TSTP Solution File: SWC015+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC015+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 10:05:34 EST 2010
% Result : Theorem 88.84s
% Output : CNFRefutation 88.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 20
% Syntax : Number of formulae : 240 ( 15 unt; 0 def)
% Number of atoms : 1003 ( 405 equ)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 1308 ( 545 ~; 623 |; 87 &)
% ( 2 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 359 ( 0 sgn 167 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax86) ).
fof(3,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax84) ).
fof(4,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax83) ).
fof(5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax82) ).
fof(6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax81) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax28) ).
fof(9,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax25) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax24) ).
fof(11,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax27) ).
fof(12,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax26) ).
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax21) ).
fof(15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax23) ).
fof(16,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax22) ).
fof(22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax78) ).
fof(23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax79) ).
fof(24,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax15) ).
fof(25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax16) ).
fof(26,axiom,
ssList(nil),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax17) ).
fof(27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax18) ).
fof(29,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X4 != X5
& ? [X6] :
( ssList(X6)
& tl(X4) = X6
& app(X3,X6) = X5
& neq(nil,X4) ) )
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& cons(X7,nil) = X1
& app(cons(X7,nil),X8) = X2 ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',co1) ).
fof(30,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X4 != X5
& ? [X6] :
( ssList(X6)
& tl(X4) = X6
& app(X3,X6) = X5
& neq(nil,X4) ) )
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& cons(X7,nil) = X1
& app(cons(X7,nil),X8) = X2 ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[29]) ).
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)
& X4 != X5
& ? [X6] :
( ssList(X6)
& tl(X4) = X6
& app(X3,X6) = X5
& neq(nil,X4) ) )
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& cons(X7,nil) = X1
& app(cons(X7,nil),X8) = X2 ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[30,theory(equality)]) ).
fof(32,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(33,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| nil = X3
| tl(app(X3,X4)) = app(tl(X3),X4) ) ),
inference(variable_rename,[status(thm)],[32]) ).
fof(34,plain,
! [X3,X4] :
( ~ ssList(X4)
| nil = X3
| tl(app(X3,X4)) = app(tl(X3),X4)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[33]) ).
cnf(35,plain,
( tl(app(X1,X2)) = app(tl(X1),X2)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[34]) ).
fof(40,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(41,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[40]) ).
cnf(42,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(43,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)],[4]) ).
fof(44,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)],[43]) ).
fof(45,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)],[44]) ).
fof(46,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)],[45]) ).
cnf(47,plain,
( nil = app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| nil != X1
| nil != X2 ),
inference(split_conjunct,[status(thm)],[46]) ).
cnf(48,plain,
( nil = X1
| ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[46]) ).
fof(50,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)],[5]) ).
fof(51,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)],[50]) ).
fof(52,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)],[51]) ).
cnf(53,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[52]) ).
fof(54,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(55,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[54]) ).
fof(56,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[55]) ).
cnf(57,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[56]) ).
fof(62,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(63,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[62]) ).
cnf(64,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[63]) ).
fof(65,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| tl(cons(X2,X1)) = X1 ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(66,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| tl(cons(X4,X3)) = X3 ) ),
inference(variable_rename,[status(thm)],[65]) ).
fof(67,plain,
! [X3,X4] :
( ~ ssItem(X4)
| tl(cons(X4,X3)) = X3
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[66]) ).
cnf(68,plain,
( tl(cons(X2,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[67]) ).
fof(69,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(70,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| ssList(tl(X2)) ),
inference(variable_rename,[status(thm)],[69]) ).
cnf(71,plain,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[70]) ).
fof(72,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssItem(X3)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(73,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)],[72]) ).
fof(74,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)],[73]) ).
cnf(75,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[74]) ).
fof(76,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(77,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[76]) ).
fof(78,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[77]) ).
cnf(79,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[78]) ).
fof(80,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| nil != cons(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(81,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3) ) ),
inference(variable_rename,[status(thm)],[80]) ).
