
$false,
inference(cn,[status(thm)],[289,theory(equality)]) ).
cnf(291,negated_conjecture,
$false,
290,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET802+4.p
% --creating new selector for [SET006+0.ax, SET006+3.ax]
% -running prover on /tmp/tmpzbGe7m/sel_SET802+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET802+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET802+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET802+4.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
%
%------------------------------------------------------------------------------