TSTP Solution File: SET697+4 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET697+4 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 03:17:02 EST 2010
% Result : Theorem 0.31s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 6
% Syntax : Number of formulae : 77 ( 14 unt; 0 def)
% Number of atoms : 232 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 254 ( 99 ~; 102 |; 43 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 144 ( 12 sgn 62 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpziCIFG/sel_SET697+4.p_1',subset) ).
fof(2,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpziCIFG/sel_SET697+4.p_1',equal_set) ).
fof(3,axiom,
! [X3,X1,X2] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmpziCIFG/sel_SET697+4.p_1',intersection) ).
fof(4,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
file('/tmp/tmpziCIFG/sel_SET697+4.p_1',difference) ).
fof(5,axiom,
! [X3] : ~ member(X3,empty_set),
file('/tmp/tmpziCIFG/sel_SET697+4.p_1',empty_set) ).
fof(6,conjecture,
! [X1,X2,X4] :
( ( subset(X1,X4)
& subset(X2,X4) )
=> ( subset(X1,X2)
<=> equal_set(intersection(X1,difference(X4,X2)),empty_set) ) ),
file('/tmp/tmpziCIFG/sel_SET697+4.p_1',thI31) ).
fof(7,negated_conjecture,
~ ! [X1,X2,X4] :
( ( subset(X1,X4)
& subset(X2,X4) )
=> ( subset(X1,X2)
<=> equal_set(intersection(X1,difference(X4,X2)),empty_set) ) ),
inference(assume_negation,[status(cth)],[6]) ).
fof(8,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[4,theory(equality)]) ).
fof(9,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).
fof(10,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(11,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)],[10]) ).
fof(12,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)],[11]) ).
fof(13,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)],[12]) ).
fof(14,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)],[13]) ).
cnf(15,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(16,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(17,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[14]) ).
fof(18,plain,
! [X1,X2] :
( ( ~ equal_set(X1,X2)
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| equal_set(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(19,plain,
! [X3,X4] :
( ( ~ equal_set(X3,X4)
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(variable_rename,[status(thm)],[18]) ).
fof(20,plain,
! [X3,X4] :
( ( subset(X3,X4)
| ~ equal_set(X3,X4) )
& ( subset(X4,X3)
| ~ equal_set(X3,X4) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(distribute,[status(thm)],[19]) ).
cnf(21,plain,
( equal_set(X1,X2)
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(23,plain,
( subset(X1,X2)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[20]) ).
fof(24,plain,
! [X3,X1,X2] :
( ( ~ member(X3,intersection(X1,X2))
| ( member(X3,X1)
& member(X3,X2) ) )
& ( ~ member(X3,X1)
| ~ member(X3,X2)
| member(X3,intersection(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(25,plain,
! [X4,X5,X6] :
( ( ~ member(X4,intersection(X5,X6))
| ( member(X4,X5)
& member(X4,X6) ) )
& ( ~ member(X4,X5)
| ~ member(X4,X6)
| member(X4,intersection(X5,X6)) ) ),
inference(variable_rename,[status(thm)],[24]) ).
fof(26,plain,
! [X4,X5,X6] :
( ( member(X4,X5)
| ~ member(X4,intersection(X5,X6)) )
& ( member(X4,X6)
| ~ member(X4,intersection(X5,X6)) )
& ( ~ member(X4,X5)
| ~ member(X4,X6)
| member(X4,intersection(X5,X6)) ) ),
inference(distribute,[status(thm)],[25]) ).
cnf(27,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[26]) ).
cnf(28,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[26]) ).
cnf(29,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[26]) ).
fof(30,plain,
! [X2,X1,X4] :
( ( ~ member(X2,difference(X4,X1))
| ( member(X2,X4)
& ~ member(X2,X1) ) )
& ( ~ member(X2,X4)
| member(X2,X1)
| member(X2,difference(X4,X1)) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(31,plain,
! [X5,X6,X7] :
( ( ~ member(X5,difference(X7,X6))
| ( member(X5,X7)
& ~ member(X5,X6) ) )
& ( ~ member(X5,X7)
| member(X5,X6)
| member(X5,difference(X7,X6)) ) ),
inference(variable_rename,[status(thm)],[30]) ).