fof(82,plain,
! [X3,X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[81]) ).
cnf(83,plain,
( ~ ssList(X1)
| nil != cons(X2,X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[82]) ).
fof(91,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| hd(cons(X2,X1)) = X2 ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(92,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| hd(cons(X4,X3)) = X4 ) ),
inference(variable_rename,[status(thm)],[91]) ).
fof(93,plain,
! [X3,X4] :
( ~ ssItem(X4)
| hd(cons(X4,X3)) = X4
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[92]) ).
cnf(94,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[93]) ).
fof(95,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(96,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| ssItem(hd(X2)) ),
inference(variable_rename,[status(thm)],[95]) ).
cnf(97,plain,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[96]) ).
fof(125,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(126,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| cons(hd(X2),tl(X2)) = X2 ),
inference(variable_rename,[status(thm)],[125]) ).
cnf(127,plain,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[126]) ).
fof(128,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X3,X2) != app(X1,X2)
| X3 = X1 ) ) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(129,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(X6,X5) != app(X4,X5)
| X6 = X4 ) ) ),
inference(variable_rename,[status(thm)],[128]) ).
fof(130,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| app(X6,X5) != app(X4,X5)
| X6 = X4
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[129]) ).
cnf(131,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| app(X3,X2) != app(X1,X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[130]) ).
fof(132,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(133,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[132]) ).
fof(134,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[133]) ).
fof(135,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)],[134]) ).
cnf(136,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[135]) ).
cnf(137,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[135]) ).
fof(138,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(139,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[138]) ).
fof(140,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[139]) ).
cnf(141,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[140]) ).
cnf(142,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[26]) ).
fof(143,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) != X1 ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(144,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) != X3 ) ),
inference(variable_rename,[status(thm)],[143]) ).
fof(145,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) != X3
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[144]) ).
cnf(146,plain,
( ~ ssList(X1)
| cons(X2,X1) != X1
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[145]) ).
fof(153,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ( ( neq(X2,nil)
& ! [X5] :
( ~ ssList(X5)
| X4 = X5
| ! [X6] :
( ~ ssList(X6)
| tl(X4) != X6
| app(X3,X6) != X5
| ~ neq(nil,X4) ) )
& ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| cons(X7,nil) != X1
| app(cons(X7,nil),X8) != X2 ) ) )
| ( neq(X2,nil)
& ~ neq(X4,nil) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(154,negated_conjecture,
? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& X10 = X12
& X9 = X11
& ( ( neq(X10,nil)
& ! [X13] :
( ~ ssList(X13)
| X12 = X13
| ! [X14] :
( ~ ssList(X14)
| tl(X12) != X14
| app(X11,X14) != X13
| ~ neq(nil,X12) ) )
& ! [X15] :
( ~ ssItem(X15)
| ! [X16] :
( ~ ssList(X16)
| cons(X15,nil) != X9
| app(cons(X15,nil),X16) != X10 ) ) )
| ( neq(X10,nil)
& ~ neq(X12,nil) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[153]) ).
fof(155,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)
& ! [X13] :
( ~ ssList(X13)
| esk10_0 = X13
| ! [X14] :
( ~ ssList(X14)
| tl(esk10_0) != X14
| app(esk9_0,X14) != X13
| ~ neq(nil,esk10_0) ) )
& ! [X15] :
( ~ ssItem(X15)
| ! [X16] :
( ~ ssList(X16)
| cons(X15,nil) != esk7_0
| app(cons(X15,nil),X16) != esk8_0 ) ) )
| ( neq(esk8_0,nil)
& ~ neq(esk10_0,nil) ) ) ),
inference(skolemize,[status(esa)],[154]) ).
fof(156,negated_conjecture,
! [X13,X14,X15,X16] :
( ( ( ( ~ ssList(X16)
| cons(X15,nil) != esk7_0
| app(cons(X15,nil),X16) != esk8_0
| ~ ssItem(X15) )
& ( ~ ssList(X14)
| tl(esk10_0) != X14
| app(esk9_0,X14) != X13
| ~ neq(nil,esk10_0)
| ~ ssList(X13)
| esk10_0 = X13 )
& 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)],[155]) ).
