TSTP Solution File: SWC123+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC123+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 10:20:44 EST 2010
% Result : Theorem 3.60s
% Output : CNFRefutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 30
% Syntax : Number of formulae : 281 ( 27 unt; 0 def)
% Number of atoms : 1257 ( 257 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 1770 ( 794 ~; 791 |; 114 &)
% ( 12 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 7 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 484 ( 0 sgn 218 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax84) ).
fof(3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax83) ).
fof(4,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax82) ).
fof(5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax81) ).
fof(7,axiom,
! [X1] :
( ssList(X1)
=> ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax46) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax28) ).
fof(9,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(X1,X2)
=> frontsegP(app(X1,X3),X2) ) ) ) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax43) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,X1) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax42) ).
fof(11,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax27) ).
fof(12,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax26) ).
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax21) ).
fof(14,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax20) ).
fof(18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( frontsegP(X1,X2)
& frontsegP(X2,X3) )
=> frontsegP(X1,X3) ) ) ) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax40) ).
fof(19,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax7) ).
fof(20,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax5) ).
fof(24,axiom,
! [X1] :
( ssItem(X1)
=> equalelemsP(cons(X1,nil)) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax73) ).
fof(26,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax58) ).
fof(27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax15) ).
fof(28,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax16) ).
fof(29,axiom,
ssList(nil),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax17) ).
fof(30,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X3) )
=> segmentP(X1,X3) ) ) ) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax53) ).
fof(33,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( segmentP(X1,X2)
=> segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax56) ).
fof(34,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',ax57) ).
fof(37,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ~ frontsegP(X4,X3)
| ~ equalelemsP(X3)
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& frontsegP(X4,X5)
& segmentP(X5,X3)
& equalelemsP(X5) )
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) ) ) ) ),
file('/tmp/tmp1oyKbE/sel_SWC123+1.p_1',co1) ).
fof(38,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ~ frontsegP(X4,X3)
| ~ equalelemsP(X3)
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& frontsegP(X4,X5)
& segmentP(X5,X3)
& equalelemsP(X5) )
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[37]) ).
fof(39,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ~ frontsegP(X4,X3)
| ~ equalelemsP(X3)
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& frontsegP(X4,X5)
& segmentP(X5,X3)
& equalelemsP(X5) )
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[38,theory(equality)]) ).
fof(41,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(42,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[41]) ).
cnf(43,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[42]) ).
fof(44,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)],[3]) ).
fof(45,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)],[44]) ).
fof(46,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)],[45]) ).
fof(47,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)],[46]) ).
cnf(48,plain,
( nil = app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| nil != X1
| nil != X2 ),
inference(split_conjunct,[status(thm)],[47]) ).
fof(51,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)],[4]) ).
fof(52,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)],[51]) ).
fof(53,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)],[52]) ).
cnf(54,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[53]) ).
fof(55,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(56,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[55]) ).
fof(57,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[56]) ).
cnf(58,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[57]) ).
fof(63,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(nil,X1)
| nil = X1 )
& ( nil != X1
| frontsegP(nil,X1) ) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(64,plain,
! [X2] :
( ~ ssList(X2)
| ( ( ~ frontsegP(nil,X2)
| nil = X2 )
& ( nil != X2
| frontsegP(nil,X2) ) ) ),
inference(variable_rename,[status(thm)],[63]) ).
fof(65,plain,
! [X2] :
( ( ~ frontsegP(nil,X2)
| nil = X2
| ~ ssList(X2) )
& ( nil != X2
| frontsegP(nil,X2)
| ~ ssList(X2) ) ),
inference(distribute,[status(thm)],[64]) ).
cnf(66,plain,
( frontsegP(nil,X1)
| ~ ssList(X1)
| nil != X1 ),
inference(split_conjunct,[status(thm)],[65]) ).
fof(68,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(69,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[68]) ).
cnf(70,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[69]) ).
fof(71,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ frontsegP(X1,X2)
| frontsegP(app(X1,X3),X2) ) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(72,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ~ frontsegP(X4,X5)
| frontsegP(app(X4,X6),X5) ) ) ),
inference(variable_rename,[status(thm)],[71]) ).
fof(73,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ~ frontsegP(X4,X5)
| frontsegP(app(X4,X6),X5)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[72]) ).
cnf(74,plain,
( frontsegP(app(X1,X3),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[73]) ).
fof(75,plain,
! [X1] :
( ~ ssList(X1)
| frontsegP(X1,X1) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(76,plain,
! [X2] :
( ~ ssList(X2)
| frontsegP(X2,X2) ),
inference(variable_rename,[status(thm)],[75]) ).
cnf(77,plain,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[76]) ).
fof(78,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssItem(X3)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(79,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)],[78]) ).
fof(80,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)],[79]) ).
