TSTP Solution File: SET587+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET587+3 : TPTP v5.0.0. Released v2.2.0.
% 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 02:58:49 EST 2010
% Result : Theorem 0.27s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 59 ( 11 unt; 0 def)
% Number of atoms : 179 ( 24 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 198 ( 78 ~; 79 |; 32 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 106 ( 6 sgn 60 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpmB1vQi/sel_SET587+3.p_1',subset_defn) ).
fof(2,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/tmp/tmpmB1vQi/sel_SET587+3.p_1',empty_defn) ).
fof(3,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpmB1vQi/sel_SET587+3.p_1',equal_defn) ).
fof(4,conjecture,
! [X1,X2] :
( difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/tmp/tmpmB1vQi/sel_SET587+3.p_1',prove_difference_empty_set) ).
fof(7,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/tmp/tmpmB1vQi/sel_SET587+3.p_1',difference_defn) ).
fof(9,axiom,
! [X1] : ~ member(X1,empty_set),
file('/tmp/tmpmB1vQi/sel_SET587+3.p_1',empty_set_defn) ).
fof(10,negated_conjecture,
~ ! [X1,X2] :
( difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
inference(assume_negation,[status(cth)],[4]) ).
fof(11,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).
fof(12,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).
fof(13,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(14,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(15,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)],[14]) ).
fof(16,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)],[15]) ).
fof(17,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)],[16]) ).
fof(18,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)],[17]) ).
cnf(19,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(20,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(21,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[18]) ).
fof(22,plain,
! [X1] :
( ( ~ empty(X1)
| ! [X2] : ~ member(X2,X1) )
& ( ? [X2] : member(X2,X1)
| empty(X1) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(23,plain,
! [X3] :
( ( ~ empty(X3)
| ! [X4] : ~ member(X4,X3) )
& ( ? [X5] : member(X5,X3)
| empty(X3) ) ),
inference(variable_rename,[status(thm)],[22]) ).
fof(24,plain,
! [X3] :
( ( ~ empty(X3)
| ! [X4] : ~ member(X4,X3) )
& ( member(esk2_1(X3),X3)
| empty(X3) ) ),
inference(skolemize,[status(esa)],[23]) ).
fof(25,plain,
! [X3,X4] :
( ( ~ member(X4,X3)
| ~ empty(X3) )
& ( member(esk2_1(X3),X3)
| empty(X3) ) ),
inference(shift_quantors,[status(thm)],[24]) ).
cnf(26,plain,
( empty(X1)
| member(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(27,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[25]) ).
fof(28,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(29,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[28]) ).
fof(30,plain,
! [X3,X4] :
( ( subset(X3,X4)
| X3 != X4 )
& ( subset(X4,X3)
| X3 != X4 )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(distribute,[status(thm)],[29]) ).
cnf(31,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[30]) ).
fof(34,negated_conjecture,
? [X1,X2] :
( ( difference(X1,X2) != empty_set
| ~ subset(X1,X2) )
& ( difference(X1,X2) = empty_set
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(35,negated_conjecture,
? [X3,X4] :
( ( difference(X3,X4) != empty_set
| ~ subset(X3,X4) )
& ( difference(X3,X4) = empty_set
| subset(X3,X4) ) ),
inference(variable_rename,[status(thm)],[34]) ).
fof(36,negated_conjecture,
( ( difference(esk3_0,esk4_0) != empty_set
| ~ subset(esk3_0,esk4_0) )
& ( difference(esk3_0,esk4_0) = empty_set
| subset(esk3_0,esk4_0) ) ),
inference(skolemize,[status(esa)],[35]) ).
cnf(37,negated_conjecture,
( subset(esk3_0,esk4_0)
| difference(esk3_0,esk4_0) = empty_set ),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(38,negated_conjecture,
( ~ subset(esk3_0,esk4_0)
| difference(esk3_0,esk4_0) != empty_set ),
inference(split_conjunct,[status(thm)],[36]) ).