fof(157,negated_conjecture,
! [X13,X14,X15,X16] :
( ( neq(esk8_0,nil)
| ~ ssList(X16)
| cons(X15,nil) != esk7_0
| app(cons(X15,nil),X16) != esk8_0
| ~ ssItem(X15) )
& ( ~ neq(esk10_0,nil)
| ~ ssList(X16)
| cons(X15,nil) != esk7_0
| app(cons(X15,nil),X16) != esk8_0
| ~ ssItem(X15) )
& ( neq(esk8_0,nil)
| ~ ssList(X14)
| tl(esk10_0) != X14
| app(esk9_0,X14) != X13
| ~ neq(nil,esk10_0)
| ~ ssList(X13)
| esk10_0 = X13 )
& ( ~ neq(esk10_0,nil)
| ~ ssList(X14)
| tl(esk10_0) != X14
| app(esk9_0,X14) != X13
| ~ neq(nil,esk10_0)
| ~ ssList(X13)
| esk10_0 = X13 )
& ( 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)],[156]) ).
cnf(158,negated_conjecture,
ssList(esk7_0),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(159,negated_conjecture,
ssList(esk8_0),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(162,negated_conjecture,
esk7_0 = esk9_0,
inference(split_conjunct,[status(thm)],[157]) ).
cnf(163,negated_conjecture,
esk8_0 = esk10_0,
inference(split_conjunct,[status(thm)],[157]) ).
cnf(165,negated_conjecture,
( neq(esk8_0,nil)
| neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(166,negated_conjecture,
( esk10_0 = X1
| ~ ssList(X1)
| ~ neq(nil,esk10_0)
| app(esk9_0,X2) != X1
| tl(esk10_0) != X2
| ~ ssList(X2)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(168,negated_conjecture,
( ~ ssItem(X1)
| app(cons(X1,nil),X2) != esk8_0
| cons(X1,nil) != esk7_0
| ~ ssList(X2)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(172,negated_conjecture,
ssList(esk10_0),
inference(rw,[status(thm)],[159,163,theory(equality)]) ).
cnf(173,negated_conjecture,
neq(esk10_0,nil),
inference(rw,[status(thm)],[165,163,theory(equality)]) ).
cnf(186,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[137,theory(equality)]) ).
cnf(199,plain,
( cons(X1,tl(cons(X1,X2))) = cons(X1,X2)
| nil = cons(X1,X2)
| ~ ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[127,94,theory(equality)]) ).
cnf(200,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(er,[status(thm)],[47,theory(equality)]) ).
cnf(201,plain,
( app(X1,nil) = nil
| nil != X1
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[200,142,theory(equality)]) ).
cnf(202,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[201,theory(equality)]) ).
cnf(231,plain,
( cons(X1,nil) = X2
| cons(X1,X3) != app(X2,X3)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[131,57,theory(equality)]) ).
cnf(242,plain,
( nil = app(X1,X2)
| ssList(app(tl(X1),X2))
| nil = X1
| ~ ssList(app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[71,35,theory(equality)]) ).
cnf(244,plain,
( tl(cons(X1,X2)) = app(tl(cons(X1,nil)),X2)
| nil = cons(X1,nil)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[35,57,theory(equality)]) ).
cnf(269,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[42,53,theory(equality)]) ).
cnf(271,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[53,64,theory(equality)]) ).
cnf(284,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[269,142,theory(equality)]) ).
cnf(285,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[284,theory(equality)]) ).
cnf(288,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[271,142,theory(equality)]) ).
cnf(289,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[288,theory(equality)]) ).
cnf(292,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[141,75,theory(equality)]) ).
cnf(294,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[83,75,theory(equality)]) ).
cnf(295,plain,
( app(cons(X1,X2),X3) != app(X2,X3)
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[146,75,theory(equality)]) ).
