TSTP Solution File: SET914+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET914+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 03:46:55 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 67 ( 19 unt; 0 def)
% Number of atoms : 273 ( 114 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 337 ( 131 ~; 135 |; 62 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 147 ( 14 sgn 82 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/tmp/tmpCsqeoV/sel_SET914+1.p_1',commutativity_k3_xboole_0) ).
fof(5,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/tmp/tmpCsqeoV/sel_SET914+1.p_1',d7_xboole_0) ).
fof(6,conjecture,
! [X1,X2,X3] :
~ ( disjoint(unordered_pair(X1,X2),X3)
& in(X1,X3) ),
file('/tmp/tmpCsqeoV/sel_SET914+1.p_1',t55_zfmisc_1) ).
fof(7,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpCsqeoV/sel_SET914+1.p_1',commutativity_k2_tarski) ).
fof(9,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/tmp/tmpCsqeoV/sel_SET914+1.p_1',d3_xboole_0) ).
fof(11,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/tmp/tmpCsqeoV/sel_SET914+1.p_1',d1_xboole_0) ).
fof(12,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/tmp/tmpCsqeoV/sel_SET914+1.p_1',d2_tarski) ).
fof(14,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( disjoint(unordered_pair(X1,X2),X3)
& in(X1,X3) ),
inference(assume_negation,[status(cth)],[6]) ).
fof(17,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).
fof(18,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(19,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[18]) ).
fof(28,plain,
! [X1,X2] :
( ( ~ disjoint(X1,X2)
| set_intersection2(X1,X2) = empty_set )
& ( set_intersection2(X1,X2) != empty_set
| disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(29,plain,
! [X3,X4] :
( ( ~ disjoint(X3,X4)
| set_intersection2(X3,X4) = empty_set )
& ( set_intersection2(X3,X4) != empty_set
| disjoint(X3,X4) ) ),
inference(variable_rename,[status(thm)],[28]) ).
cnf(31,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[29]) ).
fof(32,negated_conjecture,
? [X1,X2,X3] :
( disjoint(unordered_pair(X1,X2),X3)
& in(X1,X3) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(33,negated_conjecture,
? [X4,X5,X6] :
( disjoint(unordered_pair(X4,X5),X6)
& in(X4,X6) ),
inference(variable_rename,[status(thm)],[32]) ).
fof(34,negated_conjecture,
( disjoint(unordered_pair(esk2_0,esk3_0),esk4_0)
& in(esk2_0,esk4_0) ),
inference(skolemize,[status(esa)],[33]) ).
cnf(35,negated_conjecture,
in(esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(36,negated_conjecture,
disjoint(unordered_pair(esk2_0,esk3_0),esk4_0),
inference(split_conjunct,[status(thm)],[34]) ).
fof(37,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[7]) ).
cnf(38,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[37]) ).
fof(42,plain,
! [X1,X2,X3] :
( ( X3 != set_intersection2(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| ( in(X4,X1)
& in(X4,X2) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X2)
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ~ in(X4,X1)
| ~ in(X4,X2) )
& ( in(X4,X3)
| ( in(X4,X1)
& in(X4,X2) ) ) )
| X3 = set_intersection2(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(43,plain,
! [X5,X6,X7] :
( ( X7 != set_intersection2(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,X5)
& in(X8,X6) ) )
& ( ~ in(X8,X5)
| ~ in(X8,X6)
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ~ in(X9,X5)
| ~ in(X9,X6) )
& ( in(X9,X7)
| ( in(X9,X5)
& in(X9,X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(variable_rename,[status(thm)],[42]) ).
fof(44,plain,
! [X5,X6,X7] :
( ( X7 != set_intersection2(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,X5)
& in(X8,X6) ) )
& ( ~ in(X8,X5)
| ~ in(X8,X6)
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk6_3(X5,X6,X7),X7)
| ~ in(esk6_3(X5,X6,X7),X5)
| ~ in(esk6_3(X5,X6,X7),X6) )
& ( in(esk6_3(X5,X6,X7),X7)
| ( in(esk6_3(X5,X6,X7),X5)
& in(esk6_3(X5,X6,X7),X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(skolemize,[status(esa)],[43]) ).
