TSTP Solution File: SWC219+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC219+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 10:52:58 EST 2010
% Result : Theorem 5.24s
% Output : CNFRefutation 5.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 10
% Syntax : Number of formulae : 109 ( 14 unt; 0 def)
% Number of atoms : 554 ( 179 equ)
% Maximal formula atoms : 54 ( 5 avg)
% Number of connectives : 719 ( 274 ~; 294 |; 116 &)
% ( 1 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 188 ( 0 sgn 98 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmpn1DQGr/sel_SWC219+1.p_1',ax84) ).
fof(2,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmpn1DQGr/sel_SWC219+1.p_1',ax83) ).
fof(3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/tmp/tmpn1DQGr/sel_SWC219+1.p_1',ax82) ).
fof(4,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpn1DQGr/sel_SWC219+1.p_1',ax81) ).
fof(7,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpn1DQGr/sel_SWC219+1.p_1',ax28) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/tmp/tmpn1DQGr/sel_SWC219+1.p_1',ax27) ).
fof(16,axiom,
ssList(nil),
file('/tmp/tmpn1DQGr/sel_SWC219+1.p_1',ax17) ).
fof(19,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/tmp/tmpn1DQGr/sel_SWC219+1.p_1',ax38) ).
fof(22,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpn1DQGr/sel_SWC219+1.p_1',ax16) ).
fof(24,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ leq(X5,X8)
| leq(X8,X5) ) ) ) ) )
| ( ! [X9] :
( ssItem(X9)
=> ( cons(X9,nil) != X3
| ~ memberP(X4,X9)
| ? [X10] :
( ssItem(X10)
& X9 != X10
& memberP(X4,X10)
& leq(X10,X9) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
file('/tmp/tmpn1DQGr/sel_SWC219+1.p_1',co1) ).
fof(25,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ leq(X5,X8)
| leq(X8,X5) ) ) ) ) )
| ( ! [X9] :
( ssItem(X9)
=> ( cons(X9,nil) != X3
| ~ memberP(X4,X9)
| ? [X10] :
( ssItem(X10)
& X9 != X10
& memberP(X4,X10)
& leq(X10,X9) ) ) )
& ( 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
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ leq(X5,X8)
| leq(X8,X5) ) ) ) ) )
| ( ! [X9] :
( ssItem(X9)
=> ( cons(X9,nil) != X3
| ~ memberP(X4,X9)
| ? [X10] :
( ssItem(X10)
& X9 != X10
& memberP(X4,X10)
& leq(X10,X9) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[25,theory(equality)]) ).
fof(28,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(29,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[28]) ).
cnf(30,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( nil != app(X1,X2)
| ( nil = X2
& nil = X1 ) )
& ( nil != X2
| nil != X1
| nil = app(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(32,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( nil != app(X3,X4)
| ( nil = X4
& nil = X3 ) )
& ( nil != X4
| nil != X3
| nil = app(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[31]) ).
fof(33,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( nil != app(X3,X4)
| ( nil = X4
& nil = X3 ) )
& ( nil != X4
| nil != X3
| nil = app(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[32]) ).
fof(34,plain,
! [X3,X4] :
( ( nil = X4
| nil != app(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3) )
& ( nil = X3
| nil != app(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3) )
& ( nil != X4
| nil != X3
| nil = app(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3) ) ),
inference(distribute,[status(thm)],[33]) ).
cnf(35,plain,
( nil = app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| nil != X1
| nil != X2 ),
inference(split_conjunct,[status(thm)],[34]) ).
fof(38,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(39,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) = app(X4,app(X5,X6)) ) ) ),
inference(variable_rename,[status(thm)],[38]) ).
fof(40,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) = app(X4,app(X5,X6))
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[39]) ).
cnf(41,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[40]) ).
fof(42,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(43,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[42]) ).
fof(44,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[43]) ).
cnf(45,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[44]) ).
fof(54,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(55,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[54]) ).
cnf(56,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[55]) ).
fof(57,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssItem(X3)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(58,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssItem(X6)
| cons(X6,app(X5,X4)) = app(cons(X6,X5),X4) ) ) ),
inference(variable_rename,[status(thm)],[57]) ).
fof(59,plain,
! [X4,X5,X6] :
( ~ ssItem(X6)
| cons(X6,app(X5,X4)) = app(cons(X6,X5),X4)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[58]) ).
cnf(60,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(98,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[16]) ).
