%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC253+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 11:05:41 EST 2010
% Result : Theorem 0.61s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 16
% Syntax : Number of formulae : 184 ( 15 unt; 0 def)
% Number of atoms : 794 ( 332 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 991 ( 381 ~; 477 |; 89 &)
% ( 3 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 3 ( 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 : 235 ( 0 sgn 124 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/tmp/tmpky2VoO/sel_SWC253+1.p_1',ax86) ).
fof(3,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmpky2VoO/sel_SWC253+1.p_1',ax84) ).
fof(4,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmpky2VoO/sel_SWC253+1.p_1',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/tmpky2VoO/sel_SWC253+1.p_1',ax82) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpky2VoO/sel_SWC253+1.p_1',ax28) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/tmp/tmpky2VoO/sel_SWC253+1.p_1',ax24) ).
fof(12,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpky2VoO/sel_SWC253+1.p_1',ax26) ).
fof(16,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/tmp/tmpky2VoO/sel_SWC253+1.p_1',ax22) ).
fof(19,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
file('/tmp/tmpky2VoO/sel_SWC253+1.p_1',ax4) ).
fof(23,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/tmp/tmpky2VoO/sel_SWC253+1.p_1',ax78) ).
fof(24,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/tmp/tmpky2VoO/sel_SWC253+1.p_1',ax79) ).
fof(25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpky2VoO/sel_SWC253+1.p_1',ax15) ).
fof(26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpky2VoO/sel_SWC253+1.p_1',ax16) ).
fof(27,axiom,
ssList(nil),
file('/tmp/tmpky2VoO/sel_SWC253+1.p_1',ax17) ).
fof(29,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/tmp/tmpky2VoO/sel_SWC253+1.p_1',ax18) ).
fof(31,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X4 != X5
& ? [X6] :
( ssList(X6)
& tl(X4) = X6
& app(X3,X6) = X5
& neq(nil,X4) ) )
| singletonP(X1) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/tmp/tmpky2VoO/sel_SWC253+1.p_1',co1) ).
fof(32,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X4 != X5
& ? [X6] :
( ssList(X6)
& tl(X4) = X6
& app(X3,X6) = X5
& neq(nil,X4) ) )
| singletonP(X1) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[31]) ).
fof(34,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) ) )
| singletonP(X1) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[32,theory(equality)]) ).
fof(35,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(36,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| nil = X3
| tl(app(X3,X4)) = app(tl(X3),X4) ) ),
inference(variable_rename,[status(thm)],[35]) ).
fof(37,plain,
! [X3,X4] :
( ~ ssList(X4)
| nil = X3
| tl(app(X3,X4)) = app(tl(X3),X4)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[36]) ).
cnf(38,plain,
( tl(app(X1,X2)) = app(tl(X1),X2)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[37]) ).
fof(43,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(44,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[43]) ).
cnf(45,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[44]) ).
fof(46,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(47,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)],[46]) ).
fof(48,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)],[47]) ).
fof(49,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)],[48]) ).
cnf(51,plain,
( nil = X1
| ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[49]) ).
fof(53,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(54,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)],[53]) ).
fof(55,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)],[54]) ).
cnf(56,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[55]) ).
fof(65,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(66,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[65]) ).
cnf(67,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[66]) ).
fof(72,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(73,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| ssList(tl(X2)) ),
inference(variable_rename,[status(thm)],[72]) ).
cnf(74,plain,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[73]) ).
fof(79,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(80,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[79]) ).
fof(81,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[80]) ).
cnf(82,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[81]) ).
fof(98,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(99,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| ssItem(hd(X2)) ),
inference(variable_rename,[status(thm)],[98]) ).
cnf(100,plain,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[99]) ).
fof(112,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ singletonP(X1)
| ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) )
& ( ! [X2] :
( ~ ssItem(X2)
| cons(X2,nil) != X1 )
| singletonP(X1) ) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(113,plain,
! [X3] :
( ~ ssList(X3)
| ( ( ~ singletonP(X3)
| ? [X4] :
( ssItem(X4)
& cons(X4,nil) = X3 ) )
& ( ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X3 )
| singletonP(X3) ) ) ),
inference(variable_rename,[status(thm)],[112]) ).
fof(114,plain,
! [X3] :
( ~ ssList(X3)
| ( ( ~ singletonP(X3)
| ( ssItem(esk5_1(X3))
& cons(esk5_1(X3),nil) = X3 ) )
& ( ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X3 )
| singletonP(X3) ) ) ),
inference(skolemize,[status(esa)],[113]) ).
