TSTP Solution File: SWC327+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC327+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 11:29:01 EST 2010
% Result : Theorem 0.34s
% Output : CNFRefutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 7
% Syntax : Number of formulae : 131 ( 18 unt; 0 def)
% Number of atoms : 660 ( 294 equ)
% Maximal formula atoms : 66 ( 5 avg)
% Number of connectives : 862 ( 333 ~; 373 |; 120 &)
% ( 1 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 183 ( 0 sgn 90 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmp6-0fPb/sel_SWC327+1.p_1',ax26) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmp6-0fPb/sel_SWC327+1.p_1',ax83) ).
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmp6-0fPb/sel_SWC327+1.p_1',ax16) ).
fof(14,axiom,
ssList(nil),
file('/tmp/tmp6-0fPb/sel_SWC327+1.p_1',ax17) ).
fof(16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/tmp/tmp6-0fPb/sel_SWC327+1.p_1',ax27) ).
fof(18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmp6-0fPb/sel_SWC327+1.p_1',ax21) ).
fof(20,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ( app(X3,X5) != X4
| ~ equalelemsP(X3)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X5
& ? [X8] :
( ssList(X8)
& app(X8,cons(X6,nil)) = X3 ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( ? [X9] :
( ssList(X9)
& app(X1,X9) = X2
& ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssList(X11)
=> ( app(cons(X10,nil),X11) != X9
| ! [X12] :
( ssList(X12)
=> app(X12,cons(X10,nil)) != X1 ) ) ) )
& equalelemsP(X1) )
& ( nil != X1
| nil = X2 ) ) ) ) ) ) ),
file('/tmp/tmp6-0fPb/sel_SWC327+1.p_1',co1) ).
fof(21,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ( app(X3,X5) != X4
| ~ equalelemsP(X3)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X5
& ? [X8] :
( ssList(X8)
& app(X8,cons(X6,nil)) = X3 ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( ? [X9] :
( ssList(X9)
& app(X1,X9) = X2
& ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssList(X11)
=> ( app(cons(X10,nil),X11) != X9
| ! [X12] :
( ssList(X12)
=> app(X12,cons(X10,nil)) != X1 ) ) ) )
& equalelemsP(X1) )
& ( nil != X1
| nil = X2 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[20]) ).
fof(22,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ( app(X3,X5) != X4
| ~ equalelemsP(X3)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X5
& ? [X8] :
( ssList(X8)
& app(X8,cons(X6,nil)) = X3 ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( ? [X9] :
( ssList(X9)
& app(X1,X9) = X2
& ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssList(X11)
=> ( app(cons(X10,nil),X11) != X9
| ! [X12] :
( ssList(X12)
=> app(X12,cons(X10,nil)) != X1 ) ) ) )
& equalelemsP(X1) )
& ( nil != X1
| nil = X2 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[21,theory(equality)]) ).
fof(29,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(30,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[29]) ).
fof(31,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[30]) ).
cnf(32,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[31]) ).
fof(47,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)],[8]) ).
fof(48,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)],[47]) ).
fof(49,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)],[48]) ).
fof(50,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)],[49]) ).
cnf(51,plain,
( nil = app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| nil != X1
| nil != X2 ),
inference(split_conjunct,[status(thm)],[50]) ).
fof(81,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(82,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[81]) ).
fof(83,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[82]) ).
cnf(84,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[83]) ).
cnf(85,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[14]) ).
fof(89,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)],[16]) ).
fof(90,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)],[89]) ).
fof(91,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)],[90]) ).
cnf(92,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[91]) ).
fof(97,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| nil != cons(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(98,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3) ) ),
inference(variable_rename,[status(thm)],[97]) ).
fof(99,plain,
! [X3,X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[98]) ).
cnf(100,plain,
( ~ ssList(X1)
| nil != cons(X2,X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[99]) ).
