TSTP Solution File: SWC031+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC031+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 10:07:12 EST 2010
% Result : Theorem 5.30s
% Output : CNFRefutation 5.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 20
% Syntax : Number of formulae : 175 ( 18 unt; 0 def)
% Number of atoms : 830 ( 266 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 1145 ( 490 ~; 482 |; 126 &)
% ( 8 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 4 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 279 ( 0 sgn 142 !; 20 ?)
% 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/tmp09gWz9/sel_SWC031+1.p_1',ax67) ).
fof(5,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmp09gWz9/sel_SWC031+1.p_1',ax84) ).
fof(6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmp09gWz9/sel_SWC031+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/tmp09gWz9/sel_SWC031+1.p_1',ax82) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmp09gWz9/sel_SWC031+1.p_1',ax81) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('/tmp/tmp09gWz9/sel_SWC031+1.p_1',ax46) ).
fof(12,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmp09gWz9/sel_SWC031+1.p_1',ax28) ).
fof(15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/tmp/tmp09gWz9/sel_SWC031+1.p_1',ax27) ).
fof(16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmp09gWz9/sel_SWC031+1.p_1',ax26) ).
fof(17,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmp09gWz9/sel_SWC031+1.p_1',ax21) ).
fof(18,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/tmp/tmp09gWz9/sel_SWC031+1.p_1',ax20) ).
fof(24,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/tmp/tmp09gWz9/sel_SWC031+1.p_1',ax5) ).
fof(33,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmp09gWz9/sel_SWC031+1.p_1',ax15) ).
fof(34,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmp09gWz9/sel_SWC031+1.p_1',ax16) ).
fof(35,axiom,
ssList(nil),
file('/tmp/tmp09gWz9/sel_SWC031+1.p_1',ax17) ).
fof(41,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/tmp/tmp09gWz9/sel_SWC031+1.p_1',ax57) ).
fof(45,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ frontsegP(X4,X3)
| ~ totalorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& frontsegP(X4,X5)
& segmentP(X5,X3)
& totalorderedP(X5) )
| ( ( nil != X2
| nil = X1 )
& ( nil != X1
| nil = X2 ) ) ) ) ) ) ),
file('/tmp/tmp09gWz9/sel_SWC031+1.p_1',co1) ).
fof(46,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ frontsegP(X4,X3)
| ~ totalorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& frontsegP(X4,X5)
& segmentP(X5,X3)
& totalorderedP(X5) )
| ( ( nil != X2
| nil = X1 )
& ( nil != X1
| nil = X2 ) ) ) ) ) ) ),
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
| ~ frontsegP(X4,X3)
| ~ totalorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& frontsegP(X4,X5)
& segmentP(X5,X3)
& totalorderedP(X5) )
| ( ( nil != X2
| nil = X1 )
& ( nil != X1
| nil = X2 ) ) ) ) ) ) ),
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(87,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(nil,X1)
| nil = X1 )
& ( nil != X1
| frontsegP(nil,X1) ) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(88,plain,
! [X2] :
( ~ ssList(X2)
| ( ( ~ frontsegP(nil,X2)
| nil = X2 )
& ( nil != X2
| frontsegP(nil,X2) ) ) ),
inference(variable_rename,[status(thm)],[87]) ).
fof(89,plain,
! [X2] :
( ( ~ frontsegP(nil,X2)
| nil = X2
| ~ ssList(X2) )
& ( nil != X2
| frontsegP(nil,X2)
| ~ ssList(X2) ) ),
inference(distribute,[status(thm)],[88]) ).
cnf(91,plain,
( nil = X1
| ~ ssList(X1)
| ~ frontsegP(nil,X1) ),
inference(split_conjunct,[status(thm)],[89]) ).
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(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(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(160,plain,
( frontsegP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X3) != X1
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[157]) ).
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(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
& frontsegP(X4,X3)
& totalorderedP(X3)
& ! [X5] :
( ~ ssList(X5)
| ~ neq(X3,X5)
| ~ frontsegP(X4,X5)
| ~ segmentP(X5,X3)
| ~ totalorderedP(X5) )
& ( ( nil = X2
& nil != X1 )
| ( nil = X1
& nil != X2 ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[47]) ).
fof(253,negated_conjecture,
? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& X7 = X9
& X6 = X8
& frontsegP(X9,X8)
& totalorderedP(X8)
& ! [X10] :
( ~ ssList(X10)
| ~ neq(X8,X10)
| ~ frontsegP(X9,X10)
| ~ segmentP(X10,X8)
| ~ totalorderedP(X10) )
& ( ( nil = X7
& nil != X6 )
| ( nil = X6
& nil != X7 ) ) ) ) ) ),
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
& frontsegP(esk17_0,esk16_0)
& totalorderedP(esk16_0)
& ! [X10] :
( ~ ssList(X10)
| ~ neq(esk16_0,X10)
| ~ frontsegP(esk17_0,X10)
| ~ segmentP(X10,esk16_0)
| ~ totalorderedP(X10) )
& ( ( nil = esk15_0
& nil != esk14_0 )
| ( nil = esk14_0
& nil != esk15_0 ) ) ),
inference(skolemize,[status(esa)],[253]) ).
