TSTP Solution File: SWC098+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC098+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 10:17:01 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 3
% Syntax : Number of formulae : 71 ( 14 unt; 0 def)
% Number of atoms : 383 ( 149 equ)
% Maximal formula atoms : 46 ( 5 avg)
% Number of connectives : 491 ( 179 ~; 190 |; 102 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 36 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmp3WYh-X/sel_SWC098+1.p_1',ax21) ).
fof(16,axiom,
ssList(nil),
file('/tmp/tmp3WYh-X/sel_SWC098+1.p_1',ax17) ).
fof(24,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& cons(X5,nil) = X1
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X2,X6)
| ~ leq(X5,X6)
| X5 = X6 ) )
& memberP(X2,X5) )
| ( nil = X2
& nil = X1 )
| ( ! [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/tmp3WYh-X/sel_SWC098+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)
& cons(X5,nil) = X1
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X2,X6)
| ~ leq(X5,X6)
| X5 = X6 ) )
& memberP(X2,X5) )
| ( nil = X2
& nil = X1 )
| ( ! [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(27,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& cons(X5,nil) = X1
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X2,X6)
| ~ leq(X5,X6)
| X5 = X6 ) )
& memberP(X2,X5) )
| ( nil = X2
& nil = X1 )
| ( ! [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(65,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| nil != cons(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(66,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3) ) ),
inference(variable_rename,[status(thm)],[65]) ).
fof(67,plain,
! [X3,X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[66]) ).
cnf(68,plain,
( ~ ssList(X1)
| nil != cons(X2,X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[67]) ).
cnf(98,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[16]) ).
fof(133,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X1
| ? [X6] :
( ssItem(X6)
& memberP(X2,X6)
& leq(X5,X6)
& X5 != X6 )
| ~ memberP(X2,X5) )
& ( nil != X2
| nil != X1 )
& ( ? [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)
| cons(X13,nil) != X9
| ? [X14] :
( ssItem(X14)
& memberP(X10,X14)
& leq(X13,X14)
& X13 != X14 )
| ~ memberP(X10,X13) )
& ( nil != X10
| nil != X9 )
& ( ? [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)
| cons(X13,nil) != esk7_0
| ( ssItem(esk11_1(X13))
& memberP(esk8_0,esk11_1(X13))
& leq(X13,esk11_1(X13))
& X13 != esk11_1(X13) )
| ~ memberP(esk8_0,X13) )
& ( nil != esk8_0
| nil != esk7_0 )
& ( ( 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)
| cons(X13,nil) != esk7_0
| ( ssItem(esk11_1(X13))
& memberP(esk8_0,esk11_1(X13))
& leq(X13,esk11_1(X13))
& X13 != esk11_1(X13) )
| ~ memberP(esk8_0,X13) )
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ( nil != esk8_0
| nil != esk7_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)
| cons(X13,nil) != esk7_0
| ~ memberP(esk8_0,X13) )
& ( memberP(esk8_0,esk11_1(X13))
| ~ ssItem(X13)
| cons(X13,nil) != esk7_0
| ~ memberP(esk8_0,X13) )
& ( leq(X13,esk11_1(X13))
| ~ ssItem(X13)
| cons(X13,nil) != esk7_0
| ~ memberP(esk8_0,X13) )
& ( X13 != esk11_1(X13)
| ~ ssItem(X13)
| cons(X13,nil) != esk7_0
| ~ memberP(esk8_0,X13) )
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ( nil != esk8_0
| nil != esk7_0 )
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(distribute,[status(thm)],[136]) ).
cnf(142,negated_conjecture,
( nil != esk7_0
| nil != esk8_0 ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(143,negated_conjecture,
esk7_0 = esk9_0,
inference(split_conjunct,[status(thm)],[137]) ).
cnf(144,negated_conjecture,
esk8_0 = esk10_0,
inference(split_conjunct,[status(thm)],[137]) ).
cnf(145,negated_conjecture,
( ~ memberP(esk8_0,X1)
| cons(X1,nil) != esk7_0
| ~ ssItem(X1)
| X1 != esk11_1(X1) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(146,negated_conjecture,
( leq(X1,esk11_1(X1))
| ~ memberP(esk8_0,X1)
| cons(X1,nil) != esk7_0
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(147,negated_conjecture,
( memberP(esk8_0,esk11_1(X1))
| ~ memberP(esk8_0,X1)
| cons(X1,nil) != esk7_0
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(148,negated_conjecture,
( ssItem(esk11_1(X1))
| ~ memberP(esk8_0,X1)
| cons(X1,nil) != esk7_0
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(149,negated_conjecture,
( ssItem(esk12_0)
| nil = esk9_0 ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(150,negated_conjecture,
( ssItem(esk12_0)
| nil = esk10_0 ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(151,negated_conjecture,
( memberP(esk10_0,esk12_0)
| nil = esk9_0 ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(153,negated_conjecture,
( cons(esk12_0,nil) = esk9_0
| nil = esk9_0 ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(154,negated_conjecture,
( cons(esk12_0,nil) = esk9_0
| nil = esk10_0 ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(155,negated_conjecture,
( esk12_0 = X1
| nil = esk9_0
| ~ leq(esk12_0,X1)
| ~ memberP(esk10_0,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(159,negated_conjecture,
( esk9_0 != nil
| esk8_0 != nil ),
inference(rw,[status(thm)],[142,143,theory(equality)]) ).
