TSTP Solution File: SEU126+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU126+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 04:43:45 EST 2010
% Result : Theorem 0.33s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 17 unt; 0 def)
% Number of atoms : 206 ( 42 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 236 ( 86 ~; 98 |; 45 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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; 2 con; 0-3 aty)
% Number of variables : 115 ( 8 sgn 62 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpIx4lAx/sel_SEU126+1.p_1',d10_xboole_0) ).
fof(8,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/tmp/tmpIx4lAx/sel_SEU126+1.p_1',d2_xboole_0) ).
fof(10,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/tmp/tmpIx4lAx/sel_SEU126+1.p_1',commutativity_k2_xboole_0) ).
fof(13,conjecture,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/tmp/tmpIx4lAx/sel_SEU126+1.p_1',t12_xboole_1) ).
fof(14,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/tmp/tmpIx4lAx/sel_SEU126+1.p_1',idempotence_k2_xboole_0) ).
fof(17,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpIx4lAx/sel_SEU126+1.p_1',d3_tarski) ).
fof(20,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
inference(assume_negation,[status(cth)],[13]) ).
fof(27,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(28,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[27]) ).
fof(29,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)],[28]) ).
cnf(30,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[29]) ).
fof(44,plain,
! [X1,X2,X3] :
( ( X3 != set_union2(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| in(X4,X1)
| in(X4,X2) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X2) )
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ( ~ in(X4,X1)
& ~ in(X4,X2) ) )
& ( in(X4,X3)
| in(X4,X1)
| in(X4,X2) ) )
| X3 = set_union2(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(45,plain,
! [X5,X6,X7] :
( ( X7 != set_union2(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6) )
& ( ( ~ in(X8,X5)
& ~ in(X8,X6) )
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ( ~ in(X9,X5)
& ~ in(X9,X6) ) )
& ( in(X9,X7)
| in(X9,X5)
| in(X9,X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(variable_rename,[status(thm)],[44]) ).
fof(46,plain,
! [X5,X6,X7] :
( ( X7 != set_union2(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6) )
& ( ( ~ in(X8,X5)
& ~ in(X8,X6) )
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk2_3(X5,X6,X7),X7)
| ( ~ in(esk2_3(X5,X6,X7),X5)
& ~ in(esk2_3(X5,X6,X7),X6) ) )
& ( in(esk2_3(X5,X6,X7),X7)
| in(esk2_3(X5,X6,X7),X5)
| in(esk2_3(X5,X6,X7),X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(skolemize,[status(esa)],[45]) ).
fof(47,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6) )
& ( ( ~ in(X8,X5)
& ~ in(X8,X6) )
| in(X8,X7) ) )
| X7 != set_union2(X5,X6) )
& ( ( ( ~ in(esk2_3(X5,X6,X7),X7)
| ( ~ in(esk2_3(X5,X6,X7),X5)
& ~ in(esk2_3(X5,X6,X7),X6) ) )
& ( in(esk2_3(X5,X6,X7),X7)
| in(esk2_3(X5,X6,X7),X5)
| in(esk2_3(X5,X6,X7),X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[46]) ).
fof(48,plain,
! [X5,X6,X7,X8] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6)
| X7 != set_union2(X5,X6) )
& ( ~ in(X8,X5)
| in(X8,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(X8,X6)
| in(X8,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(esk2_3(X5,X6,X7),X5)
| ~ in(esk2_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( ~ in(esk2_3(X5,X6,X7),X6)
| ~ in(esk2_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( in(esk2_3(X5,X6,X7),X7)
| in(esk2_3(X5,X6,X7),X5)
| in(esk2_3(X5,X6,X7),X6)
| X7 = set_union2(X5,X6) ) ),
inference(distribute,[status(thm)],[47]) ).
cnf(52,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(54,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[48]) ).
fof(58,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[10]) ).
cnf(59,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[58]) ).
fof(66,negated_conjecture,
? [X1,X2] :
( subset(X1,X2)
& set_union2(X1,X2) != X2 ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(67,negated_conjecture,
? [X3,X4] :
( subset(X3,X4)
& set_union2(X3,X4) != X4 ),
inference(variable_rename,[status(thm)],[66]) ).
fof(68,negated_conjecture,
( subset(esk3_0,esk4_0)
& set_union2(esk3_0,esk4_0) != esk4_0 ),
inference(skolemize,[status(esa)],[67]) ).
cnf(69,negated_conjecture,
set_union2(esk3_0,esk4_0) != esk4_0,
inference(split_conjunct,[status(thm)],[68]) ).
cnf(70,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[68]) ).
fof(71,plain,
! [X3,X4] : set_union2(X3,X3) = X3,
inference(variable_rename,[status(thm)],[14]) ).