fof(255,negated_conjecture,
! [X10] :
( ( ~ ssList(X10)
| ~ neq(esk16_0,X10)
| ~ frontsegP(esk17_0,X10)
| ~ segmentP(X10,esk16_0)
| ~ totalorderedP(X10) )
& esk15_0 = esk17_0
& esk14_0 = esk16_0
& frontsegP(esk17_0,esk16_0)
& totalorderedP(esk16_0)
& ( ( nil = esk15_0
& nil != esk14_0 )
| ( nil = esk14_0
& nil != esk15_0 ) )
& ssList(esk17_0)
& ssList(esk16_0)
& ssList(esk15_0)
& ssList(esk14_0) ),
inference(shift_quantors,[status(thm)],[254]) ).
fof(256,negated_conjecture,
! [X10] :
( ( ~ ssList(X10)
| ~ neq(esk16_0,X10)
| ~ frontsegP(esk17_0,X10)
| ~ segmentP(X10,esk16_0)
| ~ totalorderedP(X10) )
& esk15_0 = esk17_0
& esk14_0 = esk16_0
& frontsegP(esk17_0,esk16_0)
& totalorderedP(esk16_0)
& ( nil = esk14_0
| nil = esk15_0 )
& ( nil != esk15_0
| nil = esk15_0 )
& ( nil = esk14_0
| nil != esk14_0 )
& ( nil != esk15_0
| nil != esk14_0 )
& ssList(esk17_0)
& ssList(esk16_0)
& ssList(esk15_0)
& ssList(esk14_0) ),
inference(distribute,[status(thm)],[255]) ).
cnf(257,negated_conjecture,
ssList(esk14_0),
inference(split_conjunct,[status(thm)],[256]) ).
cnf(258,negated_conjecture,
ssList(esk15_0),
inference(split_conjunct,[status(thm)],[256]) ).
cnf(261,negated_conjecture,
( nil != esk14_0
| nil != esk15_0 ),
inference(split_conjunct,[status(thm)],[256]) ).
cnf(264,negated_conjecture,
( nil = esk15_0
| nil = esk14_0 ),
inference(split_conjunct,[status(thm)],[256]) ).
cnf(266,negated_conjecture,
frontsegP(esk17_0,esk16_0),
inference(split_conjunct,[status(thm)],[256]) ).
cnf(267,negated_conjecture,
esk14_0 = esk16_0,
inference(split_conjunct,[status(thm)],[256]) ).
cnf(268,negated_conjecture,
esk15_0 = esk17_0,
inference(split_conjunct,[status(thm)],[256]) ).
cnf(269,negated_conjecture,
( ~ totalorderedP(X1)
| ~ segmentP(X1,esk16_0)
| ~ frontsegP(esk17_0,X1)
| ~ neq(esk16_0,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[256]) ).
cnf(270,negated_conjecture,
ssList(esk16_0),
inference(rw,[status(thm)],[257,267,theory(equality)]) ).
cnf(271,negated_conjecture,
ssList(esk17_0),
inference(rw,[status(thm)],[258,268,theory(equality)]) ).
cnf(272,negated_conjecture,
( esk16_0 = nil
| esk15_0 = nil ),
inference(rw,[status(thm)],[264,267,theory(equality)]) ).
cnf(273,negated_conjecture,
( esk16_0 = nil
| esk17_0 = nil ),
inference(rw,[status(thm)],[272,268,theory(equality)]) ).
cnf(275,negated_conjecture,
( frontsegP(nil,esk16_0)
| esk16_0 = nil ),
inference(spm,[status(thm)],[266,273,theory(equality)]) ).
cnf(277,negated_conjecture,
( esk16_0 != nil
| esk15_0 != nil ),
inference(rw,[status(thm)],[261,267,theory(equality)]) ).
cnf(278,negated_conjecture,
( esk16_0 != nil
| esk17_0 != nil ),
inference(rw,[status(thm)],[277,268,theory(equality)]) ).
cnf(445,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(531,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(532,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(598,negated_conjecture,
( nil = esk16_0
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[91,275,theory(equality)]) ).
cnf(601,negated_conjecture,
( nil = esk16_0
| $false ),
inference(rw,[status(thm)],[598,270,theory(equality)]) ).
cnf(602,negated_conjecture,
nil = esk16_0,
inference(cn,[status(thm)],[601,theory(equality)]) ).