fof(32,plain,
! [X5,X6,X7] :
( ( member(X5,X7)
| ~ member(X5,difference(X7,X6)) )
& ( ~ member(X5,X6)
| ~ member(X5,difference(X7,X6)) )
& ( ~ member(X5,X7)
| member(X5,X6)
| member(X5,difference(X7,X6)) ) ),
inference(distribute,[status(thm)],[31]) ).
cnf(33,plain,
( member(X1,difference(X2,X3))
| member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(34,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(35,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[32]) ).
fof(36,plain,
! [X4] : ~ member(X4,empty_set),
inference(variable_rename,[status(thm)],[9]) ).
cnf(37,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[36]) ).
fof(38,negated_conjecture,
? [X1,X2,X4] :
( subset(X1,X4)
& subset(X2,X4)
& ( ~ subset(X1,X2)
| ~ equal_set(intersection(X1,difference(X4,X2)),empty_set) )
& ( subset(X1,X2)
| equal_set(intersection(X1,difference(X4,X2)),empty_set) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(39,negated_conjecture,
? [X5,X6,X7] :
( subset(X5,X7)
& subset(X6,X7)
& ( ~ subset(X5,X6)
| ~ equal_set(intersection(X5,difference(X7,X6)),empty_set) )
& ( subset(X5,X6)
| equal_set(intersection(X5,difference(X7,X6)),empty_set) ) ),
inference(variable_rename,[status(thm)],[38]) ).
fof(40,negated_conjecture,
( subset(esk2_0,esk4_0)
& subset(esk3_0,esk4_0)
& ( ~ subset(esk2_0,esk3_0)
| ~ equal_set(intersection(esk2_0,difference(esk4_0,esk3_0)),empty_set) )
& ( subset(esk2_0,esk3_0)
| equal_set(intersection(esk2_0,difference(esk4_0,esk3_0)),empty_set) ) ),
inference(skolemize,[status(esa)],[39]) ).
cnf(41,negated_conjecture,
( equal_set(intersection(esk2_0,difference(esk4_0,esk3_0)),empty_set)
| subset(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(42,negated_conjecture,
( ~ equal_set(intersection(esk2_0,difference(esk4_0,esk3_0)),empty_set)
| ~ subset(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(44,negated_conjecture,
subset(esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(46,negated_conjecture,
( subset(intersection(esk2_0,difference(esk4_0,esk3_0)),empty_set)
| subset(esk2_0,esk3_0) ),
inference(spm,[status(thm)],[23,41,theory(equality)]) ).
cnf(49,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[37,16,theory(equality)]) ).
cnf(50,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[17,44,theory(equality)]) ).
cnf(53,negated_conjecture,
( ~ subset(esk2_0,esk3_0)
| ~ subset(empty_set,intersection(esk2_0,difference(esk4_0,esk3_0)))
| ~ subset(intersection(esk2_0,difference(esk4_0,esk3_0)),empty_set) ),
inference(spm,[status(thm)],[42,21,theory(equality)]) ).
cnf(55,plain,
( member(esk1_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[28,16,theory(equality)]) ).
cnf(56,plain,
( member(esk1_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[29,16,theory(equality)]) ).
cnf(57,plain,
( member(esk1_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[35,16,theory(equality)]) ).
cnf(58,plain,
( subset(X1,difference(X2,X3))
| member(esk1_2(X1,difference(X2,X3)),X3)
| ~ member(esk1_2(X1,difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[15,33,theory(equality)]) ).
cnf(63,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[34,16,theory(equality)]) ).
cnf(70,negated_conjecture,
( ~ subset(esk2_0,esk3_0)
| $false
| ~ subset(intersection(esk2_0,difference(esk4_0,esk3_0)),empty_set) ),
inference(rw,[status(thm)],[53,49,theory(equality)]) ).
cnf(71,negated_conjecture,
( ~ subset(esk2_0,esk3_0)
| ~ subset(intersection(esk2_0,difference(esk4_0,esk3_0)),empty_set) ),
inference(cn,[status(thm)],[70,theory(equality)]) ).
cnf(73,negated_conjecture,
( member(X1,empty_set)
| subset(esk2_0,esk3_0)
| ~ member(X1,intersection(esk2_0,difference(esk4_0,esk3_0))) ),
inference(spm,[status(thm)],[17,46,theory(equality)]) ).
cnf(75,negated_conjecture,
( subset(esk2_0,esk3_0)
| ~ member(X1,intersection(esk2_0,difference(esk4_0,esk3_0))) ),
inference(sr,[status(thm)],[73,37,theory(equality)]) ).
