TSTP Solution File: SWC022+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC022+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 10:06:23 EST 2010
% Result : Theorem 0.29s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 19
% Syntax : Number of formulae : 227 ( 15 unt; 0 def)
% Number of atoms : 1001 ( 334 equ)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 1318 ( 544 ~; 613 |; 108 &)
% ( 3 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 350 ( 0 sgn 174 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/tmp/tmp4TldNs/sel_SWC022+1.p_1',ax85) ).
fof(2,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmp4TldNs/sel_SWC022+1.p_1',ax84) ).
fof(3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmp4TldNs/sel_SWC022+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/tmp4TldNs/sel_SWC022+1.p_1',ax82) ).
fof(5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmp4TldNs/sel_SWC022+1.p_1',ax81) ).
fof(6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/tmp/tmp4TldNs/sel_SWC022+1.p_1',ax80) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/tmp/tmp4TldNs/sel_SWC022+1.p_1',ax23) ).
fof(9,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(X1,X2)
=> frontsegP(app(X1,X3),X2) ) ) ) ),
file('/tmp/tmp4TldNs/sel_SWC022+1.p_1',ax43) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,X1) ),
file('/tmp/tmp4TldNs/sel_SWC022+1.p_1',ax42) ).
fof(12,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmp4TldNs/sel_SWC022+1.p_1',ax26) ).
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmp4TldNs/sel_SWC022+1.p_1',ax21) ).
fof(15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/tmp/tmp4TldNs/sel_SWC022+1.p_1',ax27) ).
fof(19,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/tmp/tmp4TldNs/sel_SWC022+1.p_1',ax5) ).
fof(20,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/tmp/tmp4TldNs/sel_SWC022+1.p_1',ax20) ).
fof(22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/tmp/tmp4TldNs/sel_SWC022+1.p_1',ax22) ).
fof(25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmp4TldNs/sel_SWC022+1.p_1',ax15) ).
fof(26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmp4TldNs/sel_SWC022+1.p_1',ax16) ).
fof(27,axiom,
ssList(nil),
file('/tmp/tmp4TldNs/sel_SWC022+1.p_1',ax17) ).
fof(31,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& frontsegP(X2,X5)
& frontsegP(X1,X5) )
| ? [X6] :
( ssList(X6)
& X3 != X6
& ? [X7] :
( ssItem(X7)
& cons(X7,nil) = X6
& hd(X4) = X7
& neq(nil,X4) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/tmp/tmp4TldNs/sel_SWC022+1.p_1',co1) ).
fof(32,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& frontsegP(X2,X5)
& frontsegP(X1,X5) )
| ? [X6] :
( ssList(X6)
& X3 != X6
& ? [X7] :
( ssItem(X7)
& cons(X7,nil) = X6
& hd(X4) = X7
& neq(nil,X4) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[31]) ).
fof(33,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& frontsegP(X2,X5)
& frontsegP(X1,X5) )
| ? [X6] :
( ssList(X6)
& X3 != X6
& ? [X7] :
( ssItem(X7)
& cons(X7,nil) = X6
& hd(X4) = X7
& neq(nil,X4) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[32,theory(equality)]) ).
fof(34,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| nil = X1
| hd(app(X1,X2)) = hd(X1) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(35,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| nil = X3
| hd(app(X3,X4)) = hd(X3) ) ),
inference(variable_rename,[status(thm)],[34]) ).
fof(36,plain,
! [X3,X4] :
( ~ ssList(X4)
| nil = X3
| hd(app(X3,X4)) = hd(X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[35]) ).
cnf(37,plain,
( hd(app(X1,X2)) = hd(X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[36]) ).
fof(38,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(39,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[38]) ).
cnf(40,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[39]) ).
fof(41,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(42,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)],[41]) ).
fof(43,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)],[42]) ).
fof(44,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)],[43]) ).
cnf(45,plain,
( nil = app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| nil != X1
| nil != X2 ),
inference(split_conjunct,[status(thm)],[44]) ).
fof(48,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(49,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)],[48]) ).
fof(50,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)],[49]) ).
cnf(51,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[50]) ).
fof(52,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(53,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[52]) ).
fof(54,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[53]) ).
cnf(55,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[54]) ).
