TSTP Solution File: SWC108+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC108+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 10:17:57 EST 2010
% Result : Theorem 0.49s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 11
% Syntax : Number of formulae : 155 ( 14 unt; 0 def)
% Number of atoms : 681 ( 216 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 835 ( 309 ~; 396 |; 95 &)
% ( 4 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 169 ( 0 sgn 102 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmpSF08G9/sel_SWC108+1.p_1',ax84) ).
fof(2,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmpSF08G9/sel_SWC108+1.p_1',ax83) ).
fof(15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) ) ) ),
file('/tmp/tmpSF08G9/sel_SWC108+1.p_1',ax6) ).
fof(16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/tmp/tmpSF08G9/sel_SWC108+1.p_1',ax7) ).
fof(20,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/tmp/tmpSF08G9/sel_SWC108+1.p_1',ax58) ).
fof(23,axiom,
ssList(nil),
file('/tmp/tmpSF08G9/sel_SWC108+1.p_1',ax17) ).
fof(24,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( rearsegP(X1,X2)
=> rearsegP(app(X3,X1),X2) ) ) ) ),
file('/tmp/tmpSF08G9/sel_SWC108+1.p_1',ax50) ).
fof(25,axiom,
! [X1] :
( ssList(X1)
=> rearsegP(X1,nil) ),
file('/tmp/tmpSF08G9/sel_SWC108+1.p_1',ax51) ).
fof(30,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/tmpSF08G9/sel_SWC108+1.p_1',ax56) ).
fof(31,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/tmp/tmpSF08G9/sel_SWC108+1.p_1',ax57) ).
fof(33,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) )
| ( ( nil != X4
| nil != X3 )
& ( ~ neq(X3,nil)
| ~ rearsegP(X4,X3) ) ) ) ) ) ) ),
file('/tmp/tmpSF08G9/sel_SWC108+1.p_1',co1) ).
fof(34,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) )
| ( ( nil != X4
| nil != X3 )
& ( ~ neq(X3,nil)
| ~ rearsegP(X4,X3) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[33]) ).
fof(35,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) )
| ( ( nil != X4
| nil != X3 )
& ( ~ neq(X3,nil)
| ~ rearsegP(X4,X3) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[34,theory(equality)]) ).
fof(36,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(37,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[36]) ).
cnf(38,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[37]) ).
fof(39,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(40,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)],[39]) ).
fof(41,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)],[40]) ).
fof(42,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)],[41]) ).
cnf(45,plain,
( nil = X2
| ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[42]) ).
fof(98,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ rearsegP(X1,X2)
| ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) )
& ( ! [X3] :
( ~ ssList(X3)
| app(X3,X2) != X1 )
| rearsegP(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(99,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ( ( ~ rearsegP(X4,X5)
| ? [X6] :
( ssList(X6)
& app(X6,X5) = X4 ) )
& ( ! [X7] :
( ~ ssList(X7)
| app(X7,X5) != X4 )
| rearsegP(X4,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[98]) ).
fof(100,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ( ( ~ rearsegP(X4,X5)
| ( ssList(esk5_2(X4,X5))
& app(esk5_2(X4,X5),X5) = X4 ) )
& ( ! [X7] :
( ~ ssList(X7)
| app(X7,X5) != X4 )
| rearsegP(X4,X5) ) ) ) ),
inference(skolemize,[status(esa)],[99]) ).
fof(101,plain,
! [X4,X5,X7] :
( ( ( ~ ssList(X7)
| app(X7,X5) != X4
| rearsegP(X4,X5) )
& ( ~ rearsegP(X4,X5)
| ( ssList(esk5_2(X4,X5))
& app(esk5_2(X4,X5),X5) = X4 ) ) )
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[100]) ).
fof(102,plain,
! [X4,X5,X7] :
( ( ~ ssList(X7)
| app(X7,X5) != X4
| rearsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) )
& ( ssList(esk5_2(X4,X5))
| ~ rearsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) )
& ( app(esk5_2(X4,X5),X5) = X4
| ~ rearsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) ) ),
inference(distribute,[status(thm)],[101]) ).
