TSTP Solution File: SEU321+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU321+1 : TPTP v5.0.0. Released v3.3.0.
% 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 07:15:16 EST 2010
% Result : Theorem 0.19s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 10 unt; 0 def)
% Number of atoms : 146 ( 11 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 165 ( 62 ~; 54 |; 26 &)
% ( 3 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 37 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(11,axiom,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
file('/tmp/tmpNmg4n7/sel_SEU321+1.p_1',t50_subset_1) ).
fof(16,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
file('/tmp/tmpNmg4n7/sel_SEU321+1.p_1',fc1_struct_0) ).
fof(17,axiom,
( empty(empty_set)
& v1_membered(empty_set)
& v2_membered(empty_set)
& v3_membered(empty_set)
& v4_membered(empty_set)
& v5_membered(empty_set) ),
file('/tmp/tmpNmg4n7/sel_SEU321+1.p_1',fc6_membered) ).
fof(26,axiom,
! [X1,X2,X3] :
( element(X3,powerset(X1))
=> ~ ( in(X2,subset_complement(X1,X3))
& in(X2,X3) ) ),
file('/tmp/tmpNmg4n7/sel_SEU321+1.p_1',t54_subset_1) ).
fof(29,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(X3,subset_complement(the_carrier(X1),X2))
<=> ~ in(X3,X2) ) ) ) ),
file('/tmp/tmpNmg4n7/sel_SEU321+1.p_1',l40_tops_1) ).
fof(43,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(X3,subset_complement(the_carrier(X1),X2))
<=> ~ in(X3,X2) ) ) ) ),
inference(assume_negation,[status(cth)],[29]) ).
fof(44,plain,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).
fof(45,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[16,theory(equality)]) ).
fof(46,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(X3,subset_complement(the_carrier(X1),X2))
<=> ~ in(X3,X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[43,theory(equality)]) ).
fof(80,plain,
! [X1] :
( X1 = empty_set
| ! [X2] :
( ~ element(X2,powerset(X1))
| ! [X3] :
( ~ element(X3,X1)
| in(X3,X2)
| in(X3,subset_complement(X1,X2)) ) ) ),
inference(fof_nnf,[status(thm)],[44]) ).
fof(81,plain,
! [X4] :
( X4 = empty_set
| ! [X5] :
( ~ element(X5,powerset(X4))
| ! [X6] :
( ~ element(X6,X4)
| in(X6,X5)
| in(X6,subset_complement(X4,X5)) ) ) ),
inference(variable_rename,[status(thm)],[80]) ).
fof(82,plain,
! [X4,X5,X6] :
( ~ element(X6,X4)
| in(X6,X5)
| in(X6,subset_complement(X4,X5))
| ~ element(X5,powerset(X4))
| X4 = empty_set ),
inference(shift_quantors,[status(thm)],[81]) ).
cnf(83,plain,
( X1 = empty_set
| in(X3,subset_complement(X1,X2))
| in(X3,X2)
| ~ element(X2,powerset(X1))
| ~ element(X3,X1) ),
inference(split_conjunct,[status(thm)],[82]) ).
fof(97,plain,
! [X1] :
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(fof_nnf,[status(thm)],[45]) ).
fof(98,plain,
! [X2] :
( empty_carrier(X2)
| ~ one_sorted_str(X2)
| ~ empty(the_carrier(X2)) ),
inference(variable_rename,[status(thm)],[97]) ).
cnf(99,plain,
( empty_carrier(X1)
| ~ empty(the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[98]) ).
cnf(105,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[17]) ).
fof(146,plain,
! [X1,X2,X3] :
( ~ element(X3,powerset(X1))
| ~ in(X2,subset_complement(X1,X3))
| ~ in(X2,X3) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(147,plain,
! [X4,X5,X6] :
( ~ element(X6,powerset(X4))
| ~ in(X5,subset_complement(X4,X6))
| ~ in(X5,X6) ),
inference(variable_rename,[status(thm)],[146]) ).
cnf(148,plain,
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X3,X2))
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[147]) ).
fof(153,negated_conjecture,
? [X1] :
( ~ empty_carrier(X1)
& one_sorted_str(X1)
& ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& ? [X3] :
( element(X3,the_carrier(X1))
& ( ~ in(X3,subset_complement(the_carrier(X1),X2))
| in(X3,X2) )
& ( in(X3,subset_complement(the_carrier(X1),X2))
| ~ in(X3,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[46]) ).
