TSTP Solution File: SWC198+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC198+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 10:47:40 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 : 47 ( 8 unt; 0 def)
% Number of atoms : 306 ( 100 equ)
% Maximal formula atoms : 34 ( 6 avg)
% Number of connectives : 389 ( 130 ~; 138 |; 97 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 88 ( 1 sgn 47 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(12,axiom,
? [X1] :
( ssItem(X1)
& ? [X2] :
( ssItem(X2)
& X1 != X2 ) ),
file('/tmp/tmpb1vMvR/sel_SWC198+1.p_1',ax2) ).
fof(16,axiom,
ssList(nil),
file('/tmp/tmpb1vMvR/sel_SWC198+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/tmpb1vMvR/sel_SWC198+1.p_1',ax37) ).
fof(19,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/tmp/tmpb1vMvR/sel_SWC198+1.p_1',ax38) ).
fof(24,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X1,X6)
| X5 = X6 ) ) )
| ( ! [X7] :
( ssItem(X7)
=> ( cons(X7,nil) != X3
| ~ memberP(X4,X7)
| ? [X8] :
( ssItem(X8)
& X7 != X8
& memberP(X4,X8)
& leq(X7,X8) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
file('/tmp/tmpb1vMvR/sel_SWC198+1.p_1',co1) ).
fof(25,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X1,X6)
| X5 = X6 ) ) )
| ( ! [X7] :
( ssItem(X7)
=> ( cons(X7,nil) != X3
| ~ memberP(X4,X7)
| ? [X8] :
( ssItem(X8)
& X7 != X8
& memberP(X4,X8)
& leq(X7,X8) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[24]) ).
fof(26,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
| ? [X5] :
( ssItem(X5)
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X1,X6)
| X5 = X6 ) ) )
| ( ! [X7] :
( ssItem(X7)
=> ( cons(X7,nil) != X3
| ~ memberP(X4,X7)
| ? [X8] :
( ssItem(X8)
& X7 != X8
& memberP(X4,X8)
& leq(X7,X8) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[25,theory(equality)]) ).
fof(76,plain,
? [X3] :
( ssItem(X3)
& ? [X4] :
( ssItem(X4)
& X3 != X4 ) ),
inference(variable_rename,[status(thm)],[12]) ).
fof(77,plain,
( ssItem(esk3_0)
& ssItem(esk4_0)
& esk3_0 != esk4_0 ),
inference(skolemize,[status(esa)],[76]) ).
cnf(80,plain,
ssItem(esk3_0),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(98,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[16]) ).
fof(106,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(107,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)],[106]) ).
fof(108,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)],[107]) ).
fof(109,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)],[108]) ).
cnf(112,plain,
( memberP(X3,X1)
| X1 = X2
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ memberP(cons(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[109]) ).
fof(113,plain,
! [X1] :
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(114,plain,
! [X2] :
( ~ ssItem(X2)
| ~ memberP(nil,X2) ),
inference(variable_rename,[status(thm)],[113]) ).
cnf(115,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[114]) ).
fof(133,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ! [X5] :
( ~ ssItem(X5)
| ? [X6] :
( ssItem(X6)
& memberP(X1,X6)
& X5 != X6 ) )
& ( ? [X7] :
( ssItem(X7)
& cons(X7,nil) = X3
& memberP(X4,X7)
& ! [X8] :
( ~ ssItem(X8)
| X7 = X8
| ~ memberP(X4,X8)
| ~ leq(X7,X8) ) )
| ( nil = X4
& nil = X3 ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(134,negated_conjecture,
? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& X10 = X12
& X9 = X11
& ! [X13] :
( ~ ssItem(X13)
| ? [X14] :
( ssItem(X14)
& memberP(X9,X14)
& X13 != X14 ) )
& ( ? [X15] :
( ssItem(X15)
& cons(X15,nil) = X11
& memberP(X12,X15)
& ! [X16] :
( ~ ssItem(X16)
| X15 = X16
| ~ memberP(X12,X16)
| ~ leq(X15,X16) ) )
| ( nil = X12
& nil = X11 ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[133]) ).
fof(135,negated_conjecture,
( ssList(esk7_0)
& ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ! [X13] :
( ~ ssItem(X13)
| ( ssItem(esk11_1(X13))
& memberP(esk7_0,esk11_1(X13))
& X13 != esk11_1(X13) ) )
& ( ( ssItem(esk12_0)
& cons(esk12_0,nil) = esk9_0
& memberP(esk10_0,esk12_0)
& ! [X16] :
( ~ ssItem(X16)
| esk12_0 = X16
| ~ memberP(esk10_0,X16)
| ~ leq(esk12_0,X16) ) )
| ( nil = esk10_0
& nil = esk9_0 ) ) ),
inference(skolemize,[status(esa)],[134]) ).