fof(107,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ? [X5] :
( ssList(X5)
& app(X3,X5) = X4
& equalelemsP(X3)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(cons(X6,nil),X7) != X5
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X6,nil)) != X3 ) ) ) )
& ( nil = X4
| nil != X3 )
& ( ! [X9] :
( ~ ssList(X9)
| app(X1,X9) != X2
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(cons(X10,nil),X11) = X9
& ? [X12] :
( ssList(X12)
& app(X12,cons(X10,nil)) = X1 ) ) )
| ~ equalelemsP(X1) )
| ( nil = X1
& nil != X2 ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(108,negated_conjecture,
? [X13] :
( ssList(X13)
& ? [X14] :
( ssList(X14)
& ? [X15] :
( ssList(X15)
& ? [X16] :
( ssList(X16)
& X14 = X16
& X13 = X15
& ? [X17] :
( ssList(X17)
& app(X15,X17) = X16
& equalelemsP(X15)
& ! [X18] :
( ~ ssItem(X18)
| ! [X19] :
( ~ ssList(X19)
| app(cons(X18,nil),X19) != X17
| ! [X20] :
( ~ ssList(X20)
| app(X20,cons(X18,nil)) != X15 ) ) ) )
& ( nil = X16
| nil != X15 )
& ( ! [X21] :
( ~ ssList(X21)
| app(X13,X21) != X14
| ? [X22] :
( ssItem(X22)
& ? [X23] :
( ssList(X23)
& app(cons(X22,nil),X23) = X21
& ? [X24] :
( ssList(X24)
& app(X24,cons(X22,nil)) = X13 ) ) )
| ~ equalelemsP(X13) )
| ( nil = X13
& nil != X14 ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[107]) ).
fof(109,negated_conjecture,
( ssList(esk9_0)
& ssList(esk10_0)
& ssList(esk11_0)
& ssList(esk12_0)
& esk10_0 = esk12_0
& esk9_0 = esk11_0
& ssList(esk13_0)
& app(esk11_0,esk13_0) = esk12_0
& equalelemsP(esk11_0)
& ! [X18] :
( ~ ssItem(X18)
| ! [X19] :
( ~ ssList(X19)
| app(cons(X18,nil),X19) != esk13_0
| ! [X20] :
( ~ ssList(X20)
| app(X20,cons(X18,nil)) != esk11_0 ) ) )
& ( nil = esk12_0
| nil != esk11_0 )
& ( ! [X21] :
( ~ ssList(X21)
| app(esk9_0,X21) != esk10_0
| ( ssItem(esk14_1(X21))
& ssList(esk15_1(X21))
& app(cons(esk14_1(X21),nil),esk15_1(X21)) = X21
& ssList(esk16_1(X21))
& app(esk16_1(X21),cons(esk14_1(X21),nil)) = esk9_0 )
| ~ equalelemsP(esk9_0) )
| ( nil = esk9_0
& nil != esk10_0 ) ) ),
inference(skolemize,[status(esa)],[108]) ).
fof(110,negated_conjecture,
! [X18,X19,X20,X21] :
( ( ~ ssList(X21)
| app(esk9_0,X21) != esk10_0
| ( ssItem(esk14_1(X21))
& ssList(esk15_1(X21))
& app(cons(esk14_1(X21),nil),esk15_1(X21)) = X21
& ssList(esk16_1(X21))
& app(esk16_1(X21),cons(esk14_1(X21),nil)) = esk9_0 )
| ~ equalelemsP(esk9_0)
| ( nil = esk9_0
& nil != esk10_0 ) )
& ( ~ ssList(X20)
| app(X20,cons(X18,nil)) != esk11_0
| ~ ssList(X19)
| app(cons(X18,nil),X19) != esk13_0
| ~ ssItem(X18) )
& app(esk11_0,esk13_0) = esk12_0
& equalelemsP(esk11_0)
& ssList(esk13_0)
& esk10_0 = esk12_0
& esk9_0 = esk11_0
& ( nil = esk12_0
| nil != esk11_0 )
& ssList(esk12_0)
& ssList(esk11_0)
& ssList(esk10_0)
& ssList(esk9_0) ),
inference(shift_quantors,[status(thm)],[109]) ).
