TSTP Solution File: SET600+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET600+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 03:00:15 EST 2010
% Result : Theorem 0.21s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 64 ( 14 unt; 0 def)
% Number of atoms : 235 ( 88 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 272 ( 101 ~; 115 |; 48 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 105 ( 8 sgn 67 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/tmp/tmpuQ0N-6/sel_SET600+3.p_1',commutativity_of_union) ).
fof(3,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpuQ0N-6/sel_SET600+3.p_1',equal_defn) ).
fof(4,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/tmp/tmpuQ0N-6/sel_SET600+3.p_1',union_defn) ).
fof(5,conjecture,
! [X1,X2] :
( union(X1,X2) = empty_set
<=> ( X1 = empty_set
& X2 = empty_set ) ),
file('/tmp/tmpuQ0N-6/sel_SET600+3.p_1',prove_th59) ).
fof(6,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpuQ0N-6/sel_SET600+3.p_1',subset_defn) ).
fof(7,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/tmp/tmpuQ0N-6/sel_SET600+3.p_1',equal_member_defn) ).
fof(9,axiom,
! [X1] : ~ member(X1,empty_set),
file('/tmp/tmpuQ0N-6/sel_SET600+3.p_1',empty_set_defn) ).
fof(10,negated_conjecture,
~ ! [X1,X2] :
( union(X1,X2) = empty_set
<=> ( X1 = empty_set
& X2 = empty_set ) ),
inference(assume_negation,[status(cth)],[5]) ).
fof(12,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(13,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(14,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[13]) ).
fof(21,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(22,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[21]) ).
fof(23,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)],[22]) ).
cnf(24,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[23]) ).
fof(27,plain,
! [X1,X2,X3] :
( ( ~ member(X3,union(X1,X2))
| member(X3,X1)
| member(X3,X2) )
& ( ( ~ member(X3,X1)
& ~ member(X3,X2) )
| member(X3,union(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(28,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ( ~ member(X6,X4)
& ~ member(X6,X5) )
| member(X6,union(X4,X5)) ) ),
inference(variable_rename,[status(thm)],[27]) ).
fof(29,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X4)
| member(X6,union(X4,X5)) )
& ( ~ member(X6,X5)
| member(X6,union(X4,X5)) ) ),
inference(distribute,[status(thm)],[28]) ).
cnf(30,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(31,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(32,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[29]) ).
fof(33,negated_conjecture,
? [X1,X2] :
( ( union(X1,X2) != empty_set
| X1 != empty_set
| X2 != empty_set )
& ( union(X1,X2) = empty_set
| ( X1 = empty_set
& X2 = empty_set ) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(34,negated_conjecture,
? [X3,X4] :
( ( union(X3,X4) != empty_set
| X3 != empty_set
| X4 != empty_set )
& ( union(X3,X4) = empty_set
| ( X3 = empty_set
& X4 = empty_set ) ) ),
inference(variable_rename,[status(thm)],[33]) ).
fof(35,negated_conjecture,
( ( union(esk2_0,esk3_0) != empty_set
| esk2_0 != empty_set
| esk3_0 != empty_set )
& ( union(esk2_0,esk3_0) = empty_set
| ( esk2_0 = empty_set
& esk3_0 = empty_set ) ) ),
inference(skolemize,[status(esa)],[34]) ).
fof(36,negated_conjecture,
( ( union(esk2_0,esk3_0) != empty_set
| esk2_0 != empty_set
| esk3_0 != empty_set )
& ( esk2_0 = empty_set
| union(esk2_0,esk3_0) = empty_set )
& ( esk3_0 = empty_set
| union(esk2_0,esk3_0) = empty_set ) ),
inference(distribute,[status(thm)],[35]) ).
cnf(37,negated_conjecture,
( union(esk2_0,esk3_0) = empty_set
| esk3_0 = empty_set ),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(38,negated_conjecture,
( union(esk2_0,esk3_0) = empty_set
| esk2_0 = empty_set ),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(39,negated_conjecture,
( esk3_0 != empty_set
| esk2_0 != empty_set
| union(esk2_0,esk3_0) != empty_set ),
inference(split_conjunct,[status(thm)],[36]) ).
fof(40,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ member(X3,X1)
| member(X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ member(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(41,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ? [X7] :
( member(X7,X4)
& ~ member(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[40]) ).
fof(42,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( member(esk4_2(X4,X5),X4)
& ~ member(esk4_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[41]) ).
fof(43,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( member(esk4_2(X4,X5),X4)
& ~ member(esk4_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[42]) ).
fof(44,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( member(esk4_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk4_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[43]) ).
cnf(46,plain,
( subset(X1,X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[44]) ).
fof(48,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)],[7]) ).
fof(49,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)],[48]) ).
fof(50,plain,
! [X4,X5] :
( ( X4 != X5
| ! [X6] :
( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) ) )
& ( ( ( ~ member(esk5_2(X4,X5),X4)
| ~ member(esk5_2(X4,X5),X5) )
& ( member(esk5_2(X4,X5),X4)
| member(esk5_2(X4,X5),X5) ) )
| X4 = X5 ) ),
inference(skolemize,[status(esa)],[49]) ).
