TSTP Solution File: SWC077+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC077+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 10:12:34 EST 2010
% Result : Theorem 4.26s
% Output : CNFRefutation 4.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 25
% Syntax : Number of formulae : 289 ( 21 unt; 0 def)
% Number of atoms : 1273 ( 306 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 1769 ( 785 ~; 796 |; 124 &)
% ( 6 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 458 ( 0 sgn 210 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1] :
( ssItem(X1)
=> strictorderedP(cons(X1,nil)) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax68) ).
fof(5,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax84) ).
fof(6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax83) ).
fof(7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax82) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax81) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax46) ).
fof(12,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax28) ).
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(X1,X2)
=> frontsegP(app(X1,X3),X2) ) ) ) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax43) ).
fof(15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax27) ).
fof(16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax26) ).
fof(17,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax21) ).
fof(18,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax20) ).
fof(19,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,nil) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax45) ).
fof(22,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( frontsegP(X1,X2)
& frontsegP(X2,X3) )
=> frontsegP(X1,X3) ) ) ) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax40) ).
fof(23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax7) ).
fof(24,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax5) ).
fof(30,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( frontsegP(X1,X2)
& frontsegP(X2,X1) )
=> X1 = X2 ) ) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax41) ).
fof(37,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax58) ).
fof(39,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax16) ).
fof(40,axiom,
ssList(nil),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax17) ).
fof(42,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X3) )
=> segmentP(X1,X3) ) ) ) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax53) ).
fof(44,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax55) ).
fof(46,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax57) ).
fof(47,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax15) ).
fof(51,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ frontsegP(X4,X3)
| ~ strictorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ? [X6] :
( ssList(X6)
& neq(X3,X6)
& frontsegP(X4,X6)
& segmentP(X6,X3)
& strictorderedP(X6) )
| ( nil = X2
& nil = X1 ) ) ) ) ) ),
file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',co1) ).
fof(52,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ frontsegP(X4,X3)
| ~ strictorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ? [X6] :
( ssList(X6)
& neq(X3,X6)
& frontsegP(X4,X6)
& segmentP(X6,X3)
& strictorderedP(X6) )
| ( nil = X2
& nil = X1 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[51]) ).
fof(55,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ frontsegP(X4,X3)
| ~ strictorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ? [X6] :
( ssList(X6)
& neq(X3,X6)
& frontsegP(X4,X6)
& segmentP(X6,X3)
& strictorderedP(X6) )
| ( nil = X2
& nil = X1 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[52,theory(equality)]) ).
fof(61,plain,
! [X1] :
( ~ ssItem(X1)
| strictorderedP(cons(X1,nil)) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(62,plain,
! [X2] :
( ~ ssItem(X2)
| strictorderedP(cons(X2,nil)) ),
inference(variable_rename,[status(thm)],[61]) ).
cnf(63,plain,
( strictorderedP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[62]) ).
fof(68,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(69,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[68]) ).
cnf(70,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[69]) ).
fof(71,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)],[6]) ).
fof(72,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)],[71]) ).
fof(73,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)],[72]) ).
fof(74,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)],[73]) ).
cnf(77,plain,
( nil = X2
| ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[74]) ).
fof(78,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)],[7]) ).
fof(79,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)],[78]) ).
fof(80,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)],[79]) ).
cnf(81,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[80]) ).
fof(82,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(83,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[82]) ).
fof(84,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[83]) ).
cnf(85,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[84]) ).
fof(90,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(nil,X1)
| nil = X1 )
& ( nil != X1
| frontsegP(nil,X1) ) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(91,plain,
! [X2] :
( ~ ssList(X2)
| ( ( ~ frontsegP(nil,X2)
| nil = X2 )
& ( nil != X2
| frontsegP(nil,X2) ) ) ),
inference(variable_rename,[status(thm)],[90]) ).
fof(92,plain,
! [X2] :
( ( ~ frontsegP(nil,X2)
| nil = X2
| ~ ssList(X2) )
& ( nil != X2
| frontsegP(nil,X2)
| ~ ssList(X2) ) ),
inference(distribute,[status(thm)],[91]) ).
cnf(93,plain,
( frontsegP(nil,X1)
| ~ ssList(X1)
| nil != X1 ),
inference(split_conjunct,[status(thm)],[92]) ).
cnf(94,plain,
( nil = X1
| ~ ssList(X1)
| ~ frontsegP(nil,X1) ),
inference(split_conjunct,[status(thm)],[92]) ).
fof(99,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(100,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[99]) ).
cnf(101,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[100]) ).
fof(102,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ frontsegP(X1,X2)
| frontsegP(app(X1,X3),X2) ) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(103,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ~ frontsegP(X4,X5)
| frontsegP(app(X4,X6),X5) ) ) ),
inference(variable_rename,[status(thm)],[102]) ).
fof(104,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ~ frontsegP(X4,X5)
| frontsegP(app(X4,X6),X5)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[103]) ).
cnf(105,plain,
( frontsegP(app(X1,X3),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[104]) ).
fof(109,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)],[15]) ).