fof(56,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,X3) != app(X2,X1)
| X3 = X1 ) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(57,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(X5,X6) != app(X5,X4)
| X6 = X4 ) ) ),
inference(variable_rename,[status(thm)],[56]) ).
fof(58,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| app(X5,X6) != app(X5,X4)
| X6 = X4
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[57]) ).
cnf(59,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X3) != app(X2,X1)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[58]) ).
fof(63,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| hd(cons(X2,X1)) = X2 ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(64,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| hd(cons(X4,X3)) = X4 ) ),
inference(variable_rename,[status(thm)],[63]) ).
fof(65,plain,
! [X3,X4] :
( ~ ssItem(X4)
| hd(cons(X4,X3)) = X4
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[64]) ).
cnf(66,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[65]) ).
fof(67,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(68,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ~ frontsegP(X4,X5)
| frontsegP(app(X4,X6),X5) ) ) ),
inference(variable_rename,[status(thm)],[67]) ).
fof(69,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ~ frontsegP(X4,X5)
| frontsegP(app(X4,X6),X5)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[68]) ).
cnf(70,plain,
( frontsegP(app(X1,X3),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[69]) ).
fof(71,plain,
! [X1] :
( ~ ssList(X1)
| frontsegP(X1,X1) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(72,plain,
! [X2] :
( ~ ssList(X2)
| frontsegP(X2,X2) ),
inference(variable_rename,[status(thm)],[71]) ).
cnf(73,plain,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[72]) ).
fof(78,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(79,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[78]) ).
fof(80,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[79]) ).
cnf(81,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[80]) ).
fof(82,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| nil != cons(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(83,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3) ) ),
inference(variable_rename,[status(thm)],[82]) ).
fof(84,plain,
! [X3,X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[83]) ).
cnf(85,plain,
( ~ ssList(X1)
| nil != cons(X2,X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[84]) ).
fof(91,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(92,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)],[91]) ).
fof(93,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)],[92]) ).
cnf(94,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[93]) ).
fof(111,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)],[19]) ).
fof(112,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)],[111]) ).
fof(113,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ( ( ~ frontsegP(X4,X5)
| ( ssList(esk3_2(X4,X5))
& app(X5,esk3_2(X4,X5)) = X4 ) )
& ( ! [X7] :
( ~ ssList(X7)
| app(X5,X7) != X4 )
| frontsegP(X4,X5) ) ) ) ),
inference(skolemize,[status(esa)],[112]) ).
fof(114,plain,
! [X4,X5,X7] :
( ( ( ~ ssList(X7)
| app(X5,X7) != X4
| frontsegP(X4,X5) )
& ( ~ frontsegP(X4,X5)
| ( ssList(esk3_2(X4,X5))
& app(X5,esk3_2(X4,X5)) = X4 ) ) )
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[113]) ).
fof(115,plain,
! [X4,X5,X7] :
( ( ~ ssList(X7)
| app(X5,X7) != X4
| frontsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) )
& ( ssList(esk3_2(X4,X5))
| ~ frontsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) )
& ( app(X5,esk3_2(X4,X5)) = X4
| ~ frontsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) ) ),
inference(distribute,[status(thm)],[114]) ).
cnf(116,plain,
( app(X2,esk3_2(X1,X2)) = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[115]) ).
cnf(117,plain,
( ssList(esk3_2(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[115]) ).
fof(119,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(120,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssItem(X6)
& cons(X6,X5) = X4 ) ) ),
inference(variable_rename,[status(thm)],[119]) ).
fof(121,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ( ssList(esk4_1(X4))
& ssItem(esk5_1(X4))
& cons(esk5_1(X4),esk4_1(X4)) = X4 ) ),
inference(skolemize,[status(esa)],[120]) ).
fof(122,plain,
! [X4] :
( ( ssList(esk4_1(X4))
| nil = X4
| ~ ssList(X4) )
& ( ssItem(esk5_1(X4))
| nil = X4
| ~ ssList(X4) )
& ( cons(esk5_1(X4),esk4_1(X4)) = X4
| nil = X4
| ~ ssList(X4) ) ),
inference(distribute,[status(thm)],[121]) ).