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(126,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(127,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[126]) ).
fof(128,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[127]) ).
cnf(129,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[128]) ).
fof(133,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& nil != X1
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssList(X7)
| app(app(X6,cons(X5,nil)),X7) != X1
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& memberP(X7,X8)
& leq(X5,X8)
& ~ leq(X8,X5) ) ) ) )
& ( ? [X9] :
( ssItem(X9)
& cons(X9,nil) = X3
& memberP(X4,X9)
& ! [X10] :
( ~ ssItem(X10)
| X9 = X10
| ~ memberP(X4,X10)
| ~ leq(X10,X9) ) )
| ( nil = X4
& nil = X3 ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(134,negated_conjecture,
? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& ? [X13] :
( ssList(X13)
& ? [X14] :
( ssList(X14)
& X12 = X14
& X11 = X13
& nil != X11
& ! [X15] :
( ~ ssItem(X15)
| ! [X16] :
( ~ ssList(X16)
| ! [X17] :
( ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != X11
| ? [X18] :
( ssItem(X18)
& memberP(X16,X18)
& memberP(X17,X18)
& leq(X15,X18)
& ~ leq(X18,X15) ) ) ) )
& ( ? [X19] :
( ssItem(X19)
& cons(X19,nil) = X13
& memberP(X14,X19)
& ! [X20] :
( ~ ssItem(X20)
| X19 = X20
| ~ memberP(X14,X20)
| ~ leq(X20,X19) ) )
| ( nil = X14
& nil = X13 ) ) ) ) ) ),
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
& nil != esk7_0
& ! [X15] :
( ~ ssItem(X15)
| ! [X16] :
( ~ ssList(X16)
| ! [X17] :
( ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ( ssItem(esk11_3(X15,X16,X17))
& memberP(X16,esk11_3(X15,X16,X17))
& memberP(X17,esk11_3(X15,X16,X17))
& leq(X15,esk11_3(X15,X16,X17))
& ~ leq(esk11_3(X15,X16,X17),X15) ) ) ) )
& ( ( ssItem(esk12_0)
& cons(esk12_0,nil) = esk9_0
& memberP(esk10_0,esk12_0)
& ! [X20] :
( ~ ssItem(X20)
| esk12_0 = X20
| ~ memberP(esk10_0,X20)
| ~ leq(X20,esk12_0) ) )
| ( nil = esk10_0
& nil = esk9_0 ) ) ),
inference(skolemize,[status(esa)],[134]) ).
fof(136,negated_conjecture,
! [X15,X16,X17,X20] :
( ( ( ( ~ ssItem(X20)
| esk12_0 = X20
| ~ memberP(esk10_0,X20)
| ~ leq(X20,esk12_0) )
& cons(esk12_0,nil) = esk9_0
& memberP(esk10_0,esk12_0)
& ssItem(esk12_0) )
| ( nil = esk10_0
& nil = esk9_0 ) )
& ( ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ( ssItem(esk11_3(X15,X16,X17))
& memberP(X16,esk11_3(X15,X16,X17))
& memberP(X17,esk11_3(X15,X16,X17))
& leq(X15,esk11_3(X15,X16,X17))
& ~ leq(esk11_3(X15,X16,X17),X15) )
| ~ ssList(X16)
| ~ ssItem(X15) )
& esk8_0 = esk10_0
& esk7_0 = esk9_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,
! [X15,X16,X17,X20] :
( ( nil = esk10_0
| ~ ssItem(X20)
| esk12_0 = X20
| ~ memberP(esk10_0,X20)
| ~ leq(X20,esk12_0) )
& ( nil = esk9_0
| ~ ssItem(X20)
| esk12_0 = X20
| ~ memberP(esk10_0,X20)
| ~ leq(X20,esk12_0) )
& ( 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_3(X15,X16,X17))
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( memberP(X16,esk11_3(X15,X16,X17))
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( memberP(X17,esk11_3(X15,X16,X17))
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( leq(X15,esk11_3(X15,X16,X17))
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( ~ leq(esk11_3(X15,X16,X17),X15)
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& esk8_0 = esk10_0
& esk7_0 = esk9_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,
inference(split_conjunct,[status(thm)],[137]) ).
cnf(143,negated_conjecture,
esk7_0 = esk9_0,
inference(split_conjunct,[status(thm)],[137]) ).
cnf(147,negated_conjecture,
( memberP(X3,esk11_3(X1,X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk7_0
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(149,negated_conjecture,
( ssItem(esk11_3(X1,X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk7_0
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(150,negated_conjecture,
( ssItem(esk12_0)
| nil = esk9_0 ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(154,negated_conjecture,
( cons(esk12_0,nil) = esk9_0
| nil = esk9_0 ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(158,negated_conjecture,
( esk7_0 = nil
| cons(esk12_0,nil) = esk9_0 ),
inference(rw,[status(thm)],[154,143,theory(equality)]) ).