fof(115,plain,
! [X3,X5] :
( ( ( ~ ssItem(X5)
| cons(X5,nil) != X3
| singletonP(X3) )
& ( ~ singletonP(X3)
| ( ssItem(esk5_1(X3))
& cons(esk5_1(X3),nil) = X3 ) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[114]) ).
fof(116,plain,
! [X3,X5] :
( ( ~ ssItem(X5)
| cons(X5,nil) != X3
| singletonP(X3)
| ~ ssList(X3) )
& ( ssItem(esk5_1(X3))
| ~ singletonP(X3)
| ~ ssList(X3) )
& ( cons(esk5_1(X3),nil) = X3
| ~ singletonP(X3)
| ~ ssList(X3) ) ),
inference(distribute,[status(thm)],[115]) ).
cnf(119,plain,
( singletonP(X1)
| ~ ssList(X1)
| cons(X2,nil) != X1
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[116]) ).
fof(136,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(137,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| cons(hd(X2),tl(X2)) = X2 ),
inference(variable_rename,[status(thm)],[136]) ).
cnf(138,plain,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[137]) ).
fof(139,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X3,X2) != app(X1,X2)
| X3 = X1 ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(140,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(X6,X5) != app(X4,X5)
| X6 = X4 ) ) ),
inference(variable_rename,[status(thm)],[139]) ).
fof(141,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| app(X6,X5) != app(X4,X5)
| X6 = X4
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[140]) ).
cnf(142,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| app(X3,X2) != app(X1,X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[141]) ).
fof(143,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(144,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[143]) ).
fof(145,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[144]) ).
fof(146,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)],[145]) ).
cnf(147,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[146]) ).
cnf(148,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[146]) ).
fof(149,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(150,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[149]) ).
fof(151,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[150]) ).
cnf(152,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[151]) ).
cnf(153,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[27]) ).
fof(155,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) != X1 ) ),
inference(fof_nnf,[status(thm)],[29]) ).
fof(156,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) != X3 ) ),
inference(variable_rename,[status(thm)],[155]) ).
fof(157,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) != X3
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[156]) ).
cnf(158,plain,
( ~ ssList(X1)
| cons(X2,X1) != X1
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[157]) ).
fof(165,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) ) )
& ~ singletonP(X1) )
| ( neq(X2,nil)
& ~ neq(X4,nil) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(166,negated_conjecture,
? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& X8 = X10
& X7 = X9
& ( ( neq(X8,nil)
& ! [X11] :
( ~ ssList(X11)
| X10 = X11
| ! [X12] :
( ~ ssList(X12)
| tl(X10) != X12
| app(X9,X12) != X11
| ~ neq(nil,X10) ) )
& ~ singletonP(X7) )
| ( neq(X8,nil)
& ~ neq(X10,nil) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[165]) ).
fof(167,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)
| esk11_0 = X11
| ! [X12] :
( ~ ssList(X12)
| tl(esk11_0) != X12
| app(esk10_0,X12) != X11
| ~ neq(nil,esk11_0) ) )
& ~ singletonP(esk8_0) )
| ( neq(esk9_0,nil)
& ~ neq(esk11_0,nil) ) ) ),
inference(skolemize,[status(esa)],[166]) ).
fof(168,negated_conjecture,
! [X11,X12] :
( ( ( ( ~ ssList(X12)
| tl(esk11_0) != X12
| app(esk10_0,X12) != X11
| ~ neq(nil,esk11_0)
| ~ ssList(X11)
| esk11_0 = X11 )
& neq(esk9_0,nil)
& ~ singletonP(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)],[167]) ).
fof(169,negated_conjecture,
! [X11,X12] :
( ( neq(esk9_0,nil)
| ~ ssList(X12)
| tl(esk11_0) != X12
| app(esk10_0,X12) != X11
| ~ neq(nil,esk11_0)
| ~ ssList(X11)
| esk11_0 = X11 )
& ( ~ neq(esk11_0,nil)
| ~ ssList(X12)
| tl(esk11_0) != X12
| app(esk10_0,X12) != X11
| ~ neq(nil,esk11_0)
| ~ ssList(X11)
| esk11_0 = X11 )
& ( neq(esk9_0,nil)
| neq(esk9_0,nil) )
& ( ~ neq(esk11_0,nil)
| neq(esk9_0,nil) )
& ( neq(esk9_0,nil)
| ~ singletonP(esk8_0) )
& ( ~ neq(esk11_0,nil)
| ~ singletonP(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)],[168]) ).
