TSTP Solution File: SWC091+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC091+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 10:15:56 EST 2010
% Result : Theorem 4.31s
% Output : CNFRefutation 4.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 65
% Number of leaves : 25
% Syntax : Number of formulae : 293 ( 26 unt; 0 def)
% Number of atoms : 1346 ( 315 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 1916 ( 863 ~; 856 |; 135 &)
% ( 9 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 4 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 492 ( 0 sgn 202 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( totalorderedP(cons(X1,X2))
<=> ( nil = X2
| ( nil != X2
& totalorderedP(X2)
& leq(X1,hd(X2)) ) ) ) ) ),
file('/tmp/tmp2xutpp/sel_SWC091+1.p_1',ax67) ).
fof(5,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmp2xutpp/sel_SWC091+1.p_1',ax84) ).
fof(6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmp2xutpp/sel_SWC091+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/tmp2xutpp/sel_SWC091+1.p_1',ax82) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmp2xutpp/sel_SWC091+1.p_1',ax81) ).
fof(12,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmp2xutpp/sel_SWC091+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/tmp2xutpp/sel_SWC091+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/tmp2xutpp/sel_SWC091+1.p_1',ax27) ).
fof(16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmp2xutpp/sel_SWC091+1.p_1',ax26) ).
fof(17,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmp2xutpp/sel_SWC091+1.p_1',ax21) ).
fof(18,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/tmp/tmp2xutpp/sel_SWC091+1.p_1',ax20) ).
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/tmp2xutpp/sel_SWC091+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/tmp2xutpp/sel_SWC091+1.p_1',ax5) ).
fof(29,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( frontsegP(X1,X2)
& frontsegP(X2,X1) )
=> X1 = X2 ) ) ),
file('/tmp/tmp2xutpp/sel_SWC091+1.p_1',ax41) ).
fof(32,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/tmp/tmp2xutpp/sel_SWC091+1.p_1',ax58) ).
fof(33,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmp2xutpp/sel_SWC091+1.p_1',ax15) ).
fof(34,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmp2xutpp/sel_SWC091+1.p_1',ax16) ).
fof(35,axiom,
ssList(nil),
file('/tmp/tmp2xutpp/sel_SWC091+1.p_1',ax17) ).
fof(37,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X3) )
=> segmentP(X1,X3) ) ) ) ),
file('/tmp/tmp2xutpp/sel_SWC091+1.p_1',ax53) ).
fof(39,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/tmp/tmp2xutpp/sel_SWC091+1.p_1',ax55) ).
fof(41,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/tmp/tmp2xutpp/sel_SWC091+1.p_1',ax57) ).
fof(45,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ~ frontsegP(X4,X3)
| ~ totalorderedP(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)
& totalorderedP(X6) ) ) ) ) ) ),
file('/tmp/tmp2xutpp/sel_SWC091+1.p_1',co1) ).
fof(46,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ~ frontsegP(X4,X3)
| ~ totalorderedP(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)
& totalorderedP(X6) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[45]) ).
fof(47,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ~ frontsegP(X4,X3)
| ~ totalorderedP(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)
& totalorderedP(X6) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[46,theory(equality)]) ).
fof(51,plain,
! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ totalorderedP(cons(X1,X2))
| nil = X2
| ( nil != X2
& totalorderedP(X2)
& leq(X1,hd(X2)) ) )
& ( ( nil != X2
& ( nil = X2
| ~ totalorderedP(X2)
| ~ leq(X1,hd(X2)) ) )
| totalorderedP(cons(X1,X2)) ) ) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(52,plain,
! [X3] :
( ~ ssItem(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ totalorderedP(cons(X3,X4))
| nil = X4
| ( nil != X4
& totalorderedP(X4)
& leq(X3,hd(X4)) ) )
& ( ( nil != X4
& ( nil = X4
| ~ totalorderedP(X4)
| ~ leq(X3,hd(X4)) ) )
| totalorderedP(cons(X3,X4)) ) ) ) ),
inference(variable_rename,[status(thm)],[51]) ).
fof(53,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ totalorderedP(cons(X3,X4))
| nil = X4
| ( nil != X4
& totalorderedP(X4)
& leq(X3,hd(X4)) ) )
& ( ( nil != X4
& ( nil = X4
| ~ totalorderedP(X4)
| ~ leq(X3,hd(X4)) ) )
| totalorderedP(cons(X3,X4)) ) )
| ~ ssItem(X3) ),
inference(shift_quantors,[status(thm)],[52]) ).
fof(54,plain,
! [X3,X4] :
( ( nil != X4
| nil = X4
| ~ totalorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) )
& ( totalorderedP(X4)
| nil = X4
| ~ totalorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) )
& ( leq(X3,hd(X4))
| nil = X4
| ~ totalorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) )
& ( nil != X4
| totalorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) )
& ( nil = X4
| ~ totalorderedP(X4)
| ~ leq(X3,hd(X4))
| totalorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) ) ),
inference(distribute,[status(thm)],[53]) ).
