TSTP Solution File: SWC061+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC061+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 10:10:29 EST 2010
% Result : Theorem 0.73s
% Output : CNFRefutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 13
% Syntax : Number of formulae : 170 ( 14 unt; 0 def)
% Number of atoms : 740 ( 224 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 939 ( 369 ~; 425 |; 108 &)
% ( 3 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 210 ( 0 sgn 120 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmpTaxIFx/sel_SWC061+1.p_1',ax84) ).
fof(3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/tmp/tmpTaxIFx/sel_SWC061+1.p_1',ax82) ).
fof(4,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpTaxIFx/sel_SWC061+1.p_1',ax81) ).
fof(6,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpTaxIFx/sel_SWC061+1.p_1',ax28) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpTaxIFx/sel_SWC061+1.p_1',ax26) ).
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/tmp/tmpTaxIFx/sel_SWC061+1.p_1',ax7) ).
fof(17,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/tmp/tmpTaxIFx/sel_SWC061+1.p_1',ax58) ).
fof(18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpTaxIFx/sel_SWC061+1.p_1',ax15) ).
fof(19,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpTaxIFx/sel_SWC061+1.p_1',ax16) ).
fof(20,axiom,
ssList(nil),
file('/tmp/tmpTaxIFx/sel_SWC061+1.p_1',ax17) ).
fof(23,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/tmp/tmpTaxIFx/sel_SWC061+1.p_1',ax55) ).
fof(24,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( segmentP(X1,X2)
=> segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
file('/tmp/tmpTaxIFx/sel_SWC061+1.p_1',ax56) ).
fof(26,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| app(X6,cons(X5,nil)) != X3 ) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X7] :
( ssList(X7)
& neq(X7,nil)
& segmentP(X2,X7)
& segmentP(X1,X7) ) ) ) ) ) ) ),
file('/tmp/tmpTaxIFx/sel_SWC061+1.p_1',co1) ).
fof(27,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| app(X6,cons(X5,nil)) != X3 ) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X7] :
( ssList(X7)
& neq(X7,nil)
& segmentP(X2,X7)
& segmentP(X1,X7) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[26]) ).
fof(28,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| app(X6,cons(X5,nil)) != X3 ) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X7] :
( ssList(X7)
& neq(X7,nil)
& segmentP(X2,X7)
& segmentP(X1,X7) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[27,theory(equality)]) ).
fof(29,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(30,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[29]) ).
cnf(31,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[30]) ).
fof(39,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(40,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)],[39]) ).
fof(41,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)],[40]) ).
cnf(42,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(43,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(44,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[43]) ).
fof(45,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[44]) ).
cnf(46,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[45]) ).
fof(51,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(52,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[51]) ).
cnf(53,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[52]) ).
fof(58,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(59,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[58]) ).
fof(60,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[59]) ).
cnf(61,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[60]) ).
fof(84,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ segmentP(X1,X2)
| ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) )
& ( ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| app(app(X3,X2),X4) != X1 ) )
| segmentP(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(85,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ segmentP(X5,X6)
| ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& app(app(X7,X6),X8) = X5 ) ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X9,X6),X10) != X5 ) )
| segmentP(X5,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[84]) ).
fof(86,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ segmentP(X5,X6)
| ( ssList(esk5_2(X5,X6))
& ssList(esk6_2(X5,X6))
& app(app(esk5_2(X5,X6),X6),esk6_2(X5,X6)) = X5 ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X9,X6),X10) != X5 ) )
| segmentP(X5,X6) ) ) ) ),
inference(skolemize,[status(esa)],[85]) ).
fof(87,plain,
! [X5,X6,X9,X10] :
( ( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6) )
& ( ~ segmentP(X5,X6)
| ( ssList(esk5_2(X5,X6))
& ssList(esk6_2(X5,X6))
& app(app(esk5_2(X5,X6),X6),esk6_2(X5,X6)) = X5 ) ) )
| ~ ssList(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[86]) ).