cnf(307,negated_conjecture,
( esk10_0 = X1
| tl(esk10_0) != X2
| app(esk7_0,X2) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk10_0)
| ~ neq(esk10_0,nil) ),
inference(rw,[status(thm)],[166,162,theory(equality)]) ).
cnf(308,negated_conjecture,
( esk10_0 = X1
| tl(esk10_0) != X2
| app(esk7_0,X2) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk10_0)
| $false ),
inference(rw,[status(thm)],[307,173,theory(equality)]) ).
cnf(309,negated_conjecture,
( esk10_0 = X1
| tl(esk10_0) != X2
| app(esk7_0,X2) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk10_0) ),
inference(cn,[status(thm)],[308,theory(equality)]) ).
cnf(310,negated_conjecture,
( esk10_0 = X1
| nil = esk10_0
| app(esk7_0,X2) != X1
| tl(esk10_0) != X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(esk10_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[309,136,theory(equality)]) ).
cnf(312,negated_conjecture,
( esk10_0 = X1
| nil = esk10_0
| app(esk7_0,X2) != X1
| tl(esk10_0) != X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(esk10_0)
| $false ),
inference(rw,[status(thm)],[310,142,theory(equality)]) ).
cnf(313,negated_conjecture,
( esk10_0 = X1
| nil = esk10_0
| app(esk7_0,X2) != X1
| tl(esk10_0) != X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(esk10_0) ),
inference(cn,[status(thm)],[312,theory(equality)]) ).
cnf(314,negated_conjecture,
( cons(X1,nil) != esk7_0
| app(cons(X1,nil),X2) != esk10_0
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ neq(esk10_0,nil) ),
inference(rw,[status(thm)],[168,163,theory(equality)]) ).
cnf(315,negated_conjecture,
( cons(X1,nil) != esk7_0
| app(cons(X1,nil),X2) != esk10_0
| ~ ssList(X2)
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[314,173,theory(equality)]) ).
cnf(316,negated_conjecture,
( cons(X1,nil) != esk7_0
| app(cons(X1,nil),X2) != esk10_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[315,theory(equality)]) ).
cnf(330,plain,
( app(nil,nil) = nil
| ~ ssList(nil) ),
inference(er,[status(thm)],[202,theory(equality)]) ).
cnf(331,plain,
( app(nil,nil) = nil
| $false ),
inference(rw,[status(thm)],[330,142,theory(equality)]) ).
cnf(332,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[331,theory(equality)]) ).
cnf(339,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[75,332,theory(equality)]) ).
cnf(353,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[339,142,theory(equality)]) ).
cnf(354,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[353,theory(equality)]) ).
cnf(425,plain,
( cons(X1,tl(cons(X1,X2))) = cons(X1,X2)
| cons(X1,X2) = nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[199,141]) ).
cnf(426,plain,
( cons(X1,tl(cons(X1,X2))) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[425,83]) ).
cnf(518,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[294,79]) ).
cnf(526,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[518,354,theory(equality)]) ).
cnf(531,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[526,142,theory(equality)]) ).
cnf(532,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[531,theory(equality)]) ).
cnf(580,plain,
( app(cons(X1,X2),X3) != app(X2,X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[295,79]) ).
cnf(583,plain,
( cons(X1,X2) != app(nil,X2)
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[580,57,theory(equality)]) ).
cnf(591,plain,
( cons(X1,X2) != app(nil,X2)
| ~ ssItem(X1)
| $false
| ~ ssList(X2) ),
inference(rw,[status(thm)],[583,142,theory(equality)]) ).
cnf(592,plain,
( cons(X1,X2) != app(nil,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[591,theory(equality)]) ).
cnf(621,plain,
( cons(X1,X2) != app(nil,tl(cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(tl(cons(X1,X2)))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[592,426,theory(equality)]) ).
