TSTP Solution File: SWC079+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC079+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 10:12:51 EST 2010
% Result : Theorem 1.98s
% Output : CNFRefutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 69
% Number of leaves : 20
% Syntax : Number of formulae : 255 ( 14 unt; 0 def)
% Number of atoms : 1068 ( 387 equ)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 1368 ( 555 ~; 663 |; 97 &)
% ( 2 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 351 ( 0 sgn 167 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/tmp/tmpSradAx/sel_SWC079+1.p_1',ax85) ).
fof(2,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmpSradAx/sel_SWC079+1.p_1',ax84) ).
fof(3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmpSradAx/sel_SWC079+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/tmpSradAx/sel_SWC079+1.p_1',ax82) ).
fof(5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpSradAx/sel_SWC079+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/tmpSradAx/sel_SWC079+1.p_1',ax80) ).
fof(7,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpSradAx/sel_SWC079+1.p_1',ax28) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/tmp/tmpSradAx/sel_SWC079+1.p_1',ax27) ).
fof(9,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpSradAx/sel_SWC079+1.p_1',ax26) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmpSradAx/sel_SWC079+1.p_1',ax21) ).
fof(11,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/tmp/tmpSradAx/sel_SWC079+1.p_1',ax20) ).
fof(12,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/tmp/tmpSradAx/sel_SWC079+1.p_1',ax23) ).
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/tmp/tmpSradAx/sel_SWC079+1.p_1',ax22) ).
fof(22,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpSradAx/sel_SWC079+1.p_1',ax15) ).
fof(23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpSradAx/sel_SWC079+1.p_1',ax16) ).
fof(24,axiom,
ssList(nil),
file('/tmp/tmpSradAx/sel_SWC079+1.p_1',ax17) ).
fof(27,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/tmp/tmpSradAx/sel_SWC079+1.p_1',ax55) ).
fof(28,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/tmpSradAx/sel_SWC079+1.p_1',ax56) ).
fof(29,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/tmp/tmpSradAx/sel_SWC079+1.p_1',ax57) ).
fof(30,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)
& segmentP(X2,X5)
& segmentP(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/tmpSradAx/sel_SWC079+1.p_1',co1) ).
fof(31,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)
& segmentP(X2,X5)
& segmentP(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)],[30]) ).
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)
& segmentP(X2,X5)
& segmentP(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)],[31,theory(equality)]) ).
fof(33,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| nil = X1
| hd(app(X1,X2)) = hd(X1) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(34,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| nil = X3
| hd(app(X3,X4)) = hd(X3) ) ),
inference(variable_rename,[status(thm)],[33]) ).
fof(35,plain,
! [X3,X4] :
( ~ ssList(X4)
| nil = X3
| hd(app(X3,X4)) = hd(X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[34]) ).
cnf(36,plain,
( hd(app(X1,X2)) = hd(X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(38,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[37]) ).
cnf(39,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[38]) ).
fof(40,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(41,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)],[40]) ).
fof(42,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)],[41]) ).
fof(43,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)],[42]) ).
cnf(44,plain,
( nil = app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| nil != X1
| nil != X2 ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(47,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(48,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)],[47]) ).
fof(49,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)],[48]) ).
cnf(50,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[49]) ).
fof(51,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(52,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[51]) ).
fof(53,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[52]) ).
cnf(54,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[53]) ).
fof(55,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(56,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(X5,X6) != app(X5,X4)
| X6 = X4 ) ) ),
inference(variable_rename,[status(thm)],[55]) ).
fof(57,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| app(X5,X6) != app(X5,X4)
| X6 = X4
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[56]) ).
cnf(58,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X3) != app(X2,X1)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[57]) ).
fof(59,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(60,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[59]) ).
cnf(61,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[60]) ).
fof(62,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)],[8]) ).
fof(63,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)],[62]) ).
fof(64,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)],[63]) ).
cnf(65,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[64]) ).
fof(66,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(67,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[66]) ).
fof(68,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[67]) ).
cnf(69,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[68]) ).
fof(70,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| nil != cons(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(71,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3) ) ),
inference(variable_rename,[status(thm)],[70]) ).
fof(72,plain,
! [X3,X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[71]) ).
cnf(73,plain,
( ~ ssList(X1)
| nil != cons(X2,X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[72]) ).
fof(74,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(75,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssItem(X6)
& cons(X6,X5) = X4 ) ) ),
inference(variable_rename,[status(thm)],[74]) ).