fof(110,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)],[109]) ).
fof(111,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)],[110]) ).
cnf(112,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[111]) ).
fof(113,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(114,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[113]) ).
fof(115,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[114]) ).
cnf(116,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[115]) ).
fof(117,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| nil != cons(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(118,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3) ) ),
inference(variable_rename,[status(thm)],[117]) ).
fof(119,plain,
! [X3,X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[118]) ).
cnf(120,plain,
( ~ ssList(X1)
| nil != cons(X2,X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[119]) ).
fof(121,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(122,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssItem(X6)
& cons(X6,X5) = X4 ) ) ),
inference(variable_rename,[status(thm)],[121]) ).
fof(123,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ( ssList(esk1_1(X4))
& ssItem(esk2_1(X4))
& cons(esk2_1(X4),esk1_1(X4)) = X4 ) ),
inference(skolemize,[status(esa)],[122]) ).
fof(124,plain,
! [X4] :
( ( ssList(esk1_1(X4))
| nil = X4
| ~ ssList(X4) )
& ( ssItem(esk2_1(X4))
| nil = X4
| ~ ssList(X4) )
& ( cons(esk2_1(X4),esk1_1(X4)) = X4
| nil = X4
| ~ ssList(X4) ) ),
inference(distribute,[status(thm)],[123]) ).
cnf(125,plain,
( nil = X1
| cons(esk2_1(X1),esk1_1(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[124]) ).
cnf(126,plain,
( nil = X1
| ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[124]) ).
cnf(127,plain,
( nil = X1
| ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[124]) ).
fof(128,plain,
! [X1] :
( ~ ssList(X1)
| frontsegP(X1,nil) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(129,plain,
! [X2] :
( ~ ssList(X2)
| frontsegP(X2,nil) ),
inference(variable_rename,[status(thm)],[128]) ).
cnf(130,plain,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[129]) ).
fof(143,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X2,X3)
| frontsegP(X1,X3) ) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(144,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ~ frontsegP(X4,X5)
| ~ frontsegP(X5,X6)
| frontsegP(X4,X6) ) ) ),
inference(variable_rename,[status(thm)],[143]) ).
fof(145,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ~ frontsegP(X4,X5)
| ~ frontsegP(X5,X6)
| frontsegP(X4,X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[144]) ).
cnf(146,plain,
( frontsegP(X1,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X2,X3)
| ~ frontsegP(X1,X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[145]) ).
fof(147,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)],[23]) ).
fof(148,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)],[147]) ).
fof(149,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)],[148]) ).
fof(150,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)],[149]) ).
fof(151,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)],[150]) ).
cnf(155,plain,
( segmentP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[151]) ).
fof(156,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ frontsegP(X1,X2)
| ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) )
& ( ! [X3] :
( ~ ssList(X3)
| app(X2,X3) != X1 )
| frontsegP(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(157,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ( ( ~ frontsegP(X4,X5)
| ? [X6] :
( ssList(X6)
& app(X5,X6) = X4 ) )
& ( ! [X7] :
( ~ ssList(X7)
| app(X5,X7) != X4 )
| frontsegP(X4,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[156]) ).
fof(158,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ( ( ~ frontsegP(X4,X5)
| ( ssList(esk7_2(X4,X5))
& app(X5,esk7_2(X4,X5)) = X4 ) )
& ( ! [X7] :
( ~ ssList(X7)
| app(X5,X7) != X4 )
| frontsegP(X4,X5) ) ) ) ),
inference(skolemize,[status(esa)],[157]) ).
fof(159,plain,
! [X4,X5,X7] :
( ( ( ~ ssList(X7)
| app(X5,X7) != X4
| frontsegP(X4,X5) )
& ( ~ frontsegP(X4,X5)
| ( ssList(esk7_2(X4,X5))
& app(X5,esk7_2(X4,X5)) = X4 ) ) )
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[158]) ).
fof(160,plain,
! [X4,X5,X7] :
( ( ~ ssList(X7)
| app(X5,X7) != X4
| frontsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) )
& ( ssList(esk7_2(X4,X5))
| ~ frontsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) )
& ( app(X5,esk7_2(X4,X5)) = X4
| ~ frontsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) ) ),
inference(distribute,[status(thm)],[159]) ).
cnf(161,plain,
( app(X2,esk7_2(X1,X2)) = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[160]) ).
cnf(162,plain,
( ssList(esk7_2(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[160]) ).
cnf(163,plain,
( frontsegP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X3) != X1
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[160]) ).
fof(188,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[30]) ).
fof(189,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ~ frontsegP(X3,X4)
| ~ frontsegP(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[188]) ).
fof(190,plain,
! [X3,X4] :
( ~ ssList(X4)
| ~ frontsegP(X3,X4)
| ~ frontsegP(X4,X3)
| X3 = X4
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[189]) ).
cnf(191,plain,
( X1 = X2
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| ~ frontsegP(X1,X2)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[190]) ).
fof(222,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(nil,X1)
| nil = X1 )
& ( nil != X1
| segmentP(nil,X1) ) ) ),
inference(fof_nnf,[status(thm)],[37]) ).