cnf(795,plain,
( cons(hd(X1),nil) = X2
| nil = X1
| X1 != app(X2,tl(X1))
| ~ ssItem(hd(X1))
| ~ ssList(cons(hd(X1),nil))
| ~ ssList(X2)
| ~ ssList(tl(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[231,127,theory(equality)]) ).
cnf(888,plain,
( app(X1,X2) = nil
| nil = X1
| ssList(app(tl(X1),X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[242,79]) ).
cnf(889,plain,
( nil = X1
| ssList(app(tl(X1),X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[888,48]) ).
cnf(993,plain,
( app(tl(cons(X1,nil)),X2) = tl(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2) ),
inference(csr,[status(thm)],[244,532]) ).
cnf(994,plain,
( app(tl(cons(X1,nil)),X2) = tl(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[993,141,theory(equality)]) ).
cnf(996,plain,
( app(tl(cons(X1,nil)),X2) = tl(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[994,142,theory(equality)]) ).
cnf(997,plain,
( app(tl(cons(X1,nil)),X2) = tl(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[996,theory(equality)]) ).
cnf(1000,plain,
( ssList(tl(cons(X1,X2)))
| ~ ssList(X2)
| ~ ssList(tl(cons(X1,nil)))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[79,997,theory(equality)]) ).
cnf(1099,plain,
( ssList(tl(cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[1000,68,theory(equality)]) ).
cnf(1102,plain,
( ssList(tl(cons(X1,X2)))
| ~ ssItem(X1)
| $false
| ~ ssList(X2) ),
inference(rw,[status(thm)],[1099,142,theory(equality)]) ).
cnf(1103,plain,
( ssList(tl(cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[1102,theory(equality)]) ).
cnf(1964,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[285,79]) ).
cnf(1990,plain,
( app(nil,X1) = app(X1,nil)
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[289,1964,theory(equality)]) ).
cnf(2026,plain,
( app(nil,X1) = app(X1,nil)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[1990,142,theory(equality)]) ).
cnf(2027,plain,
( app(nil,X1) = app(X1,nil)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[2026,theory(equality)]) ).
cnf(2083,plain,
( tl(app(nil,X1)) = app(tl(X1),nil)
| nil = X1
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[35,2027,theory(equality)]) ).
cnf(2180,plain,
( tl(app(nil,X1)) = app(tl(X1),nil)
| nil = X1
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[2083,142,theory(equality)]) ).
cnf(2181,plain,
( tl(app(nil,X1)) = app(tl(X1),nil)
| nil = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[2180,theory(equality)]) ).
cnf(3808,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[292,79]) ).
cnf(3816,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[3808,354,theory(equality)]) ).
cnf(3837,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[3816,142,theory(equality)]) ).
cnf(3838,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[3837,theory(equality)]) ).
cnf(4703,negated_conjecture,
( esk10_0 = X1
| esk10_0 = nil
| app(esk7_0,X2) != X1
| tl(esk10_0) != X2
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[313,172,theory(equality)]) ).
cnf(4704,negated_conjecture,
( esk10_0 = X1
| esk10_0 = nil
| app(esk7_0,X2) != X1
| tl(esk10_0) != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[4703,theory(equality)]) ).
cnf(4705,negated_conjecture,
( esk10_0 = nil
| esk10_0 = X1
| app(esk7_0,tl(esk10_0)) != X1
| ~ ssList(tl(esk10_0))
| ~ ssList(X1) ),
inference(er,[status(thm)],[4704,theory(equality)]) ).
cnf(5863,negated_conjecture,
( esk10_0 = nil
| esk10_0 = X1
| app(esk7_0,tl(esk10_0)) != X1
| ~ ssList(X1)
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[4705,71,theory(equality)]) ).
cnf(5864,negated_conjecture,
( esk10_0 = nil
| esk10_0 = X1
| app(esk7_0,tl(esk10_0)) != X1
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[5863,172,theory(equality)]) ).
cnf(5865,negated_conjecture,
( esk10_0 = nil
| esk10_0 = X1
| app(esk7_0,tl(esk10_0)) != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[5864,theory(equality)]) ).
