TSTP Solution File: SWC021+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC021+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 10:06:17 EST 2010
% Result : Theorem 2.76s
% Output : CNFRefutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 15
% Syntax : Number of formulae : 146 ( 16 unt; 0 def)
% Number of atoms : 705 ( 189 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 962 ( 403 ~; 404 |; 116 &)
% ( 4 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 226 ( 0 sgn 125 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmpWx6EfD/sel_SWC021+1.p_1',ax83) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpWx6EfD/sel_SWC021+1.p_1',ax81) ).
fof(14,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,X1) ),
file('/tmp/tmpWx6EfD/sel_SWC021+1.p_1',ax42) ).
fof(15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/tmp/tmpWx6EfD/sel_SWC021+1.p_1',ax27) ).
fof(16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpWx6EfD/sel_SWC021+1.p_1',ax26) ).
fof(17,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmpWx6EfD/sel_SWC021+1.p_1',ax21) ).
fof(18,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/tmp/tmpWx6EfD/sel_SWC021+1.p_1',ax20) ).
fof(19,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,nil) ),
file('/tmp/tmpWx6EfD/sel_SWC021+1.p_1',ax45) ).
fof(24,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/tmp/tmpWx6EfD/sel_SWC021+1.p_1',ax5) ).
fof(32,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( strictorderedP(cons(X1,X2))
<=> ( nil = X2
| ( nil != X2
& strictorderedP(X2)
& lt(X1,hd(X2)) ) ) ) ) ),
file('/tmp/tmpWx6EfD/sel_SWC021+1.p_1',ax70) ).
fof(39,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpWx6EfD/sel_SWC021+1.p_1',ax16) ).
fof(40,axiom,
ssList(nil),
file('/tmp/tmpWx6EfD/sel_SWC021+1.p_1',ax17) ).
fof(46,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/tmp/tmpWx6EfD/sel_SWC021+1.p_1',ax57) ).
fof(47,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpWx6EfD/sel_SWC021+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)
& frontsegP(X2,X5)
& frontsegP(X1,X5) )
| ? [X6] :
( ssList(X6)
& neq(X3,X6)
& frontsegP(X4,X6)
& segmentP(X6,X3)
& strictorderedP(X6) )
| ( nil = X2
& nil = X1 ) ) ) ) ) ),
file('/tmp/tmpWx6EfD/sel_SWC021+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)
& frontsegP(X2,X5)
& frontsegP(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)
& frontsegP(X2,X5)
& frontsegP(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(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(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(106,plain,
! [X1] :
( ~ ssList(X1)
| frontsegP(X1,X1) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(107,plain,
! [X2] :
( ~ ssList(X2)
| frontsegP(X2,X2) ),
inference(variable_rename,[status(thm)],[106]) ).
cnf(108,plain,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[107]) ).
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(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(198,plain,
! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ strictorderedP(cons(X1,X2))
| nil = X2
| ( nil != X2
& strictorderedP(X2)
& lt(X1,hd(X2)) ) )
& ( ( nil != X2
& ( nil = X2
| ~ strictorderedP(X2)
| ~ lt(X1,hd(X2)) ) )
| strictorderedP(cons(X1,X2)) ) ) ) ),
inference(fof_nnf,[status(thm)],[32]) ).
fof(199,plain,
! [X3] :
( ~ ssItem(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ strictorderedP(cons(X3,X4))
| nil = X4
| ( nil != X4
& strictorderedP(X4)
& lt(X3,hd(X4)) ) )
& ( ( nil != X4
& ( nil = X4
| ~ strictorderedP(X4)
| ~ lt(X3,hd(X4)) ) )
| strictorderedP(cons(X3,X4)) ) ) ) ),
inference(variable_rename,[status(thm)],[198]) ).
fof(200,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ strictorderedP(cons(X3,X4))
| nil = X4
| ( nil != X4
& strictorderedP(X4)
& lt(X3,hd(X4)) ) )
& ( ( nil != X4
& ( nil = X4
| ~ strictorderedP(X4)
| ~ lt(X3,hd(X4)) ) )
| strictorderedP(cons(X3,X4)) ) )
| ~ ssItem(X3) ),
inference(shift_quantors,[status(thm)],[199]) ).
fof(201,plain,
! [X3,X4] :
( ( nil != X4
| nil = X4
| ~ strictorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) )
& ( strictorderedP(X4)
| nil = X4
| ~ strictorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) )
& ( lt(X3,hd(X4))
| nil = X4
| ~ strictorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) )
& ( nil != X4
| strictorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) )
& ( nil = X4
| ~ strictorderedP(X4)
| ~ lt(X3,hd(X4))
| strictorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) ) ),
inference(distribute,[status(thm)],[200]) ).
cnf(203,plain,
( strictorderedP(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2)
| nil != X2 ),
inference(split_conjunct,[status(thm)],[201]) ).
