TSTP Solution File: SET878+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET878+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 03:42:56 EST 2010
% Result : Theorem 0.21s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 19 unt; 0 def)
% Number of atoms : 112 ( 77 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 132 ( 51 ~; 53 |; 25 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 65 ( 4 sgn 42 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/tmp/tmpYmkFtE/sel_SET878+1.p_1',commutativity_k3_xboole_0) ).
fof(4,conjecture,
! [X1,X2] : set_intersection2(singleton(X1),unordered_pair(X1,X2)) = singleton(X1),
file('/tmp/tmpYmkFtE/sel_SET878+1.p_1',t19_zfmisc_1) ).
fof(5,axiom,
! [X1,X2] :
( in(X1,X2)
=> set_intersection2(X2,singleton(X1)) = singleton(X1) ),
file('/tmp/tmpYmkFtE/sel_SET878+1.p_1',l32_zfmisc_1) ).
fof(6,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpYmkFtE/sel_SET878+1.p_1',commutativity_k2_tarski) ).
fof(9,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/tmp/tmpYmkFtE/sel_SET878+1.p_1',d2_tarski) ).
fof(10,negated_conjecture,
~ ! [X1,X2] : set_intersection2(singleton(X1),unordered_pair(X1,X2)) = singleton(X1),
inference(assume_negation,[status(cth)],[4]) ).
fof(13,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(14,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[13]) ).
fof(20,negated_conjecture,
? [X1,X2] : set_intersection2(singleton(X1),unordered_pair(X1,X2)) != singleton(X1),
inference(fof_nnf,[status(thm)],[10]) ).
fof(21,negated_conjecture,
? [X3,X4] : set_intersection2(singleton(X3),unordered_pair(X3,X4)) != singleton(X3),
inference(variable_rename,[status(thm)],[20]) ).
fof(22,negated_conjecture,
set_intersection2(singleton(esk2_0),unordered_pair(esk2_0,esk3_0)) != singleton(esk2_0),
inference(skolemize,[status(esa)],[21]) ).
cnf(23,negated_conjecture,
set_intersection2(singleton(esk2_0),unordered_pair(esk2_0,esk3_0)) != singleton(esk2_0),
inference(split_conjunct,[status(thm)],[22]) ).
fof(24,plain,
! [X1,X2] :
( ~ in(X1,X2)
| set_intersection2(X2,singleton(X1)) = singleton(X1) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(25,plain,
! [X3,X4] :
( ~ in(X3,X4)
| set_intersection2(X4,singleton(X3)) = singleton(X3) ),
inference(variable_rename,[status(thm)],[24]) ).
cnf(26,plain,
( set_intersection2(X1,singleton(X2)) = singleton(X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[25]) ).
fof(27,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[6]) ).
cnf(28,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[27]) ).
fof(35,plain,
! [X1,X2,X3] :
( ( X3 != unordered_pair(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| X4 = X1
| X4 = X2 )
& ( ( X4 != X1
& X4 != X2 )
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ( X4 != X1
& X4 != X2 ) )
& ( in(X4,X3)
| X4 = X1
| X4 = X2 ) )
| X3 = unordered_pair(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(36,plain,
! [X5,X6,X7] :
( ( X7 != unordered_pair(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ( X9 != X5
& X9 != X6 ) )
& ( in(X9,X7)
| X9 = X5
| X9 = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(variable_rename,[status(thm)],[35]) ).
fof(37,plain,
! [X5,X6,X7] :
( ( X7 != unordered_pair(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk5_3(X5,X6,X7),X7)
| ( esk5_3(X5,X6,X7) != X5
& esk5_3(X5,X6,X7) != X6 ) )
& ( in(esk5_3(X5,X6,X7),X7)
| esk5_3(X5,X6,X7) = X5
| esk5_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(skolemize,[status(esa)],[36]) ).
fof(38,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) )
| X7 != unordered_pair(X5,X6) )
& ( ( ( ~ in(esk5_3(X5,X6,X7),X7)
| ( esk5_3(X5,X6,X7) != X5
& esk5_3(X5,X6,X7) != X6 ) )
& ( in(esk5_3(X5,X6,X7),X7)
| esk5_3(X5,X6,X7) = X5
| esk5_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[37]) ).
fof(39,plain,
! [X5,X6,X7,X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6
| X7 != unordered_pair(X5,X6) )
& ( X8 != X5
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( X8 != X6
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( esk5_3(X5,X6,X7) != X5
| ~ in(esk5_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( esk5_3(X5,X6,X7) != X6
| ~ in(esk5_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( in(esk5_3(X5,X6,X7),X7)
| esk5_3(X5,X6,X7) = X5
| esk5_3(X5,X6,X7) = X6
| X7 = unordered_pair(X5,X6) ) ),
inference(distribute,[status(thm)],[38]) ).
cnf(43,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[39]) ).
cnf(52,plain,
( in(X1,X2)
| unordered_pair(X3,X1) != X2 ),
inference(er,[status(thm)],[43,theory(equality)]) ).
cnf(54,negated_conjecture,
set_intersection2(unordered_pair(esk2_0,esk3_0),singleton(esk2_0)) != singleton(esk2_0),
inference(rw,[status(thm)],[23,14,theory(equality)]) ).
cnf(55,negated_conjecture,
~ in(esk2_0,unordered_pair(esk2_0,esk3_0)),
inference(spm,[status(thm)],[54,26,theory(equality)]) ).
cnf(65,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[52,theory(equality)]) ).
cnf(68,plain,
in(X1,unordered_pair(X1,X2)),
inference(spm,[status(thm)],[65,28,theory(equality)]) ).
cnf(78,negated_conjecture,
$false,
inference(rw,[status(thm)],[55,68,theory(equality)]) ).
cnf(79,negated_conjecture,
$false,
inference(cn,[status(thm)],[78,theory(equality)]) ).
cnf(80,negated_conjecture,
$false,
79,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET878+1.p
% --creating new selector for []
% -running prover on /tmp/tmpYmkFtE/sel_SET878+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET878+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET878+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET878+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
%
%------------------------------------------------------------------------------