cnf(170,negated_conjecture,
ssList(esk8_0),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(171,negated_conjecture,
ssList(esk9_0),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(174,negated_conjecture,
esk8_0 = esk10_0,
inference(split_conjunct,[status(thm)],[169]) ).
cnf(175,negated_conjecture,
esk9_0 = esk11_0,
inference(split_conjunct,[status(thm)],[169]) ).
cnf(176,negated_conjecture,
( ~ singletonP(esk8_0)
| ~ neq(esk11_0,nil) ),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(179,negated_conjecture,
( neq(esk9_0,nil)
| neq(esk9_0,nil) ),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(180,negated_conjecture,
( esk11_0 = X1
| ~ ssList(X1)
| ~ neq(nil,esk11_0)
| app(esk10_0,X2) != X1
| tl(esk11_0) != X2
| ~ ssList(X2)
| ~ neq(esk11_0,nil) ),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(184,negated_conjecture,
ssList(esk11_0),
inference(rw,[status(thm)],[171,175,theory(equality)]) ).
cnf(185,negated_conjecture,
neq(esk11_0,nil),
inference(rw,[status(thm)],[179,175,theory(equality)]) ).
cnf(187,negated_conjecture,
( ~ singletonP(esk8_0)
| $false ),
inference(rw,[status(thm)],[176,185,theory(equality)]) ).
cnf(188,negated_conjecture,
~ singletonP(esk8_0),
inference(cn,[status(thm)],[187,theory(equality)]) ).
cnf(205,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[148,theory(equality)]) ).
cnf(224,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(er,[status(thm)],[119,theory(equality)]) ).
cnf(227,plain,
( tl(X1) = app(tl(X1),nil)
| nil = X1
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[38,45,theory(equality)]) ).
cnf(228,plain,
( nil = app(X1,X2)
| ssList(app(tl(X1),X2))
| nil = X1
| ~ ssList(app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[74,38,theory(equality)]) ).
cnf(229,plain,
( tl(X1) = app(tl(X1),nil)
| nil = X1
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[227,153,theory(equality)]) ).
cnf(230,plain,
( tl(X1) = app(tl(X1),nil)
| nil = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[229,theory(equality)]) ).
cnf(233,plain,
( nil = X1
| X1 != tl(X1)
| ~ ssItem(hd(X1))
| ~ ssList(tl(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[158,138,theory(equality)]) ).
cnf(262,plain,
( nil = X1
| X2 != app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[142,67,theory(equality)]) ).
cnf(268,plain,
( nil = X1
| X2 != app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[262,153,theory(equality)]) ).
cnf(269,plain,
( nil = X1
| X2 != app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[268,theory(equality)]) ).
cnf(274,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[45,56,theory(equality)]) ).
cnf(276,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[56,67,theory(equality)]) ).
cnf(288,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[274,153,theory(equality)]) ).
cnf(289,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[288,theory(equality)]) ).
cnf(292,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[276,153,theory(equality)]) ).
cnf(293,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[292,theory(equality)]) ).
cnf(307,negated_conjecture,
( esk11_0 = X1
| tl(esk11_0) != X2
| app(esk8_0,X2) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk11_0)
| ~ neq(esk11_0,nil) ),
inference(rw,[status(thm)],[180,174,theory(equality)]) ).
cnf(308,negated_conjecture,
( esk11_0 = X1
| tl(esk11_0) != X2
| app(esk8_0,X2) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk11_0)
| $false ),
inference(rw,[status(thm)],[307,185,theory(equality)]) ).
cnf(309,negated_conjecture,
( esk11_0 = X1
| tl(esk11_0) != X2
| app(esk8_0,X2) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk11_0) ),
inference(cn,[status(thm)],[308,theory(equality)]) ).
cnf(310,negated_conjecture,
( esk11_0 = X1
| nil = esk11_0
| app(esk8_0,X2) != X1
| tl(esk11_0) != X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(esk11_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[309,147,theory(equality)]) ).
cnf(312,negated_conjecture,
( esk11_0 = X1
| nil = esk11_0
| app(esk8_0,X2) != X1
| tl(esk11_0) != X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(esk11_0)
| $false ),
inference(rw,[status(thm)],[310,153,theory(equality)]) ).