cnf(103,plain,
( app(esk5_2(X1,X2),X2) = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[102]) ).
cnf(104,plain,
( ssList(esk5_2(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[102]) ).
fof(106,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)],[16]) ).
fof(107,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)],[106]) ).
fof(108,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ segmentP(X5,X6)
| ( ssList(esk6_2(X5,X6))
& ssList(esk7_2(X5,X6))
& app(app(esk6_2(X5,X6),X6),esk7_2(X5,X6)) = X5 ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X9,X6),X10) != X5 ) )
| segmentP(X5,X6) ) ) ) ),
inference(skolemize,[status(esa)],[107]) ).
fof(109,plain,
! [X5,X6,X9,X10] :
( ( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6) )
& ( ~ segmentP(X5,X6)
| ( ssList(esk6_2(X5,X6))
& ssList(esk7_2(X5,X6))
& app(app(esk6_2(X5,X6),X6),esk7_2(X5,X6)) = X5 ) ) )
| ~ ssList(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[108]) ).
fof(110,plain,
! [X5,X6,X9,X10] :
( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk6_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk7_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( app(app(esk6_2(X5,X6),X6),esk7_2(X5,X6)) = X5
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) ) ),
inference(distribute,[status(thm)],[109]) ).
cnf(114,plain,
( segmentP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[110]) ).
fof(126,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(nil,X1)
| nil = X1 )
& ( nil != X1
| segmentP(nil,X1) ) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(127,plain,
! [X2] :
( ~ ssList(X2)
| ( ( ~ segmentP(nil,X2)
| nil = X2 )
& ( nil != X2
| segmentP(nil,X2) ) ) ),
inference(variable_rename,[status(thm)],[126]) ).
fof(128,plain,
! [X2] :
( ( ~ segmentP(nil,X2)
| nil = X2
| ~ ssList(X2) )
& ( nil != X2
| segmentP(nil,X2)
| ~ ssList(X2) ) ),
inference(distribute,[status(thm)],[127]) ).
cnf(129,plain,
( segmentP(nil,X1)
| ~ ssList(X1)
| nil != X1 ),
inference(split_conjunct,[status(thm)],[128]) ).
cnf(141,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[23]) ).
fof(142,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ rearsegP(X1,X2)
| rearsegP(app(X3,X1),X2) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(143,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ~ rearsegP(X4,X5)
| rearsegP(app(X6,X4),X5) ) ) ),
inference(variable_rename,[status(thm)],[142]) ).
fof(144,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ~ rearsegP(X4,X5)
| rearsegP(app(X6,X4),X5)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[143]) ).
cnf(145,plain,
( rearsegP(app(X3,X1),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[144]) ).
fof(146,plain,
! [X1] :
( ~ ssList(X1)
| rearsegP(X1,nil) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(147,plain,
! [X2] :
( ~ ssList(X2)
| rearsegP(X2,nil) ),
inference(variable_rename,[status(thm)],[146]) ).
cnf(148,plain,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[147]) ).
fof(168,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)],[30]) ).
fof(169,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)],[168]) ).
fof(170,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)],[169]) ).
cnf(171,plain,
( segmentP(app(app(X3,X1),X4),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[170]) ).
fof(172,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(173,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,nil) ),
inference(variable_rename,[status(thm)],[172]) ).
cnf(174,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[173]) ).
fof(179,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ( ( nil = X2
& nil != X1 )
| ( neq(X2,nil)
& ( ~ neq(X1,nil)
| ~ segmentP(X2,X1) ) ) )
& ( ( nil = X4
& nil = X3 )
| ( neq(X3,nil)
& rearsegP(X4,X3) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[35]) ).
fof(180,negated_conjecture,
? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& X6 = X8
& X5 = X7
& ( ( nil = X6
& nil != X5 )
| ( neq(X6,nil)
& ( ~ neq(X5,nil)
| ~ segmentP(X6,X5) ) ) )
& ( ( nil = X8
& nil = X7 )
| ( neq(X7,nil)
& rearsegP(X8,X7) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[179]) ).