cnf(159,negated_conjecture,
( esk7_0 = nil
| cons(esk12_0,nil) = esk7_0 ),
inference(rw,[status(thm)],[158,143,theory(equality)]) ).
cnf(160,negated_conjecture,
cons(esk12_0,nil) = esk7_0,
inference(sr,[status(thm)],[159,142,theory(equality)]) ).
cnf(166,negated_conjecture,
( esk7_0 = nil
| ssItem(esk12_0) ),
inference(rw,[status(thm)],[150,143,theory(equality)]) ).
cnf(167,negated_conjecture,
ssItem(esk12_0),
inference(sr,[status(thm)],[166,142,theory(equality)]) ).
cnf(184,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(er,[status(thm)],[35,theory(equality)]) ).
cnf(185,plain,
( app(X1,nil) = nil
| nil != X1
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[184,98,theory(equality)]) ).
cnf(186,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[185,theory(equality)]) ).
cnf(206,negated_conjecture,
( app(esk7_0,X1) = cons(esk12_0,X1)
| ~ ssItem(esk12_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[45,160,theory(equality)]) ).
cnf(212,plain,
( ssList(app(cons(X1,nil),X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[129,45,theory(equality)]) ).
cnf(214,negated_conjecture,
( app(esk7_0,X1) = cons(esk12_0,X1)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[206,167,theory(equality)]) ).
cnf(215,negated_conjecture,
( app(esk7_0,X1) = cons(esk12_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[214,theory(equality)]) ).
cnf(267,plain,
( app(cons(X1,X2),X3) = app(cons(X1,nil),app(X2,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[41,45,theory(equality)]) ).
cnf(341,negated_conjecture,
( ssItem(esk11_3(X1,nil,X2))
| app(cons(X1,nil),X2) != esk7_0
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(cons(X1,nil)) ),
inference(spm,[status(thm)],[149,56,theory(equality)]) ).
cnf(348,negated_conjecture,
( ssItem(esk11_3(X1,nil,X2))
| app(cons(X1,nil),X2) != esk7_0
| ~ ssItem(X1)
| ~ ssList(X2)
| $false
| ~ ssList(cons(X1,nil)) ),
inference(rw,[status(thm)],[341,98,theory(equality)]) ).
cnf(349,negated_conjecture,
( ssItem(esk11_3(X1,nil,X2))
| app(cons(X1,nil),X2) != esk7_0
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[348,theory(equality)]) ).
cnf(363,negated_conjecture,
( memberP(X1,esk11_3(X2,nil,X1))
| app(cons(X2,nil),X1) != esk7_0
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(cons(X2,nil)) ),
inference(spm,[status(thm)],[147,56,theory(equality)]) ).
cnf(370,negated_conjecture,
( memberP(X1,esk11_3(X2,nil,X1))
| app(cons(X2,nil),X1) != esk7_0
| ~ ssItem(X2)
| ~ ssList(X1)
| $false
| ~ ssList(cons(X2,nil)) ),
inference(rw,[status(thm)],[363,98,theory(equality)]) ).
cnf(371,negated_conjecture,
( memberP(X1,esk11_3(X2,nil,X1))
| app(cons(X2,nil),X1) != esk7_0
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(cons(X2,nil)) ),
inference(cn,[status(thm)],[370,theory(equality)]) ).
cnf(428,plain,
( app(nil,nil) = nil
| ~ ssList(nil) ),
inference(er,[status(thm)],[186,theory(equality)]) ).
cnf(429,plain,
( app(nil,nil) = nil
| $false ),
inference(rw,[status(thm)],[428,98,theory(equality)]) ).
cnf(430,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[429,theory(equality)]) ).
cnf(431,negated_conjecture,
( app(esk7_0,nil) = esk7_0
| ~ ssList(nil) ),
inference(spm,[status(thm)],[160,215,theory(equality)]) ).
cnf(449,negated_conjecture,
( app(esk7_0,nil) = esk7_0
| $false ),
inference(rw,[status(thm)],[431,98,theory(equality)]) ).
cnf(450,negated_conjecture,
app(esk7_0,nil) = esk7_0,
inference(cn,[status(thm)],[449,theory(equality)]) ).
cnf(541,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[60,430,theory(equality)]) ).
cnf(556,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[541,98,theory(equality)]) ).
cnf(557,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[556,theory(equality)]) ).
cnf(1256,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[212,557,theory(equality)]) ).