cnf(123,plain,
( nil = X1
| cons(esk5_1(X1),esk4_1(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[122]) ).
cnf(124,plain,
( nil = X1
| ssItem(esk5_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[122]) ).
cnf(125,plain,
( nil = X1
| ssList(esk4_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[122]) ).
fof(129,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(130,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| ssItem(hd(X2)) ),
inference(variable_rename,[status(thm)],[129]) ).
cnf(131,plain,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[130]) ).
fof(142,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(143,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[142]) ).
fof(144,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[143]) ).
fof(145,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)],[144]) ).
cnf(146,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(147,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[145]) ).
fof(148,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(149,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[148]) ).
fof(150,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[149]) ).
cnf(151,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[150]) ).
cnf(152,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[27]) ).
fof(169,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ( ( neq(X2,nil)
& ! [X5] :
( ~ ssList(X5)
| ~ neq(X5,nil)
| ~ frontsegP(X2,X5)
| ~ frontsegP(X1,X5) )
& ! [X6] :
( ~ ssList(X6)
| X3 = X6
| ! [X7] :
( ~ ssItem(X7)
| cons(X7,nil) != X6
| hd(X4) != X7
| ~ neq(nil,X4) ) ) )
| ( neq(X2,nil)
& ~ neq(X4,nil) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(170,negated_conjecture,
? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& X9 = X11
& X8 = X10
& ( ( neq(X9,nil)
& ! [X12] :
( ~ ssList(X12)
| ~ neq(X12,nil)
| ~ frontsegP(X9,X12)
| ~ frontsegP(X8,X12) )
& ! [X13] :
( ~ ssList(X13)
| X10 = X13
| ! [X14] :
( ~ ssItem(X14)
| cons(X14,nil) != X13
| hd(X11) != X14
| ~ neq(nil,X11) ) ) )
| ( neq(X9,nil)
& ~ neq(X11,nil) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[169]) ).
fof(171,negated_conjecture,
( ssList(esk7_0)
& ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ( ( neq(esk8_0,nil)
& ! [X12] :
( ~ ssList(X12)
| ~ neq(X12,nil)
| ~ frontsegP(esk8_0,X12)
| ~ frontsegP(esk7_0,X12) )
& ! [X13] :
( ~ ssList(X13)
| esk9_0 = X13
| ! [X14] :
( ~ ssItem(X14)
| cons(X14,nil) != X13
| hd(esk10_0) != X14
| ~ neq(nil,esk10_0) ) ) )
| ( neq(esk8_0,nil)
& ~ neq(esk10_0,nil) ) ) ),
inference(skolemize,[status(esa)],[170]) ).
fof(172,negated_conjecture,
! [X12,X13,X14] :
( ( ( ( ~ ssItem(X14)
| cons(X14,nil) != X13
| hd(esk10_0) != X14
| ~ neq(nil,esk10_0)
| ~ ssList(X13)
| esk9_0 = X13 )
& ( ~ ssList(X12)
| ~ neq(X12,nil)
| ~ frontsegP(esk8_0,X12)
| ~ frontsegP(esk7_0,X12) )
& neq(esk8_0,nil) )
| ( neq(esk8_0,nil)
& ~ neq(esk10_0,nil) ) )
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(shift_quantors,[status(thm)],[171]) ).
fof(173,negated_conjecture,
! [X12,X13,X14] :
( ( neq(esk8_0,nil)
| ~ ssItem(X14)
| cons(X14,nil) != X13
| hd(esk10_0) != X14
| ~ neq(nil,esk10_0)
| ~ ssList(X13)
| esk9_0 = X13 )
& ( ~ neq(esk10_0,nil)
| ~ ssItem(X14)
| cons(X14,nil) != X13
| hd(esk10_0) != X14
| ~ neq(nil,esk10_0)
| ~ ssList(X13)
| esk9_0 = X13 )
& ( neq(esk8_0,nil)
| ~ ssList(X12)
| ~ neq(X12,nil)
| ~ frontsegP(esk8_0,X12)
| ~ frontsegP(esk7_0,X12) )
& ( ~ neq(esk10_0,nil)
| ~ ssList(X12)
| ~ neq(X12,nil)
| ~ frontsegP(esk8_0,X12)
| ~ frontsegP(esk7_0,X12) )
& ( neq(esk8_0,nil)
| neq(esk8_0,nil) )
& ( ~ neq(esk10_0,nil)
| neq(esk8_0,nil) )
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(distribute,[status(thm)],[172]) ).