fof(181,negated_conjecture,
( ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& ssList(esk11_0)
& esk9_0 = esk11_0
& esk8_0 = esk10_0
& ( ( nil = esk9_0
& nil != esk8_0 )
| ( neq(esk9_0,nil)
& ( ~ neq(esk8_0,nil)
| ~ segmentP(esk9_0,esk8_0) ) ) )
& ( ( nil = esk11_0
& nil = esk10_0 )
| ( neq(esk10_0,nil)
& rearsegP(esk11_0,esk10_0) ) ) ),
inference(skolemize,[status(esa)],[180]) ).
fof(182,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)
| nil = esk9_0 )
& ( ~ neq(esk8_0,nil)
| ~ segmentP(esk9_0,esk8_0)
| nil = esk9_0 )
& ( neq(esk9_0,nil)
| nil != esk8_0 )
& ( ~ neq(esk8_0,nil)
| ~ segmentP(esk9_0,esk8_0)
| nil != esk8_0 )
& ( neq(esk10_0,nil)
| nil = esk11_0 )
& ( rearsegP(esk11_0,esk10_0)
| nil = esk11_0 )
& ( neq(esk10_0,nil)
| nil = esk10_0 )
& ( rearsegP(esk11_0,esk10_0)
| nil = esk10_0 ) ),
inference(distribute,[status(thm)],[181]) ).
cnf(183,negated_conjecture,
( nil = esk10_0
| rearsegP(esk11_0,esk10_0) ),
inference(split_conjunct,[status(thm)],[182]) ).
cnf(185,negated_conjecture,
( nil = esk11_0
| rearsegP(esk11_0,esk10_0) ),
inference(split_conjunct,[status(thm)],[182]) ).
cnf(186,negated_conjecture,
( nil = esk11_0
| neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[182]) ).
cnf(187,negated_conjecture,
( nil != esk8_0
| ~ segmentP(esk9_0,esk8_0)
| ~ neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[182]) ).
cnf(188,negated_conjecture,
( neq(esk9_0,nil)
| nil != esk8_0 ),
inference(split_conjunct,[status(thm)],[182]) ).
cnf(189,negated_conjecture,
( nil = esk9_0
| ~ segmentP(esk9_0,esk8_0)
| ~ neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[182]) ).
cnf(191,negated_conjecture,
esk8_0 = esk10_0,
inference(split_conjunct,[status(thm)],[182]) ).
cnf(192,negated_conjecture,
esk9_0 = esk11_0,
inference(split_conjunct,[status(thm)],[182]) ).
cnf(195,negated_conjecture,
ssList(esk9_0),
inference(split_conjunct,[status(thm)],[182]) ).
cnf(196,negated_conjecture,
ssList(esk8_0),
inference(split_conjunct,[status(thm)],[182]) ).
cnf(201,negated_conjecture,
( esk8_0 = nil
| rearsegP(esk11_0,esk10_0) ),
inference(rw,[status(thm)],[183,191,theory(equality)]) ).
cnf(202,negated_conjecture,
( esk8_0 = nil
| rearsegP(esk9_0,esk8_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[201,192,theory(equality)]),191,theory(equality)]) ).
cnf(205,negated_conjecture,
( esk9_0 = nil
| rearsegP(esk11_0,esk10_0) ),
inference(rw,[status(thm)],[185,192,theory(equality)]) ).
cnf(206,negated_conjecture,
( esk9_0 = nil
| rearsegP(esk9_0,esk8_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[205,192,theory(equality)]),191,theory(equality)]) ).
cnf(207,negated_conjecture,
( esk9_0 = nil
| neq(esk10_0,nil) ),
inference(rw,[status(thm)],[186,192,theory(equality)]) ).
cnf(208,negated_conjecture,
( esk9_0 = nil
| neq(esk8_0,nil) ),
inference(rw,[status(thm)],[207,191,theory(equality)]) ).
