%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC063+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 10:10:49 EST 2010
% Result : Theorem 0.51s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 14
% Syntax : Number of formulae : 171 ( 12 unt; 0 def)
% Number of atoms : 743 ( 229 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 958 ( 386 ~; 427 |; 105 &)
% ( 2 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 243 ( 0 sgn 136 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmp9MKRKd/sel_SWC063+1.p_1',ax84) ).
fof(3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/tmp/tmp9MKRKd/sel_SWC063+1.p_1',ax82) ).
fof(4,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmp9MKRKd/sel_SWC063+1.p_1',ax81) ).
fof(6,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmp9MKRKd/sel_SWC063+1.p_1',ax28) ).
fof(7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/tmp/tmp9MKRKd/sel_SWC063+1.p_1',ax27) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmp9MKRKd/sel_SWC063+1.p_1',ax26) ).
fof(9,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmp9MKRKd/sel_SWC063+1.p_1',ax21) ).
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/tmp/tmp9MKRKd/sel_SWC063+1.p_1',ax7) ).
fof(18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmp9MKRKd/sel_SWC063+1.p_1',ax15) ).
fof(19,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmp9MKRKd/sel_SWC063+1.p_1',ax16) ).
fof(20,axiom,
ssList(nil),
file('/tmp/tmp9MKRKd/sel_SWC063+1.p_1',ax17) ).
fof(23,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/tmp/tmp9MKRKd/sel_SWC063+1.p_1',ax55) ).
fof(24,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( segmentP(X1,X2)
=> segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
file('/tmp/tmp9MKRKd/sel_SWC063+1.p_1',ax56) ).
fof(26,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X3
| app(X6,cons(X5,nil)) != X4 ) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X7] :
( ssList(X7)
& neq(X7,nil)
& segmentP(X2,X7)
& segmentP(X1,X7) ) ) ) ) ) ) ),
file('/tmp/tmp9MKRKd/sel_SWC063+1.p_1',co1) ).
fof(27,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X3
| app(X6,cons(X5,nil)) != X4 ) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X7] :
( ssList(X7)
& neq(X7,nil)
& segmentP(X2,X7)
& segmentP(X1,X7) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[26]) ).
fof(28,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X3
| app(X6,cons(X5,nil)) != X4 ) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X7] :
( ssList(X7)
& neq(X7,nil)
& segmentP(X2,X7)
& segmentP(X1,X7) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[27,theory(equality)]) ).
fof(29,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(30,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[29]) ).
cnf(31,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[30]) ).
fof(39,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(40,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)],[39]) ).
fof(41,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)],[40]) ).
cnf(42,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(43,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(44,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[43]) ).
fof(45,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[44]) ).
cnf(46,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[45]) ).
fof(51,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(52,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[51]) ).
cnf(53,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[52]) ).
fof(54,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)],[7]) ).
fof(55,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)],[54]) ).
fof(56,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)],[55]) ).
cnf(57,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[56]) ).
fof(58,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(59,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[58]) ).
fof(60,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[59]) ).
cnf(61,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[60]) ).
fof(62,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| nil != cons(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(63,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3) ) ),
inference(variable_rename,[status(thm)],[62]) ).
fof(64,plain,
! [X3,X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[63]) ).
cnf(65,plain,
( ~ ssList(X1)
| nil != cons(X2,X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[64]) ).
fof(84,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ segmentP(X1,X2)
| ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) )
& ( ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| app(app(X3,X2),X4) != X1 ) )
| segmentP(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(85,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ segmentP(X5,X6)
| ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& app(app(X7,X6),X8) = X5 ) ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X9,X6),X10) != X5 ) )
| segmentP(X5,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[84]) ).
fof(86,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ segmentP(X5,X6)
| ( ssList(esk5_2(X5,X6))
& ssList(esk6_2(X5,X6))
& app(app(esk5_2(X5,X6),X6),esk6_2(X5,X6)) = X5 ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X9,X6),X10) != X5 ) )
| segmentP(X5,X6) ) ) ) ),
inference(skolemize,[status(esa)],[85]) ).