fof(76,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)],[75]) ).
fof(77,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)],[76]) ).
cnf(78,plain,
( nil = X1
| cons(esk2_1(X1),esk1_1(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(79,plain,
( nil = X1
| ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(80,plain,
( nil = X1
| ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[77]) ).
fof(81,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| hd(cons(X2,X1)) = X2 ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(82,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| hd(cons(X4,X3)) = X4 ) ),
inference(variable_rename,[status(thm)],[81]) ).
fof(83,plain,
! [X3,X4] :
( ~ ssItem(X4)
| hd(cons(X4,X3)) = X4
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[82]) ).
cnf(84,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[83]) ).
fof(85,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(86,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| ssItem(hd(X2)) ),
inference(variable_rename,[status(thm)],[85]) ).
cnf(87,plain,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[86]) ).
fof(133,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(134,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[133]) ).
fof(135,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[134]) ).
fof(136,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)],[135]) ).
cnf(137,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[136]) ).
fof(139,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(140,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[139]) ).
fof(141,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[140]) ).
cnf(142,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[141]) ).
cnf(143,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[24]) ).
fof(152,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(153,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,X2) ),
inference(variable_rename,[status(thm)],[152]) ).
cnf(154,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[153]) ).
fof(155,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)],[28]) ).
fof(156,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)],[155]) ).
fof(157,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)],[156]) ).
cnf(158,plain,
( segmentP(app(app(X3,X1),X4),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[157]) ).
fof(159,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(fof_nnf,[status(thm)],[29]) ).
fof(160,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,nil) ),
inference(variable_rename,[status(thm)],[159]) ).
cnf(161,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[160]) ).
fof(162,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)
| ~ segmentP(X2,X5)
| ~ segmentP(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)],[32]) ).
fof(163,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)
| ~ segmentP(X9,X12)
| ~ segmentP(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)],[162]) ).
fof(164,negated_conjecture,
( ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& ssList(esk11_0)
& esk9_0 = esk11_0
& esk8_0 = esk10_0
& ( ( neq(esk9_0,nil)
& ! [X12] :
( ~ ssList(X12)
| ~ neq(X12,nil)
| ~ segmentP(esk9_0,X12)
| ~ segmentP(esk8_0,X12) )
& ! [X13] :
( ~ ssList(X13)
| esk10_0 = X13
| ! [X14] :
( ~ ssItem(X14)
| cons(X14,nil) != X13
| hd(esk11_0) != X14
| ~ neq(nil,esk11_0) ) ) )
| ( neq(esk9_0,nil)
& ~ neq(esk11_0,nil) ) ) ),
inference(skolemize,[status(esa)],[163]) ).
fof(165,negated_conjecture,
! [X12,X13,X14] :
( ( ( ( ~ ssItem(X14)
| cons(X14,nil) != X13
| hd(esk11_0) != X14
| ~ neq(nil,esk11_0)
| ~ ssList(X13)
| esk10_0 = X13 )
& ( ~ ssList(X12)
| ~ neq(X12,nil)
| ~ segmentP(esk9_0,X12)
| ~ segmentP(esk8_0,X12) )
& neq(esk9_0,nil) )
| ( neq(esk9_0,nil)
& ~ neq(esk11_0,nil) ) )
& esk9_0 = esk11_0
& esk8_0 = esk10_0
& ssList(esk11_0)
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0) ),
inference(shift_quantors,[status(thm)],[164]) ).
fof(166,negated_conjecture,
! [X12,X13,X14] :
( ( neq(esk9_0,nil)
| ~ ssItem(X14)
| cons(X14,nil) != X13
| hd(esk11_0) != X14
| ~ neq(nil,esk11_0)
| ~ ssList(X13)
| esk10_0 = X13 )
& ( ~ neq(esk11_0,nil)
| ~ ssItem(X14)
| cons(X14,nil) != X13
| hd(esk11_0) != X14
| ~ neq(nil,esk11_0)
| ~ ssList(X13)
| esk10_0 = X13 )
& ( neq(esk9_0,nil)
| ~ ssList(X12)
| ~ neq(X12,nil)
| ~ segmentP(esk9_0,X12)
| ~ segmentP(esk8_0,X12) )
& ( ~ neq(esk11_0,nil)
| ~ ssList(X12)
| ~ neq(X12,nil)
| ~ segmentP(esk9_0,X12)
| ~ segmentP(esk8_0,X12) )
& ( neq(esk9_0,nil)
| neq(esk9_0,nil) )
& ( ~ neq(esk11_0,nil)
| neq(esk9_0,nil) )
& esk9_0 = esk11_0
& esk8_0 = esk10_0
& ssList(esk11_0)
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0) ),
inference(distribute,[status(thm)],[165]) ).