cnf(174,negated_conjecture,
ssList(esk7_0),
inference(split_conjunct,[status(thm)],[173]) ).
cnf(175,negated_conjecture,
ssList(esk8_0),
inference(split_conjunct,[status(thm)],[173]) ).
cnf(178,negated_conjecture,
esk7_0 = esk9_0,
inference(split_conjunct,[status(thm)],[173]) ).
cnf(179,negated_conjecture,
esk8_0 = esk10_0,
inference(split_conjunct,[status(thm)],[173]) ).
cnf(181,negated_conjecture,
( neq(esk8_0,nil)
| neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[173]) ).
cnf(182,negated_conjecture,
( ~ frontsegP(esk7_0,X1)
| ~ frontsegP(esk8_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[173]) ).
cnf(184,negated_conjecture,
( esk9_0 = X1
| ~ ssList(X1)
| ~ neq(nil,esk10_0)
| hd(esk10_0) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[173]) ).
cnf(188,negated_conjecture,
ssList(esk10_0),
inference(rw,[status(thm)],[175,179,theory(equality)]) ).
cnf(189,negated_conjecture,
neq(esk10_0,nil),
inference(rw,[status(thm)],[181,179,theory(equality)]) ).
cnf(204,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[147,theory(equality)]) ).
cnf(214,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(er,[status(thm)],[45,theory(equality)]) ).
cnf(215,plain,
( app(X1,nil) = nil
| nil != X1
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[214,152,theory(equality)]) ).
cnf(216,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[215,theory(equality)]) ).
cnf(221,plain,
( ssList(esk3_2(X1,X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[117,73,theory(equality)]) ).
cnf(224,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ frontsegP(esk7_0,X1)
| ~ frontsegP(esk10_0,X1)
| ~ neq(esk10_0,nil) ),
inference(rw,[status(thm)],[182,179,theory(equality)]) ).
cnf(225,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ frontsegP(esk7_0,X1)
| ~ frontsegP(esk10_0,X1)
| $false ),
inference(rw,[status(thm)],[224,189,theory(equality)]) ).
cnf(226,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ frontsegP(esk7_0,X1)
| ~ frontsegP(esk10_0,X1) ),
inference(cn,[status(thm)],[225,theory(equality)]) ).
cnf(228,negated_conjecture,
( X1 = nil
| ~ frontsegP(esk7_0,X1)
| ~ frontsegP(esk10_0,X1)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[226,146,theory(equality)]) ).
cnf(230,negated_conjecture,
( X1 = nil
| ~ frontsegP(esk7_0,X1)
| ~ frontsegP(esk10_0,X1)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[228,152,theory(equality)]) ).
cnf(231,negated_conjecture,
( X1 = nil
| ~ frontsegP(esk7_0,X1)
| ~ frontsegP(esk10_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[230,theory(equality)]) ).
cnf(233,plain,
( hd(X1) = esk5_1(X1)
| nil = X1
| ~ ssItem(esk5_1(X1))
| ~ ssList(esk4_1(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[66,123,theory(equality)]) ).
cnf(244,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| nil = cons(X1,nil)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[37,55,theory(equality)]) ).
cnf(256,plain,
( nil = X1
| X2 != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[59,40,theory(equality)]) ).
cnf(262,plain,
( nil = X1
| X2 != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[256,152,theory(equality)]) ).
cnf(263,plain,
( nil = X1
| X2 != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[262,theory(equality)]) ).
cnf(271,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[70,73,theory(equality)]) ).
cnf(275,plain,
( app(X1,esk3_2(X1,X1)) = X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[116,73,theory(equality)]) ).
cnf(286,negated_conjecture,
( esk7_0 = X1
| hd(esk10_0) != X2
| cons(X2,nil) != X1
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ neq(nil,esk10_0)
| ~ neq(esk10_0,nil) ),
inference(rw,[status(thm)],[184,178,theory(equality)]) ).