cnf(56,plain,
( totalorderedP(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2)
| nil != X2 ),
inference(split_conjunct,[status(thm)],[54]) ).
fof(65,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(66,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[65]) ).
cnf(67,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[66]) ).
fof(68,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(69,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)],[68]) ).
fof(70,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)],[69]) ).
fof(71,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)],[70]) ).
cnf(72,plain,
( nil = app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| nil != X1
| nil != X2 ),
inference(split_conjunct,[status(thm)],[71]) ).
fof(75,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(76,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)],[75]) ).
fof(77,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)],[76]) ).
cnf(78,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[77]) ).
fof(79,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(80,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[79]) ).
fof(81,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[80]) ).
cnf(82,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[81]) ).
fof(96,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(97,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[96]) ).
cnf(98,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[97]) ).
fof(99,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(100,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ~ frontsegP(X4,X5)
| frontsegP(app(X4,X6),X5) ) ) ),
inference(variable_rename,[status(thm)],[99]) ).
fof(101,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ~ frontsegP(X4,X5)
| frontsegP(app(X4,X6),X5)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[100]) ).
cnf(102,plain,
( frontsegP(app(X1,X3),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[101]) ).
fof(106,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(107,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)],[106]) ).
fof(108,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)],[107]) ).
cnf(109,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[108]) ).
fof(110,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(111,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[110]) ).
fof(112,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[111]) ).
cnf(113,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[112]) ).
fof(114,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| nil != cons(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(115,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3) ) ),
inference(variable_rename,[status(thm)],[114]) ).
fof(116,plain,
! [X3,X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[115]) ).
cnf(117,plain,
( ~ ssList(X1)
| nil != cons(X2,X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[116]) ).
fof(118,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(119,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssItem(X6)
& cons(X6,X5) = X4 ) ) ),
inference(variable_rename,[status(thm)],[118]) ).
fof(120,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)],[119]) ).
fof(121,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)],[120]) ).
cnf(122,plain,
( nil = X1
| cons(esk2_1(X1),esk1_1(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[121]) ).
cnf(123,plain,
( nil = X1
| ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[121]) ).
cnf(124,plain,
( nil = X1
| ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[121]) ).
fof(144,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(145,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)],[144]) ).
fof(146,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)],[145]) ).
fof(147,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)],[146]) ).
fof(148,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)],[147]) ).
cnf(152,plain,
( segmentP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[148]) ).
fof(153,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(154,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)],[153]) ).
fof(155,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)],[154]) ).
fof(156,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)],[155]) ).
fof(157,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)],[156]) ).
cnf(158,plain,
( app(X2,esk7_2(X1,X2)) = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(159,plain,
( ssList(esk7_2(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(160,plain,
( frontsegP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X3) != X1
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[157]) ).
fof(178,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[29]) ).
fof(179,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ~ frontsegP(X3,X4)
| ~ frontsegP(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[178]) ).
fof(180,plain,
! [X3,X4] :
( ~ ssList(X4)
| ~ frontsegP(X3,X4)
| ~ frontsegP(X4,X3)
| X3 = X4
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[179]) ).
cnf(181,plain,
( X1 = X2
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| ~ frontsegP(X1,X2)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[180]) ).
fof(192,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(nil,X1)
| nil = X1 )
& ( nil != X1
| segmentP(nil,X1) ) ) ),
inference(fof_nnf,[status(thm)],[32]) ).
fof(193,plain,
! [X2] :
( ~ ssList(X2)
| ( ( ~ segmentP(nil,X2)
| nil = X2 )
& ( nil != X2
| segmentP(nil,X2) ) ) ),
inference(variable_rename,[status(thm)],[192]) ).
fof(194,plain,
! [X2] :
( ( ~ segmentP(nil,X2)
| nil = X2
| ~ ssList(X2) )
& ( nil != X2
| segmentP(nil,X2)
| ~ ssList(X2) ) ),
inference(distribute,[status(thm)],[193]) ).
cnf(195,plain,
( segmentP(nil,X1)
| ~ ssList(X1)
| nil != X1 ),
inference(split_conjunct,[status(thm)],[194]) ).
fof(197,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(198,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[197]) ).
fof(199,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[198]) ).
fof(200,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)],[199]) ).
cnf(201,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[200]) ).
fof(203,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(204,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[203]) ).
fof(205,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[204]) ).
cnf(206,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[205]) ).
cnf(207,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[35]) ).
fof(221,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X3)
| segmentP(X1,X3) ) ) ),
inference(fof_nnf,[status(thm)],[37]) ).
fof(222,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ~ segmentP(X4,X5)
| ~ segmentP(X5,X6)
| segmentP(X4,X6) ) ) ),
inference(variable_rename,[status(thm)],[221]) ).
fof(223,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ~ segmentP(X4,X5)
| ~ segmentP(X5,X6)
| segmentP(X4,X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[222]) ).