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(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)
| ~ frontsegP(X2,X5)
| ~ frontsegP(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)
| ~ frontsegP(X8,X11)
| ~ frontsegP(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)
| ~ frontsegP(esk15_0,X11)
| ~ frontsegP(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)
| ~ frontsegP(esk15_0,X11)
| ~ frontsegP(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,
( ~ frontsegP(esk14_0,X1)
| ~ frontsegP(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)
| ~ frontsegP(esk16_0,X1)
| ~ frontsegP(esk15_0,X1) ),
inference(rw,[status(thm)],[299,297,theory(equality)]) ).
cnf(322,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ frontsegP(esk16_0,X1)
| ~ frontsegP(esk17_0,X1) ),
inference(rw,[status(thm)],[321,298,theory(equality)]) ).
cnf(323,negated_conjecture,
( X1 = nil
| ~ frontsegP(esk16_0,X1)
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[322,271,theory(equality)]) ).
cnf(325,negated_conjecture,
( X1 = nil
| ~ frontsegP(esk16_0,X1)
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[323,235,theory(equality)]) ).
cnf(326,negated_conjecture,
( X1 = nil
| ~ frontsegP(esk16_0,X1)
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[325,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(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(635,negated_conjecture,
( esk16_0 = nil
| ~ frontsegP(esk16_0,esk16_0)
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[326,296,theory(equality)]) ).
cnf(637,negated_conjecture,
( esk16_0 = nil
| ~ frontsegP(esk16_0,esk16_0)
| $false ),
inference(rw,[status(thm)],[635,301,theory(equality)]) ).
cnf(638,negated_conjecture,
( esk16_0 = nil
| ~ frontsegP(esk16_0,esk16_0) ),
inference(cn,[status(thm)],[637,theory(equality)]) ).
cnf(641,negated_conjecture,
( esk16_0 = nil
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[638,108,theory(equality)]) ).
cnf(642,negated_conjecture,
( esk16_0 = nil
| $false ),
inference(rw,[status(thm)],[641,301,theory(equality)]) ).
cnf(643,negated_conjecture,
esk16_0 = nil,
inference(cn,[status(thm)],[642,theory(equality)]) ).
cnf(654,negated_conjecture,
( ~ neq(nil,X1)
| ~ segmentP(X1,esk16_0)
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ strictorderedP(X1) ),
inference(rw,[status(thm)],[300,643,theory(equality)]) ).
cnf(655,negated_conjecture,
( ~ neq(nil,X1)
| ~ segmentP(X1,nil)
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ strictorderedP(X1) ),
inference(rw,[status(thm)],[654,643,theory(equality)]) ).
cnf(657,negated_conjecture,
( $false
| esk17_0 != nil ),
inference(rw,[status(thm)],[304,643,theory(equality)]) ).
cnf(658,negated_conjecture,
esk17_0 != nil,
inference(cn,[status(thm)],[657,theory(equality)]) ).
cnf(669,negated_conjecture,
( ~ neq(nil,X1)
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ strictorderedP(X1) ),
inference(csr,[status(thm)],[655,266]) ).
cnf(670,negated_conjecture,
( nil = X1
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ strictorderedP(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[669,271,theory(equality)]) ).
cnf(672,negated_conjecture,
( nil = X1
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ strictorderedP(X1)
| $false ),
inference(rw,[status(thm)],[670,235,theory(equality)]) ).
cnf(673,negated_conjecture,
( nil = X1
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ strictorderedP(X1) ),
inference(cn,[status(thm)],[672,theory(equality)]) ).
cnf(679,negated_conjecture,
( nil = cons(X1,X2)
| ~ frontsegP(esk17_0,cons(X1,X2))
| ~ ssList(cons(X1,X2))
| nil != X2
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[673,203,theory(equality)]) ).