fof(223,plain,
! [X2] :
( ~ ssList(X2)
| ( ( ~ segmentP(nil,X2)
| nil = X2 )
& ( nil != X2
| segmentP(nil,X2) ) ) ),
inference(variable_rename,[status(thm)],[222]) ).
fof(224,plain,
! [X2] :
( ( ~ segmentP(nil,X2)
| nil = X2
| ~ ssList(X2) )
& ( nil != X2
| segmentP(nil,X2)
| ~ ssList(X2) ) ),
inference(distribute,[status(thm)],[223]) ).
cnf(225,plain,
( segmentP(nil,X1)
| ~ ssList(X1)
| nil != X1 ),
inference(split_conjunct,[status(thm)],[224]) ).
fof(231,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(232,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[231]) ).
fof(233,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[232]) ).
cnf(234,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[233]) ).
cnf(235,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[40]) ).
fof(249,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X3)
| segmentP(X1,X3) ) ) ),
inference(fof_nnf,[status(thm)],[42]) ).
fof(250,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ~ segmentP(X4,X5)
| ~ segmentP(X5,X6)
| segmentP(X4,X6) ) ) ),
inference(variable_rename,[status(thm)],[249]) ).
fof(251,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ~ segmentP(X4,X5)
| ~ segmentP(X5,X6)
| segmentP(X4,X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[250]) ).
cnf(252,plain,
( segmentP(X1,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[251]) ).
fof(257,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_nnf,[status(thm)],[44]) ).
fof(258,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,X2) ),
inference(variable_rename,[status(thm)],[257]) ).
cnf(259,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[258]) ).
fof(264,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(fof_nnf,[status(thm)],[46]) ).
fof(265,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,nil) ),
inference(variable_rename,[status(thm)],[264]) ).
cnf(266,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[265]) ).
fof(267,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[47]) ).
fof(268,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[267]) ).
fof(269,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[268]) ).
fof(270,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)],[269]) ).
cnf(271,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[270]) ).
fof(286,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& frontsegP(X4,X3)
& strictorderedP(X3)
& ! [X5] :
( ~ ssList(X5)
| ~ neq(X5,nil)
| ~ segmentP(X2,X5)
| ~ segmentP(X1,X5) )
& ! [X6] :
( ~ ssList(X6)
| ~ neq(X3,X6)
| ~ frontsegP(X4,X6)
| ~ segmentP(X6,X3)
| ~ strictorderedP(X6) )
& ( nil != X2
| nil != X1 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[55]) ).
fof(287,negated_conjecture,
? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& X8 = X10
& X7 = X9
& frontsegP(X10,X9)
& strictorderedP(X9)
& ! [X11] :
( ~ ssList(X11)
| ~ neq(X11,nil)
| ~ segmentP(X8,X11)
| ~ segmentP(X7,X11) )
& ! [X12] :
( ~ ssList(X12)
| ~ neq(X9,X12)
| ~ frontsegP(X10,X12)
| ~ segmentP(X12,X9)
| ~ strictorderedP(X12) )
& ( nil != X8
| nil != X7 ) ) ) ) ),
inference(variable_rename,[status(thm)],[286]) ).
fof(288,negated_conjecture,
( ssList(esk14_0)
& ssList(esk15_0)
& ssList(esk16_0)
& ssList(esk17_0)
& esk15_0 = esk17_0
& esk14_0 = esk16_0
& frontsegP(esk17_0,esk16_0)
& strictorderedP(esk16_0)
& ! [X11] :
( ~ ssList(X11)
| ~ neq(X11,nil)
| ~ segmentP(esk15_0,X11)
| ~ segmentP(esk14_0,X11) )
& ! [X12] :
( ~ ssList(X12)
| ~ neq(esk16_0,X12)
| ~ frontsegP(esk17_0,X12)
| ~ segmentP(X12,esk16_0)
| ~ strictorderedP(X12) )
& ( nil != esk15_0
| nil != esk14_0 ) ),
inference(skolemize,[status(esa)],[287]) ).
fof(289,negated_conjecture,
! [X11,X12] :
( ( ~ ssList(X12)
| ~ neq(esk16_0,X12)
| ~ frontsegP(esk17_0,X12)
| ~ segmentP(X12,esk16_0)
| ~ strictorderedP(X12) )
& ( ~ ssList(X11)
| ~ neq(X11,nil)
| ~ segmentP(esk15_0,X11)
| ~ segmentP(esk14_0,X11) )
& esk15_0 = esk17_0
& esk14_0 = esk16_0
& frontsegP(esk17_0,esk16_0)
& strictorderedP(esk16_0)
& ( nil != esk15_0
| nil != esk14_0 )
& ssList(esk17_0)
& ssList(esk16_0)
& ssList(esk15_0)
& ssList(esk14_0) ),
inference(shift_quantors,[status(thm)],[288]) ).
cnf(290,negated_conjecture,
ssList(esk14_0),
inference(split_conjunct,[status(thm)],[289]) ).
cnf(291,negated_conjecture,
ssList(esk15_0),
inference(split_conjunct,[status(thm)],[289]) ).
