TSTP Solution File: SEU126+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU126+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 04:43:55 EST 2010
% Result : Theorem 0.25s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 16 unt; 0 def)
% Number of atoms : 73 ( 23 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 69 ( 30 ~; 24 |; 11 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 55 ( 3 sgn 33 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(5,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('/tmp/tmpgeI2X_/sel_SEU126+2.p_1',t8_xboole_1) ).
fof(7,axiom,
! [X1,X2] : subset(X1,X1),
file('/tmp/tmpgeI2X_/sel_SEU126+2.p_1',reflexivity_r1_tarski) ).
fof(12,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/tmp/tmpgeI2X_/sel_SEU126+2.p_1',commutativity_k2_xboole_0) ).
fof(14,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/tmp/tmpgeI2X_/sel_SEU126+2.p_1',t7_xboole_1) ).
fof(24,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpgeI2X_/sel_SEU126+2.p_1',d10_xboole_0) ).
fof(29,conjecture,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/tmp/tmpgeI2X_/sel_SEU126+2.p_1',t12_xboole_1) ).
fof(34,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
inference(assume_negation,[status(cth)],[29]) ).
fof(53,plain,
! [X1,X2,X3] :
( ~ subset(X1,X2)
| ~ subset(X3,X2)
| subset(set_union2(X1,X3),X2) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(54,plain,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X6,X5)
| subset(set_union2(X4,X6),X5) ),
inference(variable_rename,[status(thm)],[53]) ).
cnf(55,plain,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[54]) ).
fof(67,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[7]) ).
cnf(68,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[67]) ).
fof(84,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[12]) ).
cnf(85,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[84]) ).
fof(89,plain,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[14]) ).
cnf(90,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[89]) ).
fof(125,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(126,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[125]) ).
fof(127,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)],[126]) ).
cnf(128,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[127]) ).
fof(139,negated_conjecture,
? [X1,X2] :
( subset(X1,X2)
& set_union2(X1,X2) != X2 ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(140,negated_conjecture,
? [X3,X4] :
( subset(X3,X4)
& set_union2(X3,X4) != X4 ),
inference(variable_rename,[status(thm)],[139]) ).
fof(141,negated_conjecture,
( subset(esk6_0,esk7_0)
& set_union2(esk6_0,esk7_0) != esk7_0 ),
inference(skolemize,[status(esa)],[140]) ).
cnf(142,negated_conjecture,
set_union2(esk6_0,esk7_0) != esk7_0,
inference(split_conjunct,[status(thm)],[141]) ).
cnf(143,negated_conjecture,
subset(esk6_0,esk7_0),
inference(split_conjunct,[status(thm)],[141]) ).
cnf(178,negated_conjecture,
set_union2(esk7_0,esk6_0) != esk7_0,
inference(rw,[status(thm)],[142,85,theory(equality)]) ).
cnf(185,plain,
( set_union2(X1,X2) = X1
| ~ subset(set_union2(X1,X2),X1) ),
inference(spm,[status(thm)],[128,90,theory(equality)]) ).
cnf(402,plain,
( set_union2(X1,X2) = X1
| ~ subset(X2,X1)
| ~ subset(X1,X1) ),
inference(spm,[status(thm)],[185,55,theory(equality)]) ).
cnf(404,plain,
( set_union2(X1,X2) = X1
| ~ subset(X2,X1)
| $false ),
inference(rw,[status(thm)],[402,68,theory(equality)]) ).
cnf(405,plain,
( set_union2(X1,X2) = X1
| ~ subset(X2,X1) ),
inference(cn,[status(thm)],[404,theory(equality)]) ).
cnf(417,plain,
~ subset(esk6_0,esk7_0),
inference(spm,[status(thm)],[178,405,theory(equality)]) ).
cnf(425,plain,
$false,
inference(rw,[status(thm)],[417,143,theory(equality)]) ).
cnf(426,plain,
$false,
inference(cn,[status(thm)],[425,theory(equality)]) ).
cnf(427,plain,
$false,
426,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU126+2.p
% --creating new selector for []
% -running prover on /tmp/tmpgeI2X_/sel_SEU126+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU126+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU126+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU126+2.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
%
%------------------------------------------------------------------------------