cnf(167,negated_conjecture,
ssList(esk8_0),
inference(split_conjunct,[status(thm)],[166]) ).
cnf(168,negated_conjecture,
ssList(esk9_0),
inference(split_conjunct,[status(thm)],[166]) ).
cnf(171,negated_conjecture,
esk8_0 = esk10_0,
inference(split_conjunct,[status(thm)],[166]) ).
cnf(172,negated_conjecture,
esk9_0 = esk11_0,
inference(split_conjunct,[status(thm)],[166]) ).
cnf(174,negated_conjecture,
( neq(esk9_0,nil)
| neq(esk9_0,nil) ),
inference(split_conjunct,[status(thm)],[166]) ).
cnf(175,negated_conjecture,
( ~ segmentP(esk8_0,X1)
| ~ segmentP(esk9_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1)
| ~ neq(esk11_0,nil) ),
inference(split_conjunct,[status(thm)],[166]) ).
cnf(177,negated_conjecture,
( esk10_0 = X1
| ~ ssList(X1)
| ~ neq(nil,esk11_0)
| hd(esk11_0) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| ~ neq(esk11_0,nil) ),
inference(split_conjunct,[status(thm)],[166]) ).
cnf(181,negated_conjecture,
ssList(esk11_0),
inference(rw,[status(thm)],[168,172,theory(equality)]) ).
cnf(182,negated_conjecture,
neq(esk11_0,nil),
inference(rw,[status(thm)],[174,172,theory(equality)]) ).
cnf(207,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(er,[status(thm)],[44,theory(equality)]) ).
cnf(208,plain,
( app(X1,nil) = nil
| nil != X1
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[207,143,theory(equality)]) ).
cnf(209,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[208,theory(equality)]) ).
cnf(221,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk8_0,X1)
| ~ segmentP(esk11_0,X1)
| ~ neq(esk11_0,nil) ),
inference(rw,[status(thm)],[175,172,theory(equality)]) ).
cnf(222,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk8_0,X1)
| ~ segmentP(esk11_0,X1)
| $false ),
inference(rw,[status(thm)],[221,182,theory(equality)]) ).
cnf(223,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk8_0,X1)
| ~ segmentP(esk11_0,X1) ),
inference(cn,[status(thm)],[222,theory(equality)]) ).
cnf(224,negated_conjecture,
( ~ segmentP(esk11_0,nil)
| ~ neq(nil,nil)
| ~ ssList(nil)
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[223,161,theory(equality)]) ).
cnf(225,negated_conjecture,
( ~ segmentP(esk11_0,esk8_0)
| ~ neq(esk8_0,nil)
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[223,154,theory(equality)]) ).
cnf(226,negated_conjecture,
( ~ segmentP(esk11_0,nil)
| ~ neq(nil,nil)
| $false
| ~ ssList(esk8_0) ),
inference(rw,[status(thm)],[224,143,theory(equality)]) ).
cnf(227,negated_conjecture,
( ~ segmentP(esk11_0,nil)
| ~ neq(nil,nil)
| $false
| $false ),
inference(rw,[status(thm)],[226,167,theory(equality)]) ).
cnf(228,negated_conjecture,
( ~ segmentP(esk11_0,nil)
| ~ neq(nil,nil) ),
inference(cn,[status(thm)],[227,theory(equality)]) ).
cnf(229,negated_conjecture,
( ~ segmentP(esk11_0,esk8_0)
| ~ neq(esk8_0,nil)
| $false ),
inference(rw,[status(thm)],[225,167,theory(equality)]) ).
cnf(230,negated_conjecture,
( ~ segmentP(esk11_0,esk8_0)
| ~ neq(esk8_0,nil) ),
inference(cn,[status(thm)],[229,theory(equality)]) ).
cnf(239,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)],[36,54,theory(equality)]) ).
cnf(241,plain,
( hd(X1) = esk2_1(X1)
| nil = X1
| ~ ssItem(esk2_1(X1))
| ~ ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[84,78,theory(equality)]) ).
cnf(245,plain,
( nil = X1
| X2 != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[58,39,theory(equality)]) ).
