TSTP Solution File: SWC200+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC200+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 10:48:21 EST 2010
% Result : Theorem 0.28s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 9 unt; 0 def)
% Number of atoms : 280 ( 59 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 368 ( 141 ~; 137 |; 67 &)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 91 ( 0 sgn 50 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
file('/tmp/tmpG5vtci/sel_SWC200+1.p_1',ax4) ).
fof(16,axiom,
ssList(nil),
file('/tmp/tmpG5vtci/sel_SWC200+1.p_1',ax17) ).
fof(18,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( X1 = X2
| memberP(X3,X1) ) ) ) ) ),
file('/tmp/tmpG5vtci/sel_SWC200+1.p_1',ax37) ).
fof(19,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/tmp/tmpG5vtci/sel_SWC200+1.p_1',ax38) ).
fof(23,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ singletonP(X3)
| ? [X5] :
( ssItem(X5)
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X1,X6)
| X5 = X6 ) ) ) ) ) ) ) ),
file('/tmp/tmpG5vtci/sel_SWC200+1.p_1',co1) ).
fof(24,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ singletonP(X3)
| ? [X5] :
( ssItem(X5)
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X1,X6)
| X5 = X6 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[23]) ).
fof(25,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[19,theory(equality)]) ).
fof(27,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ singletonP(X3)
| ? [X5] :
( ssItem(X5)
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X1,X6)
| X5 = X6 ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[24,theory(equality)]) ).
fof(86,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ singletonP(X1)
| ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) )
& ( ! [X2] :
( ~ ssItem(X2)
| cons(X2,nil) != X1 )
| singletonP(X1) ) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(87,plain,
! [X3] :
( ~ ssList(X3)
| ( ( ~ singletonP(X3)
| ? [X4] :
( ssItem(X4)
& cons(X4,nil) = X3 ) )
& ( ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X3 )
| singletonP(X3) ) ) ),
inference(variable_rename,[status(thm)],[86]) ).
fof(88,plain,
! [X3] :
( ~ ssList(X3)
| ( ( ~ singletonP(X3)
| ( ssItem(esk7_1(X3))
& cons(esk7_1(X3),nil) = X3 ) )
& ( ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X3 )
| singletonP(X3) ) ) ),
inference(skolemize,[status(esa)],[87]) ).
fof(89,plain,
! [X3,X5] :
( ( ( ~ ssItem(X5)
| cons(X5,nil) != X3
| singletonP(X3) )
& ( ~ singletonP(X3)
| ( ssItem(esk7_1(X3))
& cons(esk7_1(X3),nil) = X3 ) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[88]) ).
fof(90,plain,
! [X3,X5] :
( ( ~ ssItem(X5)
| cons(X5,nil) != X3
| singletonP(X3)
| ~ ssList(X3) )
& ( ssItem(esk7_1(X3))
| ~ singletonP(X3)
| ~ ssList(X3) )
& ( cons(esk7_1(X3),nil) = X3
| ~ singletonP(X3)
| ~ ssList(X3) ) ),
inference(distribute,[status(thm)],[89]) ).
cnf(91,plain,
( cons(esk7_1(X1),nil) = X1
| ~ ssList(X1)
| ~ singletonP(X1) ),
inference(split_conjunct,[status(thm)],[90]) ).
cnf(92,plain,
( ssItem(esk7_1(X1))
| ~ ssList(X1)
| ~ singletonP(X1) ),
inference(split_conjunct,[status(thm)],[90]) ).
cnf(102,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[16]) ).
fof(110,plain,
! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssItem(X2)
| ! [X3] :
( ~ ssList(X3)
| ( ( ~ memberP(cons(X2,X3),X1)
| X1 = X2
| memberP(X3,X1) )
& ( ( X1 != X2
& ~ memberP(X3,X1) )
| memberP(cons(X2,X3),X1) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(111,plain,
! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ memberP(cons(X5,X6),X4)
| X4 = X5
| memberP(X6,X4) )
& ( ( X4 != X5
& ~ memberP(X6,X4) )
| memberP(cons(X5,X6),X4) ) ) ) ) ),
inference(variable_rename,[status(thm)],[110]) ).
fof(112,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ( ( ~ memberP(cons(X5,X6),X4)
| X4 = X5
| memberP(X6,X4) )
& ( ( X4 != X5
& ~ memberP(X6,X4) )
| memberP(cons(X5,X6),X4) ) )
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(shift_quantors,[status(thm)],[111]) ).
fof(113,plain,
! [X4,X5,X6] :
( ( ~ memberP(cons(X5,X6),X4)
| X4 = X5
| memberP(X6,X4)
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) )
& ( X4 != X5
| memberP(cons(X5,X6),X4)
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) )
& ( ~ memberP(X6,X4)
| memberP(cons(X5,X6),X4)
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ) ),
inference(distribute,[status(thm)],[112]) ).
cnf(116,plain,
( memberP(X3,X1)
| X1 = X2
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ memberP(cons(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[113]) ).
fof(117,plain,
! [X1] :
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(118,plain,
! [X2] :
( ~ ssItem(X2)
| ~ memberP(nil,X2) ),
inference(variable_rename,[status(thm)],[117]) ).
cnf(119,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[118]) ).
fof(131,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& singletonP(X3)
& ! [X5] :
( ~ ssItem(X5)
| ? [X6] :
( ssItem(X6)
& memberP(X1,X6)
& X5 != X6 ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(132,negated_conjecture,
? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& X8 = X10
& X7 = X9
& singletonP(X9)
& ! [X11] :
( ~ ssItem(X11)
| ? [X12] :
( ssItem(X12)
& memberP(X7,X12)
& X11 != X12 ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[131]) ).