fof(88,plain,
! [X5,X6,X9,X10] :
( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk5_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk6_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( app(app(esk5_2(X5,X6),X6),esk6_2(X5,X6)) = X5
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) ) ),
inference(distribute,[status(thm)],[87]) ).
cnf(92,plain,
( segmentP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[88]) ).
fof(107,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(nil,X1)
| nil = X1 )
& ( nil != X1
| segmentP(nil,X1) ) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(108,plain,
! [X2] :
( ~ ssList(X2)
| ( ( ~ segmentP(nil,X2)
| nil = X2 )
& ( nil != X2
| segmentP(nil,X2) ) ) ),
inference(variable_rename,[status(thm)],[107]) ).
fof(109,plain,
! [X2] :
( ( ~ segmentP(nil,X2)
| nil = X2
| ~ ssList(X2) )
& ( nil != X2
| segmentP(nil,X2)
| ~ ssList(X2) ) ),
inference(distribute,[status(thm)],[108]) ).
cnf(110,plain,
( segmentP(nil,X1)
| ~ ssList(X1)
| nil != X1 ),
inference(split_conjunct,[status(thm)],[109]) ).
fof(112,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(113,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[112]) ).
fof(114,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[113]) ).
fof(115,plain,
! [X3,X4] :
( ( ~ neq(X3,X4)
| X3 != X4
| ~ ssList(X4)
| ~ ssList(X3) )
& ( X3 = X4
| neq(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3) ) ),
inference(distribute,[status(thm)],[114]) ).
cnf(116,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[115]) ).
fof(118,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(119,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[118]) ).
fof(120,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[119]) ).
cnf(121,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[120]) ).
cnf(122,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[20]) ).
fof(131,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(132,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,X2) ),
inference(variable_rename,[status(thm)],[131]) ).
cnf(133,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[132]) ).
fof(134,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ~ segmentP(X1,X2)
| segmentP(app(app(X3,X1),X4),X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(135,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| ~ segmentP(X5,X6)
| segmentP(app(app(X7,X5),X8),X6) ) ) ) ),
inference(variable_rename,[status(thm)],[134]) ).
fof(136,plain,
! [X5,X6,X7,X8] :
( ~ ssList(X8)
| ~ segmentP(X5,X6)
| segmentP(app(app(X7,X5),X8),X6)
| ~ ssList(X7)
| ~ ssList(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[135]) ).
cnf(137,plain,
( segmentP(app(app(X3,X1),X4),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[136]) ).
fof(141,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ( nil = X3
| nil != X4 )
& ( ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& app(X6,cons(X5,nil)) = X3 ) )
| ~ neq(X4,nil) )
& ( ( nil = X2
& nil != X1 )
| ( neq(X2,nil)
& ! [X7] :
( ~ ssList(X7)
| ~ neq(X7,nil)
| ~ segmentP(X2,X7)
| ~ segmentP(X1,X7) ) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(142,negated_conjecture,
? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& X9 = X11
& X8 = X10
& ( nil = X10
| nil != X11 )
& ( ? [X12] :
( ssItem(X12)
& ? [X13] :
( ssList(X13)
& app(cons(X12,nil),X13) = X11
& app(X13,cons(X12,nil)) = X10 ) )
| ~ neq(X11,nil) )
& ( ( nil = X9
& nil != X8 )
| ( neq(X9,nil)
& ! [X14] :
( ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(X9,X14)
| ~ segmentP(X8,X14) ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[141]) ).
fof(143,negated_conjecture,
( ssList(esk7_0)
& ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ( nil = esk9_0
| nil != esk10_0 )
& ( ( ssItem(esk11_0)
& ssList(esk12_0)
& app(cons(esk11_0,nil),esk12_0) = esk10_0
& app(esk12_0,cons(esk11_0,nil)) = esk9_0 )
| ~ neq(esk10_0,nil) )
& ( ( nil = esk8_0
& nil != esk7_0 )
| ( neq(esk8_0,nil)
& ! [X14] :
( ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(esk8_0,X14)
| ~ segmentP(esk7_0,X14) ) ) ) ),
inference(skolemize,[status(esa)],[142]) ).