cnf(251,plain,
( nil = X1
| X2 != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[245,143,theory(equality)]) ).
cnf(252,plain,
( nil = X1
| X2 != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[251,theory(equality)]) ).
cnf(293,negated_conjecture,
( esk8_0 = X1
| hd(esk11_0) != X2
| cons(X2,nil) != X1
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ neq(nil,esk11_0)
| ~ neq(esk11_0,nil) ),
inference(rw,[status(thm)],[177,171,theory(equality)]) ).
cnf(294,negated_conjecture,
( esk8_0 = X1
| hd(esk11_0) != X2
| cons(X2,nil) != X1
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ neq(nil,esk11_0)
| $false ),
inference(rw,[status(thm)],[293,182,theory(equality)]) ).
cnf(295,negated_conjecture,
( esk8_0 = X1
| hd(esk11_0) != X2
| cons(X2,nil) != X1
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ neq(nil,esk11_0) ),
inference(cn,[status(thm)],[294,theory(equality)]) ).
cnf(296,negated_conjecture,
( esk8_0 = X1
| nil = esk11_0
| cons(X2,nil) != X1
| hd(esk11_0) != X2
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(esk11_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[295,137,theory(equality)]) ).
cnf(298,negated_conjecture,
( esk8_0 = X1
| nil = esk11_0
| cons(X2,nil) != X1
| hd(esk11_0) != X2
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(esk11_0)
| $false ),
inference(rw,[status(thm)],[296,143,theory(equality)]) ).
cnf(299,negated_conjecture,
( esk8_0 = X1
| nil = esk11_0
| cons(X2,nil) != X1
| hd(esk11_0) != X2
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(esk11_0) ),
inference(cn,[status(thm)],[298,theory(equality)]) ).
cnf(301,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[142,65,theory(equality)]) ).
cnf(304,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[73,65,theory(equality)]) ).
cnf(317,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[50,61,theory(equality)]) ).
cnf(336,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[317,143,theory(equality)]) ).
cnf(337,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[336,theory(equality)]) ).
cnf(339,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[158,154,theory(equality)]) ).
cnf(350,negated_conjecture,
( ~ neq(nil,nil)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[228,161,theory(equality)]) ).
cnf(367,negated_conjecture,
( ~ neq(nil,nil)
| $false ),
inference(rw,[status(thm)],[350,181,theory(equality)]) ).
cnf(368,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[367,theory(equality)]) ).
cnf(375,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[304,69]) ).
cnf(379,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)],[375,65,theory(equality)]) ).
cnf(384,plain,
( app(nil,nil) = nil
| ~ ssList(nil) ),
inference(er,[status(thm)],[209,theory(equality)]) ).
cnf(385,plain,
( app(nil,nil) = nil
| $false ),
inference(rw,[status(thm)],[384,143,theory(equality)]) ).
cnf(386,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[385,theory(equality)]) ).
cnf(405,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[65,386,theory(equality)]) ).
cnf(420,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[405,143,theory(equality)]) ).
cnf(421,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[420,theory(equality)]) ).
cnf(488,plain,
( app(app(cons(X1,X2),X3),X4) != nil
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[379,69]) ).
cnf(494,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)],[488,50,theory(equality)]) ).
cnf(562,plain,
( app(cons(X1,X2),app(X3,X4)) != nil
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[494,142]) ).
cnf(563,plain,
( app(cons(X1,X2),nil) != nil
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[562,386,theory(equality)]) ).
cnf(571,plain,
( app(cons(X1,X2),nil) != nil
| ~ ssItem(X1)
| $false
| ~ ssList(X2) ),
inference(rw,[status(thm)],[563,143,theory(equality)]) ).
cnf(572,plain,
( app(cons(X1,X2),nil) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[571,theory(equality)]) ).
cnf(580,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[572,54,theory(equality)]) ).
cnf(583,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[580,143,theory(equality)]) ).
cnf(584,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[583,theory(equality)]) ).
cnf(662,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2) ),
inference(csr,[status(thm)],[239,584]) ).
cnf(663,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[662,142,theory(equality)]) ).
cnf(664,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[663,143,theory(equality)]) ).
cnf(665,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[664,theory(equality)]) ).
cnf(674,plain,
( nil = cons(X1,nil)
| ssItem(hd(cons(X1,X2)))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[87,665,theory(equality)]) ).
cnf(700,plain,
( esk2_1(X1) = hd(X1)
| nil = X1
| ~ ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[241,80]) ).
