TSTP Solution File: SEU107+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU107+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 04:38:58 EST 2010
% Result : Theorem 0.19s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 15 unt; 0 def)
% Number of atoms : 123 ( 12 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 130 ( 51 ~; 47 |; 23 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 69 ( 3 sgn 46 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> prebool_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('/tmp/tmpsb-8bS/sel_SEU107+1.p_1',redefinition_k2_finsub_1) ).
fof(10,axiom,
! [X1,X2] : subset(X1,X1),
file('/tmp/tmpsb-8bS/sel_SEU107+1.p_1',reflexivity_r1_tarski) ).
fof(18,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/tmp/tmpsb-8bS/sel_SEU107+1.p_1',t37_xboole_1) ).
fof(25,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/tmp/tmpsb-8bS/sel_SEU107+1.p_1',t2_subset) ).
fof(27,axiom,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> element(prebool_difference(X1,X2,X3),X1) ),
file('/tmp/tmpsb-8bS/sel_SEU107+1.p_1',dt_k2_finsub_1) ).
fof(28,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/tmp/tmpsb-8bS/sel_SEU107+1.p_1',existence_m1_subset_1) ).
fof(33,conjecture,
! [X1] :
( ( ~ empty(X1)
& preboolean(X1) )
=> in(empty_set,X1) ),
file('/tmp/tmpsb-8bS/sel_SEU107+1.p_1',t18_finsub_1) ).
fof(34,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& preboolean(X1) )
=> in(empty_set,X1) ),
inference(assume_negation,[status(cth)],[33]) ).
fof(36,plain,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> prebool_difference(X1,X2,X3) = set_difference(X2,X3) ),
inference(fof_simplification,[status(thm)],[3,theory(equality)]) ).
fof(43,plain,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> element(prebool_difference(X1,X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[27,theory(equality)]) ).
fof(45,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& preboolean(X1) )
=> in(empty_set,X1) ),
inference(fof_simplification,[status(thm)],[34,theory(equality)]) ).
fof(56,plain,
! [X1,X2,X3] :
( empty(X1)
| ~ preboolean(X1)
| ~ element(X2,X1)
| ~ element(X3,X1)
| prebool_difference(X1,X2,X3) = set_difference(X2,X3) ),
inference(fof_nnf,[status(thm)],[36]) ).
fof(57,plain,
! [X4,X5,X6] :
( empty(X4)
| ~ preboolean(X4)
| ~ element(X5,X4)
| ~ element(X6,X4)
| prebool_difference(X4,X5,X6) = set_difference(X5,X6) ),
inference(variable_rename,[status(thm)],[56]) ).
cnf(58,plain,
( prebool_difference(X1,X2,X3) = set_difference(X2,X3)
| empty(X1)
| ~ element(X3,X1)
| ~ element(X2,X1)
| ~ preboolean(X1) ),
inference(split_conjunct,[status(thm)],[57]) ).
fof(93,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[10]) ).
cnf(94,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[93]) ).
fof(116,plain,
! [X1,X2] :
( ( set_difference(X1,X2) != empty_set
| subset(X1,X2) )
& ( ~ subset(X1,X2)
| set_difference(X1,X2) = empty_set ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(117,plain,
! [X3,X4] :
( ( set_difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| set_difference(X3,X4) = empty_set ) ),
inference(variable_rename,[status(thm)],[116]) ).
cnf(118,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[117]) ).
fof(138,plain,
! [X1,X2] :
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(139,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[138]) ).
cnf(140,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[139]) ).
fof(144,plain,
! [X1,X2,X3] :
( empty(X1)
| ~ preboolean(X1)
| ~ element(X2,X1)
| ~ element(X3,X1)
| element(prebool_difference(X1,X2,X3),X1) ),
inference(fof_nnf,[status(thm)],[43]) ).
fof(145,plain,
! [X4,X5,X6] :
( empty(X4)
| ~ preboolean(X4)
| ~ element(X5,X4)
| ~ element(X6,X4)
| element(prebool_difference(X4,X5,X6),X4) ),
inference(variable_rename,[status(thm)],[144]) ).
cnf(146,plain,
( element(prebool_difference(X1,X2,X3),X1)
| empty(X1)
| ~ element(X3,X1)
| ~ element(X2,X1)
| ~ preboolean(X1) ),
inference(split_conjunct,[status(thm)],[145]) ).
fof(147,plain,
! [X3] :
? [X4] : element(X4,X3),
inference(variable_rename,[status(thm)],[28]) ).
fof(148,plain,
! [X3] : element(esk8_1(X3),X3),
inference(skolemize,[status(esa)],[147]) ).
cnf(149,plain,
element(esk8_1(X1),X1),
inference(split_conjunct,[status(thm)],[148]) ).
fof(167,negated_conjecture,
? [X1] :
( ~ empty(X1)
& preboolean(X1)
& ~ in(empty_set,X1) ),
inference(fof_nnf,[status(thm)],[45]) ).
fof(168,negated_conjecture,
? [X2] :
( ~ empty(X2)
& preboolean(X2)
& ~ in(empty_set,X2) ),
inference(variable_rename,[status(thm)],[167]) ).
fof(169,negated_conjecture,
( ~ empty(esk11_0)
& preboolean(esk11_0)
& ~ in(empty_set,esk11_0) ),
inference(skolemize,[status(esa)],[168]) ).
cnf(170,negated_conjecture,
~ in(empty_set,esk11_0),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(171,negated_conjecture,
preboolean(esk11_0),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(172,negated_conjecture,
~ empty(esk11_0),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(185,negated_conjecture,
( empty(esk11_0)
| ~ element(empty_set,esk11_0) ),
inference(spm,[status(thm)],[170,140,theory(equality)]) ).
cnf(189,negated_conjecture,
~ element(empty_set,esk11_0),
inference(sr,[status(thm)],[185,172,theory(equality)]) ).
cnf(190,plain,
set_difference(X1,X1) = empty_set,
inference(spm,[status(thm)],[118,94,theory(equality)]) ).
cnf(223,plain,
( element(set_difference(X2,X3),X1)
| empty(X1)
| ~ preboolean(X1)
| ~ element(X3,X1)
| ~ element(X2,X1) ),
inference(spm,[status(thm)],[146,58,theory(equality)]) ).
cnf(517,plain,
( element(empty_set,X2)
| empty(X2)
| ~ preboolean(X2)
| ~ element(X1,X2) ),
inference(spm,[status(thm)],[223,190,theory(equality)]) ).
cnf(541,plain,
( element(empty_set,X1)
| empty(X1)
| ~ preboolean(X1) ),
inference(spm,[status(thm)],[517,149,theory(equality)]) ).
cnf(564,negated_conjecture,
( element(empty_set,esk11_0)
| empty(esk11_0) ),
inference(spm,[status(thm)],[541,171,theory(equality)]) ).
cnf(566,negated_conjecture,
empty(esk11_0),
inference(sr,[status(thm)],[564,189,theory(equality)]) ).
cnf(567,negated_conjecture,
$false,
inference(sr,[status(thm)],[566,172,theory(equality)]) ).
cnf(568,negated_conjecture,
$false,
567,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU107+1.p
% --creating new selector for []
% -running prover on /tmp/tmpsb-8bS/sel_SEU107+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU107+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU107+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU107+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
%
%------------------------------------------------------------------------------