fof(144,negated_conjecture,
! [X14] :
( ( ( ( ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(esk8_0,X14)
| ~ segmentP(esk7_0,X14) )
& neq(esk8_0,nil) )
| ( nil = esk8_0
& nil != esk7_0 ) )
& ssList(esk10_0)
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ( nil = esk9_0
| nil != esk10_0 )
& ( ( ssItem(esk11_0)
& ssList(esk12_0)
& app(cons(esk11_0,nil),esk12_0) = esk10_0
& app(esk12_0,cons(esk11_0,nil)) = esk9_0 )
| ~ neq(esk10_0,nil) )
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(shift_quantors,[status(thm)],[143]) ).
fof(145,negated_conjecture,
! [X14] :
( ( nil = esk8_0
| ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(esk8_0,X14)
| ~ segmentP(esk7_0,X14) )
& ( nil != esk7_0
| ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(esk8_0,X14)
| ~ segmentP(esk7_0,X14) )
& ( nil = esk8_0
| neq(esk8_0,nil) )
& ( nil != esk7_0
| neq(esk8_0,nil) )
& ssList(esk10_0)
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ( nil = esk9_0
| nil != esk10_0 )
& ( ssItem(esk11_0)
| ~ neq(esk10_0,nil) )
& ( ssList(esk12_0)
| ~ neq(esk10_0,nil) )
& ( app(cons(esk11_0,nil),esk12_0) = esk10_0
| ~ neq(esk10_0,nil) )
& ( app(esk12_0,cons(esk11_0,nil)) = esk9_0
| ~ neq(esk10_0,nil) )
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(distribute,[status(thm)],[144]) ).
cnf(146,negated_conjecture,
ssList(esk7_0),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(147,negated_conjecture,
ssList(esk8_0),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(149,negated_conjecture,
( app(esk12_0,cons(esk11_0,nil)) = esk9_0
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(150,negated_conjecture,
( app(cons(esk11_0,nil),esk12_0) = esk10_0
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(151,negated_conjecture,
( ssList(esk12_0)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(152,negated_conjecture,
( ssItem(esk11_0)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(153,negated_conjecture,
( nil = esk9_0
| nil != esk10_0 ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(154,negated_conjecture,
esk7_0 = esk9_0,
inference(split_conjunct,[status(thm)],[145]) ).
cnf(155,negated_conjecture,
esk8_0 = esk10_0,
inference(split_conjunct,[status(thm)],[145]) ).
cnf(157,negated_conjecture,
( neq(esk8_0,nil)
| nil != esk7_0 ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(158,negated_conjecture,
( neq(esk8_0,nil)
| nil = esk8_0 ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(159,negated_conjecture,
( ~ segmentP(esk7_0,X1)
| ~ segmentP(esk8_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1)
| nil != esk7_0 ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(160,negated_conjecture,
( nil = esk8_0
| ~ segmentP(esk7_0,X1)
| ~ segmentP(esk8_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(163,negated_conjecture,
ssList(esk10_0),
inference(rw,[status(thm)],[147,155,theory(equality)]) ).
cnf(164,negated_conjecture,
( esk7_0 = nil
| esk10_0 != nil ),
inference(rw,[status(thm)],[153,154,theory(equality)]) ).
cnf(165,negated_conjecture,
( esk10_0 = nil
| neq(esk8_0,nil) ),
inference(rw,[status(thm)],[158,155,theory(equality)]) ).
cnf(166,negated_conjecture,
( esk10_0 = nil
| neq(esk10_0,nil) ),
inference(rw,[status(thm)],[165,155,theory(equality)]) ).
