TSTP Solution File: SWC354+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC354+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 11:37:38 EST 2010
% Result : Theorem 1.73s
% Output : CNFRefutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 19
% Syntax : Number of formulae : 240 ( 16 unt; 0 def)
% Number of atoms : 984 ( 379 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 1247 ( 503 ~; 604 |; 88 &)
% ( 2 <=>; 50 =>; 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 : 338 ( 0 sgn 159 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/tmp/tmpAB-K7c/sel_SWC354+1.p_1',ax85) ).
fof(2,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmpAB-K7c/sel_SWC354+1.p_1',ax84) ).
fof(3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmpAB-K7c/sel_SWC354+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/tmpAB-K7c/sel_SWC354+1.p_1',ax82) ).
fof(5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpAB-K7c/sel_SWC354+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/tmpAB-K7c/sel_SWC354+1.p_1',ax80) ).
fof(7,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpAB-K7c/sel_SWC354+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/tmpAB-K7c/sel_SWC354+1.p_1',ax27) ).
fof(9,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpAB-K7c/sel_SWC354+1.p_1',ax26) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmpAB-K7c/sel_SWC354+1.p_1',ax21) ).
fof(11,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/tmp/tmpAB-K7c/sel_SWC354+1.p_1',ax20) ).
fof(12,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/tmp/tmpAB-K7c/sel_SWC354+1.p_1',ax23) ).
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/tmp/tmpAB-K7c/sel_SWC354+1.p_1',ax22) ).
fof(22,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpAB-K7c/sel_SWC354+1.p_1',ax15) ).
fof(23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpAB-K7c/sel_SWC354+1.p_1',ax16) ).
fof(24,axiom,
ssList(nil),
file('/tmp/tmpAB-K7c/sel_SWC354+1.p_1',ax17) ).
fof(27,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/tmp/tmpAB-K7c/sel_SWC354+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/tmpAB-K7c/sel_SWC354+1.p_1',ax56) ).
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)
& X3 != X5
& ? [X6] :
( ssItem(X6)
& cons(X6,nil) = X5
& hd(X4) = X6
& neq(nil,X4) ) )
| segmentP(X2,X1) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/tmp/tmpAB-K7c/sel_SWC354+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)
& X3 != X5
& ? [X6] :
( ssItem(X6)
& cons(X6,nil) = X5
& hd(X4) = X6
& neq(nil,X4) ) )
| segmentP(X2,X1) )
& ( ~ 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)
& X3 != X5
& ? [X6] :
( ssItem(X6)
& cons(X6,nil) = X5
& hd(X4) = X6
& neq(nil,X4) ) )
| segmentP(X2,X1) )
& ( ~ 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]) ).
cnf(138,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,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(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)
| X3 = X5
| ! [X6] :
( ~ ssItem(X6)
| cons(X6,nil) != X5
| hd(X4) != X6
| ~ neq(nil,X4) ) )
& ~ segmentP(X2,X1) )
| ( neq(X2,nil)
& ~ neq(X4,nil) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[32]) ).
fof(163,negated_conjecture,
? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& X8 = X10
& X7 = X9
& ( ( neq(X8,nil)
& ! [X11] :
( ~ ssList(X11)
| X9 = X11
| ! [X12] :
( ~ ssItem(X12)
| cons(X12,nil) != X11
| hd(X10) != X12
| ~ neq(nil,X10) ) )
& ~ segmentP(X8,X7) )
| ( neq(X8,nil)
& ~ neq(X10,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)
& ! [X11] :
( ~ ssList(X11)
| esk10_0 = X11
| ! [X12] :
( ~ ssItem(X12)
| cons(X12,nil) != X11
| hd(esk11_0) != X12
| ~ neq(nil,esk11_0) ) )
& ~ segmentP(esk9_0,esk8_0) )
| ( neq(esk9_0,nil)
& ~ neq(esk11_0,nil) ) ) ),
inference(skolemize,[status(esa)],[163]) ).
