TSTP Solution File: SWC120+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC120+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 10:20:29 EST 2010
% Result : Theorem 0.40s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 13
% Syntax : Number of formulae : 126 ( 14 unt; 0 def)
% Number of atoms : 555 ( 180 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 721 ( 292 ~; 320 |; 72 &)
% ( 1 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 182 ( 0 sgn 99 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpQ-E3-6/sel_SWC120+1.p_1',ax81) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpQ-E3-6/sel_SWC120+1.p_1',ax28) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/tmp/tmpQ-E3-6/sel_SWC120+1.p_1',ax24) ).
fof(11,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/tmp/tmpQ-E3-6/sel_SWC120+1.p_1',ax27) ).
fof(12,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpQ-E3-6/sel_SWC120+1.p_1',ax26) ).
fof(16,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/tmp/tmpQ-E3-6/sel_SWC120+1.p_1',ax22) ).
fof(25,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/tmp/tmpQ-E3-6/sel_SWC120+1.p_1',ax78) ).
fof(28,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpQ-E3-6/sel_SWC120+1.p_1',ax15) ).
fof(30,axiom,
ssList(nil),
file('/tmp/tmpQ-E3-6/sel_SWC120+1.p_1',ax17) ).
fof(32,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/tmp/tmpQ-E3-6/sel_SWC120+1.p_1',ax18) ).
fof(33,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/tmp/tmpQ-E3-6/sel_SWC120+1.p_1',ax55) ).
fof(34,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/tmpQ-E3-6/sel_SWC120+1.p_1',ax56) ).
fof(36,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X4 != X5
& ? [X6] :
( ssList(X6)
& tl(X4) = X6
& app(X3,X6) = X5
& neq(nil,X4) ) )
| ( neq(X1,nil)
& segmentP(X2,X1) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/tmp/tmpQ-E3-6/sel_SWC120+1.p_1',co1) ).
fof(37,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X4 != X5
& ? [X6] :
( ssList(X6)
& tl(X4) = X6
& app(X3,X6) = X5
& neq(nil,X4) ) )
| ( neq(X1,nil)
& segmentP(X2,X1) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[36]) ).
fof(38,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X4 != X5
& ? [X6] :
( ssList(X6)
& tl(X4) = X6
& app(X3,X6) = X5
& neq(nil,X4) ) )
| ( neq(X1,nil)
& segmentP(X2,X1) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[37,theory(equality)]) ).
fof(61,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(62,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[61]) ).
fof(63,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[62]) ).
cnf(64,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[63]) ).
fof(69,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(70,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[69]) ).
cnf(71,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[70]) ).
fof(76,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(77,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| ssList(tl(X2)) ),
inference(variable_rename,[status(thm)],[76]) ).
cnf(78,plain,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[77]) ).
fof(79,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)],[11]) ).
fof(80,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)],[79]) ).
fof(81,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)],[80]) ).
cnf(82,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[81]) ).
fof(83,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(84,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[83]) ).
fof(85,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[84]) ).
cnf(86,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[85]) ).
fof(102,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(103,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| ssItem(hd(X2)) ),
inference(variable_rename,[status(thm)],[102]) ).
cnf(104,plain,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[103]) ).
fof(151,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(152,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| cons(hd(X2),tl(X2)) = X2 ),
inference(variable_rename,[status(thm)],[151]) ).
cnf(153,plain,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[152]) ).
fof(163,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(164,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[163]) ).
fof(165,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[164]) ).
fof(166,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)],[165]) ).
cnf(167,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[166]) ).
cnf(168,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[166]) ).
cnf(173,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[30]) ).
fof(178,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) != X1 ) ),
inference(fof_nnf,[status(thm)],[32]) ).
fof(179,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) != X3 ) ),
inference(variable_rename,[status(thm)],[178]) ).
fof(180,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) != X3
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[179]) ).
cnf(181,plain,
( ~ ssList(X1)
| cons(X2,X1) != X1
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[180]) ).