cnf(313,negated_conjecture,
( esk11_0 = X1
| nil = esk11_0
| app(esk8_0,X2) != X1
| tl(esk11_0) != X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(esk11_0) ),
inference(cn,[status(thm)],[312,theory(equality)]) ).
cnf(371,plain,
( nil = X1
| tl(X1) != X1
| ~ ssItem(hd(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[233,74]) ).
cnf(372,plain,
( nil = X1
| tl(X1) != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[371,100]) ).
cnf(473,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[224,152,theory(equality)]) ).
cnf(475,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[473,153,theory(equality)]) ).
cnf(476,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[475,theory(equality)]) ).
cnf(529,plain,
( app(X1,X2) = nil
| nil = X1
| ssList(app(tl(X1),X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[228,82]) ).
cnf(530,plain,
( nil = X1
| ssList(app(tl(X1),X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[529,51]) ).
cnf(1081,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[289,82]) ).
cnf(1116,plain,
( app(nil,X1) = app(X1,nil)
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[293,1081,theory(equality)]) ).
cnf(1140,plain,
( app(nil,X1) = app(X1,nil)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[1116,153,theory(equality)]) ).
cnf(1141,plain,
( app(nil,X1) = app(X1,nil)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1140,theory(equality)]) ).
cnf(1223,plain,
( tl(app(nil,X1)) = app(tl(X1),nil)
| nil = X1
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[38,1141,theory(equality)]) ).
cnf(1247,plain,
( app(nil,tl(X1)) = tl(X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(tl(X1)) ),
inference(spm,[status(thm)],[230,1141,theory(equality)]) ).
cnf(1304,plain,
( tl(app(nil,X1)) = app(tl(X1),nil)
| nil = X1
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[1223,153,theory(equality)]) ).
cnf(1305,plain,
( tl(app(nil,X1)) = app(tl(X1),nil)
| nil = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1304,theory(equality)]) ).
cnf(2777,negated_conjecture,
( esk11_0 = X1
| esk11_0 = nil
| app(esk8_0,X2) != X1
| tl(esk11_0) != X2
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[313,184,theory(equality)]) ).
cnf(2778,negated_conjecture,
( esk11_0 = X1
| esk11_0 = nil
| app(esk8_0,X2) != X1
| tl(esk11_0) != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[2777,theory(equality)]) ).
cnf(2779,negated_conjecture,
( esk11_0 = nil
| esk11_0 = X1
| app(esk8_0,tl(esk11_0)) != X1
| ~ ssList(tl(esk11_0))
| ~ ssList(X1) ),
inference(er,[status(thm)],[2778,theory(equality)]) ).
cnf(4551,plain,
( app(nil,tl(X1)) = tl(X1)
| nil = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[1247,74]) ).
cnf(5262,negated_conjecture,
( esk11_0 = nil
| esk11_0 = X1
| app(esk8_0,tl(esk11_0)) != X1
| ~ ssList(X1)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[2779,74,theory(equality)]) ).
cnf(5263,negated_conjecture,
( esk11_0 = nil
| esk11_0 = X1
| app(esk8_0,tl(esk11_0)) != X1
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[5262,184,theory(equality)]) ).
cnf(5264,negated_conjecture,
( esk11_0 = nil
| esk11_0 = X1
| app(esk8_0,tl(esk11_0)) != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[5263,theory(equality)]) ).
cnf(5365,negated_conjecture,
( esk11_0 = nil
| esk11_0 = app(esk8_0,tl(esk11_0))
| ~ ssList(app(esk8_0,tl(esk11_0))) ),
inference(er,[status(thm)],[5264,theory(equality)]) ).
cnf(5370,negated_conjecture,
( app(esk8_0,tl(esk11_0)) = esk11_0
| esk11_0 = nil
| ~ ssList(tl(esk11_0))
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[5365,82,theory(equality)]) ).
cnf(5372,negated_conjecture,
( app(esk8_0,tl(esk11_0)) = esk11_0
| esk11_0 = nil
| ~ ssList(tl(esk11_0))
| $false ),
inference(rw,[status(thm)],[5370,170,theory(equality)]) ).
cnf(5373,negated_conjecture,
( app(esk8_0,tl(esk11_0)) = esk11_0
| esk11_0 = nil
| ~ ssList(tl(esk11_0)) ),
inference(cn,[status(thm)],[5372,theory(equality)]) ).
cnf(5408,negated_conjecture,
( app(esk8_0,tl(esk11_0)) = esk11_0
| esk11_0 = nil
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[5373,74,theory(equality)]) ).