cnf(160,negated_conjecture,
( esk9_0 != nil
| esk10_0 != nil ),
inference(rw,[status(thm)],[159,144,theory(equality)]) ).
cnf(174,negated_conjecture,
( esk10_0 = nil
| esk9_0 != nil
| ~ ssItem(esk12_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[68,154,theory(equality)]) ).
cnf(177,negated_conjecture,
( esk10_0 = nil
| esk9_0 != nil
| ~ ssItem(esk12_0)
| $false ),
inference(rw,[status(thm)],[174,98,theory(equality)]) ).
cnf(178,negated_conjecture,
( esk10_0 = nil
| esk9_0 != nil
| ~ ssItem(esk12_0) ),
inference(cn,[status(thm)],[177,theory(equality)]) ).
cnf(192,negated_conjecture,
( ssItem(esk11_1(X1))
| cons(X1,nil) != esk9_0
| ~ ssItem(X1)
| ~ memberP(esk8_0,X1) ),
inference(rw,[status(thm)],[148,143,theory(equality)]) ).
cnf(193,negated_conjecture,
( ssItem(esk11_1(X1))
| cons(X1,nil) != esk9_0
| ~ ssItem(X1)
| ~ memberP(esk10_0,X1) ),
inference(rw,[status(thm)],[192,144,theory(equality)]) ).
cnf(206,negated_conjecture,
( esk11_1(X1) != X1
| cons(X1,nil) != esk9_0
| ~ ssItem(X1)
| ~ memberP(esk8_0,X1) ),
inference(rw,[status(thm)],[145,143,theory(equality)]) ).
cnf(207,negated_conjecture,
( esk11_1(X1) != X1
| cons(X1,nil) != esk9_0
| ~ ssItem(X1)
| ~ memberP(esk10_0,X1) ),
inference(rw,[status(thm)],[206,144,theory(equality)]) ).
cnf(210,negated_conjecture,
( memberP(esk10_0,esk11_1(X1))
| cons(X1,nil) != esk7_0
| ~ ssItem(X1)
| ~ memberP(esk8_0,X1) ),
inference(rw,[status(thm)],[147,144,theory(equality)]) ).
cnf(211,negated_conjecture,
( memberP(esk10_0,esk11_1(X1))
| cons(X1,nil) != esk9_0
| ~ ssItem(X1)
| ~ memberP(esk8_0,X1) ),
inference(rw,[status(thm)],[210,143,theory(equality)]) ).
cnf(212,negated_conjecture,
( memberP(esk10_0,esk11_1(X1))
| cons(X1,nil) != esk9_0
| ~ ssItem(X1)
| ~ memberP(esk10_0,X1) ),
inference(rw,[status(thm)],[211,144,theory(equality)]) ).
cnf(215,negated_conjecture,
( leq(X1,esk11_1(X1))
| cons(X1,nil) != esk9_0
| ~ ssItem(X1)
| ~ memberP(esk8_0,X1) ),
inference(rw,[status(thm)],[146,143,theory(equality)]) ).
cnf(216,negated_conjecture,
( leq(X1,esk11_1(X1))
| cons(X1,nil) != esk9_0
| ~ ssItem(X1)
| ~ memberP(esk10_0,X1) ),
inference(rw,[status(thm)],[215,144,theory(equality)]) ).
cnf(361,negated_conjecture,
( esk10_0 = nil
| esk9_0 != nil ),
inference(csr,[status(thm)],[178,150]) ).
cnf(362,negated_conjecture,
esk9_0 != nil,
inference(csr,[status(thm)],[361,160]) ).
cnf(363,negated_conjecture,
ssItem(esk12_0),
inference(sr,[status(thm)],[149,362,theory(equality)]) ).
cnf(364,negated_conjecture,
memberP(esk10_0,esk12_0),
inference(sr,[status(thm)],[151,362,theory(equality)]) ).
cnf(365,negated_conjecture,
cons(esk12_0,nil) = esk9_0,
inference(sr,[status(thm)],[153,362,theory(equality)]) ).
cnf(397,negated_conjecture,
( ssItem(esk11_1(esk12_0))
| ~ memberP(esk10_0,esk12_0)
| ~ ssItem(esk12_0) ),
inference(spm,[status(thm)],[193,365,theory(equality)]) ).
