%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC229+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 10:58:04 EST 2010
% Result : Theorem 0.90s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 14
% Syntax : Number of formulae : 141 ( 17 unt; 0 def)
% Number of atoms : 661 ( 168 equ)
% Maximal formula atoms : 35 ( 4 avg)
% Number of connectives : 898 ( 378 ~; 368 |; 108 &)
% ( 4 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 236 ( 0 sgn 132 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmpqgJvNA/sel_SWC229+1.p_1',ax83) ).
fof(3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/tmp/tmpqgJvNA/sel_SWC229+1.p_1',ax82) ).
fof(4,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpqgJvNA/sel_SWC229+1.p_1',ax81) ).
fof(7,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpqgJvNA/sel_SWC229+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/tmpqgJvNA/sel_SWC229+1.p_1',ax27) ).
fof(9,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpqgJvNA/sel_SWC229+1.p_1',ax26) ).
fof(16,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
file('/tmp/tmpqgJvNA/sel_SWC229+1.p_1',ax4) ).
fof(20,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/tmp/tmpqgJvNA/sel_SWC229+1.p_1',ax58) ).
fof(21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpqgJvNA/sel_SWC229+1.p_1',ax15) ).
fof(22,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpqgJvNA/sel_SWC229+1.p_1',ax16) ).
fof(23,axiom,
ssList(nil),
file('/tmp/tmpqgJvNA/sel_SWC229+1.p_1',ax17) ).
fof(26,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/tmp/tmpqgJvNA/sel_SWC229+1.p_1',ax38) ).
fof(27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X3) )
=> segmentP(X1,X3) ) ) ) ),
file('/tmp/tmpqgJvNA/sel_SWC229+1.p_1',ax53) ).
fof(35,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ segmentP(X4,X3)
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ leq(X5,X8)
| leq(X8,X5) ) ) ) ) )
| ( ~ singletonP(X3)
& neq(X4,nil) ) ) ) ) ) ),
file('/tmp/tmpqgJvNA/sel_SWC229+1.p_1',co1) ).
fof(36,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ segmentP(X4,X3)
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ leq(X5,X8)
| leq(X8,X5) ) ) ) ) )
| ( ~ singletonP(X3)
& neq(X4,nil) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[35]) ).
fof(38,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[26,theory(equality)]) ).
fof(39,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ segmentP(X4,X3)
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ leq(X5,X8)
| leq(X8,X5) ) ) ) ) )
| ( ~ singletonP(X3)
& neq(X4,nil) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[36,theory(equality)]) ).
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)],[2]) ).
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]) ).
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)],[3]) ).
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)],[4]) ).
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(66,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(67,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[66]) ).
cnf(68,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[67]) ).
fof(69,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(70,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)],[69]) ).
fof(71,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)],[70]) ).
cnf(72,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[71]) ).
fof(73,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(74,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[73]) ).
fof(75,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[74]) ).
cnf(76,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[75]) ).
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)],[16]) ).
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(esk9_1(X3))
& cons(esk9_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(esk9_1(X3))
& cons(esk9_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(esk9_1(X3))
| ~ singletonP(X3)
| ~ ssList(X3) )
& ( cons(esk9_1(X3),nil) = X3
| ~ singletonP(X3)
| ~ ssList(X3) ) ),
inference(distribute,[status(thm)],[115]) ).
cnf(117,plain,
( cons(esk9_1(X1),nil) = X1
| ~ ssList(X1)
| ~ singletonP(X1) ),
inference(split_conjunct,[status(thm)],[116]) ).
cnf(118,plain,
( ssItem(esk9_1(X1))
| ~ ssList(X1)
| ~ singletonP(X1) ),
inference(split_conjunct,[status(thm)],[116]) ).
fof(134,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(nil,X1)
| nil = X1 )
& ( nil != X1
| segmentP(nil,X1) ) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(135,plain,
! [X2] :
( ~ ssList(X2)
| ( ( ~ segmentP(nil,X2)
| nil = X2 )
& ( nil != X2
| segmentP(nil,X2) ) ) ),
inference(variable_rename,[status(thm)],[134]) ).