fof(111,negated_conjecture,
! [X18,X19,X20,X21] :
( ( nil = esk9_0
| ssItem(esk14_1(X21))
| ~ ssList(X21)
| app(esk9_0,X21) != esk10_0
| ~ equalelemsP(esk9_0) )
& ( nil != esk10_0
| ssItem(esk14_1(X21))
| ~ ssList(X21)
| app(esk9_0,X21) != esk10_0
| ~ equalelemsP(esk9_0) )
& ( nil = esk9_0
| ssList(esk15_1(X21))
| ~ ssList(X21)
| app(esk9_0,X21) != esk10_0
| ~ equalelemsP(esk9_0) )
& ( nil != esk10_0
| ssList(esk15_1(X21))
| ~ ssList(X21)
| app(esk9_0,X21) != esk10_0
| ~ equalelemsP(esk9_0) )
& ( nil = esk9_0
| app(cons(esk14_1(X21),nil),esk15_1(X21)) = X21
| ~ ssList(X21)
| app(esk9_0,X21) != esk10_0
| ~ equalelemsP(esk9_0) )
& ( nil != esk10_0
| app(cons(esk14_1(X21),nil),esk15_1(X21)) = X21
| ~ ssList(X21)
| app(esk9_0,X21) != esk10_0
| ~ equalelemsP(esk9_0) )
& ( nil = esk9_0
| ssList(esk16_1(X21))
| ~ ssList(X21)
| app(esk9_0,X21) != esk10_0
| ~ equalelemsP(esk9_0) )
& ( nil != esk10_0
| ssList(esk16_1(X21))
| ~ ssList(X21)
| app(esk9_0,X21) != esk10_0
| ~ equalelemsP(esk9_0) )
& ( nil = esk9_0
| app(esk16_1(X21),cons(esk14_1(X21),nil)) = esk9_0
| ~ ssList(X21)
| app(esk9_0,X21) != esk10_0
| ~ equalelemsP(esk9_0) )
& ( nil != esk10_0
| app(esk16_1(X21),cons(esk14_1(X21),nil)) = esk9_0
| ~ ssList(X21)
| app(esk9_0,X21) != esk10_0
| ~ equalelemsP(esk9_0) )
& ( ~ ssList(X20)
| app(X20,cons(X18,nil)) != esk11_0
| ~ ssList(X19)
| app(cons(X18,nil),X19) != esk13_0
| ~ ssItem(X18) )
& app(esk11_0,esk13_0) = esk12_0
& equalelemsP(esk11_0)
& ssList(esk13_0)
& esk10_0 = esk12_0
& esk9_0 = esk11_0
& ( nil = esk12_0
| nil != esk11_0 )
& ssList(esk12_0)
& ssList(esk11_0)
& ssList(esk10_0)
& ssList(esk9_0) ),
inference(distribute,[status(thm)],[110]) ).
cnf(116,negated_conjecture,
( nil = esk12_0
| nil != esk11_0 ),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(117,negated_conjecture,
esk9_0 = esk11_0,
inference(split_conjunct,[status(thm)],[111]) ).
cnf(118,negated_conjecture,
esk10_0 = esk12_0,
inference(split_conjunct,[status(thm)],[111]) ).
cnf(119,negated_conjecture,
ssList(esk13_0),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(120,negated_conjecture,
equalelemsP(esk11_0),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(121,negated_conjecture,
app(esk11_0,esk13_0) = esk12_0,
inference(split_conjunct,[status(thm)],[111]) ).