cnf(287,negated_conjecture,
( esk7_0 = X1
| hd(esk10_0) != X2
| cons(X2,nil) != X1
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ neq(nil,esk10_0)
| $false ),
inference(rw,[status(thm)],[286,189,theory(equality)]) ).
cnf(288,negated_conjecture,
( esk7_0 = X1
| hd(esk10_0) != X2
| cons(X2,nil) != X1
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ neq(nil,esk10_0) ),
inference(cn,[status(thm)],[287,theory(equality)]) ).
cnf(289,negated_conjecture,
( esk7_0 = X1
| nil = esk10_0
| cons(X2,nil) != X1
| hd(esk10_0) != X2
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(esk10_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[288,146,theory(equality)]) ).
cnf(291,negated_conjecture,
( esk7_0 = X1
| nil = esk10_0
| cons(X2,nil) != X1
| hd(esk10_0) != X2
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(esk10_0)
| $false ),
inference(rw,[status(thm)],[289,152,theory(equality)]) ).
cnf(292,negated_conjecture,
( esk7_0 = X1
| nil = esk10_0
| cons(X2,nil) != X1
| hd(esk10_0) != X2
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(esk10_0) ),
inference(cn,[status(thm)],[291,theory(equality)]) ).
cnf(338,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[85,94,theory(equality)]) ).
cnf(374,negated_conjecture,
( esk7_0 = nil
| ~ frontsegP(esk10_0,esk7_0)
| ~ ssList(esk7_0) ),
inference(spm,[status(thm)],[231,73,theory(equality)]) ).
cnf(375,negated_conjecture,
( esk7_0 = nil
| ~ frontsegP(esk10_0,esk7_0)
| $false ),
inference(rw,[status(thm)],[374,174,theory(equality)]) ).
cnf(376,negated_conjecture,
( esk7_0 = nil
| ~ frontsegP(esk10_0,esk7_0) ),
inference(cn,[status(thm)],[375,theory(equality)]) ).
cnf(379,plain,
( app(nil,nil) = nil
| ~ ssList(nil) ),
inference(er,[status(thm)],[216,theory(equality)]) ).
cnf(380,plain,
( app(nil,nil) = nil
| $false ),
inference(rw,[status(thm)],[379,152,theory(equality)]) ).
cnf(381,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[380,theory(equality)]) ).
cnf(384,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[338,81]) ).
cnf(388,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)],[384,94,theory(equality)]) ).
cnf(541,plain,
( esk5_1(X1) = hd(X1)
| nil = X1
| ~ ssItem(esk5_1(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[233,125]) ).
cnf(542,plain,
( esk5_1(X1) = hd(X1)
| nil = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[541,124]) ).
cnf(544,plain,
( cons(hd(X1),esk4_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[123,542,theory(equality)]) ).
cnf(559,plain,
( frontsegP(cons(X1,X2),cons(X1,nil))
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[271,55,theory(equality)]) ).
cnf(573,plain,
( app(app(cons(X1,X2),X3),X4) != nil
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[388,81]) ).
cnf(578,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)],[573,51,theory(equality)]) ).
cnf(631,plain,
( app(cons(X1,X2),app(X3,X4)) != nil
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[578,151]) ).
cnf(632,plain,
( app(cons(X1,X2),nil) != nil
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[631,381,theory(equality)]) ).
cnf(641,plain,
( app(cons(X1,X2),nil) != nil
| ~ ssItem(X1)
| $false
| ~ ssList(X2) ),
inference(rw,[status(thm)],[632,152,theory(equality)]) ).
cnf(642,plain,
( app(cons(X1,X2),nil) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[641,theory(equality)]) ).
cnf(653,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[642,55,theory(equality)]) ).
cnf(655,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[653,152,theory(equality)]) ).
cnf(656,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[655,theory(equality)]) ).
cnf(737,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2) ),
inference(csr,[status(thm)],[244,656]) ).
cnf(738,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[737,151,theory(equality)]) ).
cnf(739,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[738,152,theory(equality)]) ).
cnf(740,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[739,theory(equality)]) ).
cnf(743,plain,
( nil = cons(X1,nil)
| ssItem(hd(cons(X1,X2)))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[131,740,theory(equality)]) ).