cnf(5409,negated_conjecture,
( app(esk8_0,tl(esk11_0)) = esk11_0
| esk11_0 = nil
| $false ),
inference(rw,[status(thm)],[5408,184,theory(equality)]) ).
cnf(5410,negated_conjecture,
( app(esk8_0,tl(esk11_0)) = esk11_0
| esk11_0 = nil ),
inference(cn,[status(thm)],[5409,theory(equality)]) ).
cnf(5414,negated_conjecture,
( tl(esk11_0) = app(tl(esk8_0),tl(esk11_0))
| nil = esk8_0
| esk11_0 = nil
| ~ ssList(tl(esk11_0))
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[38,5410,theory(equality)]) ).
cnf(5428,negated_conjecture,
( app(nil,esk11_0) = esk11_0
| esk11_0 = nil
| ~ ssList(tl(esk11_0))
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[293,5410,theory(equality)]) ).
cnf(5449,negated_conjecture,
( tl(esk11_0) = app(tl(esk8_0),tl(esk11_0))
| nil = esk8_0
| esk11_0 = nil
| ~ ssList(tl(esk11_0))
| $false ),
inference(rw,[status(thm)],[5414,170,theory(equality)]) ).
cnf(5450,negated_conjecture,
( tl(esk11_0) = app(tl(esk8_0),tl(esk11_0))
| nil = esk8_0
| esk11_0 = nil
| ~ ssList(tl(esk11_0)) ),
inference(cn,[status(thm)],[5449,theory(equality)]) ).
cnf(5477,negated_conjecture,
( app(nil,esk11_0) = esk11_0
| esk11_0 = nil
| ~ ssList(tl(esk11_0))
| $false ),
inference(rw,[status(thm)],[5428,170,theory(equality)]) ).
cnf(5478,negated_conjecture,
( app(nil,esk11_0) = esk11_0
| esk11_0 = nil
| ~ ssList(tl(esk11_0)) ),
inference(cn,[status(thm)],[5477,theory(equality)]) ).
cnf(5570,negated_conjecture,
( app(nil,esk11_0) = esk11_0
| esk11_0 = nil
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[5478,74,theory(equality)]) ).
cnf(5571,negated_conjecture,
( app(nil,esk11_0) = esk11_0
| esk11_0 = nil
| $false ),
inference(rw,[status(thm)],[5570,184,theory(equality)]) ).
cnf(5572,negated_conjecture,
( app(nil,esk11_0) = esk11_0
| esk11_0 = nil ),
inference(cn,[status(thm)],[5571,theory(equality)]) ).
cnf(5608,negated_conjecture,
( tl(esk11_0) = app(tl(esk11_0),nil)
| nil = esk11_0
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[1305,5572,theory(equality)]) ).
cnf(5708,negated_conjecture,
( tl(esk11_0) = app(tl(esk11_0),nil)
| nil = esk11_0
| $false ),
inference(rw,[status(thm)],[5608,184,theory(equality)]) ).
cnf(5709,negated_conjecture,
( tl(esk11_0) = app(tl(esk11_0),nil)
| nil = esk11_0 ),
inference(cn,[status(thm)],[5708,theory(equality)]) ).
cnf(5905,negated_conjecture,
( nil = esk11_0
| ssList(tl(esk11_0))
| ~ ssList(nil)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[530,5709,theory(equality)]) ).
cnf(5975,negated_conjecture,
( nil = esk11_0
| ssList(tl(esk11_0))
| $false
| ~ ssList(esk11_0) ),
inference(rw,[status(thm)],[5905,153,theory(equality)]) ).
cnf(5976,negated_conjecture,
( nil = esk11_0
| ssList(tl(esk11_0))
| $false
| $false ),
inference(rw,[status(thm)],[5975,184,theory(equality)]) ).
cnf(5977,negated_conjecture,
( nil = esk11_0
| ssList(tl(esk11_0)) ),
inference(cn,[status(thm)],[5976,theory(equality)]) ).
cnf(7046,negated_conjecture,
( app(tl(esk8_0),tl(esk11_0)) = tl(esk11_0)
| esk8_0 = nil
| esk11_0 = nil ),
inference(csr,[status(thm)],[5450,5977]) ).
cnf(7063,negated_conjecture,
( nil = tl(esk8_0)
| esk11_0 = nil
| esk8_0 = nil
| ~ ssList(tl(esk8_0))
| ~ ssList(tl(esk11_0)) ),
inference(spm,[status(thm)],[269,7046,theory(equality)]) ).