cnf(224,plain,
( segmentP(X1,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[223]) ).
fof(229,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(230,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,X2) ),
inference(variable_rename,[status(thm)],[229]) ).
cnf(231,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[230]) ).
fof(236,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(fof_nnf,[status(thm)],[41]) ).
fof(237,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,nil) ),
inference(variable_rename,[status(thm)],[236]) ).
cnf(238,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[237]) ).
fof(252,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& neq(X2,nil)
& frontsegP(X4,X3)
& totalorderedP(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)
| ~ totalorderedP(X6) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[47]) ).
fof(253,negated_conjecture,
? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& X8 = X10
& X7 = X9
& neq(X8,nil)
& frontsegP(X10,X9)
& totalorderedP(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)
| ~ totalorderedP(X12) ) ) ) ) ),
inference(variable_rename,[status(thm)],[252]) ).
fof(254,negated_conjecture,
( ssList(esk14_0)
& ssList(esk15_0)
& ssList(esk16_0)
& ssList(esk17_0)
& esk15_0 = esk17_0
& esk14_0 = esk16_0
& neq(esk15_0,nil)
& frontsegP(esk17_0,esk16_0)
& totalorderedP(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)
| ~ totalorderedP(X12) ) ),
inference(skolemize,[status(esa)],[253]) ).
fof(255,negated_conjecture,
! [X11,X12] :
( ( ~ ssList(X12)
| ~ neq(esk16_0,X12)
| ~ frontsegP(esk17_0,X12)
| ~ segmentP(X12,esk16_0)
| ~ totalorderedP(X12) )
& ( ~ ssList(X11)
| ~ neq(X11,nil)
| ~ segmentP(esk15_0,X11)
| ~ segmentP(esk14_0,X11) )
& esk15_0 = esk17_0
& esk14_0 = esk16_0
& neq(esk15_0,nil)
& frontsegP(esk17_0,esk16_0)
& totalorderedP(esk16_0)
& ssList(esk17_0)
& ssList(esk16_0)
& ssList(esk15_0)
& ssList(esk14_0) ),
inference(shift_quantors,[status(thm)],[254]) ).
cnf(256,negated_conjecture,
ssList(esk14_0),
inference(split_conjunct,[status(thm)],[255]) ).
cnf(257,negated_conjecture,
ssList(esk15_0),
inference(split_conjunct,[status(thm)],[255]) ).
cnf(261,negated_conjecture,
frontsegP(esk17_0,esk16_0),
inference(split_conjunct,[status(thm)],[255]) ).
cnf(262,negated_conjecture,
neq(esk15_0,nil),
inference(split_conjunct,[status(thm)],[255]) ).
cnf(263,negated_conjecture,
esk14_0 = esk16_0,
inference(split_conjunct,[status(thm)],[255]) ).
cnf(264,negated_conjecture,
esk15_0 = esk17_0,
inference(split_conjunct,[status(thm)],[255]) ).
cnf(265,negated_conjecture,
( ~ segmentP(esk14_0,X1)
| ~ segmentP(esk15_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[255]) ).
cnf(266,negated_conjecture,
( ~ totalorderedP(X1)
| ~ segmentP(X1,esk16_0)
| ~ frontsegP(esk17_0,X1)
| ~ neq(esk16_0,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[255]) ).
cnf(267,negated_conjecture,
ssList(esk16_0),
inference(rw,[status(thm)],[256,263,theory(equality)]) ).
cnf(268,negated_conjecture,
ssList(esk17_0),
inference(rw,[status(thm)],[257,264,theory(equality)]) ).
cnf(269,negated_conjecture,
neq(esk17_0,nil),
inference(rw,[status(thm)],[262,264,theory(equality)]) ).
cnf(280,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk16_0,X1)
| ~ segmentP(esk15_0,X1) ),
inference(rw,[status(thm)],[265,263,theory(equality)]) ).
cnf(281,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk16_0,X1)
| ~ segmentP(esk17_0,X1) ),
inference(rw,[status(thm)],[280,264,theory(equality)]) ).
cnf(282,negated_conjecture,
( ~ segmentP(esk16_0,esk17_0)
| ~ segmentP(esk17_0,esk17_0)
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[281,269,theory(equality)]) ).
cnf(283,negated_conjecture,
( X1 = nil
| ~ segmentP(esk16_0,X1)
| ~ segmentP(esk17_0,X1)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[281,201,theory(equality)]) ).
cnf(284,negated_conjecture,
( X1 = nil
| ~ segmentP(esk16_0,X1)
| ~ segmentP(esk17_0,X1)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[283,207,theory(equality)]) ).
cnf(285,negated_conjecture,
( X1 = nil
| ~ segmentP(esk16_0,X1)
| ~ segmentP(esk17_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[284,theory(equality)]) ).
cnf(324,negated_conjecture,
( esk16_0 = X1
| ~ segmentP(X1,esk16_0)
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1)
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[266,201,theory(equality)]) ).