fof(87,plain,
! [X5,X6,X9,X10] :
( ( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6) )
& ( ~ segmentP(X5,X6)
| ( ssList(esk5_2(X5,X6))
& ssList(esk6_2(X5,X6))
& app(app(esk5_2(X5,X6),X6),esk6_2(X5,X6)) = X5 ) ) )
| ~ ssList(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[86]) ).
fof(88,plain,
! [X5,X6,X9,X10] :
( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk5_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk6_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( app(app(esk5_2(X5,X6),X6),esk6_2(X5,X6)) = X5
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) ) ),
inference(distribute,[status(thm)],[87]) ).
cnf(92,plain,
( segmentP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[88]) ).
fof(112,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(113,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[112]) ).
fof(114,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[113]) ).
fof(115,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)],[114]) ).
cnf(116,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[115]) ).
cnf(117,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[115]) ).
fof(118,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(119,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[118]) ).
fof(120,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[119]) ).
cnf(121,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[120]) ).
cnf(122,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[20]) ).
fof(131,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(132,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,X2) ),
inference(variable_rename,[status(thm)],[131]) ).
cnf(133,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[132]) ).
fof(134,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ~ segmentP(X1,X2)
| segmentP(app(app(X3,X1),X4),X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(135,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| ~ segmentP(X5,X6)
| segmentP(app(app(X7,X5),X8),X6) ) ) ) ),
inference(variable_rename,[status(thm)],[134]) ).
fof(136,plain,
! [X5,X6,X7,X8] :
( ~ ssList(X8)
| ~ segmentP(X5,X6)
| segmentP(app(app(X7,X5),X8),X6)
| ~ ssList(X7)
| ~ ssList(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[135]) ).
cnf(137,plain,
( segmentP(app(app(X3,X1),X4),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[136]) ).
fof(141,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ( nil = X3
| nil != X4 )
& ( ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X3
& app(X6,cons(X5,nil)) = X4 ) )
| ~ neq(X4,nil) )
& ( ( nil = X2
& nil != X1 )
| ( neq(X2,nil)
& ! [X7] :
( ~ ssList(X7)
| ~ neq(X7,nil)
| ~ segmentP(X2,X7)
| ~ segmentP(X1,X7) ) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(142,negated_conjecture,
? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& X9 = X11
& X8 = X10
& ( nil = X10
| nil != X11 )
& ( ? [X12] :
( ssItem(X12)
& ? [X13] :
( ssList(X13)
& app(cons(X12,nil),X13) = X10
& app(X13,cons(X12,nil)) = X11 ) )
| ~ neq(X11,nil) )
& ( ( nil = X9
& nil != X8 )
| ( neq(X9,nil)
& ! [X14] :
( ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(X9,X14)
| ~ segmentP(X8,X14) ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[141]) ).
fof(143,negated_conjecture,
( ssList(esk7_0)
& ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ( nil = esk9_0
| nil != esk10_0 )
& ( ( ssItem(esk11_0)
& ssList(esk12_0)
& app(cons(esk11_0,nil),esk12_0) = esk9_0
& app(esk12_0,cons(esk11_0,nil)) = esk10_0 )
| ~ neq(esk10_0,nil) )
& ( ( nil = esk8_0
& nil != esk7_0 )
| ( neq(esk8_0,nil)
& ! [X14] :
( ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(esk8_0,X14)
| ~ segmentP(esk7_0,X14) ) ) ) ),
inference(skolemize,[status(esa)],[142]) ).
fof(144,negated_conjecture,
! [X14] :
( ( ( ( ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(esk8_0,X14)
| ~ segmentP(esk7_0,X14) )
& neq(esk8_0,nil) )
| ( nil = esk8_0
& nil != esk7_0 ) )
& ssList(esk10_0)
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ( nil = esk9_0
| nil != esk10_0 )
& ( ( ssItem(esk11_0)
& ssList(esk12_0)
& app(cons(esk11_0,nil),esk12_0) = esk9_0
& app(esk12_0,cons(esk11_0,nil)) = esk10_0 )
| ~ neq(esk10_0,nil) )
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(shift_quantors,[status(thm)],[143]) ).