cnf(81,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[80]) ).
fof(82,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(83,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[82]) ).
fof(84,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[83]) ).
cnf(85,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[84]) ).
fof(86,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| nil != cons(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(87,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3) ) ),
inference(variable_rename,[status(thm)],[86]) ).
fof(88,plain,
! [X3,X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[87]) ).
cnf(89,plain,
( ~ ssList(X1)
| nil != cons(X2,X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[88]) ).
fof(90,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(91,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssItem(X6)
& cons(X6,X5) = X4 ) ) ),
inference(variable_rename,[status(thm)],[90]) ).
fof(92,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)],[91]) ).
fof(93,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)],[92]) ).
cnf(94,plain,
( nil = X1
| cons(esk2_1(X1),esk1_1(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[93]) ).
cnf(95,plain,
( nil = X1
| ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[93]) ).
cnf(96,plain,
( nil = X1
| ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[93]) ).
fof(112,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X2,X3)
| frontsegP(X1,X3) ) ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(113,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ~ frontsegP(X4,X5)
| ~ frontsegP(X5,X6)
| frontsegP(X4,X6) ) ) ),
inference(variable_rename,[status(thm)],[112]) ).
fof(114,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ~ frontsegP(X4,X5)
| ~ frontsegP(X5,X6)
| frontsegP(X4,X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[113]) ).
cnf(115,plain,
( frontsegP(X1,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X2,X3)
| ~ frontsegP(X1,X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[114]) ).
fof(116,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)],[19]) ).
fof(117,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)],[116]) ).
fof(118,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)],[117]) ).
fof(119,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)],[118]) ).
fof(120,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)],[119]) ).
cnf(124,plain,
( segmentP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[120]) ).
fof(125,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)],[20]) ).
fof(126,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)],[125]) ).
fof(127,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)],[126]) ).
fof(128,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)],[127]) ).
fof(129,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)],[128]) ).
cnf(130,plain,
( app(X2,esk7_2(X1,X2)) = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[129]) ).
cnf(131,plain,
( ssList(esk7_2(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[129]) ).
cnf(132,plain,
( frontsegP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X3) != X1
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[129]) ).
fof(147,plain,
! [X1] :
( ~ ssItem(X1)
| equalelemsP(cons(X1,nil)) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(148,plain,
! [X2] :
( ~ ssItem(X2)
| equalelemsP(cons(X2,nil)) ),
inference(variable_rename,[status(thm)],[147]) ).
cnf(149,plain,
( equalelemsP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[148]) ).
fof(154,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(nil,X1)
| nil = X1 )
& ( nil != X1
| segmentP(nil,X1) ) ) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(155,plain,
! [X2] :
( ~ ssList(X2)
| ( ( ~ segmentP(nil,X2)
| nil = X2 )
& ( nil != X2
| segmentP(nil,X2) ) ) ),
inference(variable_rename,[status(thm)],[154]) ).
fof(156,plain,
! [X2] :
( ( ~ segmentP(nil,X2)
| nil = X2
| ~ ssList(X2) )
& ( nil != X2
| segmentP(nil,X2)
| ~ ssList(X2) ) ),
inference(distribute,[status(thm)],[155]) ).
cnf(157,plain,
( segmentP(nil,X1)
| ~ ssList(X1)
| nil != X1 ),
inference(split_conjunct,[status(thm)],[156]) ).
fof(159,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(160,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[159]) ).
fof(161,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[160]) ).
fof(162,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)],[161]) ).
cnf(163,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[162]) ).
fof(165,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(166,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[165]) ).
fof(167,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[166]) ).
cnf(168,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[167]) ).
cnf(169,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[29]) ).
fof(170,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X3)
| segmentP(X1,X3) ) ) ),
inference(fof_nnf,[status(thm)],[30]) ).
fof(171,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ~ segmentP(X4,X5)
| ~ segmentP(X5,X6)
| segmentP(X4,X6) ) ) ),
inference(variable_rename,[status(thm)],[170]) ).
fof(172,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ~ segmentP(X4,X5)
| ~ segmentP(X5,X6)
| segmentP(X4,X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[171]) ).
cnf(173,plain,
( segmentP(X1,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[172]) ).
fof(181,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ~ segmentP(X1,X2)
| segmentP(app(app(X3,X1),X4),X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(182,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| ~ segmentP(X5,X6)
| segmentP(app(app(X7,X5),X8),X6) ) ) ) ),
inference(variable_rename,[status(thm)],[181]) ).
fof(183,plain,
! [X5,X6,X7,X8] :
( ~ ssList(X8)
| ~ segmentP(X5,X6)
| segmentP(app(app(X7,X5),X8),X6)
| ~ ssList(X7)
| ~ ssList(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[182]) ).
cnf(184,plain,
( segmentP(app(app(X3,X1),X4),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[183]) ).