cnf(329,plain,
( segmentP(X1,X2)
| ~ segmentP(X1,nil)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1)
| nil != X2 ),
inference(spm,[status(thm)],[224,195,theory(equality)]) ).
cnf(332,plain,
( segmentP(X1,X2)
| ~ segmentP(X1,nil)
| ~ ssList(X2)
| $false
| ~ ssList(X1)
| nil != X2 ),
inference(rw,[status(thm)],[329,207,theory(equality)]) ).
cnf(333,plain,
( segmentP(X1,X2)
| ~ segmentP(X1,nil)
| ~ ssList(X2)
| ~ ssList(X1)
| nil != X2 ),
inference(cn,[status(thm)],[332,theory(equality)]) ).
cnf(334,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(er,[status(thm)],[160,theory(equality)]) ).
cnf(346,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)],[181,102,theory(equality)]) ).
cnf(411,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[152,98,theory(equality)]) ).
cnf(420,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[411,207,theory(equality)]) ).
cnf(421,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[420,theory(equality)]) ).
cnf(442,plain,
( frontsegP(X1,cons(X2,nil))
| cons(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(cons(X2,nil))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(spm,[status(thm)],[160,82,theory(equality)]) ).
cnf(458,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[67,78,theory(equality)]) ).
cnf(460,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[78,98,theory(equality)]) ).
cnf(466,plain,
( frontsegP(X1,app(X2,X3))
| app(X2,app(X3,X4)) != X1
| ~ ssList(X4)
| ~ ssList(app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[160,78,theory(equality)]) ).
cnf(476,plain,
( segmentP(X1,X2)
| app(X3,app(X2,X4)) != X1
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[152,78,theory(equality)]) ).
cnf(482,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[458,207,theory(equality)]) ).
cnf(483,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[482,theory(equality)]) ).
cnf(486,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[460,207,theory(equality)]) ).
cnf(487,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[486,theory(equality)]) ).
cnf(528,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssList(app(X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[206,109,theory(equality)]) ).
cnf(529,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssList(app(X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[117,109,theory(equality)]) ).
cnf(595,negated_conjecture,
( ~ segmentP(esk16_0,esk17_0)
| ~ segmentP(esk17_0,esk17_0)
| $false ),
inference(rw,[status(thm)],[282,268,theory(equality)]) ).
cnf(596,negated_conjecture,
( ~ segmentP(esk16_0,esk17_0)
| ~ segmentP(esk17_0,esk17_0) ),
inference(cn,[status(thm)],[595,theory(equality)]) ).
cnf(597,negated_conjecture,
( ~ segmentP(esk16_0,esk17_0)
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[596,231,theory(equality)]) ).
cnf(598,negated_conjecture,
( ~ segmentP(esk16_0,esk17_0)
| $false ),
inference(rw,[status(thm)],[597,268,theory(equality)]) ).
cnf(599,negated_conjecture,
~ segmentP(esk16_0,esk17_0),
inference(cn,[status(thm)],[598,theory(equality)]) ).
cnf(608,negated_conjecture,
( esk16_0 = X1
| ~ segmentP(X1,esk16_0)
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1)
| $false ),
inference(rw,[status(thm)],[324,267,theory(equality)]) ).
cnf(609,negated_conjecture,
( esk16_0 = X1
| ~ segmentP(X1,esk16_0)
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1) ),
inference(cn,[status(thm)],[608,theory(equality)]) ).
cnf(622,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[529,113]) ).
cnf(628,plain,
( app(app(cons(X1,X2),X3),X4) != nil
| ~ ssList(app(X2,X3))
| ~ ssList(X4)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[622,109,theory(equality)]) ).
cnf(725,plain,
( segmentP(X1,X2)
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[333,238]) ).
cnf(732,negated_conjecture,
( esk16_0 = X1
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1)
| nil != esk16_0
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[609,725,theory(equality)]) ).
cnf(742,negated_conjecture,
( esk16_0 = X1
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1)
| nil != esk16_0
| $false ),
inference(rw,[status(thm)],[732,267,theory(equality)]) ).
cnf(743,negated_conjecture,
( esk16_0 = X1
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1)
| nil != esk16_0 ),
inference(cn,[status(thm)],[742,theory(equality)]) ).
cnf(746,negated_conjecture,
( esk16_0 = cons(X1,X2)
| esk16_0 != nil
| ~ frontsegP(esk17_0,cons(X1,X2))
| ~ ssList(cons(X1,X2))
| nil != X2
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[743,56,theory(equality)]) ).
cnf(772,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[334,113]) ).
cnf(780,plain,
( frontsegP(app(X1,app(X2,X3)),app(X1,X2))
| ~ ssList(X3)
| ~ ssList(app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[772,78,theory(equality)]) ).
cnf(794,negated_conjecture,
( cons(X1,X2) = esk16_0
| esk16_0 != nil
| nil != X2
| ~ frontsegP(esk17_0,cons(X1,X2))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[746,206]) ).