cnf(7122,negated_conjecture,
( tl(esk8_0) = nil
| esk11_0 = nil
| esk8_0 = nil
| ~ ssList(tl(esk8_0)) ),
inference(csr,[status(thm)],[7063,5977]) ).
cnf(7123,negated_conjecture,
( tl(esk8_0) = nil
| esk8_0 = nil
| esk11_0 = nil
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[7122,74,theory(equality)]) ).
cnf(7124,negated_conjecture,
( tl(esk8_0) = nil
| esk8_0 = nil
| esk11_0 = nil
| $false ),
inference(rw,[status(thm)],[7123,170,theory(equality)]) ).
cnf(7125,negated_conjecture,
( tl(esk8_0) = nil
| esk8_0 = nil
| esk11_0 = nil ),
inference(cn,[status(thm)],[7124,theory(equality)]) ).
cnf(7127,negated_conjecture,
( cons(hd(esk8_0),nil) = esk8_0
| nil = esk8_0
| esk11_0 = nil
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[138,7125,theory(equality)]) ).
cnf(7157,negated_conjecture,
( cons(hd(esk8_0),nil) = esk8_0
| nil = esk8_0
| esk11_0 = nil
| $false ),
inference(rw,[status(thm)],[7127,170,theory(equality)]) ).
cnf(7158,negated_conjecture,
( cons(hd(esk8_0),nil) = esk8_0
| nil = esk8_0
| esk11_0 = nil ),
inference(cn,[status(thm)],[7157,theory(equality)]) ).
cnf(7580,negated_conjecture,
( singletonP(esk8_0)
| esk11_0 = nil
| esk8_0 = nil
| ~ ssItem(hd(esk8_0)) ),
inference(spm,[status(thm)],[476,7158,theory(equality)]) ).
cnf(7636,negated_conjecture,
( esk11_0 = nil
| esk8_0 = nil
| ~ ssItem(hd(esk8_0)) ),
inference(sr,[status(thm)],[7580,188,theory(equality)]) ).
cnf(7773,negated_conjecture,
( esk8_0 = nil
| esk11_0 = nil
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[7636,100,theory(equality)]) ).
cnf(7775,negated_conjecture,
( esk8_0 = nil
| esk11_0 = nil
| $false ),
inference(rw,[status(thm)],[7773,170,theory(equality)]) ).
cnf(7776,negated_conjecture,
( esk8_0 = nil
| esk11_0 = nil ),
inference(cn,[status(thm)],[7775,theory(equality)]) ).
cnf(7782,negated_conjecture,
( app(nil,tl(esk11_0)) = esk11_0
| esk11_0 = nil ),
inference(spm,[status(thm)],[5410,7776,theory(equality)]) ).
cnf(7831,negated_conjecture,
( esk11_0 = tl(esk11_0)
| nil = esk11_0
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[4551,7782,theory(equality)]) ).
cnf(7909,negated_conjecture,
( esk11_0 = tl(esk11_0)
| nil = esk11_0
| $false ),
inference(rw,[status(thm)],[7831,184,theory(equality)]) ).
cnf(7910,negated_conjecture,
( esk11_0 = tl(esk11_0)
| nil = esk11_0 ),
inference(cn,[status(thm)],[7909,theory(equality)]) ).
cnf(7927,negated_conjecture,
( nil = esk11_0
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[372,7910,theory(equality)]) ).
cnf(7987,negated_conjecture,
( nil = esk11_0
| $false ),
inference(rw,[status(thm)],[7927,184,theory(equality)]) ).
cnf(7988,negated_conjecture,
nil = esk11_0,
inference(cn,[status(thm)],[7987,theory(equality)]) ).
cnf(8191,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[185,7988,theory(equality)]) ).
cnf(8318,negated_conjecture,
~ ssList(nil),
inference(spm,[status(thm)],[205,8191,theory(equality)]) ).
cnf(8320,negated_conjecture,
$false,
inference(rw,[status(thm)],[8318,153,theory(equality)]) ).
cnf(8321,negated_conjecture,
$false,
inference(cn,[status(thm)],[8320,theory(equality)]) ).
cnf(8322,negated_conjecture,
$false,
8321,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC253+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpky2VoO/sel_SWC253+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC253+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC253+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC253+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
%
%------------------------------------------------------------------------------