fof(185,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(186,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,nil) ),
inference(variable_rename,[status(thm)],[185]) ).
cnf(187,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[186]) ).
fof(206,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& neq(X2,nil)
& frontsegP(X4,X3)
& equalelemsP(X3)
& ! [X5] :
( ~ ssList(X5)
| ~ neq(X3,X5)
| ~ frontsegP(X4,X5)
| ~ segmentP(X5,X3)
| ~ equalelemsP(X5) )
& ( ~ neq(X1,nil)
| ~ segmentP(X2,X1) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(207,negated_conjecture,
? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& X7 = X9
& X6 = X8
& neq(X7,nil)
& frontsegP(X9,X8)
& equalelemsP(X8)
& ! [X10] :
( ~ ssList(X10)
| ~ neq(X8,X10)
| ~ frontsegP(X9,X10)
| ~ segmentP(X10,X8)
| ~ equalelemsP(X10) )
& ( ~ neq(X6,nil)
| ~ segmentP(X7,X6) ) ) ) ) ),
inference(variable_rename,[status(thm)],[206]) ).
fof(208,negated_conjecture,
( ssList(esk12_0)
& ssList(esk13_0)
& ssList(esk14_0)
& ssList(esk15_0)
& esk13_0 = esk15_0
& esk12_0 = esk14_0
& neq(esk13_0,nil)
& frontsegP(esk15_0,esk14_0)
& equalelemsP(esk14_0)
& ! [X10] :
( ~ ssList(X10)
| ~ neq(esk14_0,X10)
| ~ frontsegP(esk15_0,X10)
| ~ segmentP(X10,esk14_0)
| ~ equalelemsP(X10) )
& ( ~ neq(esk12_0,nil)
| ~ segmentP(esk13_0,esk12_0) ) ),
inference(skolemize,[status(esa)],[207]) ).
fof(209,negated_conjecture,
! [X10] :
( ( ~ ssList(X10)
| ~ neq(esk14_0,X10)
| ~ frontsegP(esk15_0,X10)
| ~ segmentP(X10,esk14_0)
| ~ equalelemsP(X10) )
& esk13_0 = esk15_0
& esk12_0 = esk14_0
& neq(esk13_0,nil)
& frontsegP(esk15_0,esk14_0)
& equalelemsP(esk14_0)
& ( ~ neq(esk12_0,nil)
| ~ segmentP(esk13_0,esk12_0) )
& ssList(esk15_0)
& ssList(esk14_0)
& ssList(esk13_0)
& ssList(esk12_0) ),
inference(shift_quantors,[status(thm)],[208]) ).
cnf(210,negated_conjecture,
ssList(esk12_0),
inference(split_conjunct,[status(thm)],[209]) ).
cnf(211,negated_conjecture,
ssList(esk13_0),
inference(split_conjunct,[status(thm)],[209]) ).
cnf(214,negated_conjecture,
( ~ segmentP(esk13_0,esk12_0)
| ~ neq(esk12_0,nil) ),
inference(split_conjunct,[status(thm)],[209]) ).
cnf(216,negated_conjecture,
frontsegP(esk15_0,esk14_0),
inference(split_conjunct,[status(thm)],[209]) ).
cnf(217,negated_conjecture,
neq(esk13_0,nil),
inference(split_conjunct,[status(thm)],[209]) ).
cnf(218,negated_conjecture,
esk12_0 = esk14_0,
inference(split_conjunct,[status(thm)],[209]) ).
cnf(219,negated_conjecture,
esk13_0 = esk15_0,
inference(split_conjunct,[status(thm)],[209]) ).
cnf(220,negated_conjecture,
( ~ equalelemsP(X1)
| ~ segmentP(X1,esk14_0)
| ~ frontsegP(esk15_0,X1)
| ~ neq(esk14_0,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[209]) ).
cnf(221,negated_conjecture,
ssList(esk14_0),
inference(rw,[status(thm)],[210,218,theory(equality)]) ).
cnf(222,negated_conjecture,
ssList(esk15_0),
inference(rw,[status(thm)],[211,219,theory(equality)]) ).
cnf(223,negated_conjecture,
neq(esk15_0,nil),
inference(rw,[status(thm)],[217,219,theory(equality)]) ).
cnf(224,negated_conjecture,
( ~ segmentP(esk15_0,esk14_0)
| ~ neq(esk12_0,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[214,219,theory(equality)]),218,theory(equality)]) ).
cnf(225,negated_conjecture,
( ~ segmentP(esk15_0,esk14_0)
| ~ neq(esk14_0,nil) ),
inference(rw,[status(thm)],[224,218,theory(equality)]) ).
cnf(228,negated_conjecture,
( esk14_0 = nil
| ~ segmentP(esk15_0,esk14_0)
| ~ ssList(nil)
| ~ ssList(esk14_0) ),
inference(spm,[status(thm)],[225,163,theory(equality)]) ).