cnf(167,negated_conjecture,
( ssList(esk12_0)
| esk10_0 = nil ),
inference(spm,[status(thm)],[151,166,theory(equality)]) ).
cnf(168,negated_conjecture,
( ssItem(esk11_0)
| esk10_0 = nil ),
inference(spm,[status(thm)],[152,166,theory(equality)]) ).
cnf(169,negated_conjecture,
( neq(esk10_0,nil)
| esk7_0 != nil ),
inference(rw,[status(thm)],[157,155,theory(equality)]) ).
cnf(170,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(er,[status(thm)],[110,theory(equality)]) ).
cnf(171,plain,
( segmentP(nil,nil)
| $false ),
inference(rw,[status(thm)],[170,122,theory(equality)]) ).
cnf(172,plain,
segmentP(nil,nil),
inference(cn,[status(thm)],[171,theory(equality)]) ).
cnf(173,negated_conjecture,
( app(esk12_0,cons(esk11_0,nil)) = esk7_0
| ~ neq(esk10_0,nil) ),
inference(rw,[status(thm)],[149,154,theory(equality)]) ).
cnf(174,negated_conjecture,
( app(esk12_0,cons(esk11_0,nil)) = esk7_0
| esk10_0 = nil ),
inference(spm,[status(thm)],[173,166,theory(equality)]) ).
cnf(175,negated_conjecture,
( app(cons(esk11_0,nil),esk12_0) = esk10_0
| esk10_0 = nil ),
inference(spm,[status(thm)],[150,166,theory(equality)]) ).
cnf(204,negated_conjecture,
( esk10_0 = nil
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk7_0,X1)
| ~ segmentP(esk8_0,X1) ),
inference(rw,[status(thm)],[160,155,theory(equality)]) ).
cnf(205,negated_conjecture,
( esk10_0 = nil
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk7_0,X1)
| ~ segmentP(esk10_0,X1) ),
inference(rw,[status(thm)],[204,155,theory(equality)]) ).
cnf(207,negated_conjecture,
( esk10_0 = nil
| ~ segmentP(esk10_0,esk7_0)
| ~ neq(esk7_0,nil)
| ~ ssList(esk7_0) ),
inference(spm,[status(thm)],[205,133,theory(equality)]) ).
cnf(211,negated_conjecture,
( esk10_0 = nil
| ~ segmentP(esk10_0,esk7_0)
| ~ neq(esk7_0,nil)
| $false ),
inference(rw,[status(thm)],[207,146,theory(equality)]) ).
cnf(212,negated_conjecture,
( esk10_0 = nil
| ~ segmentP(esk10_0,esk7_0)
| ~ neq(esk7_0,nil) ),
inference(cn,[status(thm)],[211,theory(equality)]) ).
cnf(239,negated_conjecture,
( esk7_0 != nil
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk7_0,X1)
| ~ segmentP(esk10_0,X1) ),
inference(rw,[status(thm)],[159,155,theory(equality)]) ).
cnf(278,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| ~ ssList(nil)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X3,X2)) ),
inference(spm,[status(thm)],[92,31,theory(equality)]) ).
cnf(283,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| $false
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X3,X2)) ),
inference(rw,[status(thm)],[278,122,theory(equality)]) ).
cnf(284,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X3,X2)) ),
inference(cn,[status(thm)],[283,theory(equality)]) ).
cnf(289,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[42,53,theory(equality)]) ).
cnf(306,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[289,122,theory(equality)]) ).
cnf(307,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[306,theory(equality)]) ).
cnf(324,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[137,133,theory(equality)]) ).
cnf(394,negated_conjecture,
( esk10_0 = cons(esk11_0,esk12_0)
| esk10_0 = nil
| ~ ssItem(esk11_0)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[46,175,theory(equality)]) ).