fof(165,negated_conjecture,
! [X11,X12] :
( ( ( ( ~ ssItem(X12)
| cons(X12,nil) != X11
| hd(esk11_0) != X12
| ~ neq(nil,esk11_0)
| ~ ssList(X11)
| esk10_0 = X11 )
& neq(esk9_0,nil)
& ~ segmentP(esk9_0,esk8_0) )
| ( 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,
! [X11,X12] :
( ( neq(esk9_0,nil)
| ~ ssItem(X12)
| cons(X12,nil) != X11
| hd(esk11_0) != X12
| ~ neq(nil,esk11_0)
| ~ ssList(X11)
| esk10_0 = X11 )
& ( ~ neq(esk11_0,nil)
| ~ ssItem(X12)
| cons(X12,nil) != X11
| hd(esk11_0) != X12
| ~ neq(nil,esk11_0)
| ~ ssList(X11)
| esk10_0 = X11 )
& ( neq(esk9_0,nil)
| neq(esk9_0,nil) )
& ( ~ neq(esk11_0,nil)
| neq(esk9_0,nil) )
& ( neq(esk9_0,nil)
| ~ segmentP(esk9_0,esk8_0) )
& ( ~ neq(esk11_0,nil)
| ~ segmentP(esk9_0,esk8_0) )
& 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(173,negated_conjecture,
( ~ segmentP(esk9_0,esk8_0)
| ~ neq(esk11_0,nil) ),
inference(split_conjunct,[status(thm)],[166]) ).
cnf(176,negated_conjecture,
( neq(esk9_0,nil)
| neq(esk9_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)],[176,172,theory(equality)]) ).
cnf(188,negated_conjecture,
( $false
| ~ segmentP(esk9_0,esk8_0) ),
inference(rw,[status(thm)],[173,182,theory(equality)]) ).
cnf(189,negated_conjecture,
( $false
| ~ segmentP(esk11_0,esk8_0) ),
inference(rw,[status(thm)],[188,172,theory(equality)]) ).
cnf(190,negated_conjecture,
~ segmentP(esk11_0,esk8_0),
inference(cn,[status(thm)],[189,theory(equality)]) ).
cnf(195,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[138,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(232,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(236,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(238,plain,
( nil = X1
| X2 != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[58,39,theory(equality)]) ).
cnf(244,plain,
( nil = X1
| X2 != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[238,143,theory(equality)]) ).
cnf(245,plain,
( nil = X1
| X2 != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[244,theory(equality)]) ).
cnf(286,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(287,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)],[286,182,theory(equality)]) ).
cnf(288,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)],[287,theory(equality)]) ).
cnf(289,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)],[288,137,theory(equality)]) ).
cnf(291,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)],[289,143,theory(equality)]) ).
cnf(292,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)],[291,theory(equality)]) ).
cnf(293,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(296,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(310,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[50,61,theory(equality)]) ).
cnf(329,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[310,143,theory(equality)]) ).
cnf(330,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[329,theory(equality)]) ).
cnf(332,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[158,154,theory(equality)]) ).
cnf(361,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[296,69]) ).
cnf(365,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)],[361,65,theory(equality)]) ).
cnf(373,plain,
( app(nil,nil) = nil
| ~ ssList(nil) ),
inference(er,[status(thm)],[209,theory(equality)]) ).
cnf(374,plain,
( app(nil,nil) = nil
| $false ),
inference(rw,[status(thm)],[373,143,theory(equality)]) ).
cnf(375,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[374,theory(equality)]) ).
cnf(399,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[65,375,theory(equality)]) ).
cnf(414,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[399,143,theory(equality)]) ).
cnf(415,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[414,theory(equality)]) ).
cnf(429,plain,
( app(app(cons(X1,X2),X3),X4) != nil
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[365,69]) ).
cnf(435,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)],[429,50,theory(equality)]) ).
cnf(489,plain,
( app(cons(X1,X2),app(X3,X4)) != nil
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[435,142]) ).
cnf(490,plain,
( app(cons(X1,X2),nil) != nil
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[489,375,theory(equality)]) ).
cnf(498,plain,
( app(cons(X1,X2),nil) != nil
| ~ ssItem(X1)
| $false
| ~ ssList(X2) ),
inference(rw,[status(thm)],[490,143,theory(equality)]) ).
cnf(499,plain,
( app(cons(X1,X2),nil) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[498,theory(equality)]) ).