cnf(701,plain,
( esk2_1(X1) = hd(X1)
| nil = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[700,79]) ).
cnf(703,plain,
( cons(hd(X1),esk1_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[78,701,theory(equality)]) ).
cnf(766,plain,
( nil = X1
| cons(X2,X1) != cons(X2,nil)
| ~ ssList(X1)
| ~ ssList(cons(X2,nil))
| ~ ssItem(X2) ),
inference(spm,[status(thm)],[252,54,theory(equality)]) ).
cnf(1016,plain,
( ssItem(hd(cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2) ),
inference(csr,[status(thm)],[674,584]) ).
cnf(1017,plain,
( ssItem(hd(cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1016,142,theory(equality)]) ).
cnf(1018,plain,
( ssItem(hd(cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[1017,143,theory(equality)]) ).
cnf(1019,plain,
( ssItem(hd(cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[1018,theory(equality)]) ).
cnf(1578,negated_conjecture,
( esk8_0 = X1
| esk11_0 = nil
| cons(X2,nil) != X1
| hd(esk11_0) != X2
| ~ ssItem(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[299,181,theory(equality)]) ).
cnf(1579,negated_conjecture,
( esk8_0 = X1
| esk11_0 = nil
| cons(X2,nil) != X1
| hd(esk11_0) != X2
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1578,theory(equality)]) ).
cnf(1580,negated_conjecture,
( esk11_0 = nil
| esk8_0 = X1
| cons(hd(esk11_0),nil) != X1
| ~ ssItem(hd(esk11_0))
| ~ ssList(X1) ),
inference(er,[status(thm)],[1579,theory(equality)]) ).
cnf(1591,negated_conjecture,
( esk11_0 = nil
| esk8_0 = X1
| cons(hd(esk11_0),nil) != X1
| ~ ssList(X1)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[1580,87,theory(equality)]) ).
cnf(1592,negated_conjecture,
( esk11_0 = nil
| esk8_0 = X1
| cons(hd(esk11_0),nil) != X1
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[1591,181,theory(equality)]) ).
cnf(1593,negated_conjecture,
( esk11_0 = nil
| esk8_0 = X1
| cons(hd(esk11_0),nil) != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1592,theory(equality)]) ).
cnf(1594,negated_conjecture,
( esk11_0 = nil
| esk8_0 = cons(hd(esk11_0),nil)
| ~ ssList(cons(hd(esk11_0),nil)) ),
inference(er,[status(thm)],[1593,theory(equality)]) ).
cnf(1709,negated_conjecture,
( cons(hd(esk11_0),nil) = esk8_0
| esk11_0 = nil
| ~ ssItem(hd(esk11_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1594,142,theory(equality)]) ).
cnf(1710,negated_conjecture,
( cons(hd(esk11_0),nil) = esk8_0
| esk11_0 = nil
| ~ ssItem(hd(esk11_0))
| $false ),
inference(rw,[status(thm)],[1709,143,theory(equality)]) ).
cnf(1711,negated_conjecture,
( cons(hd(esk11_0),nil) = esk8_0
| esk11_0 = nil
| ~ ssItem(hd(esk11_0)) ),
inference(cn,[status(thm)],[1710,theory(equality)]) ).
cnf(1712,negated_conjecture,
( cons(hd(esk11_0),nil) = esk8_0
| esk11_0 = nil
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[1711,87,theory(equality)]) ).
cnf(1713,negated_conjecture,
( cons(hd(esk11_0),nil) = esk8_0
| esk11_0 = nil
| $false ),
inference(rw,[status(thm)],[1712,181,theory(equality)]) ).
cnf(1714,negated_conjecture,
( cons(hd(esk11_0),nil) = esk8_0
| esk11_0 = nil ),
inference(cn,[status(thm)],[1713,theory(equality)]) ).
cnf(1716,negated_conjecture,
( hd(esk8_0) = hd(esk11_0)
| esk11_0 = nil
| ~ ssItem(hd(esk11_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[84,1714,theory(equality)]) ).
cnf(1730,negated_conjecture,
( esk11_0 = nil
| app(esk8_0,nil) != nil
| ~ ssItem(hd(esk11_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[572,1714,theory(equality)]) ).
cnf(1733,negated_conjecture,
( app(esk8_0,nil) = esk8_0
| esk11_0 = nil
| ~ ssItem(hd(esk11_0)) ),
inference(spm,[status(thm)],[421,1714,theory(equality)]) ).