cnf(5866,negated_conjecture,
( esk10_0 = nil
| esk10_0 = app(esk7_0,tl(esk10_0))
| ~ ssList(app(esk7_0,tl(esk10_0))) ),
inference(er,[status(thm)],[5865,theory(equality)]) ).
cnf(6039,negated_conjecture,
( app(esk7_0,tl(esk10_0)) = esk10_0
| esk10_0 = nil
| ~ ssList(tl(esk10_0))
| ~ ssList(esk7_0) ),
inference(spm,[status(thm)],[5866,79,theory(equality)]) ).
cnf(6040,negated_conjecture,
( app(esk7_0,tl(esk10_0)) = esk10_0
| esk10_0 = nil
| ~ ssList(tl(esk10_0))
| $false ),
inference(rw,[status(thm)],[6039,158,theory(equality)]) ).
cnf(6041,negated_conjecture,
( app(esk7_0,tl(esk10_0)) = esk10_0
| esk10_0 = nil
| ~ ssList(tl(esk10_0)) ),
inference(cn,[status(thm)],[6040,theory(equality)]) ).
cnf(6042,negated_conjecture,
( app(esk7_0,tl(esk10_0)) = esk10_0
| esk10_0 = nil
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[6041,71,theory(equality)]) ).
cnf(6043,negated_conjecture,
( app(esk7_0,tl(esk10_0)) = esk10_0
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[6042,172,theory(equality)]) ).
cnf(6044,negated_conjecture,
( app(esk7_0,tl(esk10_0)) = esk10_0
| esk10_0 = nil ),
inference(cn,[status(thm)],[6043,theory(equality)]) ).
cnf(6058,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| esk10_0 = nil
| ~ ssList(tl(esk10_0))
| ~ ssList(esk7_0) ),
inference(spm,[status(thm)],[289,6044,theory(equality)]) ).
cnf(6101,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| esk10_0 = nil
| ~ ssList(tl(esk10_0))
| $false ),
inference(rw,[status(thm)],[6058,158,theory(equality)]) ).
cnf(6102,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| esk10_0 = nil
| ~ ssList(tl(esk10_0)) ),
inference(cn,[status(thm)],[6101,theory(equality)]) ).
cnf(6131,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| esk10_0 = nil
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[6102,71,theory(equality)]) ).
cnf(6132,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[6131,172,theory(equality)]) ).
cnf(6133,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| esk10_0 = nil ),
inference(cn,[status(thm)],[6132,theory(equality)]) ).
cnf(6174,negated_conjecture,
( tl(esk10_0) = app(tl(esk10_0),nil)
| nil = esk10_0
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[2181,6133,theory(equality)]) ).
cnf(6261,negated_conjecture,
( tl(esk10_0) = app(tl(esk10_0),nil)
| nil = esk10_0
| $false ),
inference(rw,[status(thm)],[6174,172,theory(equality)]) ).
cnf(6262,negated_conjecture,
( tl(esk10_0) = app(tl(esk10_0),nil)
| nil = esk10_0 ),
inference(cn,[status(thm)],[6261,theory(equality)]) ).
cnf(6591,negated_conjecture,
( nil = esk10_0
| ssList(tl(esk10_0))
| ~ ssList(nil)
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[889,6262,theory(equality)]) ).
cnf(6647,negated_conjecture,
( nil = esk10_0
| ssList(tl(esk10_0))
| $false
| ~ ssList(esk10_0) ),
inference(rw,[status(thm)],[6591,142,theory(equality)]) ).
cnf(6648,negated_conjecture,
( nil = esk10_0
| ssList(tl(esk10_0))
| $false
| $false ),
inference(rw,[status(thm)],[6647,172,theory(equality)]) ).
cnf(6649,negated_conjecture,
( nil = esk10_0
| ssList(tl(esk10_0)) ),
inference(cn,[status(thm)],[6648,theory(equality)]) ).