fof(51,plain,
! [X4,X5,X6] :
( ( ( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) )
| X4 != X5 )
& ( ( ( ~ member(esk5_2(X4,X5),X4)
| ~ member(esk5_2(X4,X5),X5) )
& ( member(esk5_2(X4,X5),X4)
| member(esk5_2(X4,X5),X5) ) )
| X4 = X5 ) ),
inference(shift_quantors,[status(thm)],[50]) ).
fof(52,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| X4 != X5 )
& ( ~ member(X6,X5)
| member(X6,X4)
| X4 != X5 )
& ( ~ member(esk5_2(X4,X5),X4)
| ~ member(esk5_2(X4,X5),X5)
| X4 = X5 )
& ( member(esk5_2(X4,X5),X4)
| member(esk5_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[51]) ).
cnf(53,plain,
( X1 = X2
| member(esk5_2(X1,X2),X2)
| member(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[52]) ).
fof(59,plain,
! [X2] : ~ member(X2,empty_set),
inference(variable_rename,[status(thm)],[12]) ).
cnf(60,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(72,negated_conjecture,
( member(X1,empty_set)
| esk3_0 = empty_set
| ~ member(X1,esk3_0) ),
inference(spm,[status(thm)],[30,37,theory(equality)]) ).
cnf(75,negated_conjecture,
( esk3_0 = empty_set
| ~ member(X1,esk3_0) ),
inference(sr,[status(thm)],[72,60,theory(equality)]) ).
cnf(78,negated_conjecture,
( member(X1,empty_set)
| esk2_0 = empty_set
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[31,38,theory(equality)]) ).
cnf(81,negated_conjecture,
( esk2_0 = empty_set
| ~ member(X1,esk2_0) ),
inference(sr,[status(thm)],[78,60,theory(equality)]) ).
cnf(83,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[60,46,theory(equality)]) ).
cnf(100,plain,
( empty_set = X1
| member(esk5_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[60,53,theory(equality)]) ).
cnf(109,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(spm,[status(thm)],[24,83,theory(equality)]) ).
cnf(118,negated_conjecture,
( esk3_0 = empty_set
| subset(esk3_0,X1) ),
inference(spm,[status(thm)],[75,46,theory(equality)]) ).
cnf(128,negated_conjecture,
( esk2_0 = empty_set
| subset(esk2_0,X1) ),
inference(spm,[status(thm)],[81,46,theory(equality)]) ).
cnf(142,negated_conjecture,
esk3_0 = empty_set,
inference(spm,[status(thm)],[109,118,theory(equality)]) ).
cnf(143,negated_conjecture,
esk2_0 = empty_set,
inference(spm,[status(thm)],[109,128,theory(equality)]) ).
cnf(161,negated_conjecture,
( union(empty_set,esk2_0) != empty_set
| esk2_0 != empty_set
| esk3_0 != empty_set ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[39,142,theory(equality)]),14,theory(equality)]) ).
cnf(162,negated_conjecture,
( union(empty_set,esk2_0) != empty_set
| esk2_0 != empty_set
| $false ),
inference(rw,[status(thm)],[161,142,theory(equality)]) ).
cnf(163,negated_conjecture,
( union(empty_set,esk2_0) != empty_set
| esk2_0 != empty_set ),
inference(cn,[status(thm)],[162,theory(equality)]) ).
cnf(178,negated_conjecture,
( union(empty_set,empty_set) != empty_set
| esk2_0 != empty_set ),
inference(rw,[status(thm)],[163,143,theory(equality)]) ).
cnf(179,negated_conjecture,
( union(empty_set,empty_set) != empty_set
| $false ),
inference(rw,[status(thm)],[178,143,theory(equality)]) ).
cnf(180,negated_conjecture,
union(empty_set,empty_set) != empty_set,
inference(cn,[status(thm)],[179,theory(equality)]) ).
cnf(187,plain,
( member(esk5_2(empty_set,union(X1,X2)),X2)
| member(esk5_2(empty_set,union(X1,X2)),X1)
| empty_set = union(X1,X2) ),
inference(spm,[status(thm)],[32,100,theory(equality)]) ).
cnf(231,plain,
( union(X3,X3) = empty_set
| member(esk5_2(empty_set,union(X3,X3)),X3) ),
inference(ef,[status(thm)],[187,theory(equality)]) ).
cnf(243,plain,
union(empty_set,empty_set) = empty_set,
inference(spm,[status(thm)],[60,231,theory(equality)]) ).
cnf(246,plain,
$false,
inference(sr,[status(thm)],[243,180,theory(equality)]) ).
cnf(247,plain,
$false,
246,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET600+3.p
% --creating new selector for []
% -running prover on /tmp/tmpuQ0N-6/sel_SET600+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET600+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET600+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET600+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
%
%------------------------------------------------------------------------------