cnf(229,negated_conjecture,
( esk14_0 = nil
| ~ segmentP(esk15_0,esk14_0)
| $false
| ~ ssList(esk14_0) ),
inference(rw,[status(thm)],[228,169,theory(equality)]) ).
cnf(230,negated_conjecture,
( esk14_0 = nil
| ~ segmentP(esk15_0,esk14_0)
| ~ ssList(esk14_0) ),
inference(cn,[status(thm)],[229,theory(equality)]) ).
cnf(268,negated_conjecture,
( esk14_0 = X1
| ~ segmentP(X1,esk14_0)
| ~ frontsegP(esk15_0,X1)
| ~ ssList(X1)
| ~ equalelemsP(X1)
| ~ ssList(esk14_0) ),
inference(spm,[status(thm)],[220,163,theory(equality)]) ).
cnf(280,plain,
( segmentP(X1,X2)
| ~ segmentP(X1,nil)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1)
| nil != X2 ),
inference(spm,[status(thm)],[173,157,theory(equality)]) ).
cnf(283,plain,
( segmentP(X1,X2)
| ~ segmentP(X1,nil)
| ~ ssList(X2)
| $false
| ~ ssList(X1)
| nil != X2 ),
inference(rw,[status(thm)],[280,169,theory(equality)]) ).
cnf(284,plain,
( segmentP(X1,X2)
| ~ segmentP(X1,nil)
| ~ ssList(X2)
| ~ ssList(X1)
| nil != X2 ),
inference(cn,[status(thm)],[283,theory(equality)]) ).
cnf(303,plain,
( frontsegP(X1,X2)
| ~ frontsegP(X1,app(X3,X4))
| ~ ssList(X2)
| ~ ssList(app(X3,X4))
| ~ ssList(X1)
| ~ frontsegP(X3,X2)
| ~ ssList(X4)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[115,74,theory(equality)]) ).
cnf(355,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[124,70,theory(equality)]) ).
cnf(364,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[355,169,theory(equality)]) ).
cnf(365,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[364,theory(equality)]) ).
cnf(369,plain,
( segmentP(app(X1,X2),X3)
| ~ segmentP(X1,X3)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[184,70,theory(equality)]) ).
cnf(380,plain,
( segmentP(app(X1,X2),X3)
| ~ segmentP(X1,X3)
| ~ ssList(X2)
| $false
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[369,169,theory(equality)]) ).
cnf(381,plain,
( segmentP(app(X1,X2),X3)
| ~ segmentP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[380,theory(equality)]) ).
cnf(386,plain,
( frontsegP(X1,cons(X2,nil))
| cons(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(cons(X2,nil))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(spm,[status(thm)],[132,58,theory(equality)]) ).
cnf(456,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[168,81,theory(equality)]) ).
cnf(457,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[89,81,theory(equality)]) ).
cnf(509,negated_conjecture,
( esk14_0 = nil
| ~ segmentP(esk15_0,esk14_0)
| $false ),
inference(rw,[status(thm)],[230,221,theory(equality)]) ).
cnf(510,negated_conjecture,
( esk14_0 = nil
| ~ segmentP(esk15_0,esk14_0) ),
inference(cn,[status(thm)],[509,theory(equality)]) ).
cnf(513,negated_conjecture,
( esk14_0 = X1
| ~ segmentP(X1,esk14_0)
| ~ frontsegP(esk15_0,X1)
| ~ ssList(X1)
| ~ equalelemsP(X1)
| $false ),
inference(rw,[status(thm)],[268,221,theory(equality)]) ).
cnf(514,negated_conjecture,
( esk14_0 = X1
| ~ segmentP(X1,esk14_0)
| ~ frontsegP(esk15_0,X1)
| ~ ssList(X1)
| ~ equalelemsP(X1) ),
inference(cn,[status(thm)],[513,theory(equality)]) ).
cnf(516,negated_conjecture,
( esk14_0 = cons(X1,nil)
| ~ segmentP(cons(X1,nil),esk14_0)
| ~ frontsegP(esk15_0,cons(X1,nil))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[514,149,theory(equality)]) ).
cnf(532,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[457,85]) ).
cnf(538,plain,
( app(app(cons(X1,X2),X3),X4) != nil
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[532,81,theory(equality)]) ).
cnf(669,plain,
( segmentP(X1,X2)
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[284,187]) ).
cnf(675,negated_conjecture,
( cons(X1,nil) = esk14_0
| ~ frontsegP(esk15_0,cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| nil != esk14_0
| ~ ssList(esk14_0) ),
inference(spm,[status(thm)],[516,669,theory(equality)]) ).