cnf(1740,negated_conjecture,
( ssItem(hd(esk8_0))
| esk11_0 = nil
| ~ ssItem(hd(esk11_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1019,1714,theory(equality)]) ).
cnf(1755,negated_conjecture,
( hd(esk8_0) = hd(esk11_0)
| esk11_0 = nil
| ~ ssItem(hd(esk11_0))
| $false ),
inference(rw,[status(thm)],[1716,143,theory(equality)]) ).
cnf(1756,negated_conjecture,
( hd(esk8_0) = hd(esk11_0)
| esk11_0 = nil
| ~ ssItem(hd(esk11_0)) ),
inference(cn,[status(thm)],[1755,theory(equality)]) ).
cnf(1783,negated_conjecture,
( esk11_0 = nil
| app(esk8_0,nil) != nil
| ~ ssItem(hd(esk11_0))
| $false ),
inference(rw,[status(thm)],[1730,143,theory(equality)]) ).
cnf(1784,negated_conjecture,
( esk11_0 = nil
| app(esk8_0,nil) != nil
| ~ ssItem(hd(esk11_0)) ),
inference(cn,[status(thm)],[1783,theory(equality)]) ).
cnf(1793,negated_conjecture,
( ssItem(hd(esk8_0))
| esk11_0 = nil
| ~ ssItem(hd(esk11_0))
| $false ),
inference(rw,[status(thm)],[1740,143,theory(equality)]) ).
cnf(1794,negated_conjecture,
( ssItem(hd(esk8_0))
| esk11_0 = nil
| ~ ssItem(hd(esk11_0)) ),
inference(cn,[status(thm)],[1793,theory(equality)]) ).
cnf(1813,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[301,69]) ).
cnf(1818,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1813,421,theory(equality)]) ).
cnf(1828,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[1818,143,theory(equality)]) ).
cnf(1829,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[1828,theory(equality)]) ).
cnf(1892,negated_conjecture,
( esk11_0 = nil
| ssItem(hd(esk8_0))
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[1794,87,theory(equality)]) ).
cnf(1893,negated_conjecture,
( esk11_0 = nil
| ssItem(hd(esk8_0))
| $false ),
inference(rw,[status(thm)],[1892,181,theory(equality)]) ).
cnf(1894,negated_conjecture,
( esk11_0 = nil
| ssItem(hd(esk8_0)) ),
inference(cn,[status(thm)],[1893,theory(equality)]) ).
cnf(1974,negated_conjecture,
( hd(esk8_0) = hd(esk11_0)
| esk11_0 = nil
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[1756,87,theory(equality)]) ).
cnf(1975,negated_conjecture,
( hd(esk8_0) = hd(esk11_0)
| esk11_0 = nil
| $false ),
inference(rw,[status(thm)],[1974,181,theory(equality)]) ).
cnf(1976,negated_conjecture,
( hd(esk8_0) = hd(esk11_0)
| esk11_0 = nil ),
inference(cn,[status(thm)],[1975,theory(equality)]) ).
cnf(1978,negated_conjecture,
( cons(hd(esk11_0),esk1_1(esk8_0)) = esk8_0
| nil = esk8_0
| esk11_0 = nil
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[703,1976,theory(equality)]) ).
cnf(1979,negated_conjecture,
( esk11_0 = nil
| ssItem(hd(esk11_0)) ),
inference(spm,[status(thm)],[1894,1976,theory(equality)]) ).
cnf(1982,negated_conjecture,
( cons(hd(esk11_0),esk1_1(esk8_0)) = esk8_0
| nil = esk8_0
| esk11_0 = nil
| $false ),
inference(rw,[status(thm)],[1978,167,theory(equality)]) ).
cnf(1983,negated_conjecture,
( cons(hd(esk11_0),esk1_1(esk8_0)) = esk8_0
| nil = esk8_0
| esk11_0 = nil ),
inference(cn,[status(thm)],[1982,theory(equality)]) ).
cnf(2019,negated_conjecture,
( app(esk8_0,nil) = esk8_0
| esk11_0 = nil ),
inference(csr,[status(thm)],[1733,1979]) ).
cnf(2041,negated_conjecture,
( app(nil,esk8_0) = esk8_0
| esk11_0 = nil
| ~ ssList(nil)
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[337,2019,theory(equality)]) ).