fof(182,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(183,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,X2) ),
inference(variable_rename,[status(thm)],[182]) ).
cnf(184,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[183]) ).
fof(185,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)],[34]) ).
fof(186,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)],[185]) ).
fof(187,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)],[186]) ).
cnf(188,plain,
( segmentP(app(app(X3,X1),X4),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[187]) ).
fof(192,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ( ( neq(X2,nil)
& ! [X5] :
( ~ ssList(X5)
| X4 = X5
| ! [X6] :
( ~ ssList(X6)
| tl(X4) != X6
| app(X3,X6) != X5
| ~ neq(nil,X4) ) )
& ( ~ neq(X1,nil)
| ~ segmentP(X2,X1) ) )
| ( neq(X2,nil)
& ~ neq(X4,nil) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[38]) ).
fof(193,negated_conjecture,
? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& X8 = X10
& X7 = X9
& ( ( neq(X8,nil)
& ! [X11] :
( ~ ssList(X11)
| X10 = X11
| ! [X12] :
( ~ ssList(X12)
| tl(X10) != X12
| app(X9,X12) != X11
| ~ neq(nil,X10) ) )
& ( ~ neq(X7,nil)
| ~ segmentP(X8,X7) ) )
| ( neq(X8,nil)
& ~ neq(X10,nil) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[192]) ).
fof(194,negated_conjecture,
( ssList(esk9_0)
& ssList(esk10_0)
& ssList(esk11_0)
& ssList(esk12_0)
& esk10_0 = esk12_0
& esk9_0 = esk11_0
& ( ( neq(esk10_0,nil)
& ! [X11] :
( ~ ssList(X11)
| esk12_0 = X11
| ! [X12] :
( ~ ssList(X12)
| tl(esk12_0) != X12
| app(esk11_0,X12) != X11
| ~ neq(nil,esk12_0) ) )
& ( ~ neq(esk9_0,nil)
| ~ segmentP(esk10_0,esk9_0) ) )
| ( neq(esk10_0,nil)
& ~ neq(esk12_0,nil) ) ) ),
inference(skolemize,[status(esa)],[193]) ).
fof(195,negated_conjecture,
! [X11,X12] :
( ( ( ( ~ ssList(X12)
| tl(esk12_0) != X12
| app(esk11_0,X12) != X11
| ~ neq(nil,esk12_0)
| ~ ssList(X11)
| esk12_0 = X11 )
& neq(esk10_0,nil)
& ( ~ neq(esk9_0,nil)
| ~ segmentP(esk10_0,esk9_0) ) )
| ( neq(esk10_0,nil)
& ~ neq(esk12_0,nil) ) )
& esk10_0 = esk12_0
& esk9_0 = esk11_0
& ssList(esk12_0)
& ssList(esk11_0)
& ssList(esk10_0)
& ssList(esk9_0) ),
inference(shift_quantors,[status(thm)],[194]) ).
fof(196,negated_conjecture,
! [X11,X12] :
( ( neq(esk10_0,nil)
| ~ ssList(X12)
| tl(esk12_0) != X12
| app(esk11_0,X12) != X11
| ~ neq(nil,esk12_0)
| ~ ssList(X11)
| esk12_0 = X11 )
& ( ~ neq(esk12_0,nil)
| ~ ssList(X12)
| tl(esk12_0) != X12
| app(esk11_0,X12) != X11
| ~ neq(nil,esk12_0)
| ~ ssList(X11)
| esk12_0 = X11 )
& ( neq(esk10_0,nil)
| neq(esk10_0,nil) )
& ( ~ neq(esk12_0,nil)
| neq(esk10_0,nil) )
& ( neq(esk10_0,nil)
| ~ neq(esk9_0,nil)
| ~ segmentP(esk10_0,esk9_0) )
& ( ~ neq(esk12_0,nil)
| ~ neq(esk9_0,nil)
| ~ segmentP(esk10_0,esk9_0) )
& esk10_0 = esk12_0
& esk9_0 = esk11_0
& ssList(esk12_0)
& ssList(esk11_0)
& ssList(esk10_0)
& ssList(esk9_0) ),
inference(distribute,[status(thm)],[195]) ).
