TSTP Solution File: SET800+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET800+4 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 03:40:15 EST 2010
% Result : Theorem 0.22s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 11 unt; 0 def)
% Number of atoms : 202 ( 0 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 243 ( 81 ~; 78 |; 72 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 119 ( 3 sgn 84 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmptsq9FS/sel_SET800+4.p_1',subset) ).
fof(2,axiom,
! [X4,X5,X6] :
( lower_bound(X6,X4,X5)
<=> ! [X3] :
( member(X3,X5)
=> apply(X4,X6,X3) ) ),
file('/tmp/tmptsq9FS/sel_SET800+4.p_1',lower_bound) ).
fof(4,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/tmptsq9FS/sel_SET800+4.p_1',greatest_lower_bound) ).
fof(5,conjecture,
! [X4,X5] :
( order(X4,X5)
=> ! [X9,X10] :
( ( subset(X9,X5)
& subset(X10,X5)
& subset(X9,X10) )
=> ! [X11,X12] :
( ( greatest_lower_bound(X11,X9,X4,X5)
& greatest_lower_bound(X12,X10,X4,X5) )
=> apply(X4,X12,X11) ) ) ),
file('/tmp/tmptsq9FS/sel_SET800+4.p_1',thIV12) ).
fof(6,negated_conjecture,
~ ! [X4,X5] :
( order(X4,X5)
=> ! [X9,X10] :
( ( subset(X9,X5)
& subset(X10,X5)
& subset(X9,X10) )
=> ! [X11,X12] :
( ( greatest_lower_bound(X11,X9,X4,X5)
& greatest_lower_bound(X12,X10,X4,X5) )
=> apply(X4,X12,X11) ) ) ),
inference(assume_negation,[status(cth)],[5]) ).
fof(9,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ member(X3,X1)
| member(X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ member(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(10,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ? [X7] :
( member(X7,X4)
& ~ member(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[9]) ).
fof(11,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[10]) ).
fof(12,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[11]) ).
fof(13,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( member(esk1_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk1_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[12]) ).
cnf(16,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[13]) ).
fof(17,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(18,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)],[17]) ).
fof(19,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)],[18]) ).
fof(20,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)],[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)
| lower_bound(X9,X7,X8) )
& ( ~ apply(X7,X9,esk2_3(X7,X8,X9))
| lower_bound(X9,X7,X8) ) ),
inference(distribute,[status(thm)],[20]) ).
cnf(24,plain,
( apply(X2,X1,X4)
| ~ lower_bound(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[21]) ).
fof(29,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)],[4]) ).
fof(30,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)],[29]) ).
fof(31,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)],[30]) ).
fof(32,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)],[31]) ).
fof(33,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)],[32]) ).
cnf(37,plain,
( lower_bound(X1,X3,X2)
| ~ greatest_lower_bound(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(38,plain,
( member(X1,X2)
| ~ greatest_lower_bound(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[33]) ).
fof(40,negated_conjecture,
? [X4,X5] :
( order(X4,X5)
& ? [X9,X10] :
( subset(X9,X5)
& subset(X10,X5)
& subset(X9,X10)
& ? [X11,X12] :
( greatest_lower_bound(X11,X9,X4,X5)
& greatest_lower_bound(X12,X10,X4,X5)
& ~ apply(X4,X12,X11) ) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(41,negated_conjecture,
? [X13,X14] :
( order(X13,X14)
& ? [X15,X16] :
( subset(X15,X14)
& subset(X16,X14)
& subset(X15,X16)
& ? [X17,X18] :
( greatest_lower_bound(X17,X15,X13,X14)
& greatest_lower_bound(X18,X16,X13,X14)
& ~ apply(X13,X18,X17) ) ) ),
inference(variable_rename,[status(thm)],[40]) ).
fof(42,negated_conjecture,
( order(esk4_0,esk5_0)
& subset(esk6_0,esk5_0)
& subset(esk7_0,esk5_0)
& subset(esk6_0,esk7_0)
& greatest_lower_bound(esk8_0,esk6_0,esk4_0,esk5_0)
& greatest_lower_bound(esk9_0,esk7_0,esk4_0,esk5_0)
& ~ apply(esk4_0,esk9_0,esk8_0) ),
inference(skolemize,[status(esa)],[41]) ).
cnf(43,negated_conjecture,
~ apply(esk4_0,esk9_0,esk8_0),
inference(split_conjunct,[status(thm)],[42]) ).
cnf(44,negated_conjecture,
greatest_lower_bound(esk9_0,esk7_0,esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[42]) ).
cnf(45,negated_conjecture,
greatest_lower_bound(esk8_0,esk6_0,esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[42]) ).
cnf(46,negated_conjecture,
subset(esk6_0,esk7_0),
inference(split_conjunct,[status(thm)],[42]) ).
cnf(121,negated_conjecture,
( member(X1,esk7_0)
| ~ member(X1,esk6_0) ),
inference(spm,[status(thm)],[16,46,theory(equality)]) ).
cnf(123,negated_conjecture,
member(esk8_0,esk6_0),
inference(spm,[status(thm)],[38,45,theory(equality)]) ).
cnf(127,negated_conjecture,
lower_bound(esk9_0,esk4_0,esk7_0),
inference(spm,[status(thm)],[37,44,theory(equality)]) ).
cnf(211,negated_conjecture,
( apply(esk4_0,esk9_0,X1)
| ~ member(X1,esk7_0) ),
inference(spm,[status(thm)],[24,127,theory(equality)]) ).
cnf(217,negated_conjecture,
~ member(esk8_0,esk7_0),
inference(spm,[status(thm)],[43,211,theory(equality)]) ).
cnf(236,negated_conjecture,
~ member(esk8_0,esk6_0),
inference(spm,[status(thm)],[217,121,theory(equality)]) ).
cnf(237,negated_conjecture,
$false,
inference(rw,[status(thm)],[236,123,theory(equality)]) ).
cnf(238,negated_conjecture,
$false,
inference(cn,[status(thm)],[237,theory(equality)]) ).
cnf(239,negated_conjecture,
$false,
238,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET800+4.p
% --creating new selector for [SET006+0.ax, SET006+3.ax]
% -running prover on /tmp/tmptsq9FS/sel_SET800+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET800+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET800+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET800+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
%
%------------------------------------------------------------------------------