fof(154,negated_conjecture,
? [X4] :
( ~ empty_carrier(X4)
& one_sorted_str(X4)
& ? [X5] :
( element(X5,powerset(the_carrier(X4)))
& ? [X6] :
( element(X6,the_carrier(X4))
& ( ~ in(X6,subset_complement(the_carrier(X4),X5))
| in(X6,X5) )
& ( in(X6,subset_complement(the_carrier(X4),X5))
| ~ in(X6,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[153]) ).
fof(155,negated_conjecture,
( ~ empty_carrier(esk2_0)
& one_sorted_str(esk2_0)
& element(esk3_0,powerset(the_carrier(esk2_0)))
& element(esk4_0,the_carrier(esk2_0))
& ( ~ in(esk4_0,subset_complement(the_carrier(esk2_0),esk3_0))
| in(esk4_0,esk3_0) )
& ( in(esk4_0,subset_complement(the_carrier(esk2_0),esk3_0))
| ~ in(esk4_0,esk3_0) ) ),
inference(skolemize,[status(esa)],[154]) ).
cnf(156,negated_conjecture,
( in(esk4_0,subset_complement(the_carrier(esk2_0),esk3_0))
| ~ in(esk4_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[155]) ).
cnf(157,negated_conjecture,
( in(esk4_0,esk3_0)
| ~ in(esk4_0,subset_complement(the_carrier(esk2_0),esk3_0)) ),
inference(split_conjunct,[status(thm)],[155]) ).
cnf(158,negated_conjecture,
element(esk4_0,the_carrier(esk2_0)),
inference(split_conjunct,[status(thm)],[155]) ).
cnf(159,negated_conjecture,
element(esk3_0,powerset(the_carrier(esk2_0))),
inference(split_conjunct,[status(thm)],[155]) ).
cnf(160,negated_conjecture,
one_sorted_str(esk2_0),
inference(split_conjunct,[status(thm)],[155]) ).
cnf(161,negated_conjecture,
~ empty_carrier(esk2_0),
inference(split_conjunct,[status(thm)],[155]) ).
cnf(390,negated_conjecture,
( in(esk4_0,esk3_0)
| empty_set = the_carrier(esk2_0)
| ~ element(esk3_0,powerset(the_carrier(esk2_0)))
| ~ element(esk4_0,the_carrier(esk2_0)) ),
inference(spm,[status(thm)],[157,83,theory(equality)]) ).
cnf(394,negated_conjecture,
( in(esk4_0,esk3_0)
| empty_set = the_carrier(esk2_0)
| $false
| ~ element(esk4_0,the_carrier(esk2_0)) ),
inference(rw,[status(thm)],[390,159,theory(equality)]) ).
cnf(395,negated_conjecture,
( in(esk4_0,esk3_0)
| empty_set = the_carrier(esk2_0)
| $false
| $false ),
inference(rw,[status(thm)],[394,158,theory(equality)]) ).
cnf(396,negated_conjecture,
( in(esk4_0,esk3_0)
| empty_set = the_carrier(esk2_0) ),
inference(cn,[status(thm)],[395,theory(equality)]) ).
cnf(397,negated_conjecture,
( ~ element(esk3_0,powerset(the_carrier(esk2_0)))
| ~ in(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[148,156,theory(equality)]) ).
cnf(401,negated_conjecture,
( $false
| ~ in(esk4_0,esk3_0) ),
inference(rw,[status(thm)],[397,159,theory(equality)]) ).
cnf(402,negated_conjecture,
~ in(esk4_0,esk3_0),
inference(cn,[status(thm)],[401,theory(equality)]) ).
cnf(442,negated_conjecture,
the_carrier(esk2_0) = empty_set,
inference(sr,[status(thm)],[396,402,theory(equality)]) ).
cnf(443,negated_conjecture,
( empty_carrier(esk2_0)
| ~ one_sorted_str(esk2_0)
| ~ empty(empty_set) ),
inference(spm,[status(thm)],[99,442,theory(equality)]) ).
cnf(450,negated_conjecture,
( empty_carrier(esk2_0)
| $false
| ~ empty(empty_set) ),
inference(rw,[status(thm)],[443,160,theory(equality)]) ).
cnf(451,negated_conjecture,
( empty_carrier(esk2_0)
| $false
| $false ),
inference(rw,[status(thm)],[450,105,theory(equality)]) ).
cnf(452,negated_conjecture,
empty_carrier(esk2_0),
inference(cn,[status(thm)],[451,theory(equality)]) ).
cnf(453,negated_conjecture,
$false,
inference(sr,[status(thm)],[452,161,theory(equality)]) ).
cnf(454,negated_conjecture,
$false,
453,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU321+1.p
% --creating new selector for []
% -running prover on /tmp/tmpNmg4n7/sel_SEU321+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU321+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU321+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU321+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
%
%------------------------------------------------------------------------------