cnf(566,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[499,54,theory(equality)]) ).
cnf(569,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[566,143,theory(equality)]) ).
cnf(570,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[569,theory(equality)]) ).
cnf(665,plain,
( nil = X1
| cons(X2,X1) != cons(X2,nil)
| ~ ssList(X1)
| ~ ssList(cons(X2,nil))
| ~ ssItem(X2) ),
inference(spm,[status(thm)],[245,54,theory(equality)]) ).
cnf(669,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2) ),
inference(csr,[status(thm)],[232,570]) ).
cnf(670,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[669,142,theory(equality)]) ).
cnf(671,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[670,143,theory(equality)]) ).
cnf(672,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[671,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)],[87,672,theory(equality)]) ).
cnf(700,plain,
( esk2_1(X1) = hd(X1)
| nil = X1
| ~ ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[236,80]) ).
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(1082,plain,
( ssItem(hd(cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2) ),
inference(csr,[status(thm)],[674,570]) ).
cnf(1083,plain,
( ssItem(hd(cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1082,142,theory(equality)]) ).
cnf(1084,plain,
( ssItem(hd(cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[1083,143,theory(equality)]) ).
cnf(1085,plain,
( ssItem(hd(cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[1084,theory(equality)]) ).
cnf(1517,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)],[292,181,theory(equality)]) ).
cnf(1518,negated_conjecture,
( esk8_0 = X1
| esk11_0 = nil
| cons(X2,nil) != X1
| hd(esk11_0) != X2
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1517,theory(equality)]) ).
cnf(1519,negated_conjecture,
( esk11_0 = nil
| esk8_0 = X1
| cons(hd(esk11_0),nil) != X1
| ~ ssItem(hd(esk11_0))
| ~ ssList(X1) ),
inference(er,[status(thm)],[1518,theory(equality)]) ).
cnf(1530,negated_conjecture,
( esk11_0 = nil
| esk8_0 = X1
| cons(hd(esk11_0),nil) != X1
| ~ ssList(X1)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[1519,87,theory(equality)]) ).
cnf(1531,negated_conjecture,
( esk11_0 = nil
| esk8_0 = X1
| cons(hd(esk11_0),nil) != X1
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[1530,181,theory(equality)]) ).
cnf(1532,negated_conjecture,
( esk11_0 = nil
| esk8_0 = X1
| cons(hd(esk11_0),nil) != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1531,theory(equality)]) ).
cnf(1533,negated_conjecture,
( esk11_0 = nil
| esk8_0 = cons(hd(esk11_0),nil)
| ~ ssList(cons(hd(esk11_0),nil)) ),
inference(er,[status(thm)],[1532,theory(equality)]) ).
cnf(1534,negated_conjecture,
( cons(hd(esk11_0),nil) = esk8_0
| esk11_0 = nil
| ~ ssItem(hd(esk11_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1533,142,theory(equality)]) ).
cnf(1535,negated_conjecture,
( cons(hd(esk11_0),nil) = esk8_0
| esk11_0 = nil
| ~ ssItem(hd(esk11_0))
| $false ),
inference(rw,[status(thm)],[1534,143,theory(equality)]) ).
cnf(1536,negated_conjecture,
( cons(hd(esk11_0),nil) = esk8_0
| esk11_0 = nil
| ~ ssItem(hd(esk11_0)) ),
inference(cn,[status(thm)],[1535,theory(equality)]) ).
cnf(1537,negated_conjecture,
( cons(hd(esk11_0),nil) = esk8_0
| esk11_0 = nil
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[1536,87,theory(equality)]) ).
cnf(1538,negated_conjecture,
( cons(hd(esk11_0),nil) = esk8_0
| esk11_0 = nil
| $false ),
inference(rw,[status(thm)],[1537,181,theory(equality)]) ).
cnf(1539,negated_conjecture,
( cons(hd(esk11_0),nil) = esk8_0
| esk11_0 = nil ),
inference(cn,[status(thm)],[1538,theory(equality)]) ).
cnf(1571,negated_conjecture,
( hd(esk8_0) = hd(esk11_0)
| esk11_0 = nil
| ~ ssItem(hd(esk11_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[84,1539,theory(equality)]) ).