fof(145,negated_conjecture,
! [X14] :
( ( nil = esk8_0
| ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(esk8_0,X14)
| ~ segmentP(esk7_0,X14) )
& ( nil != esk7_0
| ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(esk8_0,X14)
| ~ segmentP(esk7_0,X14) )
& ( nil = esk8_0
| neq(esk8_0,nil) )
& ( nil != esk7_0
| neq(esk8_0,nil) )
& ssList(esk10_0)
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ( nil = esk9_0
| nil != esk10_0 )
& ( ssItem(esk11_0)
| ~ neq(esk10_0,nil) )
& ( ssList(esk12_0)
| ~ neq(esk10_0,nil) )
& ( app(cons(esk11_0,nil),esk12_0) = esk9_0
| ~ neq(esk10_0,nil) )
& ( app(esk12_0,cons(esk11_0,nil)) = esk10_0
| ~ neq(esk10_0,nil) )
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(distribute,[status(thm)],[144]) ).
cnf(146,negated_conjecture,
ssList(esk7_0),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(149,negated_conjecture,
( app(esk12_0,cons(esk11_0,nil)) = esk10_0
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(150,negated_conjecture,
( app(cons(esk11_0,nil),esk12_0) = esk9_0
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(151,negated_conjecture,
( ssList(esk12_0)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(152,negated_conjecture,
( ssItem(esk11_0)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(153,negated_conjecture,
( nil = esk9_0
| nil != esk10_0 ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(154,negated_conjecture,
esk7_0 = esk9_0,
inference(split_conjunct,[status(thm)],[145]) ).
cnf(155,negated_conjecture,
esk8_0 = esk10_0,
inference(split_conjunct,[status(thm)],[145]) ).
cnf(157,negated_conjecture,
( neq(esk8_0,nil)
| nil != esk7_0 ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(158,negated_conjecture,
( neq(esk8_0,nil)
| nil = esk8_0 ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(160,negated_conjecture,
( nil = esk8_0
| ~ segmentP(esk7_0,X1)
| ~ segmentP(esk8_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[145]) ).
cnf(164,negated_conjecture,
( esk7_0 = nil
| esk10_0 != nil ),
inference(rw,[status(thm)],[153,154,theory(equality)]) ).
cnf(165,negated_conjecture,
( esk10_0 = nil
| neq(esk8_0,nil) ),
inference(rw,[status(thm)],[158,155,theory(equality)]) ).
cnf(166,negated_conjecture,
( esk10_0 = nil
| neq(esk10_0,nil) ),
inference(rw,[status(thm)],[165,155,theory(equality)]) ).
cnf(167,negated_conjecture,
( ssList(esk12_0)
| esk10_0 = nil ),
inference(spm,[status(thm)],[151,166,theory(equality)]) ).
cnf(168,negated_conjecture,
( ssItem(esk11_0)
| esk10_0 = nil ),
inference(spm,[status(thm)],[152,166,theory(equality)]) ).
cnf(169,negated_conjecture,
( neq(esk10_0,nil)
| esk7_0 != nil ),
inference(rw,[status(thm)],[157,155,theory(equality)]) ).
cnf(173,negated_conjecture,
( app(esk12_0,cons(esk11_0,nil)) = esk10_0
| esk10_0 = nil ),
inference(spm,[status(thm)],[149,166,theory(equality)]) ).
cnf(174,negated_conjecture,
( app(cons(esk11_0,nil),esk12_0) = esk7_0
| ~ neq(esk10_0,nil) ),
inference(rw,[status(thm)],[150,154,theory(equality)]) ).
cnf(175,negated_conjecture,
( app(cons(esk11_0,nil),esk12_0) = esk7_0
| esk10_0 = nil ),
inference(spm,[status(thm)],[174,166,theory(equality)]) ).
cnf(204,negated_conjecture,
( esk10_0 = nil
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk7_0,X1)
| ~ segmentP(esk8_0,X1) ),
inference(rw,[status(thm)],[160,155,theory(equality)]) ).
cnf(205,negated_conjecture,
( esk10_0 = nil
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk7_0,X1)
| ~ segmentP(esk10_0,X1) ),
inference(rw,[status(thm)],[204,155,theory(equality)]) ).