cnf(10981,plain,
( app(nil,tl(cons(X1,X2))) != cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[621,1103]) ).
cnf(20366,plain,
( cons(hd(X1),nil) = X2
| nil = X1
| app(X2,tl(X1)) != X1
| ~ ssItem(hd(X1))
| ~ ssList(cons(hd(X1),nil))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[795,71]) ).
cnf(20367,plain,
( cons(hd(X1),nil) = X2
| nil = X1
| app(X2,tl(X1)) != X1
| ~ ssItem(hd(X1))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[20366,3838]) ).
cnf(20368,plain,
( cons(hd(X1),nil) = X2
| nil = X1
| app(X2,tl(X1)) != X1
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[20367,97]) ).
cnf(20386,negated_conjecture,
( cons(hd(esk10_0),nil) = esk7_0
| nil = esk10_0
| ~ ssList(esk7_0)
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[20368,6044,theory(equality)]) ).
cnf(20402,negated_conjecture,
( cons(hd(esk10_0),nil) = esk7_0
| nil = esk10_0
| $false
| ~ ssList(esk10_0) ),
inference(rw,[status(thm)],[20386,158,theory(equality)]) ).
cnf(20403,negated_conjecture,
( cons(hd(esk10_0),nil) = esk7_0
| nil = esk10_0
| $false
| $false ),
inference(rw,[status(thm)],[20402,172,theory(equality)]) ).
cnf(20404,negated_conjecture,
( cons(hd(esk10_0),nil) = esk7_0
| nil = esk10_0 ),
inference(cn,[status(thm)],[20403,theory(equality)]) ).
cnf(20428,negated_conjecture,
( tl(esk7_0) = nil
| esk10_0 = nil
| ~ ssItem(hd(esk10_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[68,20404,theory(equality)]) ).
cnf(20431,negated_conjecture,
( hd(esk7_0) = hd(esk10_0)
| esk10_0 = nil
| ~ ssItem(hd(esk10_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[94,20404,theory(equality)]) ).
cnf(20437,negated_conjecture,
( esk10_0 = nil
| app(esk7_0,X1) != esk10_0
| ~ ssItem(hd(esk10_0))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[316,20404,theory(equality)]) ).
cnf(20497,negated_conjecture,
( esk10_0 = nil
| app(nil,tl(esk7_0)) != esk7_0
| ~ ssItem(hd(esk10_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[10981,20404,theory(equality)]) ).
cnf(20522,negated_conjecture,
( tl(esk7_0) = nil
| esk10_0 = nil
| ~ ssItem(hd(esk10_0))
| $false ),
inference(rw,[status(thm)],[20428,142,theory(equality)]) ).
cnf(20523,negated_conjecture,
( tl(esk7_0) = nil
| esk10_0 = nil
| ~ ssItem(hd(esk10_0)) ),
inference(cn,[status(thm)],[20522,theory(equality)]) ).
cnf(20528,negated_conjecture,
( hd(esk7_0) = hd(esk10_0)
| esk10_0 = nil
| ~ ssItem(hd(esk10_0))
| $false ),
inference(rw,[status(thm)],[20431,142,theory(equality)]) ).
cnf(20529,negated_conjecture,
( hd(esk7_0) = hd(esk10_0)
| esk10_0 = nil
| ~ ssItem(hd(esk10_0)) ),
inference(cn,[status(thm)],[20528,theory(equality)]) ).
cnf(20630,negated_conjecture,
( esk10_0 = nil
| app(nil,tl(esk7_0)) != esk7_0
| ~ ssItem(hd(esk10_0))
| $false ),
inference(rw,[status(thm)],[20497,142,theory(equality)]) ).
cnf(20631,negated_conjecture,
( esk10_0 = nil
| app(nil,tl(esk7_0)) != esk7_0
| ~ ssItem(hd(esk10_0)) ),
inference(cn,[status(thm)],[20630,theory(equality)]) ).
cnf(20783,negated_conjecture,
( tl(esk7_0) = nil
| esk10_0 = nil
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[20523,97,theory(equality)]) ).
