TSTP Solution File: SEU104+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU104+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 04:36:22 EST 2010
% Result : Theorem 0.28s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 12 unt; 0 def)
% Number of atoms : 166 ( 7 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 207 ( 85 ~; 67 |; 40 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 51 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(5,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/tmp/tmppy2_IM/sel_SEU104+1.p_1',t1_subset) ).
fof(19,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/tmp/tmppy2_IM/sel_SEU104+1.p_1',commutativity_k2_xboole_0) ).
fof(36,axiom,
! [X1] :
( preboolean(X1)
<=> ! [X2,X3] :
( ( in(X2,X1)
& in(X3,X1) )
=> ( in(set_union2(X2,X3),X1)
& in(set_difference(X2,X3),X1) ) ) ),
file('/tmp/tmppy2_IM/sel_SEU104+1.p_1',t10_finsub_1) ).
fof(39,axiom,
! [X1,X2] : set_union2(X1,X2) = symmetric_difference(X1,set_difference(X2,X1)),
file('/tmp/tmppy2_IM/sel_SEU104+1.p_1',t98_xboole_1) ).
fof(42,conjecture,
! [X1] :
( ~ empty(X1)
=> ( ! [X2] :
( element(X2,X1)
=> ! [X3] :
( element(X3,X1)
=> ( in(symmetric_difference(X2,X3),X1)
& in(set_difference(X2,X3),X1) ) ) )
=> preboolean(X1) ) ),
file('/tmp/tmppy2_IM/sel_SEU104+1.p_1',t15_finsub_1) ).
fof(43,negated_conjecture,
~ ! [X1] :
( ~ empty(X1)
=> ( ! [X2] :
( element(X2,X1)
=> ! [X3] :
( element(X3,X1)
=> ( in(symmetric_difference(X2,X3),X1)
& in(set_difference(X2,X3),X1) ) ) )
=> preboolean(X1) ) ),
inference(assume_negation,[status(cth)],[42]) ).
fof(54,negated_conjecture,
~ ! [X1] :
( ~ empty(X1)
=> ( ! [X2] :
( element(X2,X1)
=> ! [X3] :
( element(X3,X1)
=> ( in(symmetric_difference(X2,X3),X1)
& in(set_difference(X2,X3),X1) ) ) )
=> preboolean(X1) ) ),
inference(fof_simplification,[status(thm)],[43,theory(equality)]) ).
fof(69,plain,
! [X1,X2] :
( ~ in(X1,X2)
| element(X1,X2) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(70,plain,
! [X3,X4] :
( ~ in(X3,X4)
| element(X3,X4) ),
inference(variable_rename,[status(thm)],[69]) ).
cnf(71,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[70]) ).
fof(121,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[19]) ).
cnf(122,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[121]) ).
fof(177,plain,
! [X1] :
( ( ~ preboolean(X1)
| ! [X2,X3] :
( ~ in(X2,X1)
| ~ in(X3,X1)
| ( in(set_union2(X2,X3),X1)
& in(set_difference(X2,X3),X1) ) ) )
& ( ? [X2,X3] :
( in(X2,X1)
& in(X3,X1)
& ( ~ in(set_union2(X2,X3),X1)
| ~ in(set_difference(X2,X3),X1) ) )
| preboolean(X1) ) ),
inference(fof_nnf,[status(thm)],[36]) ).
fof(178,plain,
! [X4] :
( ( ~ preboolean(X4)
| ! [X5,X6] :
( ~ in(X5,X4)
| ~ in(X6,X4)
| ( in(set_union2(X5,X6),X4)
& in(set_difference(X5,X6),X4) ) ) )
& ( ? [X7,X8] :
( in(X7,X4)
& in(X8,X4)
& ( ~ in(set_union2(X7,X8),X4)
| ~ in(set_difference(X7,X8),X4) ) )
| preboolean(X4) ) ),
inference(variable_rename,[status(thm)],[177]) ).
fof(179,plain,
! [X4] :
( ( ~ preboolean(X4)
| ! [X5,X6] :
( ~ in(X5,X4)
| ~ in(X6,X4)
| ( in(set_union2(X5,X6),X4)
& in(set_difference(X5,X6),X4) ) ) )
& ( ( in(esk9_1(X4),X4)
& in(esk10_1(X4),X4)
& ( ~ in(set_union2(esk9_1(X4),esk10_1(X4)),X4)
| ~ in(set_difference(esk9_1(X4),esk10_1(X4)),X4) ) )
| preboolean(X4) ) ),
inference(skolemize,[status(esa)],[178]) ).