cnf(684,negated_conjecture,
( cons(X1,nil) = esk14_0
| ~ frontsegP(esk15_0,cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| nil != esk14_0
| $false ),
inference(rw,[status(thm)],[675,221,theory(equality)]) ).
cnf(685,negated_conjecture,
( cons(X1,nil) = esk14_0
| ~ frontsegP(esk15_0,cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| nil != esk14_0 ),
inference(cn,[status(thm)],[684,theory(equality)]) ).
cnf(693,plain,
( app(app(cons(X1,X2),X3),X4) != nil
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[538,85]) ).
cnf(702,plain,
( app(cons(X1,X2),app(X3,X4)) != nil
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(cons(X1,X2)) ),
inference(spm,[status(thm)],[693,54,theory(equality)]) ).
cnf(730,plain,
( app(cons(X1,X2),app(X3,X4)) != nil
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[702,168]) ).
cnf(733,plain,
( app(cons(X1,X2),nil) != nil
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X3)
| nil != X4
| nil != X3 ),
inference(spm,[status(thm)],[730,48,theory(equality)]) ).
cnf(738,plain,
( cons(X1,app(X2,X3)) != nil
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(app(X2,X3)) ),
inference(spm,[status(thm)],[730,58,theory(equality)]) ).
cnf(747,plain,
( cons(X1,app(X2,X3)) != nil
| ~ ssItem(X1)
| ~ ssList(X3)
| $false
| ~ ssList(X2)
| ~ ssList(app(X2,X3)) ),
inference(rw,[status(thm)],[738,169,theory(equality)]) ).
cnf(748,plain,
( cons(X1,app(X2,X3)) != nil
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(app(X2,X3)) ),
inference(cn,[status(thm)],[747,theory(equality)]) ).
cnf(752,plain,
( cons(X1,app(X2,X3)) != nil
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[748,85]) ).
cnf(755,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| nil != X3
| nil != X2 ),
inference(spm,[status(thm)],[752,48,theory(equality)]) ).
fof(809,plain,
( ~ epred1_0
<=> ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != nil ) ),
introduced(definition),
[split] ).
cnf(810,plain,
( epred1_0
| ~ ssItem(X1)
| cons(X1,nil) != nil ),
inference(split_equiv,[status(thm)],[809]) ).
fof(811,plain,
( ~ epred2_0
<=> ! [X3] :
( ~ ssList(X3)
| nil != X3 ) ),
introduced(definition),
[split] ).
cnf(812,plain,
( epred2_0
| ~ ssList(X3)
| nil != X3 ),
inference(split_equiv,[status(thm)],[811]) ).
fof(813,plain,
( ~ epred3_0
<=> ! [X2] :
( ~ ssList(X2)
| nil != X2 ) ),
introduced(definition),
[split] ).
cnf(814,plain,
( epred3_0
| ~ ssList(X2)
| nil != X2 ),
inference(split_equiv,[status(thm)],[813]) ).
cnf(815,plain,
( ~ epred3_0
| ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[755,809,theory(equality)]),811,theory(equality)]),813,theory(equality)]),
[split] ).
cnf(816,plain,
epred2_0,
inference(spm,[status(thm)],[812,169,theory(equality)]) ).
cnf(828,plain,
epred3_0,
inference(spm,[status(thm)],[814,169,theory(equality)]) ).
cnf(840,plain,
( $false
| ~ epred2_0
| ~ epred1_0 ),
inference(rw,[status(thm)],[815,828,theory(equality)]) ).
cnf(841,plain,
( $false
| $false
| ~ epred1_0 ),
inference(rw,[status(thm)],[840,816,theory(equality)]) ).
cnf(842,plain,
~ epred1_0,
inference(cn,[status(thm)],[841,theory(equality)]) ).
cnf(843,plain,
( ~ ssItem(X1)
| cons(X1,nil) != nil ),
inference(sr,[status(thm)],[810,842,theory(equality)]) ).
cnf(859,plain,
( frontsegP(X1,X2)
| ~ frontsegP(X1,app(X3,X4))
| ~ frontsegP(X3,X2)
| ~ ssList(X1)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[303,85]) ).
cnf(866,plain,
( frontsegP(X1,X2)
| ~ frontsegP(X1,X4)
| ~ frontsegP(X3,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(esk7_2(X4,X3))
| ~ ssList(X3)
| ~ frontsegP(X4,X3)
| ~ ssList(X4) ),
inference(spm,[status(thm)],[859,130,theory(equality)]) ).
fof(879,plain,
( ~ epred4_0
<=> ! [X2,X1] :
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,X2),nil) != nil ) ),
introduced(definition),
[split] ).
cnf(880,plain,
( epred4_0
| ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,X2),nil) != nil ),
inference(split_equiv,[status(thm)],[879]) ).
fof(881,plain,
( ~ epred5_0
<=> ! [X4] :
( ~ ssList(X4)
| nil != X4 ) ),
introduced(definition),
[split] ).