fof(136,plain,
! [X2] :
( ( ~ segmentP(nil,X2)
| nil = X2
| ~ ssList(X2) )
& ( nil != X2
| segmentP(nil,X2)
| ~ ssList(X2) ) ),
inference(distribute,[status(thm)],[135]) ).
cnf(137,plain,
( segmentP(nil,X1)
| ~ ssList(X1)
| nil != X1 ),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(138,plain,
( nil = X1
| ~ ssList(X1)
| ~ segmentP(nil,X1) ),
inference(split_conjunct,[status(thm)],[136]) ).
fof(139,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(140,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[139]) ).
fof(141,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[140]) ).
fof(142,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)],[141]) ).
cnf(143,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[142]) ).
fof(145,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(146,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[145]) ).
fof(147,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[146]) ).
cnf(148,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[147]) ).
cnf(149,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[23]) ).
fof(164,plain,
! [X1] :
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(fof_nnf,[status(thm)],[38]) ).
fof(165,plain,
! [X2] :
( ~ ssItem(X2)
| ~ memberP(nil,X2) ),
inference(variable_rename,[status(thm)],[164]) ).
cnf(166,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[165]) ).
fof(167,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X3)
| segmentP(X1,X3) ) ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(168,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ~ segmentP(X4,X5)
| ~ segmentP(X5,X6)
| segmentP(X4,X6) ) ) ),
inference(variable_rename,[status(thm)],[167]) ).
fof(169,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ~ segmentP(X4,X5)
| ~ segmentP(X5,X6)
| segmentP(X4,X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[168]) ).
cnf(170,plain,
( segmentP(X1,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[169]) ).
fof(198,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& segmentP(X4,X3)
& nil != X1
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssList(X7)
| app(app(X6,cons(X5,nil)),X7) != X1
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& memberP(X7,X8)
& leq(X5,X8)
& ~ leq(X8,X5) ) ) ) )
& ( singletonP(X3)
| ~ neq(X4,nil) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(199,negated_conjecture,
? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& X10 = X12
& X9 = X11
& segmentP(X12,X11)
& nil != X9
& ! [X13] :
( ~ ssItem(X13)
| ! [X14] :
( ~ ssList(X14)
| ! [X15] :
( ~ ssList(X15)
| app(app(X14,cons(X13,nil)),X15) != X9
| ? [X16] :
( ssItem(X16)
& memberP(X14,X16)
& memberP(X15,X16)
& leq(X13,X16)
& ~ leq(X16,X13) ) ) ) )
& ( singletonP(X11)
| ~ neq(X12,nil) ) ) ) ) ),
inference(variable_rename,[status(thm)],[198]) ).
fof(200,negated_conjecture,
( ssList(esk10_0)
& ssList(esk11_0)
& ssList(esk12_0)
& ssList(esk13_0)
& esk11_0 = esk13_0
& esk10_0 = esk12_0
& segmentP(esk13_0,esk12_0)
& nil != esk10_0
& ! [X13] :
( ~ ssItem(X13)
| ! [X14] :
( ~ ssList(X14)
| ! [X15] :
( ~ ssList(X15)
| app(app(X14,cons(X13,nil)),X15) != esk10_0
| ( ssItem(esk14_3(X13,X14,X15))
& memberP(X14,esk14_3(X13,X14,X15))
& memberP(X15,esk14_3(X13,X14,X15))
& leq(X13,esk14_3(X13,X14,X15))
& ~ leq(esk14_3(X13,X14,X15),X13) ) ) ) )
& ( singletonP(esk12_0)
| ~ neq(esk13_0,nil) ) ),
inference(skolemize,[status(esa)],[199]) ).