fof(180,plain,
! [X4,X5,X6] :
( ( ~ in(X5,X4)
| ~ in(X6,X4)
| ( in(set_union2(X5,X6),X4)
& in(set_difference(X5,X6),X4) )
| ~ preboolean(X4) )
& ( ( in(esk9_1(X4),X4)
& in(esk10_1(X4),X4)
& ( ~ in(set_union2(esk9_1(X4),esk10_1(X4)),X4)
| ~ in(set_difference(esk9_1(X4),esk10_1(X4)),X4) ) )
| preboolean(X4) ) ),
inference(shift_quantors,[status(thm)],[179]) ).
fof(181,plain,
! [X4,X5,X6] :
( ( in(set_union2(X5,X6),X4)
| ~ in(X5,X4)
| ~ in(X6,X4)
| ~ preboolean(X4) )
& ( in(set_difference(X5,X6),X4)
| ~ in(X5,X4)
| ~ in(X6,X4)
| ~ preboolean(X4) )
& ( in(esk9_1(X4),X4)
| preboolean(X4) )
& ( in(esk10_1(X4),X4)
| preboolean(X4) )
& ( ~ in(set_union2(esk9_1(X4),esk10_1(X4)),X4)
| ~ in(set_difference(esk9_1(X4),esk10_1(X4)),X4)
| preboolean(X4) ) ),
inference(distribute,[status(thm)],[180]) ).
cnf(182,plain,
( preboolean(X1)
| ~ in(set_difference(esk9_1(X1),esk10_1(X1)),X1)
| ~ in(set_union2(esk9_1(X1),esk10_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[181]) ).
cnf(183,plain,
( preboolean(X1)
| in(esk10_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[181]) ).
cnf(184,plain,
( preboolean(X1)
| in(esk9_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[181]) ).
fof(194,plain,
! [X3,X4] : set_union2(X3,X4) = symmetric_difference(X3,set_difference(X4,X3)),
inference(variable_rename,[status(thm)],[39]) ).
cnf(195,plain,
set_union2(X1,X2) = symmetric_difference(X1,set_difference(X2,X1)),
inference(split_conjunct,[status(thm)],[194]) ).
fof(202,negated_conjecture,
? [X1] :
( ~ empty(X1)
& ! [X2] :
( ~ element(X2,X1)
| ! [X3] :
( ~ element(X3,X1)
| ( in(symmetric_difference(X2,X3),X1)
& in(set_difference(X2,X3),X1) ) ) )
& ~ preboolean(X1) ),
inference(fof_nnf,[status(thm)],[54]) ).
fof(203,negated_conjecture,
? [X4] :
( ~ empty(X4)
& ! [X5] :
( ~ element(X5,X4)
| ! [X6] :
( ~ element(X6,X4)
| ( in(symmetric_difference(X5,X6),X4)
& in(set_difference(X5,X6),X4) ) ) )
& ~ preboolean(X4) ),
inference(variable_rename,[status(thm)],[202]) ).
fof(204,negated_conjecture,
( ~ empty(esk13_0)
& ! [X5] :
( ~ element(X5,esk13_0)
| ! [X6] :
( ~ element(X6,esk13_0)
| ( in(symmetric_difference(X5,X6),esk13_0)
& in(set_difference(X5,X6),esk13_0) ) ) )
& ~ preboolean(esk13_0) ),
inference(skolemize,[status(esa)],[203]) ).
fof(205,negated_conjecture,
! [X5,X6] :
( ( ~ element(X6,esk13_0)
| ( in(symmetric_difference(X5,X6),esk13_0)
& in(set_difference(X5,X6),esk13_0) )
| ~ element(X5,esk13_0) )
& ~ preboolean(esk13_0)
& ~ empty(esk13_0) ),
inference(shift_quantors,[status(thm)],[204]) ).
fof(206,negated_conjecture,
! [X5,X6] :
( ( in(symmetric_difference(X5,X6),esk13_0)
| ~ element(X6,esk13_0)
| ~ element(X5,esk13_0) )
& ( in(set_difference(X5,X6),esk13_0)
| ~ element(X6,esk13_0)
| ~ element(X5,esk13_0) )
& ~ preboolean(esk13_0)
& ~ empty(esk13_0) ),
inference(distribute,[status(thm)],[205]) ).