cnf(207,negated_conjecture,
( esk10_0 = nil
| ~ segmentP(esk10_0,esk7_0)
| ~ neq(esk7_0,nil)
| ~ ssList(esk7_0) ),
inference(spm,[status(thm)],[205,133,theory(equality)]) ).
cnf(211,negated_conjecture,
( esk10_0 = nil
| ~ segmentP(esk10_0,esk7_0)
| ~ neq(esk7_0,nil)
| $false ),
inference(rw,[status(thm)],[207,146,theory(equality)]) ).
cnf(212,negated_conjecture,
( esk10_0 = nil
| ~ segmentP(esk10_0,esk7_0)
| ~ neq(esk7_0,nil) ),
inference(cn,[status(thm)],[211,theory(equality)]) ).
cnf(213,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[117,theory(equality)]) ).
cnf(278,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| ~ ssList(nil)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X3,X2)) ),
inference(spm,[status(thm)],[92,31,theory(equality)]) ).
cnf(283,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| $false
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X3,X2)) ),
inference(rw,[status(thm)],[278,122,theory(equality)]) ).
cnf(284,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X3,X2)) ),
inference(cn,[status(thm)],[283,theory(equality)]) ).
cnf(287,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[31,42,theory(equality)]) ).
cnf(289,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[42,53,theory(equality)]) ).
cnf(302,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[287,122,theory(equality)]) ).
cnf(303,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[302,theory(equality)]) ).
cnf(306,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[289,122,theory(equality)]) ).
cnf(307,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[306,theory(equality)]) ).
cnf(311,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[65,57,theory(equality)]) ).
cnf(324,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[137,133,theory(equality)]) ).
cnf(338,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[311,61]) ).
cnf(394,negated_conjecture,
( esk7_0 = cons(esk11_0,esk12_0)
| esk10_0 = nil
| ~ ssItem(esk11_0)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[46,175,theory(equality)]) ).
cnf(402,negated_conjecture,
( esk10_0 = nil
| esk7_0 != nil
| ~ ssItem(esk11_0)
| ~ ssList(nil)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[338,175,theory(equality)]) ).
cnf(405,negated_conjecture,
( esk10_0 = nil
| esk7_0 != nil
| ~ ssItem(esk11_0)
| $false
| ~ ssList(esk12_0) ),
inference(rw,[status(thm)],[402,122,theory(equality)]) ).
cnf(406,negated_conjecture,
( esk10_0 = nil
| esk7_0 != nil
| ~ ssItem(esk11_0)
| ~ ssList(esk12_0) ),
inference(cn,[status(thm)],[405,theory(equality)]) ).
cnf(409,negated_conjecture,
( esk10_0 = nil
| esk7_0 != nil
| ~ ssItem(esk11_0) ),
inference(csr,[status(thm)],[406,167]) ).
cnf(410,negated_conjecture,
( esk10_0 = nil
| esk7_0 != nil ),
inference(csr,[status(thm)],[409,168]) ).
cnf(437,negated_conjecture,
( cons(esk11_0,esk12_0) = esk7_0
| esk10_0 = nil
| ~ ssItem(esk11_0) ),
inference(csr,[status(thm)],[394,167]) ).
cnf(438,negated_conjecture,
( cons(esk11_0,esk12_0) = esk7_0
| esk10_0 = nil ),
inference(csr,[status(thm)],[437,168]) ).
cnf(1774,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[284,61]) ).
cnf(1782,negated_conjecture,
( segmentP(X1,esk12_0)
| esk10_0 = nil
| esk7_0 != X1
| ~ ssList(cons(esk11_0,nil))
| ~ ssList(esk12_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1774,175,theory(equality)]) ).
cnf(1877,negated_conjecture,
( esk10_0 = nil
| segmentP(X1,esk12_0)
| esk7_0 != X1
| ~ ssList(cons(esk11_0,nil))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[1782,167]) ).
cnf(1878,negated_conjecture,
( esk10_0 = nil
| segmentP(X1,esk12_0)
| esk7_0 != X1
| ~ ssList(X1)
| ~ ssItem(esk11_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1877,121,theory(equality)]) ).
cnf(1879,negated_conjecture,
( esk10_0 = nil
| segmentP(X1,esk12_0)
| esk7_0 != X1
| ~ ssList(X1)
| ~ ssItem(esk11_0)
| $false ),
inference(rw,[status(thm)],[1878,122,theory(equality)]) ).