cnf(197,negated_conjecture,
ssList(esk9_0),
inference(split_conjunct,[status(thm)],[196]) ).
cnf(198,negated_conjecture,
ssList(esk10_0),
inference(split_conjunct,[status(thm)],[196]) ).
cnf(201,negated_conjecture,
esk9_0 = esk11_0,
inference(split_conjunct,[status(thm)],[196]) ).
cnf(202,negated_conjecture,
esk10_0 = esk12_0,
inference(split_conjunct,[status(thm)],[196]) ).
cnf(203,negated_conjecture,
( ~ segmentP(esk10_0,esk9_0)
| ~ neq(esk9_0,nil)
| ~ neq(esk12_0,nil) ),
inference(split_conjunct,[status(thm)],[196]) ).
cnf(206,negated_conjecture,
( neq(esk10_0,nil)
| neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[196]) ).
cnf(207,negated_conjecture,
( esk12_0 = X1
| ~ ssList(X1)
| ~ neq(nil,esk12_0)
| app(esk11_0,X2) != X1
| tl(esk12_0) != X2
| ~ ssList(X2)
| ~ neq(esk12_0,nil) ),
inference(split_conjunct,[status(thm)],[196]) ).
cnf(211,negated_conjecture,
ssList(esk12_0),
inference(rw,[status(thm)],[198,202,theory(equality)]) ).
cnf(212,negated_conjecture,
neq(esk12_0,nil),
inference(rw,[status(thm)],[206,202,theory(equality)]) ).
cnf(228,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[168,theory(equality)]) ).
cnf(229,negated_conjecture,
( ~ neq(esk9_0,nil)
| $false
| ~ segmentP(esk10_0,esk9_0) ),
inference(rw,[status(thm)],[203,212,theory(equality)]) ).
cnf(230,negated_conjecture,
( ~ neq(esk9_0,nil)
| $false
| ~ segmentP(esk12_0,esk9_0) ),
inference(rw,[status(thm)],[229,202,theory(equality)]) ).
cnf(231,negated_conjecture,
( ~ neq(esk9_0,nil)
| ~ segmentP(esk12_0,esk9_0) ),
inference(cn,[status(thm)],[230,theory(equality)]) ).
cnf(303,negated_conjecture,
( esk12_0 = X1
| tl(esk12_0) != X2
| app(esk9_0,X2) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk12_0)
| ~ neq(esk12_0,nil) ),
inference(rw,[status(thm)],[207,201,theory(equality)]) ).
cnf(304,negated_conjecture,
( esk12_0 = X1
| tl(esk12_0) != X2
| app(esk9_0,X2) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk12_0)
| $false ),
inference(rw,[status(thm)],[303,212,theory(equality)]) ).
cnf(305,negated_conjecture,
( esk12_0 = X1
| tl(esk12_0) != X2
| app(esk9_0,X2) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk12_0) ),
inference(cn,[status(thm)],[304,theory(equality)]) ).
cnf(306,negated_conjecture,
( esk12_0 = X1
| nil = esk12_0
| app(esk9_0,X2) != X1
| tl(esk12_0) != X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(esk12_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[305,167,theory(equality)]) ).
cnf(308,negated_conjecture,
( esk12_0 = X1
| nil = esk12_0
| app(esk9_0,X2) != X1
| tl(esk12_0) != X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(esk12_0)
| $false ),
inference(rw,[status(thm)],[306,173,theory(equality)]) ).
cnf(309,negated_conjecture,
( esk12_0 = X1
| nil = esk12_0
| app(esk9_0,X2) != X1
| tl(esk12_0) != X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(esk12_0) ),
inference(cn,[status(thm)],[308,theory(equality)]) ).
cnf(361,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[188,184,theory(equality)]) ).