cnf(208,negated_conjecture,
~ preboolean(esk13_0),
inference(split_conjunct,[status(thm)],[206]) ).
cnf(209,negated_conjecture,
( in(set_difference(X1,X2),esk13_0)
| ~ element(X1,esk13_0)
| ~ element(X2,esk13_0) ),
inference(split_conjunct,[status(thm)],[206]) ).
cnf(210,negated_conjecture,
( in(symmetric_difference(X1,X2),esk13_0)
| ~ element(X1,esk13_0)
| ~ element(X2,esk13_0) ),
inference(split_conjunct,[status(thm)],[206]) ).
cnf(213,plain,
symmetric_difference(X1,set_difference(X2,X1)) = symmetric_difference(X2,set_difference(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[122,195,theory(equality)]),195,theory(equality)]),
[unfolding] ).
cnf(218,plain,
( preboolean(X1)
| ~ in(symmetric_difference(esk9_1(X1),set_difference(esk10_1(X1),esk9_1(X1))),X1)
| ~ in(set_difference(esk9_1(X1),esk10_1(X1)),X1) ),
inference(rw,[status(thm)],[182,195,theory(equality)]),
[unfolding] ).
cnf(294,negated_conjecture,
( in(symmetric_difference(X2,set_difference(X1,X2)),esk13_0)
| ~ element(set_difference(X2,X1),esk13_0)
| ~ element(X1,esk13_0) ),
inference(spm,[status(thm)],[210,213,theory(equality)]) ).
cnf(573,negated_conjecture,
( preboolean(esk13_0)
| ~ in(set_difference(esk9_1(esk13_0),esk10_1(esk13_0)),esk13_0)
| ~ element(set_difference(esk9_1(esk13_0),esk10_1(esk13_0)),esk13_0)
| ~ element(esk10_1(esk13_0),esk13_0) ),
inference(spm,[status(thm)],[218,294,theory(equality)]) ).
cnf(580,negated_conjecture,
( ~ in(set_difference(esk9_1(esk13_0),esk10_1(esk13_0)),esk13_0)
| ~ element(set_difference(esk9_1(esk13_0),esk10_1(esk13_0)),esk13_0)
| ~ element(esk10_1(esk13_0),esk13_0) ),
inference(sr,[status(thm)],[573,208,theory(equality)]) ).
cnf(2660,negated_conjecture,
( ~ in(set_difference(esk9_1(esk13_0),esk10_1(esk13_0)),esk13_0)
| ~ element(esk10_1(esk13_0),esk13_0) ),
inference(csr,[status(thm)],[580,71]) ).
cnf(2661,negated_conjecture,
( ~ element(esk10_1(esk13_0),esk13_0)
| ~ element(esk9_1(esk13_0),esk13_0) ),
inference(spm,[status(thm)],[2660,209,theory(equality)]) ).
cnf(2662,negated_conjecture,
( ~ element(esk9_1(esk13_0),esk13_0)
| ~ in(esk10_1(esk13_0),esk13_0) ),
inference(spm,[status(thm)],[2661,71,theory(equality)]) ).
cnf(2663,negated_conjecture,
( ~ in(esk10_1(esk13_0),esk13_0)
| ~ in(esk9_1(esk13_0),esk13_0) ),
inference(spm,[status(thm)],[2662,71,theory(equality)]) ).
cnf(2664,negated_conjecture,
( preboolean(esk13_0)
| ~ in(esk9_1(esk13_0),esk13_0) ),
inference(spm,[status(thm)],[2663,183,theory(equality)]) ).
cnf(2665,negated_conjecture,
~ in(esk9_1(esk13_0),esk13_0),
inference(sr,[status(thm)],[2664,208,theory(equality)]) ).
cnf(2666,negated_conjecture,
preboolean(esk13_0),
inference(spm,[status(thm)],[2665,184,theory(equality)]) ).
cnf(2667,negated_conjecture,
$false,
inference(sr,[status(thm)],[2666,208,theory(equality)]) ).
cnf(2668,negated_conjecture,
$false,
2667,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU104+1.p
% --creating new selector for []
% -running prover on /tmp/tmppy2_IM/sel_SEU104+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU104+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU104+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU104+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
%
%------------------------------------------------------------------------------