TSTP Solution File: SWC125+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC125+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 10:21:01 EST 2010
% Result : Theorem 191.63s
% Output : CNFRefutation 191.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 17
% Syntax : Number of formulae : 147 ( 19 unt; 0 def)
% Number of atoms : 681 ( 169 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 917 ( 383 ~; 385 |; 103 &)
% ( 4 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 237 ( 0 sgn 139 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmp2HxPwO/sel_SWC125+1.p_4',ax83) ).
fof(7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/tmp/tmp2HxPwO/sel_SWC125+1.p_4',ax82) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmp2HxPwO/sel_SWC125+1.p_4',ax81) ).
fof(11,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmp2HxPwO/sel_SWC125+1.p_4',ax28) ).
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/tmp/tmp2HxPwO/sel_SWC125+1.p_4',ax24) ).
fof(14,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/tmp/tmp2HxPwO/sel_SWC125+1.p_4',ax27) ).
fof(15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmp2HxPwO/sel_SWC125+1.p_4',ax26) ).
fof(16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmp2HxPwO/sel_SWC125+1.p_4',ax21) ).
fof(19,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/tmp/tmp2HxPwO/sel_SWC125+1.p_4',ax22) ).
fof(22,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/tmp/tmp2HxPwO/sel_SWC125+1.p_4',ax7) ).
fof(30,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( strictorderedP(cons(X1,X2))
<=> ( nil = X2
| ( nil != X2
& strictorderedP(X2)
& lt(X1,hd(X2)) ) ) ) ) ),
file('/tmp/tmp2HxPwO/sel_SWC125+1.p_4',ax70) ).
fof(37,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmp2HxPwO/sel_SWC125+1.p_4',ax16) ).
fof(38,axiom,
ssList(nil),
file('/tmp/tmp2HxPwO/sel_SWC125+1.p_4',ax17) ).
fof(39,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/tmp/tmp2HxPwO/sel_SWC125+1.p_4',ax78) ).
fof(45,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/tmp/tmp2HxPwO/sel_SWC125+1.p_4',ax57) ).
fof(46,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmp2HxPwO/sel_SWC125+1.p_4',ax15) ).
fof(49,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ~ segmentP(X4,X3)
| ~ strictorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& segmentP(X4,X5)
& segmentP(X5,X3)
& strictorderedP(X5) )
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) ) ) ) ),
file('/tmp/tmp2HxPwO/sel_SWC125+1.p_4',co1) ).
fof(50,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ~ segmentP(X4,X3)
| ~ strictorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& segmentP(X4,X5)
& segmentP(X5,X3)
& strictorderedP(X5) )
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[49]) ).
fof(53,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ~ segmentP(X4,X3)
| ~ strictorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& segmentP(X4,X5)
& segmentP(X5,X3)
& strictorderedP(X5) )
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[50,theory(equality)]) ).
fof(69,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)],[6]) ).
fof(70,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)],[69]) ).
fof(71,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)],[70]) ).
fof(72,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)],[71]) ).
cnf(73,plain,
( nil = app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| nil != X1
| nil != X2 ),
inference(split_conjunct,[status(thm)],[72]) ).
fof(76,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)],[7]) ).
fof(77,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)],[76]) ).
fof(78,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)],[77]) ).
cnf(79,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[78]) ).
fof(80,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(81,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[80]) ).
fof(82,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[81]) ).
cnf(83,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[82]) ).
fof(92,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(93,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[92]) ).
cnf(94,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[93]) ).
fof(99,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(100,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| ssList(tl(X2)) ),
inference(variable_rename,[status(thm)],[99]) ).
cnf(101,plain,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[100]) ).
fof(102,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)],[14]) ).
fof(103,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)],[102]) ).
fof(104,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)],[103]) ).
cnf(105,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[104]) ).
fof(106,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(107,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[106]) ).
fof(108,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[107]) ).
cnf(109,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[108]) ).
fof(110,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| nil != cons(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(111,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3) ) ),
inference(variable_rename,[status(thm)],[110]) ).
fof(112,plain,
! [X3,X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[111]) ).
cnf(113,plain,
( ~ ssList(X1)
| nil != cons(X2,X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[112]) ).
fof(125,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(126,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| ssItem(hd(X2)) ),
inference(variable_rename,[status(thm)],[125]) ).
cnf(127,plain,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[126]) ).
fof(139,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)],[22]) ).
fof(140,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)],[139]) ).
fof(141,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)],[140]) ).
fof(142,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)],[141]) ).
fof(143,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)],[142]) ).
cnf(147,plain,
( segmentP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[143]) ).
fof(185,plain,
! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ strictorderedP(cons(X1,X2))
| nil = X2
| ( nil != X2
& strictorderedP(X2)
& lt(X1,hd(X2)) ) )
& ( ( nil != X2
& ( nil = X2
| ~ strictorderedP(X2)
| ~ lt(X1,hd(X2)) ) )
| strictorderedP(cons(X1,X2)) ) ) ) ),
inference(fof_nnf,[status(thm)],[30]) ).
fof(186,plain,
! [X3] :
( ~ ssItem(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ strictorderedP(cons(X3,X4))
| nil = X4
| ( nil != X4
& strictorderedP(X4)
& lt(X3,hd(X4)) ) )
& ( ( nil != X4
& ( nil = X4
| ~ strictorderedP(X4)
| ~ lt(X3,hd(X4)) ) )
| strictorderedP(cons(X3,X4)) ) ) ) ),
inference(variable_rename,[status(thm)],[185]) ).