cnf(437,negated_conjecture,
( cons(esk11_0,esk12_0) = esk10_0
| esk10_0 = nil
| ~ ssItem(esk11_0) ),
inference(csr,[status(thm)],[394,167]) ).
cnf(438,negated_conjecture,
( cons(esk11_0,esk12_0) = esk10_0
| esk10_0 = nil ),
inference(csr,[status(thm)],[437,168]) ).
cnf(1780,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[284,61]) ).
cnf(2130,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| esk10_0 = nil
| ~ ssList(esk12_0)
| ~ ssList(cons(esk11_0,nil)) ),
inference(spm,[status(thm)],[307,175,theory(equality)]) ).
cnf(3516,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| esk10_0 = nil
| ~ ssList(cons(esk11_0,nil)) ),
inference(csr,[status(thm)],[2130,167]) ).
cnf(3517,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| esk10_0 = nil
| ~ ssItem(esk11_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[3516,121,theory(equality)]) ).
cnf(3518,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| esk10_0 = nil
| ~ ssItem(esk11_0)
| $false ),
inference(rw,[status(thm)],[3517,122,theory(equality)]) ).
cnf(3519,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| esk10_0 = nil
| ~ ssItem(esk11_0) ),
inference(cn,[status(thm)],[3518,theory(equality)]) ).
cnf(3640,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| esk10_0 = nil ),
inference(csr,[status(thm)],[3519,168]) ).
cnf(3664,negated_conjecture,
( segmentP(X1,esk10_0)
| esk10_0 = nil
| esk10_0 != X1
| ~ ssList(nil)
| ~ ssList(esk10_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1780,3640,theory(equality)]) ).
cnf(3745,negated_conjecture,
( segmentP(X1,esk10_0)
| esk10_0 = nil
| esk10_0 != X1
| $false
| ~ ssList(esk10_0)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[3664,122,theory(equality)]) ).
cnf(3746,negated_conjecture,
( segmentP(X1,esk10_0)
| esk10_0 = nil
| esk10_0 != X1
| $false
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[3745,163,theory(equality)]) ).
cnf(3747,negated_conjecture,
( segmentP(X1,esk10_0)
| esk10_0 = nil
| esk10_0 != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[3746,theory(equality)]) ).
cnf(4462,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[324,53,theory(equality)]) ).
cnf(4473,negated_conjecture,
( segmentP(app(esk10_0,X1),esk12_0)
| esk10_0 = nil
| ~ ssList(X1)
| ~ ssList(cons(esk11_0,nil))
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[324,175,theory(equality)]) ).
cnf(4501,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[4462,122,theory(equality)]) ).
cnf(4502,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[4501,theory(equality)]) ).
cnf(4625,negated_conjecture,
( esk10_0 = nil
| segmentP(esk10_0,esk10_0)
| ~ ssList(esk10_0) ),
inference(er,[status(thm)],[3747,theory(equality)]) ).
cnf(4626,negated_conjecture,
( esk10_0 = nil
| segmentP(esk10_0,esk10_0)
| $false ),
inference(rw,[status(thm)],[4625,163,theory(equality)]) ).
cnf(4627,negated_conjecture,
( esk10_0 = nil
| segmentP(esk10_0,esk10_0) ),
inference(cn,[status(thm)],[4626,theory(equality)]) ).
cnf(4761,negated_conjecture,
( segmentP(esk7_0,esk12_0)
| esk10_0 = nil
| ~ ssList(cons(esk11_0,nil))
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[4502,174,theory(equality)]) ).
cnf(4822,negated_conjecture,
( esk10_0 = nil
| segmentP(esk7_0,esk12_0)
| ~ ssList(cons(esk11_0,nil)) ),
inference(csr,[status(thm)],[4761,167]) ).
cnf(4823,negated_conjecture,
( esk10_0 = nil
| segmentP(esk7_0,esk12_0)
| ~ ssItem(esk11_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[4822,121,theory(equality)]) ).