cnf(796,negated_conjecture,
( app(cons(X1,X2),X3) = esk16_0
| esk16_0 != nil
| nil != app(X2,X3)
| ~ frontsegP(esk17_0,app(cons(X1,X2),X3))
| ~ ssList(app(X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[794,109,theory(equality)]) ).
cnf(824,plain,
( X1 = app(X2,X3)
| ~ frontsegP(X1,app(X2,X3))
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[346,113]) ).
cnf(830,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)],[824,158,theory(equality)]) ).
cnf(847,plain,
( app(app(cons(X1,X2),X3),X4) != nil
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[628,113]) ).
cnf(856,plain,
( app(cons(X1,X2),app(X3,X4)) != nil
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| ~ ssList(cons(X1,X2)) ),
inference(spm,[status(thm)],[847,78,theory(equality)]) ).
cnf(908,plain,
( app(cons(X1,X2),app(X3,X4)) != nil
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[856,206]) ).
cnf(911,plain,
( app(cons(X1,X2),nil) != nil
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| nil != X4
| nil != X3 ),
inference(spm,[status(thm)],[908,72,theory(equality)]) ).
fof(1055,plain,
( ~ epred4_0
<=> ! [X2,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,X2),nil) != nil ) ),
introduced(definition),
[split] ).
cnf(1056,plain,
( epred4_0
| ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,X2),nil) != nil ),
inference(split_equiv,[status(thm)],[1055]) ).
fof(1057,plain,
( ~ epred5_0
<=> ! [X4] :
( ~ ssList(X4)
| nil != X4 ) ),
introduced(definition),
[split] ).
cnf(1058,plain,
( epred5_0
| ~ ssList(X4)
| nil != X4 ),
inference(split_equiv,[status(thm)],[1057]) ).
fof(1059,plain,
( ~ epred6_0
<=> ! [X3] :
( ~ ssList(X3)
| nil != X3 ) ),
introduced(definition),
[split] ).
cnf(1060,plain,
( epred6_0
| ~ ssList(X3)
| nil != X3 ),
inference(split_equiv,[status(thm)],[1059]) ).
cnf(1061,plain,
( ~ epred6_0
| ~ epred5_0
| ~ epred4_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[911,1055,theory(equality)]),1057,theory(equality)]),1059,theory(equality)]),
[split] ).
cnf(1062,plain,
epred5_0,
inference(spm,[status(thm)],[1058,207,theory(equality)]) ).
cnf(1075,plain,
epred6_0,
inference(spm,[status(thm)],[1060,207,theory(equality)]) ).
cnf(1088,plain,
( $false
| ~ epred5_0
| ~ epred4_0 ),
inference(rw,[status(thm)],[1061,1075,theory(equality)]) ).
cnf(1089,plain,
( $false
| $false
| ~ epred4_0 ),
inference(rw,[status(thm)],[1088,1062,theory(equality)]) ).
cnf(1090,plain,
~ epred4_0,
inference(cn,[status(thm)],[1089,theory(equality)]) ).
cnf(1095,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,X2),nil) != nil ),
inference(sr,[status(thm)],[1056,1090,theory(equality)]) ).
cnf(1098,plain,
( nil = X1
| app(X1,nil) != nil
| ~ ssList(esk1_1(X1))
| ~ ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1095,122,theory(equality)]) ).
cnf(1122,plain,
( nil = X1
| app(X1,nil) != nil
| ~ ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[1098,123]) ).
cnf(1123,plain,
( nil = X1
| app(X1,nil) != nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[1122,124]) ).
cnf(1127,plain,
( nil = app(X1,X2)
| app(X1,app(X2,nil)) != nil
| ~ ssList(app(X1,X2))
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1123,78,theory(equality)]) ).
cnf(1132,plain,
( nil = app(X1,X2)
| app(X1,app(X2,nil)) != nil
| ~ ssList(app(X1,X2))
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[1127,207,theory(equality)]) ).
cnf(1133,plain,
( nil = app(X1,X2)
| app(X1,app(X2,nil)) != nil
| ~ ssList(app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1132,theory(equality)]) ).
cnf(1134,plain,
( app(X1,X2) = nil
| app(X1,app(X2,nil)) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[1133,113]) ).
cnf(1137,plain,
( app(nil,X1) = nil
| app(X1,nil) != nil
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(app(X1,nil)) ),
inference(spm,[status(thm)],[1134,98,theory(equality)]) ).
cnf(1146,plain,
( app(nil,X1) = nil
| app(X1,nil) != nil
| ~ ssList(X1)
| $false
| ~ ssList(app(X1,nil)) ),
inference(rw,[status(thm)],[1137,207,theory(equality)]) ).
cnf(1147,plain,
( app(nil,X1) = nil
| app(X1,nil) != nil
| ~ ssList(X1)
| ~ ssList(app(X1,nil)) ),
inference(cn,[status(thm)],[1146,theory(equality)]) ).