cnf(372,plain,
( app(cons(X1,X2),X3) != app(X2,X3)
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[181,82,theory(equality)]) ).
cnf(474,plain,
( app(cons(X1,X2),X3) != app(X2,X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[372,86]) ).
cnf(478,plain,
( cons(X1,X2) != app(nil,X2)
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[474,64,theory(equality)]) ).
cnf(482,plain,
( cons(X1,X2) != app(nil,X2)
| ~ ssItem(X1)
| $false
| ~ ssList(X2) ),
inference(rw,[status(thm)],[478,173,theory(equality)]) ).
cnf(483,plain,
( cons(X1,X2) != app(nil,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[482,theory(equality)]) ).
cnf(492,plain,
( nil = X1
| X1 != app(nil,tl(X1))
| ~ ssItem(hd(X1))
| ~ ssList(tl(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[483,153,theory(equality)]) ).
cnf(499,plain,
( nil = X1
| app(nil,tl(X1)) != X1
| ~ ssItem(hd(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[492,78]) ).
cnf(500,plain,
( nil = X1
| app(nil,tl(X1)) != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[499,104]) ).
cnf(1376,negated_conjecture,
( esk12_0 = X1
| esk12_0 = nil
| app(esk9_0,X2) != X1
| tl(esk12_0) != X2
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[309,211,theory(equality)]) ).
cnf(1377,negated_conjecture,
( esk12_0 = X1
| esk12_0 = nil
| app(esk9_0,X2) != X1
| tl(esk12_0) != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1376,theory(equality)]) ).
cnf(1378,negated_conjecture,
( esk12_0 = nil
| esk12_0 = X1
| app(esk9_0,tl(esk12_0)) != X1
| ~ ssList(tl(esk12_0))
| ~ ssList(X1) ),
inference(er,[status(thm)],[1377,theory(equality)]) ).
cnf(1413,negated_conjecture,
( esk12_0 = nil
| esk12_0 = X1
| app(esk9_0,tl(esk12_0)) != X1
| ~ ssList(X1)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[1378,78,theory(equality)]) ).
cnf(1414,negated_conjecture,
( esk12_0 = nil
| esk12_0 = X1
| app(esk9_0,tl(esk12_0)) != X1
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[1413,211,theory(equality)]) ).
cnf(1415,negated_conjecture,
( esk12_0 = nil
| esk12_0 = X1
| app(esk9_0,tl(esk12_0)) != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1414,theory(equality)]) ).
cnf(1416,negated_conjecture,
( esk12_0 = nil
| esk12_0 = app(esk9_0,tl(esk12_0))
| ~ ssList(app(esk9_0,tl(esk12_0))) ),
inference(er,[status(thm)],[1415,theory(equality)]) ).
cnf(1422,negated_conjecture,
( app(esk9_0,tl(esk12_0)) = esk12_0
| esk12_0 = nil
| ~ ssList(tl(esk12_0))
| ~ ssList(esk9_0) ),
inference(spm,[status(thm)],[1416,86,theory(equality)]) ).
cnf(1423,negated_conjecture,
( app(esk9_0,tl(esk12_0)) = esk12_0
| esk12_0 = nil
| ~ ssList(tl(esk12_0))
| $false ),
inference(rw,[status(thm)],[1422,197,theory(equality)]) ).
cnf(1424,negated_conjecture,
( app(esk9_0,tl(esk12_0)) = esk12_0
| esk12_0 = nil
| ~ ssList(tl(esk12_0)) ),
inference(cn,[status(thm)],[1423,theory(equality)]) ).
cnf(1425,negated_conjecture,
( app(esk9_0,tl(esk12_0)) = esk12_0
| esk12_0 = nil
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[1424,78,theory(equality)]) ).
cnf(1426,negated_conjecture,
( app(esk9_0,tl(esk12_0)) = esk12_0
| esk12_0 = nil
| $false ),
inference(rw,[status(thm)],[1425,211,theory(equality)]) ).