cnf(4825,negated_conjecture,
( esk10_0 = nil
| segmentP(esk7_0,esk12_0)
| ~ ssItem(esk11_0)
| $false ),
inference(rw,[status(thm)],[4823,122,theory(equality)]) ).
cnf(4826,negated_conjecture,
( esk10_0 = nil
| segmentP(esk7_0,esk12_0)
| ~ ssItem(esk11_0) ),
inference(cn,[status(thm)],[4825,theory(equality)]) ).
cnf(4827,negated_conjecture,
( esk10_0 = nil
| segmentP(esk7_0,esk12_0) ),
inference(csr,[status(thm)],[4826,168]) ).
cnf(4828,negated_conjecture,
( esk10_0 = nil
| ~ segmentP(esk10_0,esk12_0)
| ~ neq(esk12_0,nil)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[205,4827,theory(equality)]) ).
cnf(4890,negated_conjecture,
( esk10_0 = nil
| ~ segmentP(esk10_0,esk12_0)
| ~ neq(esk12_0,nil) ),
inference(csr,[status(thm)],[4828,167]) ).
cnf(8502,negated_conjecture,
( esk10_0 = nil
| segmentP(app(esk10_0,X1),esk12_0)
| ~ ssList(cons(esk11_0,nil))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[4473,167]) ).
cnf(8503,negated_conjecture,
( esk10_0 = nil
| segmentP(app(esk10_0,X1),esk12_0)
| ~ ssList(X1)
| ~ ssItem(esk11_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[8502,121,theory(equality)]) ).
cnf(8505,negated_conjecture,
( esk10_0 = nil
| segmentP(app(esk10_0,X1),esk12_0)
| ~ ssList(X1)
| ~ ssItem(esk11_0)
| $false ),
inference(rw,[status(thm)],[8503,122,theory(equality)]) ).
cnf(8506,negated_conjecture,
( esk10_0 = nil
| segmentP(app(esk10_0,X1),esk12_0)
| ~ ssList(X1)
| ~ ssItem(esk11_0) ),
inference(cn,[status(thm)],[8505,theory(equality)]) ).
cnf(8507,negated_conjecture,
( esk10_0 = nil
| segmentP(app(esk10_0,X1),esk12_0)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[8506,168]) ).
cnf(8508,negated_conjecture,
( esk10_0 = nil
| segmentP(esk10_0,esk12_0)
| ~ ssList(nil)
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[8507,31,theory(equality)]) ).
cnf(8519,negated_conjecture,
( esk10_0 = nil
| segmentP(esk10_0,esk12_0)
| $false
| ~ ssList(esk10_0) ),
inference(rw,[status(thm)],[8508,122,theory(equality)]) ).
cnf(8520,negated_conjecture,
( esk10_0 = nil
| segmentP(esk10_0,esk12_0)
| $false
| $false ),
inference(rw,[status(thm)],[8519,163,theory(equality)]) ).
cnf(8521,negated_conjecture,
( esk10_0 = nil
| segmentP(esk10_0,esk12_0) ),
inference(cn,[status(thm)],[8520,theory(equality)]) ).
cnf(8537,negated_conjecture,
( esk10_0 = nil
| ~ neq(esk12_0,nil) ),
inference(spm,[status(thm)],[4890,8521,theory(equality)]) ).
cnf(8621,negated_conjecture,
( esk10_0 = nil
| esk12_0 = nil
| ~ ssList(nil)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[8537,116,theory(equality)]) ).
cnf(8623,negated_conjecture,
( esk10_0 = nil
| esk12_0 = nil
| $false
| ~ ssList(esk12_0) ),
inference(rw,[status(thm)],[8621,122,theory(equality)]) ).
cnf(8624,negated_conjecture,
( esk10_0 = nil
| esk12_0 = nil
| ~ ssList(esk12_0) ),
inference(cn,[status(thm)],[8623,theory(equality)]) ).