cnf(294,negated_conjecture,
( nil != esk14_0
| nil != esk15_0 ),
inference(split_conjunct,[status(thm)],[289]) ).
cnf(296,negated_conjecture,
frontsegP(esk17_0,esk16_0),
inference(split_conjunct,[status(thm)],[289]) ).
cnf(297,negated_conjecture,
esk14_0 = esk16_0,
inference(split_conjunct,[status(thm)],[289]) ).
cnf(298,negated_conjecture,
esk15_0 = esk17_0,
inference(split_conjunct,[status(thm)],[289]) ).
cnf(299,negated_conjecture,
( ~ segmentP(esk14_0,X1)
| ~ segmentP(esk15_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[289]) ).
cnf(300,negated_conjecture,
( ~ strictorderedP(X1)
| ~ segmentP(X1,esk16_0)
| ~ frontsegP(esk17_0,X1)
| ~ neq(esk16_0,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[289]) ).
cnf(301,negated_conjecture,
ssList(esk16_0),
inference(rw,[status(thm)],[290,297,theory(equality)]) ).
cnf(302,negated_conjecture,
ssList(esk17_0),
inference(rw,[status(thm)],[291,298,theory(equality)]) ).
cnf(303,negated_conjecture,
( esk16_0 != nil
| esk15_0 != nil ),
inference(rw,[status(thm)],[294,297,theory(equality)]) ).
cnf(304,negated_conjecture,
( esk16_0 != nil
| esk17_0 != nil ),
inference(rw,[status(thm)],[303,298,theory(equality)]) ).
cnf(321,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk16_0,X1)
| ~ segmentP(esk15_0,X1) ),
inference(rw,[status(thm)],[299,297,theory(equality)]) ).
cnf(322,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk16_0,X1)
| ~ segmentP(esk17_0,X1) ),
inference(rw,[status(thm)],[321,298,theory(equality)]) ).
cnf(323,negated_conjecture,
( X1 = nil
| ~ segmentP(esk16_0,X1)
| ~ segmentP(esk17_0,X1)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[322,271,theory(equality)]) ).
cnf(325,negated_conjecture,
( X1 = nil
| ~ segmentP(esk16_0,X1)
| ~ segmentP(esk17_0,X1)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[323,235,theory(equality)]) ).
cnf(326,negated_conjecture,
( X1 = nil
| ~ segmentP(esk16_0,X1)
| ~ segmentP(esk17_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[325,theory(equality)]) ).
cnf(350,negated_conjecture,
( esk16_0 = X1
| ~ segmentP(X1,esk16_0)
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ strictorderedP(X1)
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[300,271,theory(equality)]) ).
cnf(353,negated_conjecture,
( frontsegP(X1,esk16_0)
| ~ frontsegP(X1,esk17_0)
| ~ ssList(esk16_0)
| ~ ssList(esk17_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[146,296,theory(equality)]) ).
cnf(363,plain,
( segmentP(X1,X2)
| ~ segmentP(X1,nil)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1)
| nil != X2 ),
inference(spm,[status(thm)],[252,225,theory(equality)]) ).
cnf(366,plain,
( segmentP(X1,X2)
| ~ segmentP(X1,nil)
| ~ ssList(X2)
| $false
| ~ ssList(X1)
| nil != X2 ),
inference(rw,[status(thm)],[363,235,theory(equality)]) ).
cnf(367,plain,
( segmentP(X1,X2)
| ~ segmentP(X1,nil)
| ~ ssList(X2)
| ~ ssList(X1)
| nil != X2 ),
inference(cn,[status(thm)],[366,theory(equality)]) ).
cnf(368,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(er,[status(thm)],[163,theory(equality)]) ).
cnf(380,plain,
( X1 = app(X2,X3)
| ~ frontsegP(X1,app(X2,X3))
| ~ ssList(app(X2,X3))
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[191,105,theory(equality)]) ).
cnf(398,plain,
( nil = esk7_2(X1,X2)
| X1 != nil
| ~ ssList(esk7_2(X1,X2))
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[77,161,theory(equality)]) ).
cnf(448,plain,
( frontsegP(X1,cons(X2,nil))
| cons(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(cons(X2,nil))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(spm,[status(thm)],[163,85,theory(equality)]) ).
cnf(458,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| ~ ssList(nil)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X3,X2)) ),
inference(spm,[status(thm)],[155,70,theory(equality)]) ).
cnf(459,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[155,101,theory(equality)]) ).
cnf(467,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| $false
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X3,X2)) ),
inference(rw,[status(thm)],[458,235,theory(equality)]) ).
cnf(468,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X3,X2)) ),
inference(cn,[status(thm)],[467,theory(equality)]) ).
cnf(469,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[459,235,theory(equality)]) ).
cnf(470,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[469,theory(equality)]) ).
cnf(501,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[70,81,theory(equality)]) ).
cnf(503,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[81,101,theory(equality)]) ).
cnf(525,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[501,235,theory(equality)]) ).
cnf(526,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[525,theory(equality)]) ).
