TSTP Solution File: SET628+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET628+3 : TPTP v5.0.0. Released v2.2.0.
% 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 03:05:22 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 11 unt; 0 def)
% Number of atoms : 185 ( 25 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 215 ( 85 ~; 87 |; 35 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 89 ( 3 sgn 58 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( not_equal(X1,X2)
<=> X1 != X2 ),
file('/tmp/tmpuuBlbx/sel_SET628+3.p_1',not_equal_defn) ).
fof(2,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/tmp/tmpuuBlbx/sel_SET628+3.p_1',empty_defn) ).
fof(3,conjecture,
! [X1] :
( intersect(X1,X1)
<=> not_equal(X1,empty_set) ),
file('/tmp/tmpuuBlbx/sel_SET628+3.p_1',prove_th110) ).
fof(4,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmpuuBlbx/sel_SET628+3.p_1',intersect_defn) ).
fof(6,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/tmp/tmpuuBlbx/sel_SET628+3.p_1',equal_member_defn) ).
fof(7,axiom,
! [X1] : ~ member(X1,empty_set),
file('/tmp/tmpuuBlbx/sel_SET628+3.p_1',empty_set_defn) ).
fof(8,negated_conjecture,
~ ! [X1] :
( intersect(X1,X1)
<=> not_equal(X1,empty_set) ),
inference(assume_negation,[status(cth)],[3]) ).
fof(9,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).
fof(10,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).
fof(11,plain,
! [X1,X2] :
( ( ~ not_equal(X1,X2)
| X1 != X2 )
& ( X1 = X2
| not_equal(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(12,plain,
! [X3,X4] :
( ( ~ not_equal(X3,X4)
| X3 != X4 )
& ( X3 = X4
| not_equal(X3,X4) ) ),
inference(variable_rename,[status(thm)],[11]) ).
cnf(13,plain,
( not_equal(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[12]) ).
cnf(14,plain,
( X1 != X2
| ~ not_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[12]) ).
fof(15,plain,
! [X1] :
( ( ~ empty(X1)
| ! [X2] : ~ member(X2,X1) )
& ( ? [X2] : member(X2,X1)
| empty(X1) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(16,plain,
! [X3] :
( ( ~ empty(X3)
| ! [X4] : ~ member(X4,X3) )
& ( ? [X5] : member(X5,X3)
| empty(X3) ) ),
inference(variable_rename,[status(thm)],[15]) ).
fof(17,plain,
! [X3] :
( ( ~ empty(X3)
| ! [X4] : ~ member(X4,X3) )
& ( member(esk1_1(X3),X3)
| empty(X3) ) ),
inference(skolemize,[status(esa)],[16]) ).
fof(18,plain,
! [X3,X4] :
( ( ~ member(X4,X3)
| ~ empty(X3) )
& ( member(esk1_1(X3),X3)
| empty(X3) ) ),
inference(shift_quantors,[status(thm)],[17]) ).
cnf(19,plain,
( empty(X1)
| member(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(20,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[18]) ).
fof(21,negated_conjecture,
? [X1] :
( ( ~ intersect(X1,X1)
| ~ not_equal(X1,empty_set) )
& ( intersect(X1,X1)
| not_equal(X1,empty_set) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(22,negated_conjecture,
? [X2] :
( ( ~ intersect(X2,X2)
| ~ not_equal(X2,empty_set) )
& ( intersect(X2,X2)
| not_equal(X2,empty_set) ) ),
inference(variable_rename,[status(thm)],[21]) ).
fof(23,negated_conjecture,
( ( ~ intersect(esk2_0,esk2_0)
| ~ not_equal(esk2_0,empty_set) )
& ( intersect(esk2_0,esk2_0)
| not_equal(esk2_0,empty_set) ) ),
inference(skolemize,[status(esa)],[22]) ).
cnf(24,negated_conjecture,
( not_equal(esk2_0,empty_set)
| intersect(esk2_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(25,negated_conjecture,
( ~ not_equal(esk2_0,empty_set)
| ~ intersect(esk2_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[23]) ).
fof(26,plain,
! [X1,X2] :
( ( ~ intersect(X1,X2)
| ? [X3] :
( member(X3,X1)
& member(X3,X2) ) )
& ( ! [X3] :
( ~ member(X3,X1)
| ~ member(X3,X2) )
| intersect(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(27,plain,
! [X4,X5] :
( ( ~ intersect(X4,X5)
| ? [X6] :
( member(X6,X4)
& member(X6,X5) ) )
& ( ! [X7] :
( ~ member(X7,X4)
| ~ member(X7,X5) )
| intersect(X4,X5) ) ),
inference(variable_rename,[status(thm)],[26]) ).
fof(28,plain,
! [X4,X5] :
( ( ~ intersect(X4,X5)
| ( member(esk3_2(X4,X5),X4)
& member(esk3_2(X4,X5),X5) ) )
& ( ! [X7] :
( ~ member(X7,X4)
| ~ member(X7,X5) )
| intersect(X4,X5) ) ),
inference(skolemize,[status(esa)],[27]) ).
fof(29,plain,
! [X4,X5,X7] :
( ( ~ member(X7,X4)
| ~ member(X7,X5)
| intersect(X4,X5) )
& ( ~ intersect(X4,X5)
| ( member(esk3_2(X4,X5),X4)
& member(esk3_2(X4,X5),X5) ) ) ),
inference(shift_quantors,[status(thm)],[28]) ).