cnf(618,negated_conjecture,
( ~ neq(nil,X1)
| ~ segmentP(X1,esk16_0)
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1) ),
inference(rw,[status(thm)],[269,602,theory(equality)]) ).
cnf(619,negated_conjecture,
( ~ neq(nil,X1)
| ~ segmentP(X1,nil)
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1) ),
inference(rw,[status(thm)],[618,602,theory(equality)]) ).
cnf(620,negated_conjecture,
( $false
| esk17_0 != nil ),
inference(rw,[status(thm)],[278,602,theory(equality)]) ).
cnf(621,negated_conjecture,
esk17_0 != nil,
inference(cn,[status(thm)],[620,theory(equality)]) ).
cnf(633,negated_conjecture,
( ~ neq(nil,X1)
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1) ),
inference(csr,[status(thm)],[619,238]) ).
cnf(634,negated_conjecture,
( nil = X1
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[633,201,theory(equality)]) ).
cnf(636,negated_conjecture,
( nil = X1
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1)
| $false ),
inference(rw,[status(thm)],[634,207,theory(equality)]) ).
cnf(637,negated_conjecture,
( nil = X1
| ~ frontsegP(esk17_0,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1) ),
inference(cn,[status(thm)],[636,theory(equality)]) ).
cnf(639,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)],[637,56,theory(equality)]) ).
cnf(648,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[532,113]) ).
cnf(654,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)],[648,109,theory(equality)]) ).
cnf(668,negated_conjecture,
( cons(X1,X2) = nil
| nil != X2
| ~ frontsegP(esk17_0,cons(X1,X2))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[639,206]) ).
cnf(669,negated_conjecture,
( nil != X2
| ~ frontsegP(esk17_0,cons(X1,X2))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[668,117]) ).
cnf(934,plain,
( app(app(cons(X1,X2),X3),X4) != nil
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[654,113]) ).
cnf(943,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)],[934,78,theory(equality)]) ).
cnf(972,plain,
( app(cons(X1,X2),app(X3,X4)) != nil
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[943,206]) ).
cnf(975,plain,
( app(cons(X1,X2),nil) != nil
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| nil != X4
| nil != X3 ),
inference(spm,[status(thm)],[972,72,theory(equality)]) ).
fof(1078,plain,
( ~ epred4_0
<=> ! [X2,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,X2),nil) != nil ) ),
introduced(definition),
[split] ).
cnf(1079,plain,
( epred4_0
| ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,X2),nil) != nil ),
inference(split_equiv,[status(thm)],[1078]) ).
fof(1080,plain,
( ~ epred5_0
<=> ! [X4] :
( ~ ssList(X4)
| nil != X4 ) ),
introduced(definition),
[split] ).
cnf(1081,plain,
( epred5_0
| ~ ssList(X4)
| nil != X4 ),
inference(split_equiv,[status(thm)],[1080]) ).
fof(1082,plain,
( ~ epred6_0
<=> ! [X3] :
( ~ ssList(X3)
| nil != X3 ) ),
introduced(definition),
[split] ).
cnf(1083,plain,
( epred6_0
| ~ ssList(X3)
| nil != X3 ),
inference(split_equiv,[status(thm)],[1082]) ).
cnf(1084,plain,
( ~ epred6_0
| ~ epred5_0
| ~ epred4_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[975,1078,theory(equality)]),1080,theory(equality)]),1082,theory(equality)]),
[split] ).
cnf(1085,plain,
epred5_0,
inference(spm,[status(thm)],[1081,207,theory(equality)]) ).
cnf(1097,plain,
epred6_0,
inference(spm,[status(thm)],[1083,207,theory(equality)]) ).
cnf(1117,plain,
( $false
| ~ epred5_0
| ~ epred4_0 ),
inference(rw,[status(thm)],[1084,1097,theory(equality)]) ).
cnf(1118,plain,
( $false
| $false
| ~ epred4_0 ),
inference(rw,[status(thm)],[1117,1085,theory(equality)]) ).
cnf(1119,plain,
~ epred4_0,
inference(cn,[status(thm)],[1118,theory(equality)]) ).
cnf(1120,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,X2),nil) != nil ),
inference(sr,[status(thm)],[1079,1119,theory(equality)]) ).
cnf(1123,plain,
( nil = X1
| app(X1,nil) != nil
| ~ ssList(esk1_1(X1))
| ~ ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1120,122,theory(equality)]) ).
cnf(1274,plain,
( nil = X1
| app(X1,nil) != nil
| ~ ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[1123,123]) ).
cnf(1275,plain,
( nil = X1
| app(X1,nil) != nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[1274,124]) ).
cnf(1279,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)],[1275,78,theory(equality)]) ).
cnf(1285,plain,
( nil = app(X1,X2)
| app(X1,app(X2,nil)) != nil
| ~ ssList(app(X1,X2))
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[1279,207,theory(equality)]) ).