cnf(122,negated_conjecture,
( ~ ssItem(X1)
| app(cons(X1,nil),X2) != esk13_0
| ~ ssList(X2)
| app(X3,cons(X1,nil)) != esk11_0
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(124,negated_conjecture,
( app(esk16_1(X1),cons(esk14_1(X1),nil)) = esk9_0
| nil = esk9_0
| ~ equalelemsP(esk9_0)
| app(esk9_0,X1) != esk10_0
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(126,negated_conjecture,
( ssList(esk16_1(X1))
| nil = esk9_0
| ~ equalelemsP(esk9_0)
| app(esk9_0,X1) != esk10_0
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(127,negated_conjecture,
( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
| ~ equalelemsP(esk9_0)
| app(esk9_0,X1) != esk10_0
| ~ ssList(X1)
| nil != esk10_0 ),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(128,negated_conjecture,
( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
| nil = esk9_0
| ~ equalelemsP(esk9_0)
| app(esk9_0,X1) != esk10_0
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(129,negated_conjecture,
( ssList(esk15_1(X1))
| ~ equalelemsP(esk9_0)
| app(esk9_0,X1) != esk10_0
| ~ ssList(X1)
| nil != esk10_0 ),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(130,negated_conjecture,
( ssList(esk15_1(X1))
| nil = esk9_0
| ~ equalelemsP(esk9_0)
| app(esk9_0,X1) != esk10_0
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(131,negated_conjecture,
( ssItem(esk14_1(X1))
| ~ equalelemsP(esk9_0)
| app(esk9_0,X1) != esk10_0
| ~ ssList(X1)
| nil != esk10_0 ),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(132,negated_conjecture,
( ssItem(esk14_1(X1))
| nil = esk9_0
| ~ equalelemsP(esk9_0)
| app(esk9_0,X1) != esk10_0
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(135,negated_conjecture,
equalelemsP(esk9_0),
inference(rw,[status(thm)],[120,117,theory(equality)]) ).
cnf(138,negated_conjecture,
( esk10_0 = nil
| esk11_0 != nil ),
inference(rw,[status(thm)],[116,118,theory(equality)]) ).
cnf(139,negated_conjecture,
( esk10_0 = nil
| esk9_0 != nil ),
inference(rw,[status(thm)],[138,117,theory(equality)]) ).
cnf(140,negated_conjecture,
app(esk9_0,esk13_0) = esk12_0,
inference(rw,[status(thm)],[121,117,theory(equality)]) ).
cnf(141,negated_conjecture,
app(esk9_0,esk13_0) = esk10_0,
inference(rw,[status(thm)],[140,118,theory(equality)]) ).
cnf(167,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(er,[status(thm)],[51,theory(equality)]) ).
cnf(168,plain,
( app(X1,nil) = nil
| nil != X1
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[167,85,theory(equality)]) ).
cnf(169,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[168,theory(equality)]) ).
cnf(247,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssList(app(X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[100,92,theory(equality)]) ).
cnf(261,negated_conjecture,
( app(X3,cons(X1,nil)) != esk9_0
| app(cons(X1,nil),X2) != esk13_0
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(rw,[status(thm)],[122,117,theory(equality)]) ).
cnf(286,negated_conjecture,
( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
| app(esk9_0,X1) != esk10_0
| esk10_0 != nil
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[127,135,theory(equality)]) ).
cnf(287,negated_conjecture,
( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
| app(esk9_0,X1) != esk10_0
| esk10_0 != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[286,theory(equality)]) ).
cnf(288,negated_conjecture,
( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
| esk9_0 = nil
| app(esk9_0,X1) != esk10_0
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[128,135,theory(equality)]) ).
cnf(289,negated_conjecture,
( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
| esk9_0 = nil
| app(esk9_0,X1) != esk10_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[288,theory(equality)]) ).
cnf(292,negated_conjecture,
( app(esk16_1(X1),cons(esk14_1(X1),nil)) = esk9_0
| esk9_0 = nil
| app(esk9_0,X1) != esk10_0
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[124,135,theory(equality)]) ).
cnf(293,negated_conjecture,
( app(esk16_1(X1),cons(esk14_1(X1),nil)) = esk9_0
| esk9_0 = nil
| app(esk9_0,X1) != esk10_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[292,theory(equality)]) ).