cnf(882,plain,
( epred5_0
| ~ ssList(X4)
| nil != X4 ),
inference(split_equiv,[status(thm)],[881]) ).
fof(883,plain,
( ~ epred6_0
<=> ! [X3] :
( ~ ssList(X3)
| nil != X3 ) ),
introduced(definition),
[split] ).
cnf(884,plain,
( epred6_0
| ~ ssList(X3)
| nil != X3 ),
inference(split_equiv,[status(thm)],[883]) ).
cnf(885,plain,
( ~ epred6_0
| ~ epred5_0
| ~ epred4_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[733,879,theory(equality)]),881,theory(equality)]),883,theory(equality)]),
[split] ).
cnf(886,plain,
epred5_0,
inference(spm,[status(thm)],[882,169,theory(equality)]) ).
cnf(898,plain,
epred6_0,
inference(spm,[status(thm)],[884,169,theory(equality)]) ).
cnf(927,plain,
( $false
| ~ epred5_0
| ~ epred4_0 ),
inference(rw,[status(thm)],[885,898,theory(equality)]) ).
cnf(928,plain,
( $false
| $false
| ~ epred4_0 ),
inference(rw,[status(thm)],[927,886,theory(equality)]) ).
cnf(929,plain,
~ epred4_0,
inference(cn,[status(thm)],[928,theory(equality)]) ).
cnf(934,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,X2),nil) != nil ),
inference(sr,[status(thm)],[880,929,theory(equality)]) ).
cnf(937,plain,
( nil = X1
| app(X1,nil) != nil
| ~ ssItem(esk2_1(X1))
| ~ ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[934,94,theory(equality)]) ).
cnf(960,plain,
( nil = X1
| app(X1,nil) != nil
| ~ ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[937,96]) ).
cnf(961,plain,
( nil = X1
| app(X1,nil) != nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[960,95]) ).
cnf(965,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)],[961,54,theory(equality)]) ).
cnf(970,plain,
( nil = app(X1,X2)
| app(X1,app(X2,nil)) != nil
| ~ ssList(app(X1,X2))
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[965,169,theory(equality)]) ).
cnf(971,plain,
( nil = app(X1,X2)
| app(X1,app(X2,nil)) != nil
| ~ ssList(app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[970,theory(equality)]) ).
cnf(972,plain,
( app(X1,X2) = nil
| app(X1,app(X2,nil)) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[971,85]) ).
cnf(975,plain,
( app(nil,X1) = nil
| app(X1,nil) != nil
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(app(X1,nil)) ),
inference(spm,[status(thm)],[972,70,theory(equality)]) ).
cnf(984,plain,
( app(nil,X1) = nil
| app(X1,nil) != nil
| ~ ssList(X1)
| $false
| ~ ssList(app(X1,nil)) ),
inference(rw,[status(thm)],[975,169,theory(equality)]) ).
cnf(985,plain,
( app(nil,X1) = nil
| app(X1,nil) != nil
| ~ ssList(X1)
| ~ ssList(app(X1,nil)) ),
inference(cn,[status(thm)],[984,theory(equality)]) ).
cnf(992,plain,
( app(nil,X1) = nil
| X1 != nil
| ~ ssList(X1) ),
inference(spm,[status(thm)],[985,43,theory(equality)]) ).
cnf(993,plain,
( app(nil,nil) = nil
| ~ ssList(nil) ),
inference(spm,[status(thm)],[985,70,theory(equality)]) ).
cnf(998,plain,
( app(nil,nil) = nil
| $false ),
inference(rw,[status(thm)],[993,169,theory(equality)]) ).
cnf(999,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[998,theory(equality)]) ).
cnf(1018,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[81,999,theory(equality)]) ).
cnf(1047,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[1018,169,theory(equality)]) ).
cnf(1048,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[1047,theory(equality)]) ).
cnf(1104,plain,
( segmentP(app(nil,X2),X3)
| ~ segmentP(X1,X3)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X3)
| ~ ssList(X1)
| X1 != nil ),
inference(spm,[status(thm)],[184,992,theory(equality)]) ).
cnf(1138,plain,
( segmentP(app(nil,X2),X3)
| ~ segmentP(X1,X3)
| ~ ssList(X2)
| $false
| ~ ssList(X3)
| ~ ssList(X1)
| X1 != nil ),
inference(rw,[status(thm)],[1104,169,theory(equality)]) ).
cnf(1139,plain,
( segmentP(app(nil,X2),X3)
| ~ segmentP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| X1 != nil ),
inference(cn,[status(thm)],[1138,theory(equality)]) ).
cnf(1696,plain,
( segmentP(app(nil,X1),nil)
| X2 != nil
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[1139,187,theory(equality)]) ).