fof(136,negated_conjecture,
! [X13,X16] :
( ( ( ( ~ ssItem(X16)
| esk12_0 = X16
| ~ memberP(esk10_0,X16)
| ~ leq(esk12_0,X16) )
& cons(esk12_0,nil) = esk9_0
& memberP(esk10_0,esk12_0)
& ssItem(esk12_0) )
| ( nil = esk10_0
& nil = esk9_0 ) )
& ( ~ ssItem(X13)
| ( ssItem(esk11_1(X13))
& memberP(esk7_0,esk11_1(X13))
& X13 != esk11_1(X13) ) )
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(shift_quantors,[status(thm)],[135]) ).
fof(137,negated_conjecture,
! [X13,X16] :
( ( nil = esk10_0
| ~ ssItem(X16)
| esk12_0 = X16
| ~ memberP(esk10_0,X16)
| ~ leq(esk12_0,X16) )
& ( nil = esk9_0
| ~ ssItem(X16)
| esk12_0 = X16
| ~ memberP(esk10_0,X16)
| ~ leq(esk12_0,X16) )
& ( nil = esk10_0
| cons(esk12_0,nil) = esk9_0 )
& ( nil = esk9_0
| cons(esk12_0,nil) = esk9_0 )
& ( nil = esk10_0
| memberP(esk10_0,esk12_0) )
& ( nil = esk9_0
| memberP(esk10_0,esk12_0) )
& ( nil = esk10_0
| ssItem(esk12_0) )
& ( nil = esk9_0
| ssItem(esk12_0) )
& ( ssItem(esk11_1(X13))
| ~ ssItem(X13) )
& ( memberP(esk7_0,esk11_1(X13))
| ~ ssItem(X13) )
& ( X13 != esk11_1(X13)
| ~ ssItem(X13) )
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(distribute,[status(thm)],[136]) ).
cnf(142,negated_conjecture,
esk7_0 = esk9_0,
inference(split_conjunct,[status(thm)],[137]) ).
cnf(144,negated_conjecture,
( ~ ssItem(X1)
| X1 != esk11_1(X1) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(145,negated_conjecture,
( memberP(esk7_0,esk11_1(X1))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(146,negated_conjecture,
( ssItem(esk11_1(X1))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(147,negated_conjecture,
( ssItem(esk12_0)
| nil = esk9_0 ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(151,negated_conjecture,
( cons(esk12_0,nil) = esk9_0
| nil = esk9_0 ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(157,negated_conjecture,
( memberP(esk9_0,esk11_1(X1))
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[145,142,theory(equality)]) ).
cnf(231,negated_conjecture,
( X1 = esk12_0
| memberP(nil,X1)
| esk9_0 = nil
| ~ memberP(esk9_0,X1)
| ~ ssItem(esk12_0)
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[112,151,theory(equality)]) ).
cnf(234,negated_conjecture,
( X1 = esk12_0
| memberP(nil,X1)
| esk9_0 = nil
| ~ memberP(esk9_0,X1)
| ~ ssItem(esk12_0)
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[231,98,theory(equality)]) ).
cnf(235,negated_conjecture,
( X1 = esk12_0
| memberP(nil,X1)
| esk9_0 = nil
| ~ memberP(esk9_0,X1)
| ~ ssItem(esk12_0)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[234,theory(equality)]) ).
cnf(641,negated_conjecture,
( esk9_0 = nil
| X1 = esk12_0
| memberP(nil,X1)
| ~ memberP(esk9_0,X1)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[235,147]) ).
cnf(642,negated_conjecture,
( esk9_0 = nil
| X1 = esk12_0
| ~ memberP(esk9_0,X1)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[641,115]) ).
cnf(643,negated_conjecture,
( esk9_0 = nil
| esk11_1(X1) = esk12_0
| ~ ssItem(esk11_1(X1))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[642,157,theory(equality)]) ).
cnf(663,negated_conjecture,
( esk11_1(X1) = esk12_0
| esk9_0 = nil
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[643,146]) ).
cnf(665,negated_conjecture,
( esk9_0 = nil
| esk12_0 != X1
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[144,663,theory(equality)]) ).
cnf(671,negated_conjecture,
( esk9_0 = nil
| ~ ssItem(esk12_0) ),
inference(er,[status(thm)],[665,theory(equality)]) ).
cnf(672,negated_conjecture,
esk9_0 = nil,
inference(csr,[status(thm)],[671,147]) ).
cnf(717,negated_conjecture,
( memberP(nil,esk11_1(X1))
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[157,672,theory(equality)]) ).
cnf(740,negated_conjecture,
( ~ ssItem(esk11_1(X1))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[115,717,theory(equality)]) ).
cnf(768,negated_conjecture,
~ ssItem(X1),
inference(csr,[status(thm)],[740,146]) ).
cnf(771,plain,
$false,
inference(sr,[status(thm)],[80,768,theory(equality)]) ).
cnf(772,plain,
$false,
771,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC198+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpb1vMvR/sel_SWC198+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC198+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC198+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC198+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
%
%------------------------------------------------------------------------------