cnf(296,negated_conjecture,
( ssList(esk15_1(X1))
| app(esk9_0,X1) != esk10_0
| esk10_0 != nil
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[129,135,theory(equality)]) ).
cnf(297,negated_conjecture,
( ssList(esk15_1(X1))
| app(esk9_0,X1) != esk10_0
| esk10_0 != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[296,theory(equality)]) ).
cnf(298,negated_conjecture,
( ssItem(esk14_1(X1))
| app(esk9_0,X1) != esk10_0
| esk10_0 != nil
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[131,135,theory(equality)]) ).
cnf(299,negated_conjecture,
( ssItem(esk14_1(X1))
| app(esk9_0,X1) != esk10_0
| esk10_0 != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[298,theory(equality)]) ).
cnf(300,negated_conjecture,
( esk9_0 = nil
| ssList(esk16_1(X1))
| app(esk9_0,X1) != esk10_0
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[126,135,theory(equality)]) ).
cnf(301,negated_conjecture,
( esk9_0 = nil
| ssList(esk16_1(X1))
| app(esk9_0,X1) != esk10_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[300,theory(equality)]) ).
cnf(302,negated_conjecture,
( esk9_0 = nil
| ssList(esk15_1(X1))
| app(esk9_0,X1) != esk10_0
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[130,135,theory(equality)]) ).
cnf(303,negated_conjecture,
( esk9_0 = nil
| ssList(esk15_1(X1))
| app(esk9_0,X1) != esk10_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[302,theory(equality)]) ).
cnf(304,negated_conjecture,
( esk9_0 = nil
| ssItem(esk14_1(X1))
| app(esk9_0,X1) != esk10_0
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[132,135,theory(equality)]) ).
cnf(305,negated_conjecture,
( esk9_0 = nil
| ssItem(esk14_1(X1))
| app(esk9_0,X1) != esk10_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[304,theory(equality)]) ).
cnf(308,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[247,32]) ).
cnf(318,plain,
( app(nil,nil) = nil
| ~ ssList(nil) ),
inference(er,[status(thm)],[169,theory(equality)]) ).
cnf(319,plain,
( app(nil,nil) = nil
| $false ),
inference(rw,[status(thm)],[318,85,theory(equality)]) ).
cnf(320,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[319,theory(equality)]) ).
cnf(360,negated_conjecture,
( app(cons(esk14_1(esk13_0),nil),esk15_1(esk13_0)) = esk13_0
| esk9_0 = nil
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[289,141,theory(equality)]) ).
cnf(394,negated_conjecture,
( esk9_0 = nil
| ssList(esk16_1(esk13_0))
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[301,141,theory(equality)]) ).
cnf(399,negated_conjecture,
( esk9_0 = nil
| ssList(esk16_1(esk13_0)) ),
inference(spm,[status(thm)],[394,119,theory(equality)]) ).
cnf(400,negated_conjecture,
( esk9_0 = nil
| ssList(esk15_1(esk13_0))
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[303,141,theory(equality)]) ).
cnf(405,negated_conjecture,
( app(esk16_1(esk13_0),cons(esk14_1(esk13_0),nil)) = esk9_0
| esk9_0 = nil
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[293,141,theory(equality)]) ).
cnf(420,negated_conjecture,
( esk9_0 = nil
| ssList(esk15_1(esk13_0)) ),
inference(spm,[status(thm)],[400,119,theory(equality)]) ).
cnf(421,negated_conjecture,
( esk9_0 = nil
| ssItem(esk14_1(esk13_0))
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[305,141,theory(equality)]) ).
cnf(440,negated_conjecture,
( esk9_0 = nil
| ssItem(esk14_1(esk13_0)) ),
inference(spm,[status(thm)],[421,119,theory(equality)]) ).
cnf(506,negated_conjecture,
( app(cons(esk14_1(esk13_0),nil),esk15_1(esk13_0)) = esk13_0
| esk9_0 = nil ),
inference(spm,[status(thm)],[360,119,theory(equality)]) ).