cnf(76,negated_conjecture,
( subset(X1,esk4_0)
| ~ member(esk1_2(X1,esk4_0),esk2_0) ),
inference(spm,[status(thm)],[15,50,theory(equality)]) ).
cnf(85,plain,
( subset(intersection(X1,difference(X2,X3)),X4)
| ~ member(esk1_2(intersection(X1,difference(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[34,55,theory(equality)]) ).
cnf(88,negated_conjecture,
( subset(esk2_0,esk3_0)
| ~ member(X1,difference(esk4_0,esk3_0))
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[75,27,theory(equality)]) ).
cnf(134,negated_conjecture,
subset(difference(esk2_0,X1),esk4_0),
inference(spm,[status(thm)],[76,57,theory(equality)]) ).
cnf(147,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,difference(esk2_0,X2)) ),
inference(spm,[status(thm)],[17,134,theory(equality)]) ).
cnf(323,negated_conjecture,
( member(esk1_2(difference(esk2_0,X1),X2),esk4_0)
| subset(difference(esk2_0,X1),X2) ),
inference(spm,[status(thm)],[147,16,theory(equality)]) ).
cnf(330,negated_conjecture,
( member(esk1_2(difference(esk2_0,X1),difference(esk4_0,X2)),X2)
| subset(difference(esk2_0,X1),difference(esk4_0,X2)) ),
inference(spm,[status(thm)],[58,323,theory(equality)]) ).
cnf(1434,negated_conjecture,
subset(difference(esk2_0,X1),difference(esk4_0,X1)),
inference(spm,[status(thm)],[63,330,theory(equality)]) ).
cnf(1471,negated_conjecture,
( member(X1,difference(esk4_0,X2))
| ~ member(X1,difference(esk2_0,X2)) ),
inference(spm,[status(thm)],[17,1434,theory(equality)]) ).
cnf(1532,negated_conjecture,
( subset(esk2_0,esk3_0)
| ~ member(X1,esk2_0)
| ~ member(X1,difference(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[88,1471,theory(equality)]) ).
cnf(1544,negated_conjecture,
( subset(esk2_0,esk3_0)
| ~ member(X1,difference(esk2_0,esk3_0)) ),
inference(csr,[status(thm)],[1532,35]) ).
cnf(1546,negated_conjecture,
( subset(esk2_0,esk3_0)
| member(X1,esk3_0)
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[1544,33,theory(equality)]) ).
cnf(1622,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk2_0) ),
inference(csr,[status(thm)],[1546,17]) ).
cnf(1623,negated_conjecture,
( member(esk1_2(esk2_0,X1),esk3_0)
| subset(esk2_0,X1) ),
inference(spm,[status(thm)],[1622,16,theory(equality)]) ).
cnf(1625,negated_conjecture,
( member(esk1_2(intersection(esk2_0,X1),X2),esk3_0)
| subset(intersection(esk2_0,X1),X2) ),
inference(spm,[status(thm)],[1622,56,theory(equality)]) ).
cnf(1688,negated_conjecture,
subset(esk2_0,esk3_0),
inference(spm,[status(thm)],[15,1623,theory(equality)]) ).
cnf(1739,negated_conjecture,
( ~ subset(intersection(esk2_0,difference(esk4_0,esk3_0)),empty_set)
| $false ),
inference(rw,[status(thm)],[71,1688,theory(equality)]) ).
cnf(1740,negated_conjecture,
~ subset(intersection(esk2_0,difference(esk4_0,esk3_0)),empty_set),
inference(cn,[status(thm)],[1739,theory(equality)]) ).
cnf(1986,negated_conjecture,
subset(intersection(esk2_0,difference(X1,esk3_0)),X2),
inference(spm,[status(thm)],[85,1625,theory(equality)]) ).
cnf(1993,negated_conjecture,
$false,
inference(rw,[status(thm)],[1740,1986,theory(equality)]) ).
cnf(1994,negated_conjecture,
$false,
inference(cn,[status(thm)],[1993,theory(equality)]) ).
cnf(1995,negated_conjecture,
$false,
1994,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET697+4.p
% --creating new selector for [SET006+0.ax]
% -running prover on /tmp/tmpziCIFG/sel_SET697+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET697+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET697+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET697+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
%
%------------------------------------------------------------------------------