fof(45,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ in(X8,X7)
| ( in(X8,X5)
& in(X8,X6) ) )
& ( ~ in(X8,X5)
| ~ in(X8,X6)
| in(X8,X7) ) )
| X7 != set_intersection2(X5,X6) )
& ( ( ( ~ in(esk6_3(X5,X6,X7),X7)
| ~ in(esk6_3(X5,X6,X7),X5)
| ~ in(esk6_3(X5,X6,X7),X6) )
& ( in(esk6_3(X5,X6,X7),X7)
| ( in(esk6_3(X5,X6,X7),X5)
& in(esk6_3(X5,X6,X7),X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[44]) ).
fof(46,plain,
! [X5,X6,X7,X8] :
( ( in(X8,X5)
| ~ in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( in(X8,X6)
| ~ in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( ~ in(X8,X5)
| ~ in(X8,X6)
| in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( ~ in(esk6_3(X5,X6,X7),X7)
| ~ in(esk6_3(X5,X6,X7),X5)
| ~ in(esk6_3(X5,X6,X7),X6)
| X7 = set_intersection2(X5,X6) )
& ( in(esk6_3(X5,X6,X7),X5)
| in(esk6_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) )
& ( in(esk6_3(X5,X6,X7),X6)
| in(esk6_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) ) ),
inference(distribute,[status(thm)],[45]) ).
cnf(47,plain,
( X1 = set_intersection2(X2,X3)
| in(esk6_3(X2,X3,X1),X1)
| in(esk6_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[46]) ).
cnf(50,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[46]) ).
cnf(51,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[46]) ).
fof(56,plain,
! [X1] :
( ( X1 != empty_set
| ! [X2] : ~ in(X2,X1) )
& ( ? [X2] : in(X2,X1)
| X1 = empty_set ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(57,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( ? [X5] : in(X5,X3)
| X3 = empty_set ) ),
inference(variable_rename,[status(thm)],[56]) ).
fof(58,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( in(esk7_1(X3),X3)
| X3 = empty_set ) ),
inference(skolemize,[status(esa)],[57]) ).
fof(59,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| X3 != empty_set )
& ( in(esk7_1(X3),X3)
| X3 = empty_set ) ),
inference(shift_quantors,[status(thm)],[58]) ).
cnf(61,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[59]) ).
fof(62,plain,
! [X1,X2,X3] :
( ( X3 != unordered_pair(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| X4 = X1
| X4 = X2 )
& ( ( X4 != X1
& X4 != X2 )
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ( X4 != X1
& X4 != X2 ) )
& ( in(X4,X3)
| X4 = X1
| X4 = X2 ) )
| X3 = unordered_pair(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(63,plain,
! [X5,X6,X7] :
( ( X7 != unordered_pair(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ( X9 != X5
& X9 != X6 ) )
& ( in(X9,X7)
| X9 = X5
| X9 = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(variable_rename,[status(thm)],[62]) ).
fof(64,plain,
! [X5,X6,X7] :
( ( X7 != unordered_pair(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
| ( esk8_3(X5,X6,X7) != X5
& esk8_3(X5,X6,X7) != X6 ) )
& ( in(esk8_3(X5,X6,X7),X7)
| esk8_3(X5,X6,X7) = X5
| esk8_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(skolemize,[status(esa)],[63]) ).
fof(65,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) )
| X7 != unordered_pair(X5,X6) )
& ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
| ( esk8_3(X5,X6,X7) != X5
& esk8_3(X5,X6,X7) != X6 ) )
& ( in(esk8_3(X5,X6,X7),X7)
| esk8_3(X5,X6,X7) = X5
| esk8_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[64]) ).
fof(66,plain,
! [X5,X6,X7,X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6
| X7 != unordered_pair(X5,X6) )
& ( X8 != X5
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( X8 != X6
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( esk8_3(X5,X6,X7) != X5
| ~ in(esk8_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( esk8_3(X5,X6,X7) != X6
| ~ in(esk8_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( in(esk8_3(X5,X6,X7),X7)
| esk8_3(X5,X6,X7) = X5
| esk8_3(X5,X6,X7) = X6
| X7 = unordered_pair(X5,X6) ) ),
inference(distribute,[status(thm)],[65]) ).