cnf(72,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[71]) ).
fof(79,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ in(X3,X1)
| in(X3,X2) ) )
& ( ? [X3] :
( in(X3,X1)
& ~ in(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(80,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ? [X7] :
( in(X7,X4)
& ~ in(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[79]) ).
fof(81,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk6_2(X4,X5),X4)
& ~ in(esk6_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[80]) ).
fof(82,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk6_2(X4,X5),X4)
& ~ in(esk6_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[81]) ).
fof(83,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk6_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk6_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[82]) ).
cnf(84,plain,
( subset(X1,X2)
| ~ in(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[83]) ).
cnf(85,plain,
( subset(X1,X2)
| in(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[83]) ).
cnf(86,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[83]) ).
cnf(99,negated_conjecture,
set_union2(esk4_0,esk3_0) != esk4_0,
inference(rw,[status(thm)],[69,59,theory(equality)]) ).
cnf(118,negated_conjecture,
( in(X1,esk4_0)
| ~ in(X1,esk3_0) ),
inference(spm,[status(thm)],[86,70,theory(equality)]) ).
cnf(120,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[52,theory(equality)]) ).
cnf(134,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(er,[status(thm)],[54,theory(equality)]) ).
cnf(180,negated_conjecture,
( in(esk6_2(esk3_0,X1),esk4_0)
| subset(esk3_0,X1) ),
inference(spm,[status(thm)],[118,85,theory(equality)]) ).
cnf(205,plain,
( subset(X1,set_union2(X2,X3))
| ~ in(esk6_2(X1,set_union2(X2,X3)),X3) ),
inference(spm,[status(thm)],[84,120,theory(equality)]) ).
cnf(277,plain,
( in(esk6_2(set_union2(X1,X2),X3),X2)
| in(esk6_2(set_union2(X1,X2),X3),X1)
| subset(set_union2(X1,X2),X3) ),
inference(spm,[status(thm)],[134,85,theory(equality)]) ).
cnf(295,plain,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[205,85,theory(equality)]) ).
cnf(296,negated_conjecture,
subset(esk3_0,set_union2(X1,esk4_0)),
inference(spm,[status(thm)],[205,180,theory(equality)]) ).
cnf(304,negated_conjecture,
( in(X1,set_union2(X2,esk4_0))
| ~ in(X1,esk3_0) ),
inference(spm,[status(thm)],[86,296,theory(equality)]) ).
cnf(311,plain,
subset(X1,set_union2(X1,X2)),
inference(spm,[status(thm)],[295,59,theory(equality)]) ).
cnf(496,negated_conjecture,
( subset(X1,set_union2(X2,esk4_0))
| ~ in(esk6_2(X1,set_union2(X2,esk4_0)),esk3_0) ),
inference(spm,[status(thm)],[84,304,theory(equality)]) ).
cnf(884,negated_conjecture,
( subset(X1,esk4_0)
| ~ in(esk6_2(X1,esk4_0),esk3_0) ),
inference(spm,[status(thm)],[496,72,theory(equality)]) ).
cnf(1126,negated_conjecture,
( subset(set_union2(esk3_0,X1),esk4_0)
| in(esk6_2(set_union2(esk3_0,X1),esk4_0),X1) ),
inference(spm,[status(thm)],[884,277,theory(equality)]) ).
cnf(1155,negated_conjecture,
subset(set_union2(esk3_0,esk4_0),esk4_0),
inference(spm,[status(thm)],[84,1126,theory(equality)]) ).
cnf(1163,negated_conjecture,
subset(set_union2(esk4_0,esk3_0),esk4_0),
inference(rw,[status(thm)],[1155,59,theory(equality)]) ).
cnf(1169,negated_conjecture,
( esk4_0 = set_union2(esk4_0,esk3_0)
| ~ subset(esk4_0,set_union2(esk4_0,esk3_0)) ),
inference(spm,[status(thm)],[30,1163,theory(equality)]) ).
cnf(1173,negated_conjecture,
( esk4_0 = set_union2(esk4_0,esk3_0)
| $false ),
inference(rw,[status(thm)],[1169,311,theory(equality)]) ).
cnf(1174,negated_conjecture,
esk4_0 = set_union2(esk4_0,esk3_0),
inference(cn,[status(thm)],[1173,theory(equality)]) ).
cnf(1175,negated_conjecture,
$false,
inference(sr,[status(thm)],[1174,99,theory(equality)]) ).
cnf(1176,negated_conjecture,
$false,
1175,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU126+1.p
% --creating new selector for []
% -running prover on /tmp/tmpIx4lAx/sel_SEU126+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU126+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU126+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU126+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
%
%------------------------------------------------------------------------------