fof(30,plain,
! [X4,X5,X7] :
( ( ~ member(X7,X4)
| ~ member(X7,X5)
| intersect(X4,X5) )
& ( member(esk3_2(X4,X5),X4)
| ~ intersect(X4,X5) )
& ( member(esk3_2(X4,X5),X5)
| ~ intersect(X4,X5) ) ),
inference(distribute,[status(thm)],[29]) ).
cnf(31,plain,
( member(esk3_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[30]) ).
cnf(33,plain,
( intersect(X1,X2)
| ~ member(X3,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[30]) ).
fof(37,plain,
! [X1,X2] :
( ( X1 != X2
| ! [X3] :
( ( ~ member(X3,X1)
| member(X3,X2) )
& ( ~ member(X3,X2)
| member(X3,X1) ) ) )
& ( ? [X3] :
( ( ~ member(X3,X1)
| ~ member(X3,X2) )
& ( member(X3,X1)
| member(X3,X2) ) )
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(38,plain,
! [X4,X5] :
( ( X4 != X5
| ! [X6] :
( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) ) )
& ( ? [X7] :
( ( ~ member(X7,X4)
| ~ member(X7,X5) )
& ( member(X7,X4)
| member(X7,X5) ) )
| X4 = X5 ) ),
inference(variable_rename,[status(thm)],[37]) ).
fof(39,plain,
! [X4,X5] :
( ( X4 != X5
| ! [X6] :
( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) ) )
& ( ( ( ~ member(esk4_2(X4,X5),X4)
| ~ member(esk4_2(X4,X5),X5) )
& ( member(esk4_2(X4,X5),X4)
| member(esk4_2(X4,X5),X5) ) )
| X4 = X5 ) ),
inference(skolemize,[status(esa)],[38]) ).
fof(40,plain,
! [X4,X5,X6] :
( ( ( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) )
| X4 != X5 )
& ( ( ( ~ member(esk4_2(X4,X5),X4)
| ~ member(esk4_2(X4,X5),X5) )
& ( member(esk4_2(X4,X5),X4)
| member(esk4_2(X4,X5),X5) ) )
| X4 = X5 ) ),
inference(shift_quantors,[status(thm)],[39]) ).
fof(41,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| X4 != X5 )
& ( ~ member(X6,X5)
| member(X6,X4)
| X4 != X5 )
& ( ~ member(esk4_2(X4,X5),X4)
| ~ member(esk4_2(X4,X5),X5)
| X4 = X5 )
& ( member(esk4_2(X4,X5),X4)
| member(esk4_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[40]) ).
cnf(42,plain,
( X1 = X2
| member(esk4_2(X1,X2),X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(46,plain,
! [X2] : ~ member(X2,empty_set),
inference(variable_rename,[status(thm)],[10]) ).
cnf(47,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[46]) ).
cnf(48,plain,
~ not_equal(X1,X1),
inference(er,[status(thm)],[14,theory(equality)]) ).
cnf(52,negated_conjecture,
( member(esk3_2(esk2_0,esk2_0),esk2_0)
| not_equal(esk2_0,empty_set) ),
inference(spm,[status(thm)],[31,24,theory(equality)]) ).
cnf(56,plain,
( empty_set = X1
| member(esk4_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[47,42,theory(equality)]) ).
cnf(62,plain,
( intersect(X1,X2)
| empty(X2)
| ~ member(esk1_1(X2),X1) ),
inference(spm,[status(thm)],[33,19,theory(equality)]) ).
cnf(65,plain,
( intersect(X1,X1)
| empty(X1) ),
inference(spm,[status(thm)],[62,19,theory(equality)]) ).
cnf(66,negated_conjecture,
( empty(esk2_0)
| ~ not_equal(esk2_0,empty_set) ),
inference(spm,[status(thm)],[25,65,theory(equality)]) ).
cnf(70,negated_conjecture,
( empty(esk2_0)
| esk2_0 = empty_set ),
inference(spm,[status(thm)],[66,13,theory(equality)]) ).
cnf(76,negated_conjecture,
( not_equal(esk2_0,empty_set)
| ~ empty(esk2_0) ),
inference(spm,[status(thm)],[20,52,theory(equality)]) ).
cnf(80,plain,
( empty_set = X1
| ~ empty(X1) ),
inference(spm,[status(thm)],[20,56,theory(equality)]) ).
cnf(86,negated_conjecture,
empty_set = esk2_0,
inference(spm,[status(thm)],[80,70,theory(equality)]) ).
cnf(88,plain,
~ member(X1,esk2_0),
inference(rw,[status(thm)],[47,86,theory(equality)]) ).
cnf(94,negated_conjecture,
( not_equal(esk2_0,esk2_0)
| ~ empty(esk2_0) ),
inference(rw,[status(thm)],[76,86,theory(equality)]) ).
cnf(95,negated_conjecture,
~ empty(esk2_0),
inference(sr,[status(thm)],[94,48,theory(equality)]) ).
cnf(103,plain,
empty(esk2_0),
inference(spm,[status(thm)],[88,19,theory(equality)]) ).
cnf(107,plain,
$false,
inference(sr,[status(thm)],[103,95,theory(equality)]) ).
cnf(108,plain,
$false,
107,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET628+3.p
% --creating new selector for []
% -running prover on /tmp/tmpuuBlbx/sel_SET628+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET628+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET628+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET628+3.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
%
%------------------------------------------------------------------------------