cnf(1583,negated_conjecture,
( esk11_0 = nil
| app(esk8_0,nil) != nil
| ~ ssItem(hd(esk11_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[499,1539,theory(equality)]) ).
cnf(1586,negated_conjecture,
( app(esk8_0,nil) = esk8_0
| esk11_0 = nil
| ~ ssItem(hd(esk11_0)) ),
inference(spm,[status(thm)],[415,1539,theory(equality)]) ).
cnf(1595,negated_conjecture,
( ssItem(hd(esk8_0))
| esk11_0 = nil
| ~ ssItem(hd(esk11_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1085,1539,theory(equality)]) ).
cnf(1611,negated_conjecture,
( hd(esk8_0) = hd(esk11_0)
| esk11_0 = nil
| ~ ssItem(hd(esk11_0))
| $false ),
inference(rw,[status(thm)],[1571,143,theory(equality)]) ).
cnf(1612,negated_conjecture,
( hd(esk8_0) = hd(esk11_0)
| esk11_0 = nil
| ~ ssItem(hd(esk11_0)) ),
inference(cn,[status(thm)],[1611,theory(equality)]) ).
cnf(1635,negated_conjecture,
( esk11_0 = nil
| app(esk8_0,nil) != nil
| ~ ssItem(hd(esk11_0))
| $false ),
inference(rw,[status(thm)],[1583,143,theory(equality)]) ).
cnf(1636,negated_conjecture,
( esk11_0 = nil
| app(esk8_0,nil) != nil
| ~ ssItem(hd(esk11_0)) ),
inference(cn,[status(thm)],[1635,theory(equality)]) ).
cnf(1649,negated_conjecture,
( ssItem(hd(esk8_0))
| esk11_0 = nil
| ~ ssItem(hd(esk11_0))
| $false ),
inference(rw,[status(thm)],[1595,143,theory(equality)]) ).
cnf(1650,negated_conjecture,
( ssItem(hd(esk8_0))
| esk11_0 = nil
| ~ ssItem(hd(esk11_0)) ),
inference(cn,[status(thm)],[1649,theory(equality)]) ).
cnf(1663,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[293,69]) ).
cnf(1668,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1663,415,theory(equality)]) ).
cnf(1677,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[1668,143,theory(equality)]) ).
cnf(1678,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[1677,theory(equality)]) ).
cnf(1683,negated_conjecture,
( esk11_0 = nil
| ssItem(hd(esk8_0))
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[1650,87,theory(equality)]) ).
cnf(1684,negated_conjecture,
( esk11_0 = nil
| ssItem(hd(esk8_0))
| $false ),
inference(rw,[status(thm)],[1683,181,theory(equality)]) ).
cnf(1685,negated_conjecture,
( esk11_0 = nil
| ssItem(hd(esk8_0)) ),
inference(cn,[status(thm)],[1684,theory(equality)]) ).
cnf(1769,negated_conjecture,
( hd(esk8_0) = hd(esk11_0)
| esk11_0 = nil
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[1612,87,theory(equality)]) ).
cnf(1770,negated_conjecture,
( hd(esk8_0) = hd(esk11_0)
| esk11_0 = nil
| $false ),
inference(rw,[status(thm)],[1769,181,theory(equality)]) ).
cnf(1771,negated_conjecture,
( hd(esk8_0) = hd(esk11_0)
| esk11_0 = nil ),
inference(cn,[status(thm)],[1770,theory(equality)]) ).
cnf(1822,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)],[703,1771,theory(equality)]) ).
cnf(1823,negated_conjecture,
( esk11_0 = nil
| ssItem(hd(esk11_0)) ),
inference(spm,[status(thm)],[1685,1771,theory(equality)]) ).
cnf(1826,negated_conjecture,
( cons(hd(esk11_0),esk1_1(esk8_0)) = esk8_0
| nil = esk8_0
| esk11_0 = nil
| $false ),
inference(rw,[status(thm)],[1822,167,theory(equality)]) ).
cnf(1827,negated_conjecture,
( cons(hd(esk11_0),esk1_1(esk8_0)) = esk8_0
| nil = esk8_0
| esk11_0 = nil ),
inference(cn,[status(thm)],[1826,theory(equality)]) ).