cnf(1286,plain,
( nil = app(X1,X2)
| app(X1,app(X2,nil)) != nil
| ~ ssList(app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1285,theory(equality)]) ).
cnf(1365,plain,
( app(X1,X2) = nil
| app(X1,app(X2,nil)) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[1286,113]) ).
cnf(1369,plain,
( app(nil,X1) = nil
| app(X1,nil) != nil
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(app(X1,nil)) ),
inference(spm,[status(thm)],[1365,98,theory(equality)]) ).
cnf(1381,plain,
( app(nil,X1) = nil
| app(X1,nil) != nil
| ~ ssList(X1)
| $false
| ~ ssList(app(X1,nil)) ),
inference(rw,[status(thm)],[1369,207,theory(equality)]) ).
cnf(1382,plain,
( app(nil,X1) = nil
| app(X1,nil) != nil
| ~ ssList(X1)
| ~ ssList(app(X1,nil)) ),
inference(cn,[status(thm)],[1381,theory(equality)]) ).
cnf(1406,plain,
( app(nil,X1) = nil
| X1 != nil
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1382,67,theory(equality)]) ).
cnf(1442,plain,
( cons(X1,nil) = app(cons(X1,nil),X2)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssItem(X1)
| X2 != nil ),
inference(spm,[status(thm)],[109,1406,theory(equality)]) ).
cnf(1483,plain,
( cons(X1,nil) = app(cons(X1,nil),X2)
| $false
| ~ ssList(X2)
| ~ ssItem(X1)
| X2 != nil ),
inference(rw,[status(thm)],[1442,207,theory(equality)]) ).
cnf(1484,plain,
( cons(X1,nil) = app(cons(X1,nil),X2)
| ~ ssList(X2)
| ~ ssItem(X1)
| X2 != nil ),
inference(cn,[status(thm)],[1483,theory(equality)]) ).
cnf(3635,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)],[445,122,theory(equality)]) ).
cnf(3638,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)],[3635,theory(equality)]) ).
cnf(11953,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[531,113]) ).
cnf(11965,plain,
( ssList(cons(X1,nil))
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssItem(X1)
| X2 != nil ),
inference(spm,[status(thm)],[11953,1484,theory(equality)]) ).
cnf(11987,plain,
( ssList(cons(X1,nil))
| $false
| ~ ssList(X2)
| ~ ssItem(X1)
| X2 != nil ),
inference(rw,[status(thm)],[11965,207,theory(equality)]) ).
cnf(11988,plain,
( ssList(cons(X1,nil))
| ~ ssList(X2)
| ~ ssItem(X1)
| X2 != nil ),
inference(cn,[status(thm)],[11987,theory(equality)]) ).
cnf(11994,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[11988,207,theory(equality)]) ).
cnf(99088,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)],[3638,123]) ).
cnf(99089,plain,
( nil = X1
| frontsegP(X1,cons(esk2_1(X1),nil))
| ~ ssList(cons(esk2_1(X1),nil))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[99088,124]) ).
cnf(99095,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)],[669,99089,theory(equality)]) ).
cnf(99187,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)],[99095,207,theory(equality)]) ).
cnf(99188,negated_conjecture,
( nil = esk17_0
| $false
| ~ ssItem(esk2_1(esk17_0))
| ~ ssList(cons(esk2_1(esk17_0),nil))
| $false ),
inference(rw,[status(thm)],[99187,271,theory(equality)]) ).
cnf(99189,negated_conjecture,
( nil = esk17_0
| ~ ssItem(esk2_1(esk17_0))
| ~ ssList(cons(esk2_1(esk17_0),nil)) ),
inference(cn,[status(thm)],[99188,theory(equality)]) ).
cnf(99190,negated_conjecture,
( ~ ssItem(esk2_1(esk17_0))
| ~ ssList(cons(esk2_1(esk17_0),nil)) ),
inference(sr,[status(thm)],[99189,621,theory(equality)]) ).
cnf(99252,negated_conjecture,
~ ssItem(esk2_1(esk17_0)),
inference(csr,[status(thm)],[99190,11994]) ).
cnf(99253,negated_conjecture,
( nil = esk17_0
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[99252,123,theory(equality)]) ).
cnf(99255,negated_conjecture,
( nil = esk17_0
| $false ),
inference(rw,[status(thm)],[99253,271,theory(equality)]) ).
cnf(99256,negated_conjecture,
nil = esk17_0,
inference(cn,[status(thm)],[99255,theory(equality)]) ).
cnf(99257,negated_conjecture,
$false,
inference(sr,[status(thm)],[99256,621,theory(equality)]) ).
cnf(99258,negated_conjecture,
$false,
99257,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC031+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmp09gWz9/sel_SWC031+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC031+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC031+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC031+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
%
%------------------------------------------------------------------------------