fof(54,plain,
! [X1,X2,X3] :
( ( ~ member(X3,difference(X1,X2))
| ( member(X3,X1)
& ~ member(X3,X2) ) )
& ( ~ member(X3,X1)
| member(X3,X2)
| member(X3,difference(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(55,plain,
! [X4,X5,X6] :
( ( ~ member(X6,difference(X4,X5))
| ( member(X6,X4)
& ~ member(X6,X5) ) )
& ( ~ member(X6,X4)
| member(X6,X5)
| member(X6,difference(X4,X5)) ) ),
inference(variable_rename,[status(thm)],[54]) ).
fof(56,plain,
! [X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,difference(X4,X5)) )
& ( ~ member(X6,X5)
| ~ member(X6,difference(X4,X5)) )
& ( ~ member(X6,X4)
| member(X6,X5)
| member(X6,difference(X4,X5)) ) ),
inference(distribute,[status(thm)],[55]) ).
cnf(57,plain,
( member(X1,difference(X2,X3))
| member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[56]) ).
cnf(58,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[56]) ).
cnf(59,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[56]) ).
fof(62,plain,
! [X2] : ~ member(X2,empty_set),
inference(variable_rename,[status(thm)],[13]) ).
cnf(63,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[62]) ).
cnf(66,plain,
( empty(difference(X1,X2))
| ~ member(esk2_1(difference(X1,X2)),X2) ),
inference(spm,[status(thm)],[58,26,theory(equality)]) ).
cnf(69,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[63,20,theory(equality)]) ).
cnf(70,plain,
( subset(X1,X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[27,20,theory(equality)]) ).
cnf(76,plain,
( member(esk2_1(difference(X1,X2)),X1)
| empty(difference(X1,X2)) ),
inference(spm,[status(thm)],[59,26,theory(equality)]) ).
cnf(83,plain,
( member(esk1_2(X1,X2),difference(X1,X3))
| member(esk1_2(X1,X2),X3)
| subset(X1,X2) ),
inference(spm,[status(thm)],[57,20,theory(equality)]) ).
cnf(110,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(spm,[status(thm)],[31,69,theory(equality)]) ).
cnf(114,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(spm,[status(thm)],[110,70,theory(equality)]) ).
cnf(417,negated_conjecture,
( member(esk1_2(esk3_0,X1),empty_set)
| member(esk1_2(esk3_0,X1),esk4_0)
| subset(esk3_0,X1)
| subset(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[83,37,theory(equality)]) ).
cnf(430,negated_conjecture,
( member(esk1_2(esk3_0,X1),esk4_0)
| subset(esk3_0,X1)
| subset(esk3_0,esk4_0) ),
inference(sr,[status(thm)],[417,63,theory(equality)]) ).
cnf(433,negated_conjecture,
subset(esk3_0,esk4_0),
inference(spm,[status(thm)],[19,430,theory(equality)]) ).
cnf(438,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,esk3_0) ),
inference(spm,[status(thm)],[21,433,theory(equality)]) ).
cnf(447,negated_conjecture,
( difference(esk3_0,esk4_0) != empty_set
| $false ),
inference(rw,[status(thm)],[38,433,theory(equality)]) ).
cnf(448,negated_conjecture,
difference(esk3_0,esk4_0) != empty_set,
inference(cn,[status(thm)],[447,theory(equality)]) ).
cnf(473,negated_conjecture,
( member(esk2_1(difference(esk3_0,X1)),esk4_0)
| empty(difference(esk3_0,X1)) ),
inference(spm,[status(thm)],[438,76,theory(equality)]) ).
cnf(561,negated_conjecture,
empty(difference(esk3_0,esk4_0)),
inference(spm,[status(thm)],[66,473,theory(equality)]) ).
cnf(571,negated_conjecture,
difference(esk3_0,esk4_0) = empty_set,
inference(spm,[status(thm)],[114,561,theory(equality)]) ).
cnf(580,negated_conjecture,
$false,
inference(sr,[status(thm)],[571,448,theory(equality)]) ).
cnf(581,negated_conjecture,
$false,
580,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET587+3.p
% --creating new selector for []
% -running prover on /tmp/tmpmB1vQi/sel_SET587+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET587+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET587+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET587+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
%
%------------------------------------------------------------------------------