cnf(529,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[503,235,theory(equality)]) ).
cnf(530,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[529,theory(equality)]) ).
cnf(564,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssList(app(X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[234,112,theory(equality)]) ).
cnf(565,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssList(app(X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[120,112,theory(equality)]) ).
cnf(635,negated_conjecture,
( esk17_0 = nil
| ~ segmentP(esk16_0,esk17_0)
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[326,259,theory(equality)]) ).
cnf(636,negated_conjecture,
( esk17_0 = nil
| ~ segmentP(esk16_0,esk17_0)
| $false ),
inference(rw,[status(thm)],[635,302,theory(equality)]) ).
cnf(637,negated_conjecture,
( esk17_0 = nil
| ~ segmentP(esk16_0,esk17_0) ),
inference(cn,[status(thm)],[636,theory(equality)]) ).
cnf(638,negated_conjecture,
( esk16_0 = X1
| ~ segmentP(X1,esk16_0)
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ strictorderedP(X1)
| $false ),
inference(rw,[status(thm)],[350,301,theory(equality)]) ).
cnf(639,negated_conjecture,
( esk16_0 = X1
| ~ segmentP(X1,esk16_0)
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ strictorderedP(X1) ),
inference(cn,[status(thm)],[638,theory(equality)]) ).
cnf(664,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[565,116]) ).
cnf(675,negated_conjecture,
( frontsegP(X1,esk16_0)
| ~ frontsegP(X1,esk17_0)
| $false
| ~ ssList(esk17_0)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[353,301,theory(equality)]) ).
cnf(676,negated_conjecture,
( frontsegP(X1,esk16_0)
| ~ frontsegP(X1,esk17_0)
| $false
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[675,302,theory(equality)]) ).
cnf(677,negated_conjecture,
( frontsegP(X1,esk16_0)
| ~ frontsegP(X1,esk17_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[676,theory(equality)]) ).
cnf(679,negated_conjecture,
( frontsegP(nil,esk16_0)
| ~ ssList(nil)
| nil != esk17_0
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[677,93,theory(equality)]) ).
cnf(684,negated_conjecture,
( frontsegP(nil,esk16_0)
| $false
| nil != esk17_0
| ~ ssList(esk17_0) ),
inference(rw,[status(thm)],[679,235,theory(equality)]) ).
cnf(685,negated_conjecture,
( frontsegP(nil,esk16_0)
| $false
| nil != esk17_0
| $false ),
inference(rw,[status(thm)],[684,302,theory(equality)]) ).
cnf(686,negated_conjecture,
( frontsegP(nil,esk16_0)
| nil != esk17_0 ),
inference(cn,[status(thm)],[685,theory(equality)]) ).
cnf(689,negated_conjecture,
( nil = esk16_0
| ~ ssList(esk16_0)
| esk17_0 != nil ),
inference(spm,[status(thm)],[94,686,theory(equality)]) ).
cnf(692,negated_conjecture,
( nil = esk16_0
| $false
| esk17_0 != nil ),
inference(rw,[status(thm)],[689,301,theory(equality)]) ).
cnf(693,negated_conjecture,
( nil = esk16_0
| esk17_0 != nil ),
inference(cn,[status(thm)],[692,theory(equality)]) ).
cnf(700,negated_conjecture,
esk17_0 != nil,
inference(csr,[status(thm)],[693,304]) ).
cnf(730,plain,
( segmentP(X1,X2)
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[367,266]) ).
cnf(736,negated_conjecture,
( esk16_0 = X1
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ strictorderedP(X1)
| nil != esk16_0
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[639,730,theory(equality)]) ).
cnf(744,negated_conjecture,
( esk16_0 = X1
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ strictorderedP(X1)
| nil != esk16_0
| $false ),
inference(rw,[status(thm)],[736,301,theory(equality)]) ).
cnf(745,negated_conjecture,
( esk16_0 = X1
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ strictorderedP(X1)
| nil != esk16_0 ),
inference(cn,[status(thm)],[744,theory(equality)]) ).
cnf(747,negated_conjecture,
( esk16_0 = cons(X1,nil)
| esk16_0 != nil
| ~ frontsegP(esk17_0,cons(X1,nil))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[745,63,theory(equality)]) ).
cnf(773,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[368,116]) ).
cnf(781,plain,
( frontsegP(app(X1,app(X2,X3)),app(X1,X2))
| ~ ssList(X3)
| ~ ssList(app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[773,81,theory(equality)]) ).
cnf(843,plain,
( X1 = app(X2,X3)
| ~ frontsegP(X1,app(X2,X3))
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[380,116]) ).
cnf(849,plain,
( X1 = X3
| ~ frontsegP(X1,X3)
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(esk7_2(X3,X2))
| ~ ssList(X2)
| ~ frontsegP(X3,X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[843,161,theory(equality)]) ).
cnf(1139,plain,
( esk7_2(X1,X2) = nil
| X1 != nil
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[398,162]) ).
cnf(1141,plain,
( app(X1,nil) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2)
| X2 != nil ),
inference(spm,[status(thm)],[161,1139,theory(equality)]) ).