fof(201,negated_conjecture,
! [X13,X14,X15] :
( ( ~ ssList(X15)
| app(app(X14,cons(X13,nil)),X15) != esk10_0
| ( ssItem(esk14_3(X13,X14,X15))
& memberP(X14,esk14_3(X13,X14,X15))
& memberP(X15,esk14_3(X13,X14,X15))
& leq(X13,esk14_3(X13,X14,X15))
& ~ leq(esk14_3(X13,X14,X15),X13) )
| ~ ssList(X14)
| ~ ssItem(X13) )
& esk11_0 = esk13_0
& esk10_0 = esk12_0
& segmentP(esk13_0,esk12_0)
& nil != esk10_0
& ( singletonP(esk12_0)
| ~ neq(esk13_0,nil) )
& ssList(esk13_0)
& ssList(esk12_0)
& ssList(esk11_0)
& ssList(esk10_0) ),
inference(shift_quantors,[status(thm)],[200]) ).
fof(202,negated_conjecture,
! [X13,X14,X15] :
( ( ssItem(esk14_3(X13,X14,X15))
| ~ ssList(X15)
| app(app(X14,cons(X13,nil)),X15) != esk10_0
| ~ ssList(X14)
| ~ ssItem(X13) )
& ( memberP(X14,esk14_3(X13,X14,X15))
| ~ ssList(X15)
| app(app(X14,cons(X13,nil)),X15) != esk10_0
| ~ ssList(X14)
| ~ ssItem(X13) )
& ( memberP(X15,esk14_3(X13,X14,X15))
| ~ ssList(X15)
| app(app(X14,cons(X13,nil)),X15) != esk10_0
| ~ ssList(X14)
| ~ ssItem(X13) )
& ( leq(X13,esk14_3(X13,X14,X15))
| ~ ssList(X15)
| app(app(X14,cons(X13,nil)),X15) != esk10_0
| ~ ssList(X14)
| ~ ssItem(X13) )
& ( ~ leq(esk14_3(X13,X14,X15),X13)
| ~ ssList(X15)
| app(app(X14,cons(X13,nil)),X15) != esk10_0
| ~ ssList(X14)
| ~ ssItem(X13) )
& esk11_0 = esk13_0
& esk10_0 = esk12_0
& segmentP(esk13_0,esk12_0)
& nil != esk10_0
& ( singletonP(esk12_0)
| ~ neq(esk13_0,nil) )
& ssList(esk13_0)
& ssList(esk12_0)
& ssList(esk11_0)
& ssList(esk10_0) ),
inference(distribute,[status(thm)],[201]) ).
cnf(203,negated_conjecture,
ssList(esk10_0),
inference(split_conjunct,[status(thm)],[202]) ).
cnf(204,negated_conjecture,
ssList(esk11_0),
inference(split_conjunct,[status(thm)],[202]) ).
cnf(207,negated_conjecture,
( singletonP(esk12_0)
| ~ neq(esk13_0,nil) ),
inference(split_conjunct,[status(thm)],[202]) ).
cnf(208,negated_conjecture,
nil != esk10_0,
inference(split_conjunct,[status(thm)],[202]) ).
cnf(209,negated_conjecture,
segmentP(esk13_0,esk12_0),
inference(split_conjunct,[status(thm)],[202]) ).
cnf(210,negated_conjecture,
esk10_0 = esk12_0,
inference(split_conjunct,[status(thm)],[202]) ).
cnf(211,negated_conjecture,
esk11_0 = esk13_0,
inference(split_conjunct,[status(thm)],[202]) ).
cnf(214,negated_conjecture,
( memberP(X3,esk14_3(X1,X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk10_0
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[202]) ).
cnf(216,negated_conjecture,
( ssItem(esk14_3(X1,X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk10_0
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[202]) ).
cnf(217,negated_conjecture,
ssList(esk13_0),
inference(rw,[status(thm)],[204,211,theory(equality)]) ).
cnf(220,negated_conjecture,
segmentP(esk13_0,esk10_0),
inference(rw,[status(thm)],[209,210,theory(equality)]) ).
cnf(221,negated_conjecture,
( singletonP(esk10_0)
| ~ neq(esk13_0,nil) ),
inference(rw,[status(thm)],[207,210,theory(equality)]) ).
cnf(229,negated_conjecture,
( singletonP(esk10_0)
| esk13_0 = nil
| ~ ssList(nil)
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[221,143,theory(equality)]) ).