fof(133,negated_conjecture,
( ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& ssList(esk11_0)
& esk9_0 = esk11_0
& esk8_0 = esk10_0
& singletonP(esk10_0)
& ! [X11] :
( ~ ssItem(X11)
| ( ssItem(esk12_1(X11))
& memberP(esk8_0,esk12_1(X11))
& X11 != esk12_1(X11) ) ) ),
inference(skolemize,[status(esa)],[132]) ).
fof(134,negated_conjecture,
! [X11] :
( ( ~ ssItem(X11)
| ( ssItem(esk12_1(X11))
& memberP(esk8_0,esk12_1(X11))
& X11 != esk12_1(X11) ) )
& esk9_0 = esk11_0
& esk8_0 = esk10_0
& singletonP(esk10_0)
& ssList(esk11_0)
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0) ),
inference(shift_quantors,[status(thm)],[133]) ).
fof(135,negated_conjecture,
! [X11] :
( ( ssItem(esk12_1(X11))
| ~ ssItem(X11) )
& ( memberP(esk8_0,esk12_1(X11))
| ~ ssItem(X11) )
& ( X11 != esk12_1(X11)
| ~ ssItem(X11) )
& esk9_0 = esk11_0
& esk8_0 = esk10_0
& singletonP(esk10_0)
& ssList(esk11_0)
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0) ),
inference(distribute,[status(thm)],[134]) ).
cnf(136,negated_conjecture,
ssList(esk8_0),
inference(split_conjunct,[status(thm)],[135]) ).
cnf(140,negated_conjecture,
singletonP(esk10_0),
inference(split_conjunct,[status(thm)],[135]) ).
cnf(141,negated_conjecture,
esk8_0 = esk10_0,
inference(split_conjunct,[status(thm)],[135]) ).
cnf(143,negated_conjecture,
( ~ ssItem(X1)
| X1 != esk12_1(X1) ),
inference(split_conjunct,[status(thm)],[135]) ).
cnf(144,negated_conjecture,
( memberP(esk8_0,esk12_1(X1))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[135]) ).
cnf(145,negated_conjecture,
( ssItem(esk12_1(X1))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[135]) ).
cnf(146,negated_conjecture,
singletonP(esk8_0),
inference(rw,[status(thm)],[140,141,theory(equality)]) ).
cnf(200,plain,
( X1 = esk7_1(X2)
| memberP(nil,X1)
| ~ memberP(X2,X1)
| ~ ssItem(esk7_1(X2))
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ singletonP(X2)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[116,91,theory(equality)]) ).
cnf(202,plain,
( X1 = esk7_1(X2)
| memberP(nil,X1)
| ~ memberP(X2,X1)
| ~ ssItem(esk7_1(X2))
| ~ ssItem(X1)
| $false
| ~ singletonP(X2)
| ~ ssList(X2) ),
inference(rw,[status(thm)],[200,102,theory(equality)]) ).
cnf(203,plain,
( X1 = esk7_1(X2)
| memberP(nil,X1)
| ~ memberP(X2,X1)
| ~ ssItem(esk7_1(X2))
| ~ ssItem(X1)
| ~ singletonP(X2)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[202,theory(equality)]) ).
cnf(663,plain,
( X1 = esk7_1(X2)
| memberP(nil,X1)
| ~ singletonP(X2)
| ~ memberP(X2,X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[203,92]) ).
cnf(664,plain,
( X1 = esk7_1(X2)
| ~ singletonP(X2)
| ~ memberP(X2,X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[663,119]) ).
cnf(665,negated_conjecture,
( esk12_1(X1) = esk7_1(esk8_0)
| ~ singletonP(esk8_0)
| ~ ssItem(esk12_1(X1))
| ~ ssList(esk8_0)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[664,144,theory(equality)]) ).
cnf(670,negated_conjecture,
( esk12_1(X1) = esk7_1(esk8_0)
| $false
| ~ ssItem(esk12_1(X1))
| ~ ssList(esk8_0)
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[665,146,theory(equality)]) ).
cnf(671,negated_conjecture,
( esk12_1(X1) = esk7_1(esk8_0)
| $false
| ~ ssItem(esk12_1(X1))
| $false
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[670,136,theory(equality)]) ).
cnf(672,negated_conjecture,
( esk12_1(X1) = esk7_1(esk8_0)
| ~ ssItem(esk12_1(X1))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[671,theory(equality)]) ).
cnf(673,negated_conjecture,
( esk12_1(X1) = esk7_1(esk8_0)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[672,145]) ).
cnf(677,negated_conjecture,
( esk7_1(esk8_0) != X1
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[143,673,theory(equality)]) ).
cnf(716,negated_conjecture,
~ ssItem(esk7_1(esk8_0)),
inference(er,[status(thm)],[677,theory(equality)]) ).
cnf(718,negated_conjecture,
( ~ singletonP(esk8_0)
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[716,92,theory(equality)]) ).
cnf(721,negated_conjecture,
( $false
| ~ ssList(esk8_0) ),
inference(rw,[status(thm)],[718,146,theory(equality)]) ).
cnf(722,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[721,136,theory(equality)]) ).
cnf(723,negated_conjecture,
$false,
inference(cn,[status(thm)],[722,theory(equality)]) ).
cnf(724,negated_conjecture,
$false,
723,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC200+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpG5vtci/sel_SWC200+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC200+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC200+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC200+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
%
%------------------------------------------------------------------------------