cnf(1266,plain,
( app(nil,nil) = X1
| X1 != nil
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1141,130,theory(equality)]) ).
cnf(1277,plain,
( app(nil,nil) = X1
| X1 != nil
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[1266,235,theory(equality)]) ).
cnf(1278,plain,
( app(nil,nil) = X1
| X1 != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1277,theory(equality)]) ).
cnf(1516,plain,
app(nil,nil) = nil,
inference(spm,[status(thm)],[1278,235,theory(equality)]) ).
cnf(1542,plain,
( app(nil,X1) = app(nil,app(nil,X1))
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[81,1516,theory(equality)]) ).
cnf(1543,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssList(nil)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[112,1516,theory(equality)]) ).
cnf(1571,plain,
( app(nil,X1) = app(nil,app(nil,X1))
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[1542,235,theory(equality)]) ).
cnf(1572,plain,
( app(nil,X1) = app(nil,app(nil,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1571,theory(equality)]) ).
cnf(1573,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| $false
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[1543,235,theory(equality)]) ).
cnf(1574,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[1573,theory(equality)]) ).
cnf(1817,plain,
( cons(X1,nil) != nil
| ~ ssList(nil)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[664,1574,theory(equality)]) ).
cnf(1858,plain,
( cons(X1,nil) != nil
| $false
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[1817,235,theory(equality)]) ).
cnf(1859,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[1858,theory(equality)]) ).
cnf(2165,plain,
( frontsegP(X1,cons(esk2_1(X2),nil))
| nil = X2
| X2 != X1
| ~ ssList(cons(esk2_1(X2),nil))
| ~ ssList(esk1_1(X2))
| ~ ssList(X1)
| ~ ssItem(esk2_1(X2))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[448,125,theory(equality)]) ).
cnf(2169,plain,
( frontsegP(X1,cons(esk2_1(X1),nil))
| nil = X1
| ~ ssList(cons(esk2_1(X1),nil))
| ~ ssList(esk1_1(X1))
| ~ ssList(X1)
| ~ ssItem(esk2_1(X1)) ),
inference(er,[status(thm)],[2165,theory(equality)]) ).
cnf(3106,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[468,116]) ).
cnf(3192,plain,
( segmentP(X1,X2)
| X3 != X1
| ~ ssList(esk7_2(X3,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X3,X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[470,161,theory(equality)]) ).
cnf(3213,plain,
( segmentP(X1,X2)
| ~ ssList(esk7_2(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X1,X2) ),
inference(er,[status(thm)],[3192,theory(equality)]) ).
cnf(4761,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[526,116]) ).
cnf(4817,plain,
( app(nil,X1) = app(X1,nil)
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[530,4761,theory(equality)]) ).
cnf(4873,plain,
( app(nil,X1) = app(X1,nil)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[4817,235,theory(equality)]) ).
cnf(4874,plain,
( app(nil,X1) = app(X1,nil)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[4873,theory(equality)]) ).
cnf(5168,plain,
( frontsegP(X1,X2)
| app(nil,X2) != X1
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[163,4874,theory(equality)]) ).
cnf(5229,plain,
( app(nil,app(X1,nil)) = app(X1,nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1572,4874,theory(equality)]) ).
cnf(5250,plain,
( segmentP(X1,X2)
| app(X2,nil) != X1
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[3106,4874,theory(equality)]) ).
cnf(5324,plain,
( frontsegP(X1,X2)
| app(nil,X2) != X1
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[5168,235,theory(equality)]) ).
cnf(5325,plain,
( frontsegP(X1,X2)
| app(nil,X2) != X1
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[5324,theory(equality)]) ).
cnf(5477,plain,
( segmentP(X1,X2)
| app(X2,nil) != X1
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[5250,235,theory(equality)]) ).
cnf(5478,plain,
( segmentP(X1,X2)
| app(X2,nil) != X1
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[5477,theory(equality)]) ).
cnf(10830,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[564,116]) ).
cnf(10838,plain,
( ssList(cons(X1,nil))
| ~ ssList(nil)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[10830,1574,theory(equality)]) ).
cnf(10860,plain,
( ssList(cons(X1,nil))
| $false
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[10838,235,theory(equality)]) ).
cnf(10861,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[10860,theory(equality)]) ).
cnf(12478,negated_conjecture,
( esk17_0 = nil
| app(esk17_0,nil) != esk16_0
| ~ ssList(esk17_0)
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[637,5478,theory(equality)]) ).
cnf(12499,negated_conjecture,
( esk17_0 = nil
| app(esk17_0,nil) != esk16_0
| $false
| ~ ssList(esk16_0) ),
inference(rw,[status(thm)],[12478,302,theory(equality)]) ).
cnf(12500,negated_conjecture,
( esk17_0 = nil
| app(esk17_0,nil) != esk16_0
| $false
| $false ),
inference(rw,[status(thm)],[12499,301,theory(equality)]) ).
cnf(12501,negated_conjecture,
( esk17_0 = nil
| app(esk17_0,nil) != esk16_0 ),
inference(cn,[status(thm)],[12500,theory(equality)]) ).