cnf(1880,negated_conjecture,
( esk10_0 = nil
| segmentP(X1,esk12_0)
| esk7_0 != X1
| ~ ssList(X1)
| ~ ssItem(esk11_0) ),
inference(cn,[status(thm)],[1879,theory(equality)]) ).
cnf(1882,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[303,61]) ).
cnf(2098,negated_conjecture,
( esk10_0 = nil
| segmentP(X1,esk12_0)
| esk7_0 != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[1880,168]) ).
cnf(2099,negated_conjecture,
( esk10_0 = nil
| segmentP(esk7_0,esk12_0)
| ~ ssList(esk7_0) ),
inference(er,[status(thm)],[2098,theory(equality)]) ).
cnf(2100,negated_conjecture,
( esk10_0 = nil
| segmentP(esk7_0,esk12_0)
| $false ),
inference(rw,[status(thm)],[2099,146,theory(equality)]) ).
cnf(2101,negated_conjecture,
( esk10_0 = nil
| segmentP(esk7_0,esk12_0) ),
inference(cn,[status(thm)],[2100,theory(equality)]) ).
cnf(2102,negated_conjecture,
( esk10_0 = nil
| ~ segmentP(esk10_0,esk12_0)
| ~ neq(esk12_0,nil)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[205,2101,theory(equality)]) ).
cnf(2163,plain,
( app(X1,nil) = app(nil,X1)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1882,307,theory(equality)]) ).
cnf(2226,plain,
( app(X1,nil) = app(nil,X1)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[2163,122,theory(equality)]) ).
cnf(2227,plain,
( app(X1,nil) = app(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[2226,theory(equality)]) ).
cnf(2236,negated_conjecture,
( esk10_0 = nil
| ~ segmentP(esk10_0,esk12_0)
| ~ neq(esk12_0,nil) ),
inference(csr,[status(thm)],[2102,167]) ).
cnf(4368,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[324,53,theory(equality)]) ).
cnf(4406,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[4368,122,theory(equality)]) ).
cnf(4407,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[4406,theory(equality)]) ).
cnf(4843,negated_conjecture,
( segmentP(esk10_0,esk12_0)
| esk10_0 = nil
| ~ ssList(cons(esk11_0,nil))
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[4407,173,theory(equality)]) ).
cnf(4855,plain,
( segmentP(app(nil,X1),X1)
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[4407,2227,theory(equality)]) ).
cnf(4880,plain,
( segmentP(app(nil,X1),X1)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[4855,122,theory(equality)]) ).
cnf(4881,plain,
( segmentP(app(nil,X1),X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[4880,theory(equality)]) ).
cnf(4907,negated_conjecture,
( esk10_0 = nil
| segmentP(esk10_0,esk12_0)
| ~ ssList(cons(esk11_0,nil)) ),
inference(csr,[status(thm)],[4843,167]) ).
cnf(4908,negated_conjecture,
( esk10_0 = nil
| segmentP(esk10_0,esk12_0)
| ~ ssItem(esk11_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[4907,121,theory(equality)]) ).
cnf(4910,negated_conjecture,
( esk10_0 = nil
| segmentP(esk10_0,esk12_0)
| ~ ssItem(esk11_0)
| $false ),
inference(rw,[status(thm)],[4908,122,theory(equality)]) ).
cnf(4911,negated_conjecture,
( esk10_0 = nil
| segmentP(esk10_0,esk12_0)
| ~ ssItem(esk11_0) ),
inference(cn,[status(thm)],[4910,theory(equality)]) ).
cnf(4912,negated_conjecture,
( esk10_0 = nil
| segmentP(esk10_0,esk12_0) ),
inference(csr,[status(thm)],[4911,168]) ).
cnf(4919,negated_conjecture,
( esk10_0 = nil
| ~ neq(esk12_0,nil) ),
inference(spm,[status(thm)],[2236,4912,theory(equality)]) ).
cnf(4932,negated_conjecture,
( esk10_0 = nil
| esk12_0 = nil
| ~ ssList(nil)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[4919,116,theory(equality)]) ).