cnf(1155,plain,
( app(nil,nil) = nil
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1147,98,theory(equality)]) ).
cnf(1160,plain,
( app(nil,nil) = nil
| $false ),
inference(rw,[status(thm)],[1155,207,theory(equality)]) ).
cnf(1161,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[1160,theory(equality)]) ).
cnf(1179,plain,
( app(nil,X1) = app(nil,app(nil,X1))
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[78,1161,theory(equality)]) ).
cnf(1180,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssList(nil)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[109,1161,theory(equality)]) ).
cnf(1207,plain,
( app(nil,X1) = app(nil,app(nil,X1))
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[1179,207,theory(equality)]) ).
cnf(1208,plain,
( app(nil,X1) = app(nil,app(nil,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1207,theory(equality)]) ).
cnf(1209,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| $false
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[1180,207,theory(equality)]) ).
cnf(1210,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[1209,theory(equality)]) ).
cnf(2293,plain,
( segmentP(X1,X2)
| X3 != X1
| ~ ssList(esk7_2(X3,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X3,X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[421,158,theory(equality)]) ).
cnf(2310,plain,
( segmentP(X1,X2)
| ~ ssList(esk7_2(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X1,X2) ),
inference(er,[status(thm)],[2293,theory(equality)]) ).
cnf(3986,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)],[442,122,theory(equality)]) ).
cnf(3990,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)],[3986,theory(equality)]) ).
cnf(4879,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[483,113]) ).
cnf(4942,plain,
( app(nil,X1) = app(X1,nil)
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[487,4879,theory(equality)]) ).
cnf(4991,plain,
( app(nil,X1) = app(X1,nil)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[4942,207,theory(equality)]) ).
cnf(4992,plain,
( app(nil,X1) = app(X1,nil)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[4991,theory(equality)]) ).
cnf(5089,plain,
( app(nil,app(X1,nil)) = app(X1,nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1208,4992,theory(equality)]) ).
cnf(6382,plain,
( frontsegP(X1,app(X2,X3))
| app(X2,app(X3,X4)) != X1
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X4) ),
inference(csr,[status(thm)],[466,113]) ).
cnf(9863,plain,
( frontsegP(X1,app(nil,X2))
| app(X2,nil) != X1
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[6382,5089,theory(equality)]) ).
cnf(9880,plain,
( segmentP(X1,X2)
| app(X2,nil) != X1
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[476,5089,theory(equality)]) ).
cnf(10015,plain,
( frontsegP(X1,app(nil,X2))
| app(X2,nil) != X1
| $false
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(rw,[status(thm)],[9863,207,theory(equality)]) ).
cnf(10016,plain,
( frontsegP(X1,app(nil,X2))
| app(X2,nil) != X1
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[10015,theory(equality)]) ).
cnf(10045,plain,
( segmentP(X1,X2)
| app(X2,nil) != X1
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[9880,207,theory(equality)]) ).
cnf(10046,plain,
( segmentP(X1,X2)
| app(X2,nil) != X1
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[10045,theory(equality)]) ).
cnf(10108,negated_conjecture,
( app(esk17_0,nil) != esk16_0
| ~ ssList(esk17_0)
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[599,10046,theory(equality)]) ).
cnf(10128,negated_conjecture,
( app(esk17_0,nil) != esk16_0
| $false
| ~ ssList(esk16_0) ),
inference(rw,[status(thm)],[10108,268,theory(equality)]) ).
cnf(10129,negated_conjecture,
( app(esk17_0,nil) != esk16_0
| $false
| $false ),
inference(rw,[status(thm)],[10128,267,theory(equality)]) ).
cnf(10130,negated_conjecture,
app(esk17_0,nil) != esk16_0,
inference(cn,[status(thm)],[10129,theory(equality)]) ).
cnf(10155,negated_conjecture,
( esk17_0 != esk16_0
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[10130,67,theory(equality)]) ).
cnf(10160,negated_conjecture,
( esk17_0 != esk16_0
| $false ),
inference(rw,[status(thm)],[10155,268,theory(equality)]) ).
cnf(10161,negated_conjecture,
esk17_0 != esk16_0,
inference(cn,[status(thm)],[10160,theory(equality)]) ).
cnf(11325,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[528,113]) ).
cnf(11332,plain,
( ssList(cons(X1,nil))
| ~ ssList(nil)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[11325,1210,theory(equality)]) ).
cnf(11352,plain,
( ssList(cons(X1,nil))
| $false
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[11332,207,theory(equality)]) ).
cnf(11353,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[11352,theory(equality)]) ).
cnf(16218,plain,
( frontsegP(X1,X2)
| app(X2,nil) != X1
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[10016,98,theory(equality)]) ).
cnf(17684,plain,
( frontsegP(app(X1,app(X2,X3)),app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[780,113]) ).
cnf(17769,plain,
( frontsegP(app(X1,nil),app(nil,X1))
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[17684,5089,theory(equality)]) ).