cnf(1702,plain,
( segmentP(app(nil,X1),nil)
| X2 != nil
| ~ ssList(X1)
| $false
| ~ ssList(X2) ),
inference(rw,[status(thm)],[1696,169,theory(equality)]) ).
cnf(1703,plain,
( segmentP(app(nil,X1),nil)
| X2 != nil
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[1702,theory(equality)]) ).
cnf(1731,plain,
( segmentP(app(nil,X1),nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1703,169,theory(equality)]) ).
cnf(1742,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1731,999,theory(equality)]) ).
cnf(1753,plain,
( segmentP(nil,nil)
| $false ),
inference(rw,[status(thm)],[1742,169,theory(equality)]) ).
cnf(1754,plain,
segmentP(nil,nil),
inference(cn,[status(thm)],[1753,theory(equality)]) ).
cnf(2285,plain,
( segmentP(X1,X2)
| X3 != X1
| ~ ssList(esk7_2(X3,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X3,X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[365,130,theory(equality)]) ).
cnf(2304,plain,
( segmentP(X1,X2)
| ~ ssList(esk7_2(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X1,X2) ),
inference(er,[status(thm)],[2285,theory(equality)]) ).
cnf(2844,plain,
( segmentP(X2,X3)
| ~ segmentP(X1,X3)
| ~ ssList(esk7_2(X2,X1))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[381,130,theory(equality)]) ).
cnf(3548,plain,
( frontsegP(X1,cons(esk2_1(X2),nil))
| nil = X2
| X2 != X1
| ~ ssItem(esk2_1(X2))
| ~ ssList(cons(esk2_1(X2),nil))
| ~ ssList(esk1_1(X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[386,94,theory(equality)]) ).
cnf(3550,plain,
( frontsegP(X1,cons(esk2_1(X1),nil))
| nil = X1
| ~ ssItem(esk2_1(X1))
| ~ ssList(cons(esk2_1(X1),nil))
| ~ ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(er,[status(thm)],[3548,theory(equality)]) ).
cnf(11665,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[456,85]) ).
cnf(11673,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[11665,1048,theory(equality)]) ).
cnf(11696,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[11673,169,theory(equality)]) ).
cnf(11697,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[11696,theory(equality)]) ).
cnf(22501,plain,
( frontsegP(X1,X2)
| ~ frontsegP(X4,X3)
| ~ frontsegP(X1,X4)
| ~ frontsegP(X3,X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[866,131]) ).
cnf(44742,plain,
( segmentP(X1,X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[2304,131]) ).
cnf(44746,negated_conjecture,
( esk14_0 = nil
| ~ frontsegP(esk15_0,esk14_0)
| ~ ssList(esk14_0)
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[510,44742,theory(equality)]) ).
cnf(44772,negated_conjecture,
( esk14_0 = nil
| $false
| ~ ssList(esk14_0)
| ~ ssList(esk15_0) ),
inference(rw,[status(thm)],[44746,216,theory(equality)]) ).
cnf(44773,negated_conjecture,
( esk14_0 = nil
| $false
| $false
| ~ ssList(esk15_0) ),
inference(rw,[status(thm)],[44772,221,theory(equality)]) ).
cnf(44774,negated_conjecture,
( esk14_0 = nil
| $false
| $false
| $false ),
inference(rw,[status(thm)],[44773,222,theory(equality)]) ).
cnf(44775,negated_conjecture,
esk14_0 = nil,
inference(cn,[status(thm)],[44774,theory(equality)]) ).
cnf(44805,negated_conjecture,
frontsegP(esk15_0,nil),
inference(rw,[status(thm)],[216,44775,theory(equality)]) ).
cnf(45037,negated_conjecture,
( cons(X1,nil) = nil
| esk14_0 != nil
| ~ frontsegP(esk15_0,cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(rw,[status(thm)],[685,44775,theory(equality)]) ).
cnf(45038,negated_conjecture,
( cons(X1,nil) = nil
| $false
| ~ frontsegP(esk15_0,cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(rw,[status(thm)],[45037,44775,theory(equality)]) ).
cnf(45039,negated_conjecture,
( cons(X1,nil) = nil
| ~ frontsegP(esk15_0,cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[45038,theory(equality)]) ).
cnf(45062,negated_conjecture,
( ~ neq(nil,nil)
| ~ segmentP(esk15_0,esk14_0) ),
inference(rw,[status(thm)],[225,44775,theory(equality)]) ).
cnf(45063,negated_conjecture,
( ~ neq(nil,nil)
| ~ segmentP(esk15_0,nil) ),
inference(rw,[status(thm)],[45062,44775,theory(equality)]) ).
cnf(45072,negated_conjecture,
( frontsegP(esk15_0,X1)
| ~ frontsegP(X2,X1)
| ~ frontsegP(nil,X2)
| ~ ssList(X1)
| ~ ssList(esk15_0)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[22501,44805,theory(equality)]) ).