cnf(212,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(er,[status(thm)],[129,theory(equality)]) ).
cnf(213,plain,
( segmentP(nil,nil)
| $false ),
inference(rw,[status(thm)],[212,141,theory(equality)]) ).
cnf(214,plain,
segmentP(nil,nil),
inference(cn,[status(thm)],[213,theory(equality)]) ).
cnf(215,negated_conjecture,
( esk9_0 = nil
| ~ segmentP(esk9_0,esk8_0) ),
inference(csr,[status(thm)],[189,208]) ).
cnf(245,negated_conjecture,
( ssList(esk5_2(esk9_0,esk8_0))
| esk8_0 = nil
| ~ ssList(esk8_0)
| ~ ssList(esk9_0) ),
inference(spm,[status(thm)],[104,202,theory(equality)]) ).
cnf(246,negated_conjecture,
( ssList(esk5_2(esk9_0,esk8_0))
| esk9_0 = nil
| ~ ssList(esk8_0)
| ~ ssList(esk9_0) ),
inference(spm,[status(thm)],[104,206,theory(equality)]) ).
cnf(249,negated_conjecture,
( ssList(esk5_2(esk9_0,esk8_0))
| esk8_0 = nil
| $false
| ~ ssList(esk9_0) ),
inference(rw,[status(thm)],[245,196,theory(equality)]) ).
cnf(250,negated_conjecture,
( ssList(esk5_2(esk9_0,esk8_0))
| esk8_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[249,195,theory(equality)]) ).
cnf(251,negated_conjecture,
( ssList(esk5_2(esk9_0,esk8_0))
| esk8_0 = nil ),
inference(cn,[status(thm)],[250,theory(equality)]) ).
cnf(252,negated_conjecture,
( ssList(esk5_2(esk9_0,esk8_0))
| esk9_0 = nil
| $false
| ~ ssList(esk9_0) ),
inference(rw,[status(thm)],[246,196,theory(equality)]) ).
cnf(253,negated_conjecture,
( ssList(esk5_2(esk9_0,esk8_0))
| esk9_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[252,195,theory(equality)]) ).
cnf(254,negated_conjecture,
( ssList(esk5_2(esk9_0,esk8_0))
| esk9_0 = nil ),
inference(cn,[status(thm)],[253,theory(equality)]) ).
cnf(292,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[145,148,theory(equality)]) ).
cnf(296,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| $false
| ~ ssList(X2) ),
inference(rw,[status(thm)],[292,141,theory(equality)]) ).
cnf(297,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[296,theory(equality)]) ).
cnf(307,plain,
( app(esk5_2(X1,nil),nil) = X1
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[103,148,theory(equality)]) ).
cnf(309,negated_conjecture,
( app(esk5_2(esk9_0,esk8_0),esk8_0) = esk9_0
| esk8_0 = nil
| ~ ssList(esk8_0)
| ~ ssList(esk9_0) ),
inference(spm,[status(thm)],[103,202,theory(equality)]) ).
cnf(310,negated_conjecture,
( app(esk5_2(esk9_0,esk8_0),esk8_0) = esk9_0
| esk9_0 = nil
| ~ ssList(esk8_0)
| ~ ssList(esk9_0) ),
inference(spm,[status(thm)],[103,206,theory(equality)]) ).
cnf(311,plain,
( app(esk5_2(X1,nil),nil) = X1
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[307,141,theory(equality)]) ).
cnf(312,plain,
( app(esk5_2(X1,nil),nil) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[311,theory(equality)]) ).
cnf(313,negated_conjecture,
( app(esk5_2(esk9_0,esk8_0),esk8_0) = esk9_0
| esk8_0 = nil
| $false
| ~ ssList(esk9_0) ),
inference(rw,[status(thm)],[309,196,theory(equality)]) ).
cnf(314,negated_conjecture,
( app(esk5_2(esk9_0,esk8_0),esk8_0) = esk9_0
| esk8_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[313,195,theory(equality)]) ).