cnf(70,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[66]) ).
cnf(83,negated_conjecture,
set_intersection2(unordered_pair(esk2_0,esk3_0),esk4_0) = empty_set,
inference(spm,[status(thm)],[31,36,theory(equality)]) ).
cnf(84,negated_conjecture,
set_intersection2(esk4_0,unordered_pair(esk2_0,esk3_0)) = empty_set,
inference(rw,[status(thm)],[83,19,theory(equality)]) ).
cnf(87,plain,
( in(X1,X2)
| unordered_pair(X3,X1) != X2 ),
inference(er,[status(thm)],[70,theory(equality)]) ).
cnf(89,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[51,theory(equality)]) ).
cnf(102,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[50,theory(equality)]) ).
cnf(109,plain,
( set_intersection2(X2,X3) = X1
| in(esk6_3(X2,X3,X1),X3)
| empty_set != X1 ),
inference(spm,[status(thm)],[61,47,theory(equality)]) ).
cnf(130,plain,
( set_intersection2(X2,X1) = X3
| empty_set != X1
| empty_set != X3 ),
inference(spm,[status(thm)],[61,109,theory(equality)]) ).
cnf(140,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[87,theory(equality)]) ).
cnf(143,plain,
( set_intersection2(X1,X2) = empty_set
| empty_set != X2 ),
inference(er,[status(thm)],[130,theory(equality)]) ).
cnf(156,plain,
in(X1,unordered_pair(X1,X2)),
inference(spm,[status(thm)],[140,38,theory(equality)]) ).
cnf(188,plain,
( in(X1,X2)
| ~ in(X1,empty_set)
| empty_set != X2 ),
inference(spm,[status(thm)],[89,143,theory(equality)]) ).
cnf(197,plain,
( empty_set != X2
| ~ in(X1,empty_set) ),
inference(csr,[status(thm)],[188,61]) ).
fof(198,plain,
( ~ epred1_0
<=> ! [X2] : empty_set != X2 ),
introduced(definition),
[split] ).
cnf(199,plain,
( epred1_0
| empty_set != X2 ),
inference(split_equiv,[status(thm)],[198]) ).
fof(200,plain,
( ~ epred2_0
<=> ! [X1] : ~ in(X1,empty_set) ),
introduced(definition),
[split] ).
cnf(201,plain,
( epred2_0
| ~ in(X1,empty_set) ),
inference(split_equiv,[status(thm)],[200]) ).
cnf(202,plain,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[197,198,theory(equality)]),200,theory(equality)]),
[split] ).
cnf(203,plain,
epred1_0,
inference(er,[status(thm)],[199,theory(equality)]) ).
cnf(205,plain,
( ~ epred2_0
| $false ),
inference(rw,[status(thm)],[202,203,theory(equality)]) ).
cnf(206,plain,
~ epred2_0,
inference(cn,[status(thm)],[205,theory(equality)]) ).
cnf(207,plain,
~ in(X1,empty_set),
inference(sr,[status(thm)],[201,206,theory(equality)]) ).
cnf(313,negated_conjecture,
( in(X1,empty_set)
| ~ in(X1,unordered_pair(esk2_0,esk3_0))
| ~ in(X1,esk4_0) ),
inference(spm,[status(thm)],[102,84,theory(equality)]) ).
cnf(329,negated_conjecture,
( ~ in(X1,unordered_pair(esk2_0,esk3_0))
| ~ in(X1,esk4_0) ),
inference(sr,[status(thm)],[313,207,theory(equality)]) ).
cnf(333,negated_conjecture,
~ in(esk2_0,esk4_0),
inference(spm,[status(thm)],[329,156,theory(equality)]) ).
cnf(342,negated_conjecture,
$false,
inference(rw,[status(thm)],[333,35,theory(equality)]) ).
cnf(343,negated_conjecture,
$false,
inference(cn,[status(thm)],[342,theory(equality)]) ).
cnf(344,negated_conjecture,
$false,
343,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET914+1.p
% --creating new selector for []
% -running prover on /tmp/tmpCsqeoV/sel_SET914+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET914+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET914+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET914+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
%
%------------------------------------------------------------------------------