cnf(17876,plain,
( frontsegP(app(X1,nil),app(nil,X1))
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[17769,207,theory(equality)]) ).
cnf(17877,plain,
( frontsegP(app(X1,nil),app(nil,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[17876,theory(equality)]) ).
cnf(18138,negated_conjecture,
( app(cons(X1,X2),X3) = esk16_0
| app(X2,X3) != nil
| esk16_0 != nil
| ~ frontsegP(esk17_0,app(cons(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[796,113]) ).
cnf(18333,plain,
( frontsegP(X1,app(nil,X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[17877,67,theory(equality)]) ).
cnf(18479,plain,
( frontsegP(X1,app(X1,nil))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[18333,4992,theory(equality)]) ).
cnf(18809,plain,
( X1 = X3
| ~ frontsegP(X3,X2)
| ~ frontsegP(X1,X3)
| ~ frontsegP(X2,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[830,159]) ).
cnf(18810,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)],[18809,261,theory(equality)]) ).
cnf(18860,negated_conjecture,
( esk17_0 = esk16_0
| ~ frontsegP(X1,esk17_0)
| ~ frontsegP(esk16_0,X1)
| $false
| ~ ssList(X1)
| ~ ssList(esk16_0) ),
inference(rw,[status(thm)],[18810,268,theory(equality)]) ).
cnf(18861,negated_conjecture,
( esk17_0 = esk16_0
| ~ frontsegP(X1,esk17_0)
| ~ frontsegP(esk16_0,X1)
| $false
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[18860,267,theory(equality)]) ).
cnf(18862,negated_conjecture,
( esk17_0 = esk16_0
| ~ frontsegP(X1,esk17_0)
| ~ frontsegP(esk16_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[18861,theory(equality)]) ).
cnf(18863,negated_conjecture,
( ~ frontsegP(X1,esk17_0)
| ~ frontsegP(esk16_0,X1)
| ~ ssList(X1) ),
inference(sr,[status(thm)],[18862,10161,theory(equality)]) ).
cnf(19057,negated_conjecture,
( ~ frontsegP(esk16_0,X1)
| ~ ssList(X1)
| app(esk17_0,nil) != X1
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[18863,16218,theory(equality)]) ).
cnf(19092,negated_conjecture,
( ~ frontsegP(esk16_0,X1)
| ~ ssList(X1)
| app(esk17_0,nil) != X1
| $false ),
inference(rw,[status(thm)],[19057,268,theory(equality)]) ).
cnf(19093,negated_conjecture,
( ~ frontsegP(esk16_0,X1)
| ~ ssList(X1)
| app(esk17_0,nil) != X1 ),
inference(cn,[status(thm)],[19092,theory(equality)]) ).
cnf(20368,negated_conjecture,
( app(esk17_0,nil) != app(esk16_0,nil)
| ~ ssList(app(esk16_0,nil))
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[19093,18479,theory(equality)]) ).
cnf(20411,negated_conjecture,
( app(esk17_0,nil) != app(esk16_0,nil)
| ~ ssList(app(esk16_0,nil))
| $false ),
inference(rw,[status(thm)],[20368,267,theory(equality)]) ).
cnf(20412,negated_conjecture,
( app(esk17_0,nil) != app(esk16_0,nil)
| ~ ssList(app(esk16_0,nil)) ),
inference(cn,[status(thm)],[20411,theory(equality)]) ).
cnf(27148,negated_conjecture,
( app(esk17_0,nil) != app(esk16_0,nil)
| ~ ssList(nil)
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[20412,113,theory(equality)]) ).
cnf(27155,negated_conjecture,
( app(esk17_0,nil) != app(esk16_0,nil)
| $false
| ~ ssList(esk16_0) ),
inference(rw,[status(thm)],[27148,207,theory(equality)]) ).
cnf(27156,negated_conjecture,
( app(esk17_0,nil) != app(esk16_0,nil)
| $false
| $false ),
inference(rw,[status(thm)],[27155,267,theory(equality)]) ).
cnf(27157,negated_conjecture,
app(esk17_0,nil) != app(esk16_0,nil),
inference(cn,[status(thm)],[27156,theory(equality)]) ).
cnf(27175,negated_conjecture,
( esk17_0 != app(esk16_0,nil)
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[27157,67,theory(equality)]) ).
cnf(27180,negated_conjecture,
( esk17_0 != app(esk16_0,nil)
| $false ),
inference(rw,[status(thm)],[27175,268,theory(equality)]) ).
cnf(27181,negated_conjecture,
esk17_0 != app(esk16_0,nil),
inference(cn,[status(thm)],[27180,theory(equality)]) ).
cnf(46432,plain,
( segmentP(X1,X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[2310,159]) ).
cnf(46438,negated_conjecture,
( X1 = nil
| ~ segmentP(esk16_0,X1)
| ~ ssList(X1)
| ~ frontsegP(esk17_0,X1)
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[285,46432,theory(equality)]) ).