cnf(315,negated_conjecture,
( app(esk5_2(esk9_0,esk8_0),esk8_0) = esk9_0
| esk8_0 = nil ),
inference(cn,[status(thm)],[314,theory(equality)]) ).
cnf(316,negated_conjecture,
( app(esk5_2(esk9_0,esk8_0),esk8_0) = esk9_0
| esk9_0 = nil
| $false
| ~ ssList(esk9_0) ),
inference(rw,[status(thm)],[310,196,theory(equality)]) ).
cnf(317,negated_conjecture,
( app(esk5_2(esk9_0,esk8_0),esk8_0) = esk9_0
| esk9_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[316,195,theory(equality)]) ).
cnf(318,negated_conjecture,
( app(esk5_2(esk9_0,esk8_0),esk8_0) = esk9_0
| esk9_0 = nil ),
inference(cn,[status(thm)],[317,theory(equality)]) ).
cnf(445,plain,
( segmentP(app(app(X1,nil),X2),nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[171,214,theory(equality)]) ).
cnf(453,plain,
( segmentP(app(app(X1,nil),X2),nil)
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[445,141,theory(equality)]) ).
cnf(454,plain,
( segmentP(app(app(X1,nil),X2),nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[453,theory(equality)]) ).
cnf(620,negated_conjecture,
( nil = esk8_0
| esk9_0 != nil
| ~ ssList(esk8_0)
| ~ ssList(esk5_2(esk9_0,esk8_0)) ),
inference(spm,[status(thm)],[45,315,theory(equality)]) ).
cnf(627,negated_conjecture,
( segmentP(X1,esk8_0)
| esk8_0 = nil
| app(esk9_0,X2) != X1
| ~ ssList(X2)
| ~ ssList(esk5_2(esk9_0,esk8_0))
| ~ ssList(esk8_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[114,315,theory(equality)]) ).
cnf(634,negated_conjecture,
( nil = esk8_0
| esk9_0 != nil
| $false
| ~ ssList(esk5_2(esk9_0,esk8_0)) ),
inference(rw,[status(thm)],[620,196,theory(equality)]) ).
cnf(635,negated_conjecture,
( nil = esk8_0
| esk9_0 != nil
| ~ ssList(esk5_2(esk9_0,esk8_0)) ),
inference(cn,[status(thm)],[634,theory(equality)]) ).
cnf(648,negated_conjecture,
( segmentP(X1,esk8_0)
| esk8_0 = nil
| app(esk9_0,X2) != X1
| ~ ssList(X2)
| ~ ssList(esk5_2(esk9_0,esk8_0))
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[627,196,theory(equality)]) ).
cnf(649,negated_conjecture,
( segmentP(X1,esk8_0)
| esk8_0 = nil
| app(esk9_0,X2) != X1
| ~ ssList(X2)
| ~ ssList(esk5_2(esk9_0,esk8_0))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[648,theory(equality)]) ).
cnf(656,negated_conjecture,
( esk8_0 = nil
| esk9_0 != nil ),
inference(csr,[status(thm)],[635,251]) ).
cnf(765,negated_conjecture,
( rearsegP(esk9_0,nil)
| esk9_0 = nil
| ~ ssList(esk5_2(esk9_0,esk8_0))
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[297,318,theory(equality)]) ).
cnf(785,negated_conjecture,
( rearsegP(esk9_0,nil)
| esk9_0 = nil
| ~ ssList(esk5_2(esk9_0,esk8_0))
| $false ),
inference(rw,[status(thm)],[765,196,theory(equality)]) ).
cnf(786,negated_conjecture,
( rearsegP(esk9_0,nil)
| esk9_0 = nil
| ~ ssList(esk5_2(esk9_0,esk8_0)) ),
inference(cn,[status(thm)],[785,theory(equality)]) ).
cnf(921,negated_conjecture,
( esk9_0 = nil
| rearsegP(esk9_0,nil) ),
inference(csr,[status(thm)],[786,254]) ).