cnf(1427,negated_conjecture,
( app(esk9_0,tl(esk12_0)) = esk12_0
| esk12_0 = nil ),
inference(cn,[status(thm)],[1426,theory(equality)]) ).
cnf(4349,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[361,71,theory(equality)]) ).
cnf(4384,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[4349,173,theory(equality)]) ).
cnf(4385,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[4384,theory(equality)]) ).
cnf(4837,negated_conjecture,
( segmentP(esk12_0,esk9_0)
| esk12_0 = nil
| ~ ssList(tl(esk12_0))
| ~ ssList(esk9_0) ),
inference(spm,[status(thm)],[4385,1427,theory(equality)]) ).
cnf(4863,negated_conjecture,
( segmentP(esk12_0,esk9_0)
| esk12_0 = nil
| ~ ssList(tl(esk12_0))
| $false ),
inference(rw,[status(thm)],[4837,197,theory(equality)]) ).
cnf(4864,negated_conjecture,
( segmentP(esk12_0,esk9_0)
| esk12_0 = nil
| ~ ssList(tl(esk12_0)) ),
inference(cn,[status(thm)],[4863,theory(equality)]) ).
cnf(4879,negated_conjecture,
( esk12_0 = nil
| segmentP(esk12_0,esk9_0)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[4864,78,theory(equality)]) ).
cnf(4880,negated_conjecture,
( esk12_0 = nil
| segmentP(esk12_0,esk9_0)
| $false ),
inference(rw,[status(thm)],[4879,211,theory(equality)]) ).
cnf(4881,negated_conjecture,
( esk12_0 = nil
| segmentP(esk12_0,esk9_0) ),
inference(cn,[status(thm)],[4880,theory(equality)]) ).
cnf(4952,negated_conjecture,
( esk12_0 = nil
| ~ neq(esk9_0,nil) ),
inference(spm,[status(thm)],[231,4881,theory(equality)]) ).
cnf(4977,negated_conjecture,
( esk12_0 = nil
| esk9_0 = nil
| ~ ssList(nil)
| ~ ssList(esk9_0) ),
inference(spm,[status(thm)],[4952,167,theory(equality)]) ).
cnf(4979,negated_conjecture,
( esk12_0 = nil
| esk9_0 = nil
| $false
| ~ ssList(esk9_0) ),
inference(rw,[status(thm)],[4977,173,theory(equality)]) ).
cnf(4980,negated_conjecture,
( esk12_0 = nil
| esk9_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[4979,197,theory(equality)]) ).
cnf(4981,negated_conjecture,
( esk12_0 = nil
| esk9_0 = nil ),
inference(cn,[status(thm)],[4980,theory(equality)]) ).
cnf(4985,negated_conjecture,
( app(nil,tl(esk12_0)) = esk12_0
| esk12_0 = nil ),
inference(spm,[status(thm)],[1427,4981,theory(equality)]) ).
cnf(5068,negated_conjecture,
( nil = esk12_0
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[500,4985,theory(equality)]) ).
cnf(5120,negated_conjecture,
( nil = esk12_0
| $false ),
inference(rw,[status(thm)],[5068,211,theory(equality)]) ).
cnf(5121,negated_conjecture,
nil = esk12_0,
inference(cn,[status(thm)],[5120,theory(equality)]) ).
cnf(5173,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[212,5121,theory(equality)]) ).
cnf(5260,negated_conjecture,
~ ssList(nil),
inference(spm,[status(thm)],[228,5173,theory(equality)]) ).
cnf(5262,negated_conjecture,
$false,
inference(rw,[status(thm)],[5260,173,theory(equality)]) ).
cnf(5263,negated_conjecture,
$false,
inference(cn,[status(thm)],[5262,theory(equality)]) ).
cnf(5264,negated_conjecture,
$false,
5263,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC120+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpQ-E3-6/sel_SWC120+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC120+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC120+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC120+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
%
%------------------------------------------------------------------------------