TSTP Solution File: SET798+4 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET798+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 03:40:06 EST 2010
% Result : Theorem 0.22s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 6 unt; 0 def)
% Number of atoms : 122 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 135 ( 44 ~; 42 |; 39 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 83 ( 0 sgn 52 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpUY_9Wh/sel_SET798+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/tmpUY_9Wh/sel_SET798+4.p_1',lower_bound) ).
fof(4,conjecture,
! [X4,X5] :
( order(X4,X5)
=> ! [X3,X7] :
( ( subset(X3,X5)
& subset(X7,X5)
& subset(X3,X7) )
=> ! [X6] :
( lower_bound(X6,X4,X7)
=> lower_bound(X6,X4,X3) ) ) ),
file('/tmp/tmpUY_9Wh/sel_SET798+4.p_1',thIV10) ).
fof(5,negated_conjecture,
~ ! [X4,X5] :
( order(X4,X5)
=> ! [X3,X7] :
( ( subset(X3,X5)
& subset(X7,X5)
& subset(X3,X7) )
=> ! [X6] :
( lower_bound(X6,X4,X7)
=> lower_bound(X6,X4,X3) ) ) ),
inference(assume_negation,[status(cth)],[4]) ).
fof(8,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(9,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)],[8]) ).
fof(10,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)],[9]) ).
fof(11,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)],[10]) ).
fof(12,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)],[11]) ).
cnf(15,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[12]) ).
fof(16,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(17,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)],[16]) ).
fof(18,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)],[17]) ).
fof(19,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)],[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)
| lower_bound(X9,X7,X8) )
& ( ~ apply(X7,X9,esk2_3(X7,X8,X9))
| lower_bound(X9,X7,X8) ) ),
inference(distribute,[status(thm)],[19]) ).
cnf(21,plain,
( lower_bound(X1,X2,X3)
| ~ apply(X2,X1,esk2_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(22,plain,
( lower_bound(X1,X2,X3)
| member(esk2_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(23,plain,
( apply(X2,X1,X4)
| ~ lower_bound(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[20]) ).
fof(28,negated_conjecture,
? [X4,X5] :
( order(X4,X5)
& ? [X3,X7] :
( subset(X3,X5)
& subset(X7,X5)
& subset(X3,X7)
& ? [X6] :
( lower_bound(X6,X4,X7)
& ~ lower_bound(X6,X4,X3) ) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(29,negated_conjecture,
? [X8,X9] :
( order(X8,X9)
& ? [X10,X11] :
( subset(X10,X9)
& subset(X11,X9)
& subset(X10,X11)
& ? [X12] :
( lower_bound(X12,X8,X11)
& ~ lower_bound(X12,X8,X10) ) ) ),
inference(variable_rename,[status(thm)],[28]) ).
fof(30,negated_conjecture,
( order(esk3_0,esk4_0)
& subset(esk5_0,esk4_0)
& subset(esk6_0,esk4_0)
& subset(esk5_0,esk6_0)
& lower_bound(esk7_0,esk3_0,esk6_0)
& ~ lower_bound(esk7_0,esk3_0,esk5_0) ),
inference(skolemize,[status(esa)],[29]) ).
cnf(31,negated_conjecture,
~ lower_bound(esk7_0,esk3_0,esk5_0),
inference(split_conjunct,[status(thm)],[30]) ).
cnf(32,negated_conjecture,
lower_bound(esk7_0,esk3_0,esk6_0),
inference(split_conjunct,[status(thm)],[30]) ).
cnf(33,negated_conjecture,
subset(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[30]) ).
cnf(109,negated_conjecture,
( member(X1,esk6_0)
| ~ member(X1,esk5_0) ),
inference(spm,[status(thm)],[15,33,theory(equality)]) ).
cnf(111,negated_conjecture,
( apply(esk3_0,esk7_0,X1)
| ~ member(X1,esk6_0) ),
inference(spm,[status(thm)],[23,32,theory(equality)]) ).
cnf(206,negated_conjecture,
( lower_bound(esk7_0,esk3_0,X1)
| ~ member(esk2_3(esk3_0,X1,esk7_0),esk6_0) ),
inference(spm,[status(thm)],[21,111,theory(equality)]) ).
cnf(222,negated_conjecture,
( lower_bound(esk7_0,esk3_0,X1)
| ~ member(esk2_3(esk3_0,X1,esk7_0),esk5_0) ),
inference(spm,[status(thm)],[206,109,theory(equality)]) ).
cnf(224,negated_conjecture,
lower_bound(esk7_0,esk3_0,esk5_0),
inference(spm,[status(thm)],[222,22,theory(equality)]) ).
cnf(225,negated_conjecture,
$false,
inference(sr,[status(thm)],[224,31,theory(equality)]) ).
cnf(226,negated_conjecture,
$false,
225,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET798+4.p
% --creating new selector for [SET006+0.ax, SET006+3.ax]
% -running prover on /tmp/tmpUY_9Wh/sel_SET798+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET798+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET798+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET798+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
%
%------------------------------------------------------------------------------