cnf(45102,negated_conjecture,
( frontsegP(esk15_0,X1)
| ~ frontsegP(X2,X1)
| ~ frontsegP(nil,X2)
| ~ ssList(X1)
| $false
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(rw,[status(thm)],[45072,222,theory(equality)]) ).
cnf(45103,negated_conjecture,
( frontsegP(esk15_0,X1)
| ~ frontsegP(X2,X1)
| ~ frontsegP(nil,X2)
| ~ ssList(X1)
| $false
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[45102,169,theory(equality)]) ).
cnf(45104,negated_conjecture,
( frontsegP(esk15_0,X1)
| ~ frontsegP(X2,X1)
| ~ frontsegP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[45103,theory(equality)]) ).
cnf(47688,negated_conjecture,
( cons(X1,nil) = nil
| ~ frontsegP(esk15_0,cons(X1,nil))
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[45039,11697]) ).
cnf(47689,negated_conjecture,
( ~ frontsegP(esk15_0,cons(X1,nil))
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[47688,843]) ).
cnf(58022,plain,
( segmentP(X2,X3)
| ~ segmentP(X1,X3)
| ~ frontsegP(X2,X1)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[2844,131]) ).
cnf(68242,negated_conjecture,
( frontsegP(esk15_0,X1)
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2)
| nil != X2 ),
inference(spm,[status(thm)],[45104,66,theory(equality)]) ).
cnf(68753,negated_conjecture,
( frontsegP(esk15_0,X1)
| nil != X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[68242,77,theory(equality)]) ).
cnf(68936,negated_conjecture,
( segmentP(esk15_0,X1)
| ~ segmentP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(esk15_0)
| nil != X2 ),
inference(spm,[status(thm)],[58022,68753,theory(equality)]) ).
cnf(68999,negated_conjecture,
( segmentP(esk15_0,X1)
| ~ segmentP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2)
| $false
| nil != X2 ),
inference(rw,[status(thm)],[68936,222,theory(equality)]) ).
cnf(69000,negated_conjecture,
( segmentP(esk15_0,X1)
| ~ segmentP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2)
| nil != X2 ),
inference(cn,[status(thm)],[68999,theory(equality)]) ).
cnf(69960,negated_conjecture,
( segmentP(esk15_0,nil)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[69000,1754,theory(equality)]) ).
cnf(70048,negated_conjecture,
( segmentP(esk15_0,nil)
| $false ),
inference(rw,[status(thm)],[69960,169,theory(equality)]) ).
cnf(70049,negated_conjecture,
segmentP(esk15_0,nil),
inference(cn,[status(thm)],[70048,theory(equality)]) ).
cnf(70130,negated_conjecture,
( ~ neq(nil,nil)
| $false ),
inference(rw,[status(thm)],[45063,70049,theory(equality)]) ).
cnf(70131,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[70130,theory(equality)]) ).
cnf(74269,plain,
( nil = X1
| frontsegP(X1,cons(esk2_1(X1),nil))
| ~ ssItem(esk2_1(X1))
| ~ ssList(cons(esk2_1(X1),nil))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[3550,96]) ).
cnf(74270,plain,
( nil = X1
| frontsegP(X1,cons(esk2_1(X1),nil))
| ~ ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[74269,11697]) ).
cnf(74271,plain,
( nil = X1
| frontsegP(X1,cons(esk2_1(X1),nil))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[74270,95]) ).
cnf(74306,negated_conjecture,
( nil = esk15_0
| ~ ssItem(esk2_1(esk15_0))
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[47689,74271,theory(equality)]) ).
cnf(74359,negated_conjecture,
( nil = esk15_0
| ~ ssItem(esk2_1(esk15_0))
| $false ),
inference(rw,[status(thm)],[74306,222,theory(equality)]) ).
cnf(74360,negated_conjecture,
( nil = esk15_0
| ~ ssItem(esk2_1(esk15_0)) ),
inference(cn,[status(thm)],[74359,theory(equality)]) ).
cnf(74393,negated_conjecture,
( esk15_0 = nil
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[74360,95,theory(equality)]) ).
cnf(74394,negated_conjecture,
( esk15_0 = nil
| $false ),
inference(rw,[status(thm)],[74393,222,theory(equality)]) ).
cnf(74395,negated_conjecture,
esk15_0 = nil,
inference(cn,[status(thm)],[74394,theory(equality)]) ).
cnf(74402,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[223,74395,theory(equality)]) ).
cnf(74403,negated_conjecture,
$false,
inference(sr,[status(thm)],[74402,70131,theory(equality)]) ).
cnf(74404,negated_conjecture,
$false,
74403,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC123+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmp1oyKbE/sel_SWC123+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC123+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC123+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC123+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
%
%------------------------------------------------------------------------------