cnf(2042,negated_conjecture,
( esk11_0 = nil
| esk8_0 != nil
| ~ ssItem(hd(esk11_0)) ),
inference(spm,[status(thm)],[1784,2019,theory(equality)]) ).
cnf(2103,negated_conjecture,
( app(nil,esk8_0) = esk8_0
| esk11_0 = nil
| $false
| ~ ssList(esk8_0) ),
inference(rw,[status(thm)],[2041,143,theory(equality)]) ).
cnf(2104,negated_conjecture,
( app(nil,esk8_0) = esk8_0
| esk11_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[2103,167,theory(equality)]) ).
cnf(2105,negated_conjecture,
( app(nil,esk8_0) = esk8_0
| esk11_0 = nil ),
inference(cn,[status(thm)],[2104,theory(equality)]) ).
cnf(2108,negated_conjecture,
( esk11_0 = nil
| esk8_0 != nil ),
inference(csr,[status(thm)],[2042,1979]) ).
cnf(2868,negated_conjecture,
( cons(hd(esk11_0),esk1_1(esk8_0)) = esk8_0
| esk11_0 = nil ),
inference(csr,[status(thm)],[1983,2108]) ).
cnf(4136,negated_conjecture,
( segmentP(app(esk8_0,X1),esk8_0)
| esk11_0 = nil
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[339,2105,theory(equality)]) ).
cnf(4164,negated_conjecture,
( segmentP(app(esk8_0,X1),esk8_0)
| esk11_0 = nil
| ~ ssList(X1)
| $false
| ~ ssList(esk8_0) ),
inference(rw,[status(thm)],[4136,143,theory(equality)]) ).
cnf(4165,negated_conjecture,
( segmentP(app(esk8_0,X1),esk8_0)
| esk11_0 = nil
| ~ ssList(X1)
| $false
| $false ),
inference(rw,[status(thm)],[4164,167,theory(equality)]) ).
cnf(4166,negated_conjecture,
( segmentP(app(esk8_0,X1),esk8_0)
| esk11_0 = nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[4165,theory(equality)]) ).
cnf(7326,plain,
( nil = X1
| cons(X2,X1) != cons(X2,nil)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[766,1829]) ).
cnf(7331,negated_conjecture,
( nil = X1
| esk11_0 = nil
| cons(hd(esk11_0),X1) != esk8_0
| ~ ssItem(hd(esk11_0))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[7326,1714,theory(equality)]) ).
cnf(7341,negated_conjecture,
( esk11_0 = nil
| nil = X1
| cons(hd(esk11_0),X1) != esk8_0
| ~ ssList(X1) ),
inference(csr,[status(thm)],[7331,1979]) ).
cnf(7344,negated_conjecture,
( esk11_0 = nil
| nil = esk1_1(esk8_0)
| ~ ssList(esk1_1(esk8_0)) ),
inference(spm,[status(thm)],[7341,2868,theory(equality)]) ).
cnf(7352,negated_conjecture,
( esk1_1(esk8_0) = nil
| esk11_0 = nil
| nil = esk8_0
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[7344,80,theory(equality)]) ).
cnf(7353,negated_conjecture,
( esk1_1(esk8_0) = nil
| esk11_0 = nil
| nil = esk8_0
| $false ),
inference(rw,[status(thm)],[7352,167,theory(equality)]) ).
cnf(7354,negated_conjecture,
( esk1_1(esk8_0) = nil
| esk11_0 = nil
| nil = esk8_0 ),
inference(cn,[status(thm)],[7353,theory(equality)]) ).
cnf(7355,negated_conjecture,
( esk1_1(esk8_0) = nil
| esk11_0 = nil ),
inference(csr,[status(thm)],[7354,2108]) ).
cnf(7361,negated_conjecture,
( cons(hd(esk8_0),nil) = esk8_0
| nil = esk8_0
| esk11_0 = nil
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[703,7355,theory(equality)]) ).
cnf(7379,negated_conjecture,
( cons(hd(esk8_0),nil) = esk8_0
| nil = esk8_0
| esk11_0 = nil
| $false ),
inference(rw,[status(thm)],[7361,167,theory(equality)]) ).
cnf(7380,negated_conjecture,
( cons(hd(esk8_0),nil) = esk8_0
| nil = esk8_0
| esk11_0 = nil ),
inference(cn,[status(thm)],[7379,theory(equality)]) ).
cnf(7438,negated_conjecture,
( cons(hd(esk8_0),nil) = esk8_0
| esk11_0 = nil ),
inference(csr,[status(thm)],[7380,2108]) ).
