TSTP Solution File: SEU153+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU153+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 04:53:53 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 14 unt; 0 def)
% Number of atoms : 225 ( 79 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 282 ( 111 ~; 110 |; 52 &)
% ( 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 : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 103 ( 3 sgn 70 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/tmp/tmpeVvzjF/sel_SEU153+1.p_1',commutativity_k3_xboole_0) ).
fof(7,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/tmp/tmpeVvzjF/sel_SEU153+1.p_1',d7_xboole_0) ).
fof(8,conjecture,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
file('/tmp/tmpeVvzjF/sel_SEU153+1.p_1',l25_zfmisc_1) ).
fof(10,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpeVvzjF/sel_SEU153+1.p_1',d1_tarski) ).
fof(12,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/tmp/tmpeVvzjF/sel_SEU153+1.p_1',d3_xboole_0) ).
fof(14,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/tmp/tmpeVvzjF/sel_SEU153+1.p_1',d1_xboole_0) ).
fof(16,negated_conjecture,
~ ! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
inference(assume_negation,[status(cth)],[8]) ).
fof(19,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[14,theory(equality)]) ).
fof(20,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(21,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[20]) ).
fof(32,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)],[7]) ).
fof(33,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)],[32]) ).
cnf(35,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[33]) ).
fof(36,negated_conjecture,
? [X1,X2] :
( disjoint(singleton(X1),X2)
& in(X1,X2) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(37,negated_conjecture,
? [X3,X4] :
( disjoint(singleton(X3),X4)
& in(X3,X4) ),
inference(variable_rename,[status(thm)],[36]) ).
fof(38,negated_conjecture,
( disjoint(singleton(esk2_0),esk3_0)
& in(esk2_0,esk3_0) ),
inference(skolemize,[status(esa)],[37]) ).
cnf(39,negated_conjecture,
in(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[38]) ).
cnf(40,negated_conjecture,
disjoint(singleton(esk2_0),esk3_0),
inference(split_conjunct,[status(thm)],[38]) ).
fof(42,plain,
! [X1,X2] :
( ( X2 != singleton(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1 )
& ( X3 != X1
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| X3 != X1 )
& ( in(X3,X2)
| X3 = X1 ) )
| X2 = singleton(X1) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(43,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| X7 != X4 )
& ( in(X7,X5)
| X7 = X4 ) )
| X5 = singleton(X4) ) ),
inference(variable_rename,[status(thm)],[42]) ).
fof(44,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) != X4 )
& ( in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[43]) ).
fof(45,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) != X4 )
& ( in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[44]) ).
fof(46,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[45]) ).
cnf(49,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[46]) ).
fof(54,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)],[12]) ).
fof(55,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)],[54]) ).
fof(56,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)],[55]) ).
fof(57,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)],[56]) ).
fof(58,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)],[57]) ).
cnf(62,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[58]) ).
fof(68,plain,
! [X1] :
( ( X1 != empty_set
| ! [X2] : ~ in(X2,X1) )
& ( ? [X2] : in(X2,X1)
| X1 = empty_set ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(69,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( ? [X5] : in(X5,X3)
| X3 = empty_set ) ),
inference(variable_rename,[status(thm)],[68]) ).
fof(70,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( in(esk7_1(X3),X3)
| X3 = empty_set ) ),
inference(skolemize,[status(esa)],[69]) ).
fof(71,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| X3 != empty_set )
& ( in(esk7_1(X3),X3)
| X3 = empty_set ) ),
inference(shift_quantors,[status(thm)],[70]) ).
cnf(73,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[71]) ).
cnf(80,plain,
( in(X1,X2)
| singleton(X1) != X2 ),
inference(er,[status(thm)],[49,theory(equality)]) ).
cnf(87,negated_conjecture,
set_intersection2(singleton(esk2_0),esk3_0) = empty_set,
inference(spm,[status(thm)],[35,40,theory(equality)]) ).
cnf(88,negated_conjecture,
set_intersection2(esk3_0,singleton(esk2_0)) = empty_set,
inference(rw,[status(thm)],[87,21,theory(equality)]) ).
cnf(135,negated_conjecture,
( in(X1,X2)
| empty_set != X2
| ~ in(X1,singleton(esk2_0))
| ~ in(X1,esk3_0) ),
inference(spm,[status(thm)],[62,88,theory(equality)]) ).
cnf(139,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[80,theory(equality)]) ).
cnf(267,negated_conjecture,
( empty_set != X2
| ~ in(X1,singleton(esk2_0))
| ~ in(X1,esk3_0) ),
inference(csr,[status(thm)],[135,73]) ).
fof(268,plain,
( ~ epred3_0
<=> ! [X2] : empty_set != X2 ),
introduced(definition),
[split] ).
cnf(269,plain,
( epred3_0
| empty_set != X2 ),
inference(split_equiv,[status(thm)],[268]) ).
fof(270,plain,
( ~ epred4_0
<=> ! [X1] :
( ~ in(X1,esk3_0)
| ~ in(X1,singleton(esk2_0)) ) ),
introduced(definition),
[split] ).
cnf(271,plain,
( epred4_0
| ~ in(X1,esk3_0)
| ~ in(X1,singleton(esk2_0)) ),
inference(split_equiv,[status(thm)],[270]) ).
cnf(272,negated_conjecture,
( ~ epred4_0
| ~ epred3_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[267,268,theory(equality)]),270,theory(equality)]),
[split] ).
cnf(273,negated_conjecture,
epred3_0,
inference(er,[status(thm)],[269,theory(equality)]) ).
cnf(275,negated_conjecture,
( ~ epred4_0
| $false ),
inference(rw,[status(thm)],[272,273,theory(equality)]) ).
cnf(276,negated_conjecture,
~ epred4_0,
inference(cn,[status(thm)],[275,theory(equality)]) ).
cnf(278,negated_conjecture,
( ~ in(X1,esk3_0)
| ~ in(X1,singleton(esk2_0)) ),
inference(sr,[status(thm)],[271,276,theory(equality)]) ).
cnf(279,negated_conjecture,
~ in(esk2_0,esk3_0),
inference(spm,[status(thm)],[278,139,theory(equality)]) ).
cnf(288,negated_conjecture,
$false,
inference(rw,[status(thm)],[279,39,theory(equality)]) ).
cnf(289,negated_conjecture,
$false,
inference(cn,[status(thm)],[288,theory(equality)]) ).
cnf(290,negated_conjecture,
$false,
289,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU153+1.p
% --creating new selector for []
% -running prover on /tmp/tmpeVvzjF/sel_SEU153+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU153+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU153+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU153+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
%
%------------------------------------------------------------------------------