cnf(230,negated_conjecture,
( singletonP(esk10_0)
| esk13_0 = nil
| $false
| ~ ssList(esk13_0) ),
inference(rw,[status(thm)],[229,149,theory(equality)]) ).
cnf(231,negated_conjecture,
( singletonP(esk10_0)
| esk13_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[230,217,theory(equality)]) ).
cnf(232,negated_conjecture,
( singletonP(esk10_0)
| esk13_0 = nil ),
inference(cn,[status(thm)],[231,theory(equality)]) ).
cnf(339,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[53,68,theory(equality)]) ).
cnf(358,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[339,149,theory(equality)]) ).
cnf(359,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[358,theory(equality)]) ).
cnf(364,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[148,72,theory(equality)]) ).
cnf(385,negated_conjecture,
( segmentP(X1,esk10_0)
| ~ segmentP(X1,esk13_0)
| ~ ssList(esk10_0)
| ~ ssList(esk13_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[170,220,theory(equality)]) ).
cnf(389,negated_conjecture,
( segmentP(X1,esk10_0)
| ~ segmentP(X1,esk13_0)
| $false
| ~ ssList(esk13_0)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[385,203,theory(equality)]) ).
cnf(390,negated_conjecture,
( segmentP(X1,esk10_0)
| ~ segmentP(X1,esk13_0)
| $false
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[389,217,theory(equality)]) ).
cnf(391,negated_conjecture,
( segmentP(X1,esk10_0)
| ~ segmentP(X1,esk13_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[390,theory(equality)]) ).
cnf(408,negated_conjecture,
( ssItem(esk14_3(X1,nil,X2))
| app(cons(X1,nil),X2) != esk10_0
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(cons(X1,nil)) ),
inference(spm,[status(thm)],[216,68,theory(equality)]) ).
cnf(417,negated_conjecture,
( ssItem(esk14_3(X1,nil,X2))
| app(cons(X1,nil),X2) != esk10_0
| ~ ssItem(X1)
| ~ ssList(X2)
| $false
| ~ ssList(cons(X1,nil)) ),
inference(rw,[status(thm)],[408,149,theory(equality)]) ).
cnf(418,negated_conjecture,
( ssItem(esk14_3(X1,nil,X2))
| app(cons(X1,nil),X2) != esk10_0
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[417,theory(equality)]) ).
cnf(465,negated_conjecture,
( ~ ssItem(esk14_3(X1,X2,nil))
| app(app(X2,cons(X1,nil)),nil) != esk10_0
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[166,214,theory(equality)]) ).
cnf(468,negated_conjecture,
( ~ ssItem(esk14_3(X1,X2,nil))
| app(app(X2,cons(X1,nil)),nil) != esk10_0
| ~ ssItem(X1)
| $false
| ~ ssList(X2) ),
inference(rw,[status(thm)],[465,149,theory(equality)]) ).
cnf(469,negated_conjecture,
( ~ ssItem(esk14_3(X1,X2,nil))
| app(app(X2,cons(X1,nil)),nil) != esk10_0
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[468,theory(equality)]) ).
cnf(538,negated_conjecture,
( segmentP(nil,esk10_0)
| ~ ssList(nil)
| nil != esk13_0
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[391,137,theory(equality)]) ).
cnf(541,negated_conjecture,
( segmentP(nil,esk10_0)
| $false
| nil != esk13_0
| ~ ssList(esk13_0) ),
inference(rw,[status(thm)],[538,149,theory(equality)]) ).
cnf(542,negated_conjecture,
( segmentP(nil,esk10_0)
| $false
| nil != esk13_0
| $false ),
inference(rw,[status(thm)],[541,217,theory(equality)]) ).
cnf(543,negated_conjecture,
( segmentP(nil,esk10_0)
| nil != esk13_0 ),
inference(cn,[status(thm)],[542,theory(equality)]) ).
cnf(549,negated_conjecture,
( nil = esk10_0
| ~ ssList(esk10_0)
| esk13_0 != nil ),
inference(spm,[status(thm)],[138,543,theory(equality)]) ).
cnf(552,negated_conjecture,
( nil = esk10_0
| $false
| esk13_0 != nil ),
inference(rw,[status(thm)],[549,203,theory(equality)]) ).