cnf(8625,negated_conjecture,
( esk10_0 = nil
| esk12_0 = nil ),
inference(csr,[status(thm)],[8624,167]) ).
cnf(8631,negated_conjecture,
( cons(esk11_0,nil) = esk10_0
| esk10_0 = nil ),
inference(spm,[status(thm)],[438,8625,theory(equality)]) ).
cnf(8695,negated_conjecture,
( app(esk12_0,esk10_0) = esk7_0
| esk10_0 = nil ),
inference(spm,[status(thm)],[174,8631,theory(equality)]) ).
cnf(9054,negated_conjecture,
( app(nil,esk10_0) = esk7_0
| esk10_0 = nil ),
inference(spm,[status(thm)],[8695,8625,theory(equality)]) ).
cnf(9690,negated_conjecture,
( esk7_0 = esk10_0
| esk10_0 = nil
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[53,9054,theory(equality)]) ).
cnf(9773,negated_conjecture,
( esk7_0 = esk10_0
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[9690,163,theory(equality)]) ).
cnf(9774,negated_conjecture,
( esk7_0 = esk10_0
| esk10_0 = nil ),
inference(cn,[status(thm)],[9773,theory(equality)]) ).
cnf(9965,negated_conjecture,
( esk10_0 = nil
| ~ segmentP(esk10_0,esk10_0)
| ~ neq(esk10_0,nil) ),
inference(spm,[status(thm)],[212,9774,theory(equality)]) ).
cnf(10175,negated_conjecture,
( esk10_0 = nil
| ~ segmentP(esk10_0,esk10_0) ),
inference(csr,[status(thm)],[9965,166]) ).
cnf(10176,negated_conjecture,
esk10_0 = nil,
inference(csr,[status(thm)],[10175,4627]) ).
cnf(10533,negated_conjecture,
( esk7_0 != nil
| ~ segmentP(esk7_0,X1)
| ~ segmentP(nil,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[239,10176,theory(equality)]) ).
cnf(10539,negated_conjecture,
( neq(nil,nil)
| esk7_0 != nil ),
inference(rw,[status(thm)],[169,10176,theory(equality)]) ).
cnf(10542,negated_conjecture,
( esk7_0 = nil
| $false ),
inference(rw,[status(thm)],[164,10176,theory(equality)]) ).
cnf(10543,negated_conjecture,
esk7_0 = nil,
inference(cn,[status(thm)],[10542,theory(equality)]) ).
cnf(10561,negated_conjecture,
( $false
| ~ segmentP(esk7_0,X1)
| ~ segmentP(nil,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[10533,10543,theory(equality)]) ).
cnf(10562,negated_conjecture,
( $false
| ~ segmentP(nil,X1)
| ~ segmentP(nil,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[10561,10543,theory(equality)]) ).
cnf(10563,negated_conjecture,
( ~ segmentP(nil,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[10562,theory(equality)]) ).
cnf(10564,negated_conjecture,
( ~ neq(nil,nil)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[10563,172,theory(equality)]) ).
cnf(10567,negated_conjecture,
( ~ neq(nil,nil)
| $false ),
inference(rw,[status(thm)],[10564,122,theory(equality)]) ).
cnf(10568,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[10567,theory(equality)]) ).
cnf(10577,negated_conjecture,
( neq(nil,nil)
| $false ),
inference(rw,[status(thm)],[10539,10543,theory(equality)]) ).
cnf(10578,negated_conjecture,
neq(nil,nil),
inference(cn,[status(thm)],[10577,theory(equality)]) ).
cnf(10579,negated_conjecture,
$false,
inference(sr,[status(thm)],[10578,10568,theory(equality)]) ).
cnf(10580,negated_conjecture,
$false,
10579,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC061+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpTaxIFx/sel_SWC061+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC061+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC061+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC061+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
%
%------------------------------------------------------------------------------