cnf(20784,negated_conjecture,
( tl(esk7_0) = nil
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[20783,172,theory(equality)]) ).
cnf(20785,negated_conjecture,
( tl(esk7_0) = nil
| esk10_0 = nil ),
inference(cn,[status(thm)],[20784,theory(equality)]) ).
cnf(21647,negated_conjecture,
( esk10_0 = nil
| app(nil,tl(esk7_0)) != esk7_0
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[20631,97,theory(equality)]) ).
cnf(21648,negated_conjecture,
( esk10_0 = nil
| app(nil,tl(esk7_0)) != esk7_0
| $false ),
inference(rw,[status(thm)],[21647,172,theory(equality)]) ).
cnf(21649,negated_conjecture,
( esk10_0 = nil
| app(nil,tl(esk7_0)) != esk7_0 ),
inference(cn,[status(thm)],[21648,theory(equality)]) ).
cnf(21654,negated_conjecture,
( esk10_0 = nil
| app(nil,nil) != esk7_0 ),
inference(spm,[status(thm)],[21649,20785,theory(equality)]) ).
cnf(21657,negated_conjecture,
( esk10_0 = nil
| nil != esk7_0 ),
inference(rw,[status(thm)],[21654,332,theory(equality)]) ).
cnf(22737,negated_conjecture,
( hd(esk7_0) = hd(esk10_0)
| esk10_0 = nil
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[20529,97,theory(equality)]) ).
cnf(22738,negated_conjecture,
( hd(esk7_0) = hd(esk10_0)
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[22737,172,theory(equality)]) ).
cnf(22739,negated_conjecture,
( hd(esk7_0) = hd(esk10_0)
| esk10_0 = nil ),
inference(cn,[status(thm)],[22738,theory(equality)]) ).
cnf(22749,negated_conjecture,
( nil = esk7_0
| ssItem(hd(esk10_0))
| esk10_0 = nil
| ~ ssList(esk7_0) ),
inference(spm,[status(thm)],[97,22739,theory(equality)]) ).
cnf(22759,negated_conjecture,
( nil = esk7_0
| ssItem(hd(esk10_0))
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[22749,158,theory(equality)]) ).
cnf(22760,negated_conjecture,
( nil = esk7_0
| ssItem(hd(esk10_0))
| esk10_0 = nil ),
inference(cn,[status(thm)],[22759,theory(equality)]) ).
cnf(22775,negated_conjecture,
( esk10_0 = nil
| ssItem(hd(esk10_0)) ),
inference(csr,[status(thm)],[22760,21657]) ).
cnf(921402,negated_conjecture,
( esk10_0 = nil
| app(esk7_0,X1) != esk10_0
| ~ ssList(X1) ),
inference(csr,[status(thm)],[20437,22775]) ).
cnf(921407,negated_conjecture,
( esk10_0 = nil
| ~ ssList(tl(esk10_0)) ),
inference(spm,[status(thm)],[921402,6044,theory(equality)]) ).
cnf(921486,negated_conjecture,
esk10_0 = nil,
inference(csr,[status(thm)],[921407,6649]) ).
cnf(921489,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[173,921486,theory(equality)]) ).
cnf(923816,negated_conjecture,
~ ssList(nil),
inference(spm,[status(thm)],[186,921489,theory(equality)]) ).
cnf(923818,negated_conjecture,
$false,
inference(rw,[status(thm)],[923816,142,theory(equality)]) ).
cnf(923819,negated_conjecture,
$false,
inference(cn,[status(thm)],[923818,theory(equality)]) ).
cnf(923820,negated_conjecture,
$false,
923819,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC015+1.p
% --creating new selector for [SWC001+0.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpsLcjbr/sel_SWC015+1.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpsLcjbr/sel_SWC015+1.p_2 with time limit 81
% -prover status Theorem
% Problem SWC015+1.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC015+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC015+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
%
%------------------------------------------------------------------------------