cnf(12502,negated_conjecture,
app(esk17_0,nil) != esk16_0,
inference(sr,[status(thm)],[12501,700,theory(equality)]) ).
cnf(12541,negated_conjecture,
( esk17_0 != esk16_0
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[12502,70,theory(equality)]) ).
cnf(12546,negated_conjecture,
( esk17_0 != esk16_0
| $false ),
inference(rw,[status(thm)],[12541,302,theory(equality)]) ).
cnf(12547,negated_conjecture,
esk17_0 != esk16_0,
inference(cn,[status(thm)],[12546,theory(equality)]) ).
cnf(17304,plain,
( frontsegP(app(X1,app(X2,X3)),app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[781,116]) ).
cnf(17396,plain,
( frontsegP(app(X1,nil),app(nil,X1))
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[17304,5229,theory(equality)]) ).
cnf(17496,plain,
( frontsegP(app(X1,nil),app(nil,X1))
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[17396,235,theory(equality)]) ).
cnf(17497,plain,
( frontsegP(app(X1,nil),app(nil,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[17496,theory(equality)]) ).
cnf(18269,plain,
( frontsegP(X1,app(nil,X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[17497,70,theory(equality)]) ).
cnf(18860,plain,
( X1 = X3
| ~ frontsegP(X3,X2)
| ~ frontsegP(X1,X3)
| ~ frontsegP(X2,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[849,162]) ).
cnf(18861,negated_conjecture,
( esk17_0 = esk16_0
| ~ frontsegP(X1,esk17_0)
| ~ frontsegP(esk16_0,X1)
| ~ ssList(esk17_0)
| ~ ssList(X1)
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[18860,296,theory(equality)]) ).
cnf(18908,negated_conjecture,
( esk17_0 = esk16_0
| ~ frontsegP(X1,esk17_0)
| ~ frontsegP(esk16_0,X1)
| $false
| ~ ssList(X1)
| ~ ssList(esk16_0) ),
inference(rw,[status(thm)],[18861,302,theory(equality)]) ).
cnf(18909,negated_conjecture,
( esk17_0 = esk16_0
| ~ frontsegP(X1,esk17_0)
| ~ frontsegP(esk16_0,X1)
| $false
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[18908,301,theory(equality)]) ).
cnf(18910,negated_conjecture,
( esk17_0 = esk16_0
| ~ frontsegP(X1,esk17_0)
| ~ frontsegP(esk16_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[18909,theory(equality)]) ).
cnf(18911,negated_conjecture,
( ~ frontsegP(X1,esk17_0)
| ~ frontsegP(esk16_0,X1)
| ~ ssList(X1) ),
inference(sr,[status(thm)],[18910,12547,theory(equality)]) ).
cnf(18981,negated_conjecture,
( ~ frontsegP(esk16_0,X1)
| ~ ssList(X1)
| app(nil,esk17_0) != X1
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[18911,5325,theory(equality)]) ).
cnf(19012,negated_conjecture,
( ~ frontsegP(esk16_0,X1)
| ~ ssList(X1)
| app(nil,esk17_0) != X1
| $false ),
inference(rw,[status(thm)],[18981,302,theory(equality)]) ).
cnf(19013,negated_conjecture,
( ~ frontsegP(esk16_0,X1)
| ~ ssList(X1)
| app(nil,esk17_0) != X1 ),
inference(cn,[status(thm)],[19012,theory(equality)]) ).
cnf(19358,negated_conjecture,
( app(nil,esk17_0) != app(nil,esk16_0)
| ~ ssList(app(nil,esk16_0))
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[19013,18269,theory(equality)]) ).
cnf(19387,negated_conjecture,
( app(nil,esk17_0) != app(nil,esk16_0)
| ~ ssList(app(nil,esk16_0))
| $false ),
inference(rw,[status(thm)],[19358,301,theory(equality)]) ).
cnf(19388,negated_conjecture,
( app(nil,esk17_0) != app(nil,esk16_0)
| ~ ssList(app(nil,esk16_0)) ),
inference(cn,[status(thm)],[19387,theory(equality)]) ).
cnf(22034,negated_conjecture,
( app(nil,esk17_0) != app(nil,esk16_0)
| ~ ssList(esk16_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[19388,116,theory(equality)]) ).
cnf(22040,negated_conjecture,
( app(nil,esk17_0) != app(nil,esk16_0)
| $false
| ~ ssList(nil) ),
inference(rw,[status(thm)],[22034,301,theory(equality)]) ).
cnf(22041,negated_conjecture,
( app(nil,esk17_0) != app(nil,esk16_0)
| $false
| $false ),
inference(rw,[status(thm)],[22040,235,theory(equality)]) ).
cnf(22042,negated_conjecture,
app(nil,esk17_0) != app(nil,esk16_0),
inference(cn,[status(thm)],[22041,theory(equality)]) ).
cnf(22051,negated_conjecture,
( esk17_0 != app(nil,esk16_0)
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[22042,101,theory(equality)]) ).