cnf(1265,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[1256,98,theory(equality)]) ).
cnf(1266,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[1265,theory(equality)]) ).
cnf(2593,plain,
( app(cons(X1,X2),X3) = app(cons(X1,nil),app(X2,X3))
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[267,1266]) ).
cnf(2597,plain,
( app(cons(X1,X2),nil) = app(cons(X1,nil),X2)
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[2593,30,theory(equality)]) ).
cnf(2681,plain,
( app(cons(X1,X2),nil) = app(cons(X1,nil),X2)
| ~ ssItem(X1)
| $false
| ~ ssList(X2) ),
inference(rw,[status(thm)],[2597,98,theory(equality)]) ).
cnf(2682,plain,
( app(cons(X1,X2),nil) = app(cons(X1,nil),X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[2681,theory(equality)]) ).
cnf(7737,negated_conjecture,
( ssItem(esk11_3(X1,nil,X2))
| app(cons(X1,nil),X2) != esk7_0
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[349,1266]) ).
cnf(9379,negated_conjecture,
( memberP(X1,esk11_3(X2,nil,X1))
| app(cons(X2,nil),X1) != esk7_0
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[371,1266]) ).
cnf(119177,negated_conjecture,
( app(cons(esk12_0,X1),nil) = app(esk7_0,X1)
| ~ ssItem(esk12_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[2682,160,theory(equality)]) ).
cnf(119589,negated_conjecture,
( app(cons(esk12_0,X1),nil) = app(esk7_0,X1)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[119177,167,theory(equality)]) ).
cnf(119590,negated_conjecture,
( app(cons(esk12_0,X1),nil) = app(esk7_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[119589,theory(equality)]) ).
cnf(132336,negated_conjecture,
( ssItem(esk11_3(esk12_0,nil,nil))
| app(esk7_0,nil) != esk7_0
| ~ ssItem(esk12_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[7737,119590,theory(equality)]) ).
cnf(132342,negated_conjecture,
( memberP(nil,esk11_3(esk12_0,nil,nil))
| app(esk7_0,nil) != esk7_0
| ~ ssItem(esk12_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[9379,119590,theory(equality)]) ).
cnf(132630,negated_conjecture,
( ssItem(esk11_3(esk12_0,nil,nil))
| $false
| ~ ssItem(esk12_0)
| ~ ssList(nil) ),
inference(rw,[status(thm)],[132336,450,theory(equality)]) ).
cnf(132631,negated_conjecture,
( ssItem(esk11_3(esk12_0,nil,nil))
| $false
| $false
| ~ ssList(nil) ),
inference(rw,[status(thm)],[132630,167,theory(equality)]) ).
cnf(132632,negated_conjecture,
( ssItem(esk11_3(esk12_0,nil,nil))
| $false
| $false
| $false ),
inference(rw,[status(thm)],[132631,98,theory(equality)]) ).
cnf(132633,negated_conjecture,
ssItem(esk11_3(esk12_0,nil,nil)),
inference(cn,[status(thm)],[132632,theory(equality)]) ).
cnf(132654,negated_conjecture,
( memberP(nil,esk11_3(esk12_0,nil,nil))
| $false
| ~ ssItem(esk12_0)
| ~ ssList(nil) ),
inference(rw,[status(thm)],[132342,450,theory(equality)]) ).
cnf(132655,negated_conjecture,
( memberP(nil,esk11_3(esk12_0,nil,nil))
| $false
| $false
| ~ ssList(nil) ),
inference(rw,[status(thm)],[132654,167,theory(equality)]) ).
cnf(132656,negated_conjecture,
( memberP(nil,esk11_3(esk12_0,nil,nil))
| $false
| $false
| $false ),
inference(rw,[status(thm)],[132655,98,theory(equality)]) ).
cnf(132657,negated_conjecture,
memberP(nil,esk11_3(esk12_0,nil,nil)),
inference(cn,[status(thm)],[132656,theory(equality)]) ).
cnf(135338,negated_conjecture,
~ ssItem(esk11_3(esk12_0,nil,nil)),
inference(spm,[status(thm)],[115,132657,theory(equality)]) ).
cnf(135345,negated_conjecture,
$false,
inference(rw,[status(thm)],[135338,132633,theory(equality)]) ).
cnf(135346,negated_conjecture,
$false,
inference(cn,[status(thm)],[135345,theory(equality)]) ).
cnf(135347,negated_conjecture,
$false,
135346,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC219+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpn1DQGr/sel_SWC219+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC219+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC219+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC219+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
%
%------------------------------------------------------------------------------