cnf(802,negated_conjecture,
( cons(X1,X2) = nil
| nil != X2
| ~ frontsegP(esk17_0,cons(X1,X2))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[679,234]) ).
cnf(803,negated_conjecture,
( nil != X2
| ~ frontsegP(esk17_0,cons(X1,X2))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[802,120]) ).
cnf(1035,plain,
( esk7_2(X1,X2) = nil
| X1 != nil
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[398,162]) ).
cnf(1037,plain,
( app(X1,nil) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2)
| X2 != nil ),
inference(spm,[status(thm)],[161,1035,theory(equality)]) ).
cnf(1065,plain,
( app(nil,nil) = X1
| X1 != nil
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1037,130,theory(equality)]) ).
cnf(1074,plain,
( app(nil,nil) = X1
| X1 != nil
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[1065,235,theory(equality)]) ).
cnf(1075,plain,
( app(nil,nil) = X1
| X1 != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1074,theory(equality)]) ).
cnf(1194,plain,
app(nil,nil) = nil,
inference(spm,[status(thm)],[1075,235,theory(equality)]) ).
cnf(1228,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssList(nil)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[112,1194,theory(equality)]) ).
cnf(1256,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| $false
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[1228,235,theory(equality)]) ).
cnf(1257,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[1256,theory(equality)]) ).
cnf(2152,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(2155,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)],[2152,theory(equality)]) ).
cnf(9715,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[564,116]) ).
cnf(9723,plain,
( ssList(cons(X1,nil))
| ~ ssList(nil)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[9715,1257,theory(equality)]) ).
cnf(9744,plain,
( ssList(cons(X1,nil))
| $false
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[9723,235,theory(equality)]) ).
cnf(9745,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[9744,theory(equality)]) ).
cnf(51311,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)],[2155,126]) ).
cnf(51312,plain,
( nil = X1
| frontsegP(X1,cons(esk2_1(X1),nil))
| ~ ssList(cons(esk2_1(X1),nil))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[51311,127]) ).
cnf(51320,negated_conjecture,
( nil = esk17_0
| ~ ssList(nil)
| ~ ssItem(esk2_1(esk17_0))
| ~ ssList(cons(esk2_1(esk17_0),nil))
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[803,51312,theory(equality)]) ).
cnf(51398,negated_conjecture,
( nil = esk17_0
| $false
| ~ ssItem(esk2_1(esk17_0))
| ~ ssList(cons(esk2_1(esk17_0),nil))
| ~ ssList(esk17_0) ),
inference(rw,[status(thm)],[51320,235,theory(equality)]) ).
cnf(51399,negated_conjecture,
( nil = esk17_0
| $false
| ~ ssItem(esk2_1(esk17_0))
| ~ ssList(cons(esk2_1(esk17_0),nil))
| $false ),
inference(rw,[status(thm)],[51398,302,theory(equality)]) ).
cnf(51400,negated_conjecture,
( nil = esk17_0
| ~ ssItem(esk2_1(esk17_0))
| ~ ssList(cons(esk2_1(esk17_0),nil)) ),
inference(cn,[status(thm)],[51399,theory(equality)]) ).
cnf(51401,negated_conjecture,
( ~ ssItem(esk2_1(esk17_0))
| ~ ssList(cons(esk2_1(esk17_0),nil)) ),
inference(sr,[status(thm)],[51400,658,theory(equality)]) ).
cnf(51453,negated_conjecture,
~ ssItem(esk2_1(esk17_0)),
inference(csr,[status(thm)],[51401,9745]) ).
cnf(51454,negated_conjecture,
( nil = esk17_0
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[51453,126,theory(equality)]) ).
cnf(51456,negated_conjecture,
( nil = esk17_0
| $false ),
inference(rw,[status(thm)],[51454,302,theory(equality)]) ).
cnf(51457,negated_conjecture,
nil = esk17_0,
inference(cn,[status(thm)],[51456,theory(equality)]) ).
cnf(51458,negated_conjecture,
$false,
inference(sr,[status(thm)],[51457,658,theory(equality)]) ).
cnf(51459,negated_conjecture,
$false,
51458,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC021+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpWx6EfD/sel_SWC021+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC021+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC021+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC021+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
%
%------------------------------------------------------------------------------