cnf(553,negated_conjecture,
( nil = esk10_0
| esk13_0 != nil ),
inference(cn,[status(thm)],[552,theory(equality)]) ).
cnf(554,negated_conjecture,
esk13_0 != nil,
inference(sr,[status(thm)],[553,208,theory(equality)]) ).
cnf(562,negated_conjecture,
singletonP(esk10_0),
inference(sr,[status(thm)],[232,554,theory(equality)]) ).
cnf(632,plain,
( app(nil,nil) = nil
| ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| nil != X1 ),
inference(spm,[status(thm)],[359,47,theory(equality)]) ).
cnf(692,plain,
( app(nil,nil) = nil
| nil != X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[632,149,theory(equality)]) ).
cnf(702,plain,
app(nil,nil) = nil,
inference(spm,[status(thm)],[692,149,theory(equality)]) ).
cnf(720,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[72,702,theory(equality)]) ).
cnf(743,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[720,149,theory(equality)]) ).
cnf(744,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[743,theory(equality)]) ).
cnf(901,negated_conjecture,
( app(cons(X1,nil),nil) != esk10_0
| ~ ssItem(esk14_3(X1,nil,nil))
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(cons(X1,nil)) ),
inference(spm,[status(thm)],[469,68,theory(equality)]) ).
cnf(908,negated_conjecture,
( app(cons(X1,nil),nil) != esk10_0
| ~ ssItem(esk14_3(X1,nil,nil))
| ~ ssItem(X1)
| $false
| ~ ssList(cons(X1,nil)) ),
inference(rw,[status(thm)],[901,149,theory(equality)]) ).
cnf(909,negated_conjecture,
( app(cons(X1,nil),nil) != esk10_0
| ~ ssItem(esk14_3(X1,nil,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[908,theory(equality)]) ).
cnf(6214,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[364,76]) ).
cnf(6222,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[6214,744,theory(equality)]) ).
cnf(6242,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[6222,149,theory(equality)]) ).
cnf(6243,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[6242,theory(equality)]) ).
cnf(7943,negated_conjecture,
( ssItem(esk14_3(X1,nil,X2))
| app(cons(X1,nil),X2) != esk10_0
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[418,6243]) ).
cnf(7944,negated_conjecture,
( app(cons(X1,nil),nil) != esk10_0
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[909,7943,theory(equality)]) ).
cnf(7946,negated_conjecture,
( app(cons(X1,nil),nil) != esk10_0
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| $false ),
inference(rw,[status(thm)],[7944,149,theory(equality)]) ).
cnf(7947,negated_conjecture,
( app(cons(X1,nil),nil) != esk10_0
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[7946,theory(equality)]) ).
cnf(7950,negated_conjecture,
( app(cons(X1,nil),nil) != esk10_0
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[7947,6243]) ).
cnf(7954,negated_conjecture,
( cons(X1,nil) != esk10_0
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[7950,57,theory(equality)]) ).
cnf(7963,negated_conjecture,
( cons(X1,nil) != esk10_0
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[7954,149,theory(equality)]) ).
cnf(7964,negated_conjecture,
( cons(X1,nil) != esk10_0
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[7963,theory(equality)]) ).
cnf(7971,negated_conjecture,
( X1 != esk10_0
| ~ ssItem(esk9_1(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[7964,117,theory(equality)]) ).
cnf(15863,negated_conjecture,
( X1 != esk10_0
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[7971,118]) ).
cnf(15864,negated_conjecture,
~ ssList(esk10_0),
inference(spm,[status(thm)],[15863,562,theory(equality)]) ).
cnf(15866,negated_conjecture,
$false,
inference(rw,[status(thm)],[15864,203,theory(equality)]) ).
cnf(15867,negated_conjecture,
$false,
inference(cn,[status(thm)],[15866,theory(equality)]) ).
cnf(15868,negated_conjecture,
$false,
15867,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC229+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpqgJvNA/sel_SWC229+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC229+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC229+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC229+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
%
%------------------------------------------------------------------------------