TSTP Solution File: SET695+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET695+4 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 03:12:27 EST 2010
% Result : Theorem 0.49s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 44 ( 7 unt; 0 def)
% Number of atoms : 142 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 153 ( 55 ~; 61 |; 29 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 85 ( 2 sgn 39 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmp0ItzMd/sel_SET695+4.p_1',subset) ).
fof(2,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
file('/tmp/tmp0ItzMd/sel_SET695+4.p_1',difference) ).
fof(3,conjecture,
! [X1,X2,X4] :
( ( subset(X1,X4)
& subset(X2,X4) )
=> ( subset(X1,X2)
<=> subset(difference(X4,X2),difference(X4,X1)) ) ),
file('/tmp/tmp0ItzMd/sel_SET695+4.p_1',thI24) ).
fof(4,negated_conjecture,
~ ! [X1,X2,X4] :
( ( subset(X1,X4)
& subset(X2,X4) )
=> ( subset(X1,X2)
<=> subset(difference(X4,X2),difference(X4,X1)) ) ),
inference(assume_negation,[status(cth)],[3]) ).
fof(5,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).
fof(6,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(7,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)],[6]) ).
fof(8,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)],[7]) ).
fof(9,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)],[8]) ).
fof(10,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)],[9]) ).
cnf(11,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[10]) ).
cnf(12,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[10]) ).
cnf(13,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[10]) ).
fof(14,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)],[5]) ).
fof(15,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)],[14]) ).
fof(16,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)],[15]) ).
cnf(17,plain,
( member(X1,difference(X2,X3))
| member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(18,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(19,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[16]) ).
fof(20,negated_conjecture,
? [X1,X2,X4] :
( subset(X1,X4)
& subset(X2,X4)
& ( ~ subset(X1,X2)
| ~ subset(difference(X4,X2),difference(X4,X1)) )
& ( subset(X1,X2)
| subset(difference(X4,X2),difference(X4,X1)) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(21,negated_conjecture,
? [X5,X6,X7] :
( subset(X5,X7)
& subset(X6,X7)
& ( ~ subset(X5,X6)
| ~ subset(difference(X7,X6),difference(X7,X5)) )
& ( subset(X5,X6)
| subset(difference(X7,X6),difference(X7,X5)) ) ),
inference(variable_rename,[status(thm)],[20]) ).
fof(22,negated_conjecture,
( subset(esk2_0,esk4_0)
& subset(esk3_0,esk4_0)
& ( ~ subset(esk2_0,esk3_0)
| ~ subset(difference(esk4_0,esk3_0),difference(esk4_0,esk2_0)) )
& ( subset(esk2_0,esk3_0)
| subset(difference(esk4_0,esk3_0),difference(esk4_0,esk2_0)) ) ),
inference(skolemize,[status(esa)],[21]) ).
cnf(23,negated_conjecture,
( subset(difference(esk4_0,esk3_0),difference(esk4_0,esk2_0))
| subset(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(24,negated_conjecture,
( ~ subset(difference(esk4_0,esk3_0),difference(esk4_0,esk2_0))
| ~ subset(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(26,negated_conjecture,
subset(esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(29,plain,
( member(esk1_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[19,12,theory(equality)]) ).
cnf(30,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[18,12,theory(equality)]) ).
cnf(31,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[13,26,theory(equality)]) ).
cnf(33,negated_conjecture,
( member(X1,difference(esk4_0,esk2_0))
| subset(esk2_0,esk3_0)
| ~ member(X1,difference(esk4_0,esk3_0)) ),
inference(spm,[status(thm)],[13,23,theory(equality)]) ).
cnf(34,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)],[11,17,theory(equality)]) ).
cnf(77,negated_conjecture,
( subset(esk2_0,esk3_0)
| ~ member(X1,esk2_0)
| ~ member(X1,difference(esk4_0,esk3_0)) ),
inference(spm,[status(thm)],[18,33,theory(equality)]) ).
cnf(88,negated_conjecture,
( subset(esk2_0,esk3_0)
| member(X1,esk3_0)
| ~ member(X1,esk2_0)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[77,17,theory(equality)]) ).
cnf(104,plain,
( member(esk1_2(difference(X1,X2),difference(X1,X3)),X3)
| subset(difference(X1,X2),difference(X1,X3)) ),
inference(spm,[status(thm)],[34,29,theory(equality)]) ).
cnf(815,negated_conjecture,
( member(X1,esk3_0)
| subset(esk2_0,esk3_0)
| ~ member(X1,esk2_0) ),
inference(csr,[status(thm)],[88,31]) ).
cnf(816,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk2_0) ),
inference(csr,[status(thm)],[815,13]) ).
cnf(817,negated_conjecture,
( member(esk1_2(esk2_0,X1),esk3_0)
| subset(esk2_0,X1) ),
inference(spm,[status(thm)],[816,12,theory(equality)]) ).
cnf(832,negated_conjecture,
subset(esk2_0,esk3_0),
inference(spm,[status(thm)],[11,817,theory(equality)]) ).
cnf(851,negated_conjecture,
( ~ subset(difference(esk4_0,esk3_0),difference(esk4_0,esk2_0))
| $false ),
inference(rw,[status(thm)],[24,832,theory(equality)]) ).
cnf(852,negated_conjecture,
~ subset(difference(esk4_0,esk3_0),difference(esk4_0,esk2_0)),
inference(cn,[status(thm)],[851,theory(equality)]) ).
cnf(1107,negated_conjecture,
( member(esk1_2(difference(X1,X2),difference(X1,esk2_0)),esk3_0)
| subset(difference(X1,X2),difference(X1,esk2_0)) ),
inference(spm,[status(thm)],[816,104,theory(equality)]) ).
cnf(4134,negated_conjecture,
subset(difference(X1,esk3_0),difference(X1,esk2_0)),
inference(spm,[status(thm)],[30,1107,theory(equality)]) ).
cnf(4147,negated_conjecture,
$false,
inference(rw,[status(thm)],[852,4134,theory(equality)]) ).
cnf(4148,negated_conjecture,
$false,
inference(cn,[status(thm)],[4147,theory(equality)]) ).
cnf(4149,negated_conjecture,
$false,
4148,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET695+4.p
% --creating new selector for [SET006+0.ax]
% -running prover on /tmp/tmp0ItzMd/sel_SET695+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET695+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET695+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET695+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
%
%------------------------------------------------------------------------------