cnf(579,negated_conjecture,
( ssList(esk13_0)
| esk9_0 = nil
| ~ ssList(esk15_1(esk13_0))
| ~ ssList(cons(esk14_1(esk13_0),nil)) ),
inference(spm,[status(thm)],[32,506,theory(equality)]) ).
cnf(623,negated_conjecture,
( esk9_0 = nil
| ssList(esk13_0)
| ~ ssList(cons(esk14_1(esk13_0),nil)) ),
inference(csr,[status(thm)],[579,420]) ).
cnf(624,negated_conjecture,
( esk9_0 = nil
| ssList(esk13_0)
| ~ ssList(nil)
| ~ ssItem(esk14_1(esk13_0)) ),
inference(spm,[status(thm)],[623,84,theory(equality)]) ).
cnf(625,negated_conjecture,
( esk9_0 = nil
| ssList(esk13_0)
| $false
| ~ ssItem(esk14_1(esk13_0)) ),
inference(rw,[status(thm)],[624,85,theory(equality)]) ).
cnf(626,negated_conjecture,
( esk9_0 = nil
| ssList(esk13_0)
| ~ ssItem(esk14_1(esk13_0)) ),
inference(cn,[status(thm)],[625,theory(equality)]) ).
cnf(627,negated_conjecture,
( esk9_0 = nil
| ssList(esk13_0) ),
inference(csr,[status(thm)],[626,440]) ).
cnf(682,negated_conjecture,
( app(esk16_1(esk13_0),cons(esk14_1(esk13_0),nil)) = esk9_0
| esk9_0 = nil ),
inference(csr,[status(thm)],[405,627]) ).
cnf(692,negated_conjecture,
( esk9_0 = nil
| app(cons(esk14_1(esk13_0),nil),X1) != esk13_0
| ~ ssList(esk16_1(esk13_0))
| ~ ssList(X1)
| ~ ssItem(esk14_1(esk13_0)) ),
inference(spm,[status(thm)],[261,682,theory(equality)]) ).
cnf(1862,negated_conjecture,
( esk9_0 = nil
| app(cons(esk14_1(esk13_0),nil),X1) != esk13_0
| ~ ssList(esk16_1(esk13_0))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[692,440]) ).
cnf(1863,negated_conjecture,
( esk9_0 = nil
| app(cons(esk14_1(esk13_0),nil),X1) != esk13_0
| ~ ssList(X1) ),
inference(csr,[status(thm)],[1862,399]) ).
cnf(1866,negated_conjecture,
( esk9_0 = nil
| ~ ssList(esk15_1(esk13_0)) ),
inference(spm,[status(thm)],[1863,506,theory(equality)]) ).
cnf(1874,negated_conjecture,
esk9_0 = nil,
inference(csr,[status(thm)],[1866,420]) ).
cnf(1934,negated_conjecture,
( ssItem(esk14_1(X1))
| app(nil,X1) != esk10_0
| esk10_0 != nil
| ~ ssList(X1) ),
inference(rw,[status(thm)],[299,1874,theory(equality)]) ).
cnf(1938,negated_conjecture,
( ssList(esk15_1(X1))
| app(nil,X1) != esk10_0
| esk10_0 != nil
| ~ ssList(X1) ),
inference(rw,[status(thm)],[297,1874,theory(equality)]) ).
cnf(1939,negated_conjecture,
( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
| app(nil,X1) != esk10_0
| esk10_0 != nil
| ~ ssList(X1) ),
inference(rw,[status(thm)],[287,1874,theory(equality)]) ).
cnf(1942,negated_conjecture,
( esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[139,1874,theory(equality)]) ).
cnf(1943,negated_conjecture,
esk10_0 = nil,
inference(cn,[status(thm)],[1942,theory(equality)]) ).
cnf(1991,negated_conjecture,
( ssItem(esk14_1(X1))
| app(nil,X1) != nil
| esk10_0 != nil
| ~ ssList(X1) ),
inference(rw,[status(thm)],[1934,1943,theory(equality)]) ).