cnf(7442,negated_conjecture,
( app(esk8_0,X1) = cons(hd(esk8_0),X1)
| esk11_0 = nil
| ~ ssItem(hd(esk8_0))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[54,7438,theory(equality)]) ).
cnf(9321,negated_conjecture,
( cons(hd(esk8_0),X1) = app(esk8_0,X1)
| esk11_0 = nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[7442,1894]) ).
cnf(9367,negated_conjecture,
( cons(hd(esk11_0),X1) = app(esk8_0,X1)
| esk11_0 = nil
| ~ ssList(X1) ),
inference(spm,[status(thm)],[9321,1976,theory(equality)]) ).
cnf(10235,negated_conjecture,
( app(esk8_0,esk1_1(esk11_0)) = esk11_0
| nil = esk11_0
| ~ ssList(esk11_0)
| ~ ssList(esk1_1(esk11_0)) ),
inference(spm,[status(thm)],[703,9367,theory(equality)]) ).
cnf(10343,negated_conjecture,
( app(esk8_0,esk1_1(esk11_0)) = esk11_0
| nil = esk11_0
| $false
| ~ ssList(esk1_1(esk11_0)) ),
inference(rw,[status(thm)],[10235,181,theory(equality)]) ).
cnf(10344,negated_conjecture,
( app(esk8_0,esk1_1(esk11_0)) = esk11_0
| nil = esk11_0
| ~ ssList(esk1_1(esk11_0)) ),
inference(cn,[status(thm)],[10343,theory(equality)]) ).
cnf(37178,negated_conjecture,
( app(esk8_0,esk1_1(esk11_0)) = esk11_0
| esk11_0 = nil
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[10344,80,theory(equality)]) ).
cnf(37179,negated_conjecture,
( app(esk8_0,esk1_1(esk11_0)) = esk11_0
| esk11_0 = nil
| $false ),
inference(rw,[status(thm)],[37178,181,theory(equality)]) ).
cnf(37180,negated_conjecture,
( app(esk8_0,esk1_1(esk11_0)) = esk11_0
| esk11_0 = nil ),
inference(cn,[status(thm)],[37179,theory(equality)]) ).
cnf(37218,negated_conjecture,
( esk11_0 = nil
| segmentP(esk11_0,esk8_0)
| ~ ssList(esk1_1(esk11_0)) ),
inference(spm,[status(thm)],[4166,37180,theory(equality)]) ).
cnf(38143,negated_conjecture,
( esk11_0 = nil
| segmentP(esk11_0,esk8_0)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[37218,80,theory(equality)]) ).
cnf(38144,negated_conjecture,
( esk11_0 = nil
| segmentP(esk11_0,esk8_0)
| $false ),
inference(rw,[status(thm)],[38143,181,theory(equality)]) ).
cnf(38145,negated_conjecture,
( esk11_0 = nil
| segmentP(esk11_0,esk8_0) ),
inference(cn,[status(thm)],[38144,theory(equality)]) ).
cnf(38152,negated_conjecture,
( esk11_0 = nil
| ~ neq(esk8_0,nil) ),
inference(spm,[status(thm)],[230,38145,theory(equality)]) ).
cnf(38171,negated_conjecture,
( esk11_0 = nil
| esk8_0 = nil
| ~ ssList(nil)
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[38152,137,theory(equality)]) ).
cnf(38173,negated_conjecture,
( esk11_0 = nil
| esk8_0 = nil
| $false
| ~ ssList(esk8_0) ),
inference(rw,[status(thm)],[38171,143,theory(equality)]) ).
cnf(38174,negated_conjecture,
( esk11_0 = nil
| esk8_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[38173,167,theory(equality)]) ).
cnf(38175,negated_conjecture,
( esk11_0 = nil
| esk8_0 = nil ),
inference(cn,[status(thm)],[38174,theory(equality)]) ).
cnf(38176,negated_conjecture,
esk11_0 = nil,
inference(csr,[status(thm)],[38175,2108]) ).
cnf(38179,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[182,38176,theory(equality)]) ).
cnf(38180,negated_conjecture,
$false,
inference(sr,[status(thm)],[38179,368,theory(equality)]) ).
cnf(38181,negated_conjecture,
$false,
38180,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC079+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpSradAx/sel_SWC079+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC079+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC079+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC079+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
%
%------------------------------------------------------------------------------