cnf(22055,negated_conjecture,
( esk17_0 != app(nil,esk16_0)
| $false ),
inference(rw,[status(thm)],[22051,302,theory(equality)]) ).
cnf(22056,negated_conjecture,
esk17_0 != app(nil,esk16_0),
inference(cn,[status(thm)],[22055,theory(equality)]) ).
cnf(51088,plain,
( nil = X1
| frontsegP(X1,cons(esk2_1(X1),nil))
| ~ ssList(cons(esk2_1(X1),nil))
| ~ ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[2169,126]) ).
cnf(51089,plain,
( nil = X1
| frontsegP(X1,cons(esk2_1(X1),nil))
| ~ ssList(cons(esk2_1(X1),nil))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[51088,127]) ).
cnf(78322,plain,
( segmentP(X1,X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[3213,162]) ).
cnf(78327,negated_conjecture,
( X1 = nil
| ~ segmentP(esk16_0,X1)
| ~ ssList(X1)
| ~ frontsegP(esk17_0,X1)
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[326,78322,theory(equality)]) ).
cnf(78371,negated_conjecture,
( X1 = nil
| ~ segmentP(esk16_0,X1)
| ~ ssList(X1)
| ~ frontsegP(esk17_0,X1)
| $false ),
inference(rw,[status(thm)],[78327,302,theory(equality)]) ).
cnf(78372,negated_conjecture,
( X1 = nil
| ~ segmentP(esk16_0,X1)
| ~ ssList(X1)
| ~ frontsegP(esk17_0,X1) ),
inference(cn,[status(thm)],[78371,theory(equality)]) ).
cnf(78648,negated_conjecture,
( esk16_0 = nil
| ~ frontsegP(esk17_0,esk16_0)
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[78372,259,theory(equality)]) ).
cnf(78675,negated_conjecture,
( esk16_0 = nil
| $false
| ~ ssList(esk16_0) ),
inference(rw,[status(thm)],[78648,296,theory(equality)]) ).
cnf(78676,negated_conjecture,
( esk16_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[78675,301,theory(equality)]) ).
cnf(78677,negated_conjecture,
esk16_0 = nil,
inference(cn,[status(thm)],[78676,theory(equality)]) ).
cnf(78750,negated_conjecture,
nil != esk17_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[22056,78677,theory(equality)]),1516,theory(equality)]) ).
cnf(79435,negated_conjecture,
( cons(X1,nil) = nil
| esk16_0 != nil
| ~ frontsegP(esk17_0,cons(X1,nil))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[747,78677,theory(equality)]) ).
cnf(79436,negated_conjecture,
( cons(X1,nil) = nil
| $false
| ~ frontsegP(esk17_0,cons(X1,nil))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[79435,78677,theory(equality)]) ).
cnf(79437,negated_conjecture,
( cons(X1,nil) = nil
| ~ frontsegP(esk17_0,cons(X1,nil))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[79436,theory(equality)]) ).
cnf(80659,negated_conjecture,
( cons(X1,nil) = nil
| ~ frontsegP(esk17_0,cons(X1,nil))
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[79437,10861]) ).
cnf(80660,negated_conjecture,
( ~ frontsegP(esk17_0,cons(X1,nil))
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[80659,1859]) ).
cnf(80670,negated_conjecture,
( nil = esk17_0
| ~ ssItem(esk2_1(esk17_0))
| ~ ssList(cons(esk2_1(esk17_0),nil))
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[80660,51089,theory(equality)]) ).
cnf(80683,negated_conjecture,
( nil = esk17_0
| ~ ssItem(esk2_1(esk17_0))
| ~ ssList(cons(esk2_1(esk17_0),nil))
| $false ),
inference(rw,[status(thm)],[80670,302,theory(equality)]) ).
cnf(80684,negated_conjecture,
( nil = esk17_0
| ~ ssItem(esk2_1(esk17_0))
| ~ ssList(cons(esk2_1(esk17_0),nil)) ),
inference(cn,[status(thm)],[80683,theory(equality)]) ).
cnf(80685,negated_conjecture,
( ~ ssItem(esk2_1(esk17_0))
| ~ ssList(cons(esk2_1(esk17_0),nil)) ),
inference(sr,[status(thm)],[80684,78750,theory(equality)]) ).
cnf(80745,negated_conjecture,
~ ssItem(esk2_1(esk17_0)),
inference(csr,[status(thm)],[80685,10861]) ).
cnf(80746,negated_conjecture,
( nil = esk17_0
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[80745,126,theory(equality)]) ).
cnf(80748,negated_conjecture,
( nil = esk17_0
| $false ),
inference(rw,[status(thm)],[80746,302,theory(equality)]) ).
cnf(80749,negated_conjecture,
nil = esk17_0,
inference(cn,[status(thm)],[80748,theory(equality)]) ).
cnf(80750,negated_conjecture,
$false,
inference(sr,[status(thm)],[80749,78750,theory(equality)]) ).
cnf(80751,negated_conjecture,
$false,
80750,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC077+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpeS6kvB/sel_SWC077+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC077+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC077+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC077+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
%
%------------------------------------------------------------------------------