cnf(1992,negated_conjecture,
( ssItem(esk14_1(X1))
| app(nil,X1) != nil
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[1991,1943,theory(equality)]) ).
cnf(1993,negated_conjecture,
( ssItem(esk14_1(X1))
| app(nil,X1) != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1992,theory(equality)]) ).
cnf(1994,negated_conjecture,
( ssItem(esk14_1(nil))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1993,320,theory(equality)]) ).
cnf(2001,negated_conjecture,
( ssItem(esk14_1(nil))
| $false ),
inference(rw,[status(thm)],[1994,85,theory(equality)]) ).
cnf(2002,negated_conjecture,
ssItem(esk14_1(nil)),
inference(cn,[status(thm)],[2001,theory(equality)]) ).
cnf(2053,negated_conjecture,
( ssList(esk15_1(X1))
| app(nil,X1) != nil
| esk10_0 != nil
| ~ ssList(X1) ),
inference(rw,[status(thm)],[1938,1943,theory(equality)]) ).
cnf(2054,negated_conjecture,
( ssList(esk15_1(X1))
| app(nil,X1) != nil
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[2053,1943,theory(equality)]) ).
cnf(2055,negated_conjecture,
( ssList(esk15_1(X1))
| app(nil,X1) != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[2054,theory(equality)]) ).
cnf(2056,negated_conjecture,
( ssList(esk15_1(nil))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[2055,320,theory(equality)]) ).
cnf(2063,negated_conjecture,
( ssList(esk15_1(nil))
| $false ),
inference(rw,[status(thm)],[2056,85,theory(equality)]) ).
cnf(2064,negated_conjecture,
ssList(esk15_1(nil)),
inference(cn,[status(thm)],[2063,theory(equality)]) ).
cnf(2172,negated_conjecture,
( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
| app(nil,X1) != nil
| esk10_0 != nil
| ~ ssList(X1) ),
inference(rw,[status(thm)],[1939,1943,theory(equality)]) ).
cnf(2173,negated_conjecture,
( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
| app(nil,X1) != nil
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[2172,1943,theory(equality)]) ).
cnf(2174,negated_conjecture,
( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
| app(nil,X1) != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[2173,theory(equality)]) ).
cnf(2175,negated_conjecture,
( app(cons(esk14_1(nil),nil),esk15_1(nil)) = nil
| ~ ssList(nil) ),
inference(spm,[status(thm)],[2174,320,theory(equality)]) ).
cnf(2183,negated_conjecture,
( app(cons(esk14_1(nil),nil),esk15_1(nil)) = nil
| $false ),
inference(rw,[status(thm)],[2175,85,theory(equality)]) ).
cnf(2184,negated_conjecture,
app(cons(esk14_1(nil),nil),esk15_1(nil)) = nil,
inference(cn,[status(thm)],[2183,theory(equality)]) ).
cnf(2201,negated_conjecture,
( ~ ssList(nil)
| ~ ssList(esk15_1(nil))
| ~ ssItem(esk14_1(nil)) ),
inference(spm,[status(thm)],[308,2184,theory(equality)]) ).
cnf(2239,negated_conjecture,
( $false
| ~ ssList(esk15_1(nil))
| ~ ssItem(esk14_1(nil)) ),
inference(rw,[status(thm)],[2201,85,theory(equality)]) ).
cnf(2240,negated_conjecture,
( $false
| $false
| ~ ssItem(esk14_1(nil)) ),
inference(rw,[status(thm)],[2239,2064,theory(equality)]) ).
cnf(2241,negated_conjecture,
( $false
| $false
| $false ),
inference(rw,[status(thm)],[2240,2002,theory(equality)]) ).
cnf(2242,negated_conjecture,
$false,
inference(cn,[status(thm)],[2241,theory(equality)]) ).
cnf(2243,negated_conjecture,
$false,
2242,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC327+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmp6-0fPb/sel_SWC327+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC327+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC327+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC327+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
%
%------------------------------------------------------------------------------