cnf(46478,negated_conjecture,
( X1 = nil
| ~ segmentP(esk16_0,X1)
| ~ ssList(X1)
| ~ frontsegP(esk17_0,X1)
| $false ),
inference(rw,[status(thm)],[46438,268,theory(equality)]) ).
cnf(46479,negated_conjecture,
( X1 = nil
| ~ segmentP(esk16_0,X1)
| ~ ssList(X1)
| ~ frontsegP(esk17_0,X1) ),
inference(cn,[status(thm)],[46478,theory(equality)]) ).
cnf(46818,negated_conjecture,
( esk16_0 = nil
| ~ frontsegP(esk17_0,esk16_0)
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[46479,231,theory(equality)]) ).
cnf(46839,negated_conjecture,
( esk16_0 = nil
| $false
| ~ ssList(esk16_0) ),
inference(rw,[status(thm)],[46818,261,theory(equality)]) ).
cnf(46840,negated_conjecture,
( esk16_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[46839,267,theory(equality)]) ).
cnf(46841,negated_conjecture,
esk16_0 = nil,
inference(cn,[status(thm)],[46840,theory(equality)]) ).
cnf(46898,negated_conjecture,
nil != esk17_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[27181,46841,theory(equality)]),1161,theory(equality)]) ).
cnf(47181,negated_conjecture,
( app(cons(X1,X2),X3) = nil
| app(X2,X3) != nil
| esk16_0 != nil
| ~ frontsegP(esk17_0,app(cons(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[18138,46841,theory(equality)]) ).
cnf(47182,negated_conjecture,
( app(cons(X1,X2),X3) = nil
| app(X2,X3) != nil
| $false
| ~ frontsegP(esk17_0,app(cons(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[47181,46841,theory(equality)]) ).
cnf(47183,negated_conjecture,
( app(cons(X1,X2),X3) = nil
| app(X2,X3) != nil
| ~ frontsegP(esk17_0,app(cons(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[47182,theory(equality)]) ).
cnf(48001,negated_conjecture,
( app(X2,X3) != nil
| ~ frontsegP(esk17_0,app(cons(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[47183,622]) ).
cnf(48009,negated_conjecture,
( app(nil,nil) != nil
| ~ frontsegP(esk17_0,cons(X1,nil))
| ~ ssList(nil)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[48001,1210,theory(equality)]) ).
cnf(48051,negated_conjecture,
( $false
| ~ frontsegP(esk17_0,cons(X1,nil))
| ~ ssList(nil)
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[48009,1161,theory(equality)]) ).
cnf(48052,negated_conjecture,
( $false
| ~ frontsegP(esk17_0,cons(X1,nil))
| $false
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[48051,207,theory(equality)]) ).
cnf(48053,negated_conjecture,
( ~ frontsegP(esk17_0,cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[48052,theory(equality)]) ).
cnf(82271,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)],[3990,123]) ).
cnf(82272,plain,
( nil = X1
| frontsegP(X1,cons(esk2_1(X1),nil))
| ~ ssList(cons(esk2_1(X1),nil))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[82271,124]) ).
cnf(82320,negated_conjecture,
( nil = esk17_0
| ~ ssItem(esk2_1(esk17_0))
| ~ ssList(cons(esk2_1(esk17_0),nil))
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[48053,82272,theory(equality)]) ).
cnf(82381,negated_conjecture,
( nil = esk17_0
| ~ ssItem(esk2_1(esk17_0))
| ~ ssList(cons(esk2_1(esk17_0),nil))
| $false ),
inference(rw,[status(thm)],[82320,268,theory(equality)]) ).
cnf(82382,negated_conjecture,
( nil = esk17_0
| ~ ssItem(esk2_1(esk17_0))
| ~ ssList(cons(esk2_1(esk17_0),nil)) ),
inference(cn,[status(thm)],[82381,theory(equality)]) ).
cnf(82383,negated_conjecture,
( ~ ssItem(esk2_1(esk17_0))
| ~ ssList(cons(esk2_1(esk17_0),nil)) ),
inference(sr,[status(thm)],[82382,46898,theory(equality)]) ).
cnf(82400,negated_conjecture,
~ ssItem(esk2_1(esk17_0)),
inference(csr,[status(thm)],[82383,11353]) ).
cnf(82401,negated_conjecture,
( nil = esk17_0
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[82400,123,theory(equality)]) ).
cnf(82403,negated_conjecture,
( nil = esk17_0
| $false ),
inference(rw,[status(thm)],[82401,268,theory(equality)]) ).
cnf(82404,negated_conjecture,
nil = esk17_0,
inference(cn,[status(thm)],[82403,theory(equality)]) ).
cnf(82405,negated_conjecture,
$false,
inference(sr,[status(thm)],[82404,46898,theory(equality)]) ).
cnf(82406,negated_conjecture,
$false,
82405,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC091+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmp2xutpp/sel_SWC091+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC091+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC091+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC091+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
%
%------------------------------------------------------------------------------