cnf(4934,negated_conjecture,
( esk10_0 = nil
| esk12_0 = nil
| $false
| ~ ssList(esk12_0) ),
inference(rw,[status(thm)],[4932,122,theory(equality)]) ).
cnf(4935,negated_conjecture,
( esk10_0 = nil
| esk12_0 = nil
| ~ ssList(esk12_0) ),
inference(cn,[status(thm)],[4934,theory(equality)]) ).
cnf(4994,negated_conjecture,
( esk10_0 = nil
| esk12_0 = nil ),
inference(csr,[status(thm)],[4935,167]) ).
cnf(5000,negated_conjecture,
( cons(esk11_0,nil) = esk7_0
| esk10_0 = nil ),
inference(spm,[status(thm)],[438,4994,theory(equality)]) ).
cnf(5090,negated_conjecture,
( app(esk12_0,esk7_0) = esk10_0
| esk10_0 = nil ),
inference(spm,[status(thm)],[173,5000,theory(equality)]) ).
cnf(5278,negated_conjecture,
( app(nil,esk7_0) = esk10_0
| esk10_0 = nil ),
inference(spm,[status(thm)],[5090,4994,theory(equality)]) ).
cnf(5600,negated_conjecture,
( segmentP(esk10_0,esk7_0)
| esk10_0 = nil
| ~ ssList(esk7_0) ),
inference(spm,[status(thm)],[4881,5278,theory(equality)]) ).
cnf(5725,negated_conjecture,
( segmentP(esk10_0,esk7_0)
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[5600,146,theory(equality)]) ).
cnf(5726,negated_conjecture,
( segmentP(esk10_0,esk7_0)
| esk10_0 = nil ),
inference(cn,[status(thm)],[5725,theory(equality)]) ).
cnf(5814,negated_conjecture,
( esk10_0 = nil
| ~ neq(esk7_0,nil) ),
inference(spm,[status(thm)],[212,5726,theory(equality)]) ).
cnf(5904,negated_conjecture,
( esk10_0 = nil
| esk7_0 = nil
| ~ ssList(nil)
| ~ ssList(esk7_0) ),
inference(spm,[status(thm)],[5814,116,theory(equality)]) ).
cnf(5907,negated_conjecture,
( esk10_0 = nil
| esk7_0 = nil
| $false
| ~ ssList(esk7_0) ),
inference(rw,[status(thm)],[5904,122,theory(equality)]) ).
cnf(5908,negated_conjecture,
( esk10_0 = nil
| esk7_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[5907,146,theory(equality)]) ).
cnf(5909,negated_conjecture,
( esk10_0 = nil
| esk7_0 = nil ),
inference(cn,[status(thm)],[5908,theory(equality)]) ).
cnf(5910,negated_conjecture,
esk10_0 = nil,
inference(csr,[status(thm)],[5909,410]) ).
cnf(6126,negated_conjecture,
( neq(nil,nil)
| esk7_0 != nil ),
inference(rw,[status(thm)],[169,5910,theory(equality)]) ).
cnf(6129,negated_conjecture,
( esk7_0 = nil
| $false ),
inference(rw,[status(thm)],[164,5910,theory(equality)]) ).
cnf(6130,negated_conjecture,
esk7_0 = nil,
inference(cn,[status(thm)],[6129,theory(equality)]) ).
cnf(6149,negated_conjecture,
( neq(nil,nil)
| $false ),
inference(rw,[status(thm)],[6126,6130,theory(equality)]) ).
cnf(6150,negated_conjecture,
neq(nil,nil),
inference(cn,[status(thm)],[6149,theory(equality)]) ).
cnf(6151,negated_conjecture,
~ ssList(nil),
inference(spm,[status(thm)],[213,6150,theory(equality)]) ).
cnf(6157,negated_conjecture,
$false,
inference(rw,[status(thm)],[6151,122,theory(equality)]) ).
cnf(6158,negated_conjecture,
$false,
inference(cn,[status(thm)],[6157,theory(equality)]) ).
cnf(6159,negated_conjecture,
$false,
6158,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC063+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmp9MKRKd/sel_SWC063+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC063+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC063+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC063+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
%
%------------------------------------------------------------------------------