cnf(1861,negated_conjecture,
( app(esk8_0,nil) = esk8_0
| esk11_0 = nil ),
inference(csr,[status(thm)],[1586,1823]) ).
cnf(1883,negated_conjecture,
( esk11_0 = nil
| esk8_0 != nil
| ~ ssItem(hd(esk11_0)) ),
inference(spm,[status(thm)],[1636,1861,theory(equality)]) ).
cnf(1946,negated_conjecture,
( esk11_0 = nil
| esk8_0 != nil ),
inference(csr,[status(thm)],[1883,1823]) ).
cnf(2316,negated_conjecture,
( app(nil,esk8_0) = esk8_0
| esk11_0 = nil
| ~ ssList(nil)
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[330,1861,theory(equality)]) ).
cnf(2369,negated_conjecture,
( app(nil,esk8_0) = esk8_0
| esk11_0 = nil
| $false
| ~ ssList(esk8_0) ),
inference(rw,[status(thm)],[2316,143,theory(equality)]) ).
cnf(2370,negated_conjecture,
( app(nil,esk8_0) = esk8_0
| esk11_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[2369,167,theory(equality)]) ).
cnf(2371,negated_conjecture,
( app(nil,esk8_0) = esk8_0
| esk11_0 = nil ),
inference(cn,[status(thm)],[2370,theory(equality)]) ).
cnf(2945,negated_conjecture,
( cons(hd(esk11_0),esk1_1(esk8_0)) = esk8_0
| esk11_0 = nil ),
inference(csr,[status(thm)],[1827,1946]) ).
cnf(4144,negated_conjecture,
( segmentP(app(esk8_0,X1),esk8_0)
| esk11_0 = nil
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[332,2371,theory(equality)]) ).
cnf(4170,negated_conjecture,
( segmentP(app(esk8_0,X1),esk8_0)
| esk11_0 = nil
| ~ ssList(X1)
| $false
| ~ ssList(esk8_0) ),
inference(rw,[status(thm)],[4144,143,theory(equality)]) ).
cnf(4171,negated_conjecture,
( segmentP(app(esk8_0,X1),esk8_0)
| esk11_0 = nil
| ~ ssList(X1)
| $false
| $false ),
inference(rw,[status(thm)],[4170,167,theory(equality)]) ).
cnf(4172,negated_conjecture,
( segmentP(app(esk8_0,X1),esk8_0)
| esk11_0 = nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[4171,theory(equality)]) ).
cnf(7341,plain,
( nil = X1
| cons(X2,X1) != cons(X2,nil)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[665,1678]) ).
cnf(7346,negated_conjecture,
( nil = X1
| esk11_0 = nil
| cons(hd(esk11_0),X1) != esk8_0
| ~ ssItem(hd(esk11_0))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[7341,1539,theory(equality)]) ).
cnf(7360,negated_conjecture,
( esk11_0 = nil
| nil = X1
| cons(hd(esk11_0),X1) != esk8_0
| ~ ssList(X1) ),
inference(csr,[status(thm)],[7346,1823]) ).
cnf(7363,negated_conjecture,
( esk11_0 = nil
| nil = esk1_1(esk8_0)
| ~ ssList(esk1_1(esk8_0)) ),
inference(spm,[status(thm)],[7360,2945,theory(equality)]) ).
cnf(7371,negated_conjecture,
( esk1_1(esk8_0) = nil
| esk11_0 = nil
| nil = esk8_0
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[7363,80,theory(equality)]) ).
cnf(7372,negated_conjecture,
( esk1_1(esk8_0) = nil
| esk11_0 = nil
| nil = esk8_0
| $false ),
inference(rw,[status(thm)],[7371,167,theory(equality)]) ).
cnf(7373,negated_conjecture,
( esk1_1(esk8_0) = nil
| esk11_0 = nil
| nil = esk8_0 ),
inference(cn,[status(thm)],[7372,theory(equality)]) ).
cnf(7374,negated_conjecture,
( esk1_1(esk8_0) = nil
| esk11_0 = nil ),
inference(csr,[status(thm)],[7373,1946]) ).