cnf(923,negated_conjecture,
( ssList(esk5_2(esk9_0,nil))
| esk9_0 = nil
| ~ ssList(nil)
| ~ ssList(esk9_0) ),
inference(spm,[status(thm)],[104,921,theory(equality)]) ).
cnf(926,negated_conjecture,
( app(esk5_2(esk9_0,nil),nil) = esk9_0
| esk9_0 = nil
| ~ ssList(nil)
| ~ ssList(esk9_0) ),
inference(spm,[status(thm)],[103,921,theory(equality)]) ).
cnf(930,negated_conjecture,
( ssList(esk5_2(esk9_0,nil))
| esk9_0 = nil
| $false
| ~ ssList(esk9_0) ),
inference(rw,[status(thm)],[923,141,theory(equality)]) ).
cnf(931,negated_conjecture,
( ssList(esk5_2(esk9_0,nil))
| esk9_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[930,195,theory(equality)]) ).
cnf(932,negated_conjecture,
( ssList(esk5_2(esk9_0,nil))
| esk9_0 = nil ),
inference(cn,[status(thm)],[931,theory(equality)]) ).
cnf(939,negated_conjecture,
( app(esk5_2(esk9_0,nil),nil) = esk9_0
| esk9_0 = nil
| $false
| ~ ssList(esk9_0) ),
inference(rw,[status(thm)],[926,141,theory(equality)]) ).
cnf(940,negated_conjecture,
( app(esk5_2(esk9_0,nil),nil) = esk9_0
| esk9_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[939,195,theory(equality)]) ).
cnf(941,negated_conjecture,
( app(esk5_2(esk9_0,nil),nil) = esk9_0
| esk9_0 = nil ),
inference(cn,[status(thm)],[940,theory(equality)]) ).
cnf(1214,negated_conjecture,
( esk9_0 = esk5_2(esk9_0,nil)
| esk9_0 = nil
| ~ ssList(esk5_2(esk9_0,nil)) ),
inference(spm,[status(thm)],[38,941,theory(equality)]) ).
cnf(1586,negated_conjecture,
( esk5_2(esk9_0,nil) = esk9_0
| esk9_0 = nil ),
inference(csr,[status(thm)],[1214,932]) ).
cnf(1590,negated_conjecture,
( app(esk9_0,nil) = esk9_0
| esk9_0 = nil
| ~ ssList(esk9_0) ),
inference(spm,[status(thm)],[312,1586,theory(equality)]) ).
cnf(1598,negated_conjecture,
( app(esk9_0,nil) = esk9_0
| esk9_0 = nil
| $false ),
inference(rw,[status(thm)],[1590,195,theory(equality)]) ).
cnf(1599,negated_conjecture,
( app(esk9_0,nil) = esk9_0
| esk9_0 = nil ),
inference(cn,[status(thm)],[1598,theory(equality)]) ).
cnf(1774,plain,
( segmentP(app(X1,X2),nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[454,38,theory(equality)]) ).
cnf(2000,negated_conjecture,
( segmentP(esk9_0,nil)
| esk9_0 = nil
| ~ ssList(nil)
| ~ ssList(esk9_0) ),
inference(spm,[status(thm)],[1774,1599,theory(equality)]) ).
cnf(2033,negated_conjecture,
( segmentP(esk9_0,nil)
| esk9_0 = nil
| $false
| ~ ssList(esk9_0) ),
inference(rw,[status(thm)],[2000,141,theory(equality)]) ).
cnf(2034,negated_conjecture,
( segmentP(esk9_0,nil)
| esk9_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[2033,195,theory(equality)]) ).
cnf(2035,negated_conjecture,
( segmentP(esk9_0,nil)
| esk9_0 = nil ),
inference(cn,[status(thm)],[2034,theory(equality)]) ).
cnf(7913,negated_conjecture,
( esk8_0 = nil
| segmentP(X1,esk8_0)
| app(esk9_0,X2) != X1
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[649,251]) ).
cnf(7915,negated_conjecture,
( esk8_0 = nil
| segmentP(X1,esk8_0)
| esk9_0 != X1
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(esk9_0) ),
inference(spm,[status(thm)],[7913,38,theory(equality)]) ).
