TSTP Solution File: SET907+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET907+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 03:46:04 EST 2010
% Result : Theorem 0.24s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 16 unt; 0 def)
% Number of atoms : 66 ( 19 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 57 ( 22 ~; 16 |; 15 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 32 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('/tmp/tmpDyUzIZ/sel_SET907+1.p_1',t38_zfmisc_1) ).
fof(2,conjecture,
! [X1,X2,X3] :
( ( in(X1,X2)
& in(X3,X2) )
=> set_union2(unordered_pair(X1,X3),X2) = X2 ),
file('/tmp/tmpDyUzIZ/sel_SET907+1.p_1',t48_zfmisc_1) ).
fof(5,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/tmp/tmpDyUzIZ/sel_SET907+1.p_1',commutativity_k2_xboole_0) ).
fof(7,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpDyUzIZ/sel_SET907+1.p_1',commutativity_k2_tarski) ).
fof(8,axiom,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/tmp/tmpDyUzIZ/sel_SET907+1.p_1',t12_xboole_1) ).
fof(13,negated_conjecture,
~ ! [X1,X2,X3] :
( ( in(X1,X2)
& in(X3,X2) )
=> set_union2(unordered_pair(X1,X3),X2) = X2 ),
inference(assume_negation,[status(cth)],[2]) ).
fof(18,plain,
! [X1,X2,X3] :
( ( ~ subset(unordered_pair(X1,X2),X3)
| ( in(X1,X3)
& in(X2,X3) ) )
& ( ~ in(X1,X3)
| ~ in(X2,X3)
| subset(unordered_pair(X1,X2),X3) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(19,plain,
! [X4,X5,X6] :
( ( ~ subset(unordered_pair(X4,X5),X6)
| ( in(X4,X6)
& in(X5,X6) ) )
& ( ~ in(X4,X6)
| ~ in(X5,X6)
| subset(unordered_pair(X4,X5),X6) ) ),
inference(variable_rename,[status(thm)],[18]) ).
fof(20,plain,
! [X4,X5,X6] :
( ( in(X4,X6)
| ~ subset(unordered_pair(X4,X5),X6) )
& ( in(X5,X6)
| ~ subset(unordered_pair(X4,X5),X6) )
& ( ~ in(X4,X6)
| ~ in(X5,X6)
| subset(unordered_pair(X4,X5),X6) ) ),
inference(distribute,[status(thm)],[19]) ).
cnf(21,plain,
( subset(unordered_pair(X1,X2),X3)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[20]) ).
fof(24,negated_conjecture,
? [X1,X2,X3] :
( in(X1,X2)
& in(X3,X2)
& set_union2(unordered_pair(X1,X3),X2) != X2 ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(25,negated_conjecture,
? [X4,X5,X6] :
( in(X4,X5)
& in(X6,X5)
& set_union2(unordered_pair(X4,X6),X5) != X5 ),
inference(variable_rename,[status(thm)],[24]) ).
fof(26,negated_conjecture,
( in(esk1_0,esk2_0)
& in(esk3_0,esk2_0)
& set_union2(unordered_pair(esk1_0,esk3_0),esk2_0) != esk2_0 ),
inference(skolemize,[status(esa)],[25]) ).
cnf(27,negated_conjecture,
set_union2(unordered_pair(esk1_0,esk3_0),esk2_0) != esk2_0,
inference(split_conjunct,[status(thm)],[26]) ).
cnf(28,negated_conjecture,
in(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[26]) ).
cnf(29,negated_conjecture,
in(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[26]) ).
fof(36,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(37,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[36]) ).
fof(41,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[7]) ).
cnf(42,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[41]) ).
fof(43,plain,
! [X1,X2] :
( ~ subset(X1,X2)
| set_union2(X1,X2) = X2 ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(44,plain,
! [X3,X4] :
( ~ subset(X3,X4)
| set_union2(X3,X4) = X4 ),
inference(variable_rename,[status(thm)],[43]) ).
cnf(45,plain,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(64,negated_conjecture,
set_union2(esk2_0,unordered_pair(esk1_0,esk3_0)) != esk2_0,
inference(rw,[status(thm)],[27,37,theory(equality)]) ).
cnf(77,negated_conjecture,
( subset(unordered_pair(X1,esk1_0),esk2_0)
| ~ in(X1,esk2_0) ),
inference(spm,[status(thm)],[21,29,theory(equality)]) ).
cnf(96,negated_conjecture,
subset(unordered_pair(esk3_0,esk1_0),esk2_0),
inference(spm,[status(thm)],[77,28,theory(equality)]) ).
cnf(97,negated_conjecture,
subset(unordered_pair(esk1_0,esk3_0),esk2_0),
inference(rw,[status(thm)],[96,42,theory(equality)]) ).
cnf(114,negated_conjecture,
set_union2(unordered_pair(esk1_0,esk3_0),esk2_0) = esk2_0,
inference(spm,[status(thm)],[45,97,theory(equality)]) ).
cnf(117,negated_conjecture,
set_union2(esk2_0,unordered_pair(esk1_0,esk3_0)) = esk2_0,
inference(rw,[status(thm)],[114,37,theory(equality)]) ).
cnf(118,negated_conjecture,
$false,
inference(sr,[status(thm)],[117,64,theory(equality)]) ).
cnf(119,negated_conjecture,
$false,
118,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET907+1.p
% --creating new selector for []
% -running prover on /tmp/tmpDyUzIZ/sel_SET907+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET907+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET907+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET907+1.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
%
%------------------------------------------------------------------------------