%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET885+1 : TPTP v5.0.0. Released v3.2.0.
% 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 03:43:29 EST 2010
% Result : Theorem 0.21s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 11 unt; 0 def)
% Number of atoms : 213 ( 115 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 268 ( 98 ~; 109 |; 53 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 108 ( 4 sgn 70 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpA2VQAp/sel_SET885+1.p_1',commutativity_k2_tarski) ).
fof(3,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpA2VQAp/sel_SET885+1.p_1',d1_tarski) ).
fof(4,conjecture,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),singleton(X3))
=> X1 = X3 ),
file('/tmp/tmpA2VQAp/sel_SET885+1.p_1',t26_zfmisc_1) ).
fof(7,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpA2VQAp/sel_SET885+1.p_1',d3_tarski) ).
fof(8,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/tmp/tmpA2VQAp/sel_SET885+1.p_1',d2_tarski) ).
fof(10,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),singleton(X3))
=> X1 = X3 ),
inference(assume_negation,[status(cth)],[4]) ).
fof(16,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[2]) ).
cnf(17,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[16]) ).
fof(18,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)],[3]) ).
fof(19,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)],[18]) ).
fof(20,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) != X4 )
& ( in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[19]) ).
fof(21,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) != X4 )
& ( in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[20]) ).
fof(22,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[21]) ).
cnf(26,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(27,negated_conjecture,
? [X1,X2,X3] :
( subset(unordered_pair(X1,X2),singleton(X3))
& X1 != X3 ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(28,negated_conjecture,
? [X4,X5,X6] :
( subset(unordered_pair(X4,X5),singleton(X6))
& X4 != X6 ),
inference(variable_rename,[status(thm)],[27]) ).
fof(29,negated_conjecture,
( subset(unordered_pair(esk3_0,esk4_0),singleton(esk5_0))
& esk3_0 != esk5_0 ),
inference(skolemize,[status(esa)],[28]) ).
cnf(30,negated_conjecture,
esk3_0 != esk5_0,
inference(split_conjunct,[status(thm)],[29]) ).
cnf(31,negated_conjecture,
subset(unordered_pair(esk3_0,esk4_0),singleton(esk5_0)),
inference(split_conjunct,[status(thm)],[29]) ).
fof(38,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ in(X3,X1)
| in(X3,X2) ) )
& ( ? [X3] :
( in(X3,X1)
& ~ in(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(39,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ? [X7] :
( in(X7,X4)
& ~ in(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[38]) ).
fof(40,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk7_2(X4,X5),X4)
& ~ in(esk7_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[39]) ).
fof(41,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk7_2(X4,X5),X4)
& ~ in(esk7_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[40]) ).
fof(42,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk7_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk7_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[41]) ).
cnf(45,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[42]) ).
fof(46,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)],[8]) ).
fof(47,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)],[46]) ).
fof(48,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)],[47]) ).
fof(49,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)],[48]) ).
fof(50,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)],[49]) ).
cnf(54,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[50]) ).
cnf(64,plain,
( in(X1,X2)
| unordered_pair(X3,X1) != X2 ),
inference(er,[status(thm)],[54,theory(equality)]) ).
cnf(67,negated_conjecture,
( in(X1,singleton(esk5_0))
| ~ in(X1,unordered_pair(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[45,31,theory(equality)]) ).
cnf(90,negated_conjecture,
( X1 = X2
| singleton(X1) != singleton(esk5_0)
| ~ in(X2,unordered_pair(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[26,67,theory(equality)]) ).
cnf(95,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[64,theory(equality)]) ).
cnf(98,plain,
in(X1,unordered_pair(X1,X2)),
inference(spm,[status(thm)],[95,17,theory(equality)]) ).
cnf(163,negated_conjecture,
( X1 = esk4_0
| singleton(X1) != singleton(esk5_0) ),
inference(spm,[status(thm)],[90,95,theory(equality)]) ).
cnf(168,negated_conjecture,
esk5_0 = esk4_0,
inference(er,[status(thm)],[163,theory(equality)]) ).
cnf(175,negated_conjecture,
( X1 = X2
| singleton(X1) != singleton(esk5_0)
| ~ in(X2,unordered_pair(esk3_0,esk5_0)) ),
inference(rw,[status(thm)],[90,168,theory(equality)]) ).
cnf(200,negated_conjecture,
( X1 = esk3_0
| singleton(X1) != singleton(esk5_0) ),
inference(spm,[status(thm)],[175,98,theory(equality)]) ).
cnf(204,negated_conjecture,
esk5_0 = esk3_0,
inference(er,[status(thm)],[200,theory(equality)]) ).
cnf(205,negated_conjecture,
$false,
inference(sr,[status(thm)],[204,30,theory(equality)]) ).
cnf(206,negated_conjecture,
$false,
205,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET885+1.p
% --creating new selector for []
% -running prover on /tmp/tmpA2VQAp/sel_SET885+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET885+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET885+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET885+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
%
%------------------------------------------------------------------------------