cnf(7921,negated_conjecture,
( esk8_0 = nil
| segmentP(X1,esk8_0)
| esk9_0 != X1
| $false
| ~ ssList(X1)
| ~ ssList(esk9_0) ),
inference(rw,[status(thm)],[7915,141,theory(equality)]) ).
cnf(7922,negated_conjecture,
( esk8_0 = nil
| segmentP(X1,esk8_0)
| esk9_0 != X1
| $false
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[7921,195,theory(equality)]) ).
cnf(7923,negated_conjecture,
( esk8_0 = nil
| segmentP(X1,esk8_0)
| esk9_0 != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[7922,theory(equality)]) ).
cnf(7936,negated_conjecture,
( esk8_0 = nil
| segmentP(esk9_0,esk8_0)
| ~ ssList(esk9_0) ),
inference(er,[status(thm)],[7923,theory(equality)]) ).
cnf(7937,negated_conjecture,
( esk8_0 = nil
| segmentP(esk9_0,esk8_0)
| $false ),
inference(rw,[status(thm)],[7936,195,theory(equality)]) ).
cnf(7938,negated_conjecture,
( esk8_0 = nil
| segmentP(esk9_0,esk8_0) ),
inference(cn,[status(thm)],[7937,theory(equality)]) ).
cnf(7939,negated_conjecture,
( esk9_0 = nil
| esk8_0 = nil ),
inference(spm,[status(thm)],[215,7938,theory(equality)]) ).
cnf(7964,negated_conjecture,
esk8_0 = nil,
inference(csr,[status(thm)],[7939,656]) ).
cnf(8051,negated_conjecture,
( $false
| ~ segmentP(esk9_0,esk8_0)
| ~ neq(esk8_0,nil) ),
inference(rw,[status(thm)],[187,7964,theory(equality)]) ).
cnf(8052,negated_conjecture,
( $false
| ~ segmentP(esk9_0,nil)
| ~ neq(esk8_0,nil) ),
inference(rw,[status(thm)],[8051,7964,theory(equality)]) ).
cnf(8053,negated_conjecture,
( $false
| ~ segmentP(esk9_0,nil)
| ~ neq(nil,nil) ),
inference(rw,[status(thm)],[8052,7964,theory(equality)]) ).
cnf(8054,negated_conjecture,
( ~ segmentP(esk9_0,nil)
| ~ neq(nil,nil) ),
inference(cn,[status(thm)],[8053,theory(equality)]) ).
cnf(8055,negated_conjecture,
( esk9_0 = nil
| ~ segmentP(esk9_0,nil) ),
inference(rw,[status(thm)],[215,7964,theory(equality)]) ).
cnf(8056,negated_conjecture,
( neq(esk9_0,nil)
| $false ),
inference(rw,[status(thm)],[188,7964,theory(equality)]) ).
cnf(8057,negated_conjecture,
neq(esk9_0,nil),
inference(cn,[status(thm)],[8056,theory(equality)]) ).
cnf(8065,negated_conjecture,
( ~ neq(nil,nil)
| ~ ssList(esk9_0) ),
inference(spm,[status(thm)],[8054,174,theory(equality)]) ).
cnf(8067,negated_conjecture,
( ~ neq(nil,nil)
| $false ),
inference(rw,[status(thm)],[8065,195,theory(equality)]) ).
cnf(8068,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[8067,theory(equality)]) ).
cnf(8114,negated_conjecture,
esk9_0 = nil,
inference(csr,[status(thm)],[8055,2035]) ).
cnf(8115,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[8057,8114,theory(equality)]) ).
cnf(8116,negated_conjecture,
$false,
inference(sr,[status(thm)],[8115,8068,theory(equality)]) ).
cnf(8117,negated_conjecture,
$false,
8116,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC108+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpSF08G9/sel_SWC108+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC108+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC108+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC108+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
%
%------------------------------------------------------------------------------