cnf(7380,negated_conjecture,
( cons(hd(esk8_0),nil) = esk8_0
| nil = esk8_0
| esk11_0 = nil
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[703,7374,theory(equality)]) ).
cnf(7398,negated_conjecture,
( cons(hd(esk8_0),nil) = esk8_0
| nil = esk8_0
| esk11_0 = nil
| $false ),
inference(rw,[status(thm)],[7380,167,theory(equality)]) ).
cnf(7399,negated_conjecture,
( cons(hd(esk8_0),nil) = esk8_0
| nil = esk8_0
| esk11_0 = nil ),
inference(cn,[status(thm)],[7398,theory(equality)]) ).
cnf(7457,negated_conjecture,
( cons(hd(esk8_0),nil) = esk8_0
| esk11_0 = nil ),
inference(csr,[status(thm)],[7399,1946]) ).
cnf(7461,negated_conjecture,
( app(esk8_0,X1) = cons(hd(esk8_0),X1)
| esk11_0 = nil
| ~ ssItem(hd(esk8_0))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[54,7457,theory(equality)]) ).
cnf(9341,negated_conjecture,
( cons(hd(esk8_0),X1) = app(esk8_0,X1)
| esk11_0 = nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[7461,1685]) ).
cnf(9386,negated_conjecture,
( cons(hd(esk11_0),X1) = app(esk8_0,X1)
| esk11_0 = nil
| ~ ssList(X1) ),
inference(spm,[status(thm)],[9341,1771,theory(equality)]) ).
cnf(9894,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)],[703,9386,theory(equality)]) ).
cnf(9999,negated_conjecture,
( app(esk8_0,esk1_1(esk11_0)) = esk11_0
| nil = esk11_0
| $false
| ~ ssList(esk1_1(esk11_0)) ),
inference(rw,[status(thm)],[9894,181,theory(equality)]) ).
cnf(10000,negated_conjecture,
( app(esk8_0,esk1_1(esk11_0)) = esk11_0
| nil = esk11_0
| ~ ssList(esk1_1(esk11_0)) ),
inference(cn,[status(thm)],[9999,theory(equality)]) ).
cnf(30865,negated_conjecture,
( app(esk8_0,esk1_1(esk11_0)) = esk11_0
| esk11_0 = nil
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[10000,80,theory(equality)]) ).
cnf(30866,negated_conjecture,
( app(esk8_0,esk1_1(esk11_0)) = esk11_0
| esk11_0 = nil
| $false ),
inference(rw,[status(thm)],[30865,181,theory(equality)]) ).
cnf(30867,negated_conjecture,
( app(esk8_0,esk1_1(esk11_0)) = esk11_0
| esk11_0 = nil ),
inference(cn,[status(thm)],[30866,theory(equality)]) ).
cnf(30906,negated_conjecture,
( esk11_0 = nil
| segmentP(esk11_0,esk8_0)
| ~ ssList(esk1_1(esk11_0)) ),
inference(spm,[status(thm)],[4172,30867,theory(equality)]) ).
cnf(31027,negated_conjecture,
( esk11_0 = nil
| ~ ssList(esk1_1(esk11_0)) ),
inference(sr,[status(thm)],[30906,190,theory(equality)]) ).
cnf(31106,negated_conjecture,
( esk11_0 = nil
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[31027,80,theory(equality)]) ).
cnf(31107,negated_conjecture,
( esk11_0 = nil
| $false ),
inference(rw,[status(thm)],[31106,181,theory(equality)]) ).
cnf(31108,negated_conjecture,
esk11_0 = nil,
inference(cn,[status(thm)],[31107,theory(equality)]) ).
cnf(31111,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[182,31108,theory(equality)]) ).
cnf(31525,negated_conjecture,
~ ssList(nil),
inference(spm,[status(thm)],[195,31111,theory(equality)]) ).
cnf(31527,negated_conjecture,
$false,
inference(rw,[status(thm)],[31525,143,theory(equality)]) ).
cnf(31528,negated_conjecture,
$false,
inference(cn,[status(thm)],[31527,theory(equality)]) ).
cnf(31529,negated_conjecture,
$false,
31528,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC354+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpAB-K7c/sel_SWC354+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC354+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC354+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC354+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
%
%------------------------------------------------------------------------------