cnf(863,plain,
( nil = esk3_2(X1,X1)
| ~ ssList(esk3_2(X1,X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[263,275,theory(equality)]) ).
cnf(993,plain,
( esk3_2(X1,X1) = nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[863,221]) ).
cnf(1005,plain,
( ssItem(hd(cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2) ),
inference(csr,[status(thm)],[743,656]) ).
cnf(1006,plain,
( ssItem(hd(cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1005,151,theory(equality)]) ).
cnf(1007,plain,
( ssItem(hd(cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[1006,152,theory(equality)]) ).
cnf(1008,plain,
( ssItem(hd(cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[1007,theory(equality)]) ).
cnf(1108,plain,
( frontsegP(cons(X1,X2),cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[559,151,theory(equality)]) ).
cnf(1109,plain,
( frontsegP(cons(X1,X2),cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[1108,152,theory(equality)]) ).
cnf(1110,plain,
( frontsegP(cons(X1,X2),cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[1109,theory(equality)]) ).
cnf(1215,negated_conjecture,
( esk7_0 = X1
| esk10_0 = nil
| cons(X2,nil) != X1
| hd(esk10_0) != X2
| ~ ssItem(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[292,188,theory(equality)]) ).
cnf(1216,negated_conjecture,
( esk7_0 = X1
| esk10_0 = nil
| cons(X2,nil) != X1
| hd(esk10_0) != X2
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1215,theory(equality)]) ).
cnf(1217,negated_conjecture,
( esk10_0 = nil
| esk7_0 = X1
| cons(hd(esk10_0),nil) != X1
| ~ ssItem(hd(esk10_0))
| ~ ssList(X1) ),
inference(er,[status(thm)],[1216,theory(equality)]) ).
cnf(1250,negated_conjecture,
( esk10_0 = nil
| esk7_0 = X1
| cons(hd(esk10_0),nil) != X1
| ~ ssList(X1)
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[1217,131,theory(equality)]) ).
cnf(1251,negated_conjecture,
( esk10_0 = nil
| esk7_0 = X1
| cons(hd(esk10_0),nil) != X1
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[1250,188,theory(equality)]) ).
cnf(1252,negated_conjecture,
( esk10_0 = nil
| esk7_0 = X1
| cons(hd(esk10_0),nil) != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1251,theory(equality)]) ).
cnf(1253,negated_conjecture,
( esk10_0 = nil
| esk7_0 = cons(hd(esk10_0),nil)
| ~ ssList(cons(hd(esk10_0),nil)) ),
inference(er,[status(thm)],[1252,theory(equality)]) ).
cnf(1254,negated_conjecture,
( cons(hd(esk10_0),nil) = esk7_0
| esk10_0 = nil
| ~ ssItem(hd(esk10_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1253,151,theory(equality)]) ).
cnf(1255,negated_conjecture,
( cons(hd(esk10_0),nil) = esk7_0
| esk10_0 = nil
| ~ ssItem(hd(esk10_0))
| $false ),
inference(rw,[status(thm)],[1254,152,theory(equality)]) ).
cnf(1256,negated_conjecture,
( cons(hd(esk10_0),nil) = esk7_0
| esk10_0 = nil
| ~ ssItem(hd(esk10_0)) ),
inference(cn,[status(thm)],[1255,theory(equality)]) ).
cnf(1257,negated_conjecture,
( cons(hd(esk10_0),nil) = esk7_0
| esk10_0 = nil
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[1256,131,theory(equality)]) ).
cnf(1258,negated_conjecture,
( cons(hd(esk10_0),nil) = esk7_0
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[1257,188,theory(equality)]) ).
cnf(1259,negated_conjecture,
( cons(hd(esk10_0),nil) = esk7_0
| esk10_0 = nil ),
inference(cn,[status(thm)],[1258,theory(equality)]) ).
cnf(1281,negated_conjecture,
( hd(esk7_0) = hd(esk10_0)
| esk10_0 = nil
| ~ ssItem(hd(esk10_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[66,1259,theory(equality)]) ).
cnf(1299,negated_conjecture,
( esk10_0 = nil
| app(esk7_0,nil) != nil
| ~ ssItem(hd(esk10_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[642,1259,theory(equality)]) ).