cnf(398,negated_conjecture,
( memberP(esk10_0,esk11_1(esk12_0))
| ~ memberP(esk10_0,esk12_0)
| ~ ssItem(esk12_0) ),
inference(spm,[status(thm)],[212,365,theory(equality)]) ).
cnf(399,negated_conjecture,
( leq(esk12_0,esk11_1(esk12_0))
| ~ memberP(esk10_0,esk12_0)
| ~ ssItem(esk12_0) ),
inference(spm,[status(thm)],[216,365,theory(equality)]) ).
cnf(419,negated_conjecture,
( ssItem(esk11_1(esk12_0))
| $false
| ~ ssItem(esk12_0) ),
inference(rw,[status(thm)],[397,364,theory(equality)]) ).
cnf(420,negated_conjecture,
( ssItem(esk11_1(esk12_0))
| $false
| $false ),
inference(rw,[status(thm)],[419,363,theory(equality)]) ).
cnf(421,negated_conjecture,
ssItem(esk11_1(esk12_0)),
inference(cn,[status(thm)],[420,theory(equality)]) ).
cnf(422,negated_conjecture,
( memberP(esk10_0,esk11_1(esk12_0))
| $false
| ~ ssItem(esk12_0) ),
inference(rw,[status(thm)],[398,364,theory(equality)]) ).
cnf(423,negated_conjecture,
( memberP(esk10_0,esk11_1(esk12_0))
| $false
| $false ),
inference(rw,[status(thm)],[422,363,theory(equality)]) ).
cnf(424,negated_conjecture,
memberP(esk10_0,esk11_1(esk12_0)),
inference(cn,[status(thm)],[423,theory(equality)]) ).
cnf(425,negated_conjecture,
( leq(esk12_0,esk11_1(esk12_0))
| $false
| ~ ssItem(esk12_0) ),
inference(rw,[status(thm)],[399,364,theory(equality)]) ).
cnf(426,negated_conjecture,
( leq(esk12_0,esk11_1(esk12_0))
| $false
| $false ),
inference(rw,[status(thm)],[425,363,theory(equality)]) ).
cnf(427,negated_conjecture,
leq(esk12_0,esk11_1(esk12_0)),
inference(cn,[status(thm)],[426,theory(equality)]) ).
cnf(456,negated_conjecture,
( esk9_0 = nil
| esk12_0 = esk11_1(esk12_0)
| ~ leq(esk12_0,esk11_1(esk12_0))
| ~ ssItem(esk11_1(esk12_0)) ),
inference(spm,[status(thm)],[155,424,theory(equality)]) ).
cnf(468,negated_conjecture,
( esk9_0 = nil
| esk12_0 = esk11_1(esk12_0)
| ~ leq(esk12_0,esk11_1(esk12_0))
| $false ),
inference(rw,[status(thm)],[456,421,theory(equality)]) ).
cnf(469,negated_conjecture,
( esk9_0 = nil
| esk12_0 = esk11_1(esk12_0)
| ~ leq(esk12_0,esk11_1(esk12_0)) ),
inference(cn,[status(thm)],[468,theory(equality)]) ).
cnf(470,negated_conjecture,
( esk11_1(esk12_0) = esk12_0
| ~ leq(esk12_0,esk11_1(esk12_0)) ),
inference(sr,[status(thm)],[469,362,theory(equality)]) ).
cnf(517,negated_conjecture,
( esk11_1(esk12_0) = esk12_0
| $false ),
inference(rw,[status(thm)],[470,427,theory(equality)]) ).
cnf(518,negated_conjecture,
esk11_1(esk12_0) = esk12_0,
inference(cn,[status(thm)],[517,theory(equality)]) ).
cnf(519,negated_conjecture,
( cons(esk12_0,nil) != esk9_0
| ~ memberP(esk10_0,esk12_0)
| ~ ssItem(esk12_0) ),
inference(spm,[status(thm)],[207,518,theory(equality)]) ).
cnf(527,negated_conjecture,
( $false
| ~ memberP(esk10_0,esk12_0)
| ~ ssItem(esk12_0) ),
inference(rw,[status(thm)],[519,365,theory(equality)]) ).
cnf(528,negated_conjecture,
( $false
| $false
| ~ ssItem(esk12_0) ),
inference(rw,[status(thm)],[527,364,theory(equality)]) ).
cnf(529,negated_conjecture,
( $false
| $false
| $false ),
inference(rw,[status(thm)],[528,363,theory(equality)]) ).
cnf(530,negated_conjecture,
$false,
inference(cn,[status(thm)],[529,theory(equality)]) ).
cnf(531,negated_conjecture,
$false,
530,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC098+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmp3WYh-X/sel_SWC098+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC098+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC098+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC098+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
%
%------------------------------------------------------------------------------