cnf(1311,negated_conjecture,
( ssItem(hd(esk7_0))
| esk10_0 = nil
| ~ ssItem(hd(esk10_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1008,1259,theory(equality)]) ).
cnf(1314,negated_conjecture,
( frontsegP(esk7_0,cons(hd(esk10_0),nil))
| esk10_0 = nil
| ~ ssItem(hd(esk10_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1110,1259,theory(equality)]) ).
cnf(1315,negated_conjecture,
( frontsegP(cons(hd(esk10_0),X1),esk7_0)
| esk10_0 = nil
| ~ ssItem(hd(esk10_0))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1110,1259,theory(equality)]) ).
cnf(1324,negated_conjecture,
( hd(esk7_0) = hd(esk10_0)
| esk10_0 = nil
| ~ ssItem(hd(esk10_0))
| $false ),
inference(rw,[status(thm)],[1281,152,theory(equality)]) ).
cnf(1325,negated_conjecture,
( hd(esk7_0) = hd(esk10_0)
| esk10_0 = nil
| ~ ssItem(hd(esk10_0)) ),
inference(cn,[status(thm)],[1324,theory(equality)]) ).
cnf(1360,negated_conjecture,
( esk10_0 = nil
| app(esk7_0,nil) != nil
| ~ ssItem(hd(esk10_0))
| $false ),
inference(rw,[status(thm)],[1299,152,theory(equality)]) ).
cnf(1361,negated_conjecture,
( esk10_0 = nil
| app(esk7_0,nil) != nil
| ~ ssItem(hd(esk10_0)) ),
inference(cn,[status(thm)],[1360,theory(equality)]) ).
cnf(1374,negated_conjecture,
( ssItem(hd(esk7_0))
| esk10_0 = nil
| ~ ssItem(hd(esk10_0))
| $false ),
inference(rw,[status(thm)],[1311,152,theory(equality)]) ).
cnf(1375,negated_conjecture,
( ssItem(hd(esk7_0))
| esk10_0 = nil
| ~ ssItem(hd(esk10_0)) ),
inference(cn,[status(thm)],[1374,theory(equality)]) ).
cnf(1380,negated_conjecture,
( frontsegP(esk7_0,cons(hd(esk10_0),nil))
| esk10_0 = nil
| ~ ssItem(hd(esk10_0))
| $false ),
inference(rw,[status(thm)],[1314,152,theory(equality)]) ).
cnf(1381,negated_conjecture,
( frontsegP(esk7_0,cons(hd(esk10_0),nil))
| esk10_0 = nil
| ~ ssItem(hd(esk10_0)) ),
inference(cn,[status(thm)],[1380,theory(equality)]) ).
cnf(1398,negated_conjecture,
( esk10_0 = nil
| ssItem(hd(esk7_0))
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[1375,131,theory(equality)]) ).
cnf(1399,negated_conjecture,
( esk10_0 = nil
| ssItem(hd(esk7_0))
| $false ),
inference(rw,[status(thm)],[1398,188,theory(equality)]) ).
cnf(1400,negated_conjecture,
( esk10_0 = nil
| ssItem(hd(esk7_0)) ),
inference(cn,[status(thm)],[1399,theory(equality)]) ).
cnf(1450,negated_conjecture,
( hd(esk7_0) = hd(esk10_0)
| esk10_0 = nil
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[1325,131,theory(equality)]) ).
cnf(1451,negated_conjecture,
( hd(esk7_0) = hd(esk10_0)
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[1450,188,theory(equality)]) ).
cnf(1452,negated_conjecture,
( hd(esk7_0) = hd(esk10_0)
| esk10_0 = nil ),
inference(cn,[status(thm)],[1451,theory(equality)]) ).
cnf(1455,negated_conjecture,
( esk10_0 = nil
| ssItem(hd(esk10_0)) ),
inference(spm,[status(thm)],[1400,1452,theory(equality)]) ).
cnf(1475,negated_conjecture,
( esk10_0 = nil
| frontsegP(esk7_0,cons(hd(esk10_0),nil)) ),
inference(csr,[status(thm)],[1381,1455]) ).
cnf(1483,negated_conjecture,
( esk10_0 = nil
| frontsegP(esk7_0,esk7_0) ),
inference(spm,[status(thm)],[1475,1259,theory(equality)]) ).
cnf(1500,negated_conjecture,
( app(esk7_0,esk3_2(esk7_0,esk7_0)) = esk7_0
| esk10_0 = nil
| ~ ssList(esk7_0) ),
inference(spm,[status(thm)],[116,1483,theory(equality)]) ).
cnf(1508,negated_conjecture,
( app(esk7_0,esk3_2(esk7_0,esk7_0)) = esk7_0
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[1500,174,theory(equality)]) ).
cnf(1509,negated_conjecture,
( app(esk7_0,esk3_2(esk7_0,esk7_0)) = esk7_0
| esk10_0 = nil ),
inference(cn,[status(thm)],[1508,theory(equality)]) ).
cnf(1585,negated_conjecture,
( app(esk7_0,nil) = esk7_0
| esk10_0 = nil
| ~ ssList(esk7_0) ),
inference(spm,[status(thm)],[1509,993,theory(equality)]) ).
cnf(1620,negated_conjecture,
( app(esk7_0,nil) = esk7_0
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[1585,174,theory(equality)]) ).
cnf(1621,negated_conjecture,
( app(esk7_0,nil) = esk7_0
| esk10_0 = nil ),
inference(cn,[status(thm)],[1620,theory(equality)]) ).
cnf(1643,negated_conjecture,
( esk10_0 = nil
| esk7_0 != nil
| ~ ssItem(hd(esk10_0)) ),
inference(spm,[status(thm)],[1361,1621,theory(equality)]) ).
cnf(1698,negated_conjecture,
( esk10_0 = nil
| esk7_0 != nil ),
inference(csr,[status(thm)],[1643,1455]) ).
cnf(2458,negated_conjecture,
( esk10_0 = nil
| frontsegP(cons(hd(esk10_0),X1),esk7_0)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[1315,1455]) ).
cnf(2465,negated_conjecture,
( esk10_0 = nil
| frontsegP(esk10_0,esk7_0)
| ~ ssList(esk4_1(esk10_0))
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[2458,544,theory(equality)]) ).
cnf(2478,negated_conjecture,
( esk10_0 = nil
| frontsegP(esk10_0,esk7_0)
| ~ ssList(esk4_1(esk10_0))
| $false ),
inference(rw,[status(thm)],[2465,188,theory(equality)]) ).
cnf(2479,negated_conjecture,
( esk10_0 = nil
| frontsegP(esk10_0,esk7_0)
| ~ ssList(esk4_1(esk10_0)) ),
inference(cn,[status(thm)],[2478,theory(equality)]) ).
cnf(2484,negated_conjecture,
( esk10_0 = nil
| frontsegP(esk10_0,esk7_0)
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[2479,125,theory(equality)]) ).
cnf(2485,negated_conjecture,
( esk10_0 = nil
| frontsegP(esk10_0,esk7_0)
| $false ),
inference(rw,[status(thm)],[2484,188,theory(equality)]) ).
cnf(2486,negated_conjecture,
( esk10_0 = nil
| frontsegP(esk10_0,esk7_0) ),
inference(cn,[status(thm)],[2485,theory(equality)]) ).
cnf(2492,negated_conjecture,
( esk7_0 = nil
| esk10_0 = nil ),
inference(spm,[status(thm)],[376,2486,theory(equality)]) ).
cnf(2594,negated_conjecture,
esk10_0 = nil,
inference(csr,[status(thm)],[2492,1698]) ).
cnf(2597,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[189,2594,theory(equality)]) ).
cnf(2649,negated_conjecture,
~ ssList(nil),
inference(spm,[status(thm)],[204,2597,theory(equality)]) ).
cnf(2651,negated_conjecture,
$false,
inference(rw,[status(thm)],[2649,152,theory(equality)]) ).
cnf(2652,negated_conjecture,
$false,
inference(cn,[status(thm)],[2651,theory(equality)]) ).
cnf(2653,negated_conjecture,
$false,
2652,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC022+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmp4TldNs/sel_SWC022+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC022+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC022+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC022+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
%
%------------------------------------------------------------------------------