fof(187,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ strictorderedP(cons(X3,X4))
| nil = X4
| ( nil != X4
& strictorderedP(X4)
& lt(X3,hd(X4)) ) )
& ( ( nil != X4
& ( nil = X4
| ~ strictorderedP(X4)
| ~ lt(X3,hd(X4)) ) )
| strictorderedP(cons(X3,X4)) ) )
| ~ ssItem(X3) ),
inference(shift_quantors,[status(thm)],[186]) ).
fof(188,plain,
! [X3,X4] :
( ( nil != X4
| nil = X4
| ~ strictorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) )
& ( strictorderedP(X4)
| nil = X4
| ~ strictorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) )
& ( lt(X3,hd(X4))
| nil = X4
| ~ strictorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) )
& ( nil != X4
| strictorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) )
& ( nil = X4
| ~ strictorderedP(X4)
| ~ lt(X3,hd(X4))
| strictorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) ) ),
inference(distribute,[status(thm)],[187]) ).
cnf(190,plain,
( strictorderedP(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2)
| nil != X2 ),
inference(split_conjunct,[status(thm)],[188]) ).
fof(218,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[37]) ).
fof(219,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[218]) ).
fof(220,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[219]) ).
cnf(221,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[220]) ).
cnf(222,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[38]) ).
fof(223,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(224,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| cons(hd(X2),tl(X2)) = X2 ),
inference(variable_rename,[status(thm)],[223]) ).
cnf(225,plain,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[224]) ).
fof(254,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(fof_nnf,[status(thm)],[45]) ).
fof(255,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,nil) ),
inference(variable_rename,[status(thm)],[254]) ).
cnf(256,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[255]) ).
fof(257,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[46]) ).
fof(258,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[257]) ).
fof(259,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[258]) ).
fof(260,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)],[259]) ).
cnf(261,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[260]) ).
fof(270,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& neq(X2,nil)
& segmentP(X4,X3)
& strictorderedP(X3)
& ! [X5] :
( ~ ssList(X5)
| ~ neq(X3,X5)
| ~ segmentP(X4,X5)
| ~ segmentP(X5,X3)
| ~ strictorderedP(X5) )
& ( ~ neq(X1,nil)
| ~ segmentP(X2,X1) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[53]) ).
fof(271,negated_conjecture,
? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& X7 = X9
& X6 = X8
& neq(X7,nil)
& segmentP(X9,X8)
& strictorderedP(X8)
& ! [X10] :
( ~ ssList(X10)
| ~ neq(X8,X10)
| ~ segmentP(X9,X10)
| ~ segmentP(X10,X8)
| ~ strictorderedP(X10) )
& ( ~ neq(X6,nil)
| ~ segmentP(X7,X6) ) ) ) ) ),
inference(variable_rename,[status(thm)],[270]) ).
fof(272,negated_conjecture,
( ssList(esk14_0)
& ssList(esk15_0)
& ssList(esk16_0)
& ssList(esk17_0)
& esk15_0 = esk17_0
& esk14_0 = esk16_0
& neq(esk15_0,nil)
& segmentP(esk17_0,esk16_0)
& strictorderedP(esk16_0)
& ! [X10] :
( ~ ssList(X10)
| ~ neq(esk16_0,X10)
| ~ segmentP(esk17_0,X10)
| ~ segmentP(X10,esk16_0)
| ~ strictorderedP(X10) )
& ( ~ neq(esk14_0,nil)
| ~ segmentP(esk15_0,esk14_0) ) ),
inference(skolemize,[status(esa)],[271]) ).
fof(273,negated_conjecture,
! [X10] :
( ( ~ ssList(X10)
| ~ neq(esk16_0,X10)
| ~ segmentP(esk17_0,X10)
| ~ segmentP(X10,esk16_0)
| ~ strictorderedP(X10) )
& esk15_0 = esk17_0
& esk14_0 = esk16_0
& neq(esk15_0,nil)
& segmentP(esk17_0,esk16_0)
& strictorderedP(esk16_0)
& ( ~ neq(esk14_0,nil)
| ~ segmentP(esk15_0,esk14_0) )
& ssList(esk17_0)
& ssList(esk16_0)
& ssList(esk15_0)
& ssList(esk14_0) ),
inference(shift_quantors,[status(thm)],[272]) ).
cnf(274,negated_conjecture,
ssList(esk14_0),
inference(split_conjunct,[status(thm)],[273]) ).
cnf(275,negated_conjecture,
ssList(esk15_0),
inference(split_conjunct,[status(thm)],[273]) ).
cnf(278,negated_conjecture,
( ~ segmentP(esk15_0,esk14_0)
| ~ neq(esk14_0,nil) ),
inference(split_conjunct,[status(thm)],[273]) ).
cnf(280,negated_conjecture,
segmentP(esk17_0,esk16_0),
inference(split_conjunct,[status(thm)],[273]) ).
cnf(281,negated_conjecture,
neq(esk15_0,nil),
inference(split_conjunct,[status(thm)],[273]) ).
cnf(282,negated_conjecture,
esk14_0 = esk16_0,
inference(split_conjunct,[status(thm)],[273]) ).
cnf(283,negated_conjecture,
esk15_0 = esk17_0,
inference(split_conjunct,[status(thm)],[273]) ).
cnf(284,negated_conjecture,
( ~ strictorderedP(X1)
| ~ segmentP(X1,esk16_0)
| ~ segmentP(esk17_0,X1)
| ~ neq(esk16_0,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[273]) ).
cnf(285,negated_conjecture,
ssList(esk16_0),
inference(rw,[status(thm)],[274,282,theory(equality)]) ).
cnf(286,negated_conjecture,
ssList(esk17_0),
inference(rw,[status(thm)],[275,283,theory(equality)]) ).
cnf(287,negated_conjecture,
neq(esk17_0,nil),
inference(rw,[status(thm)],[281,283,theory(equality)]) ).
cnf(288,negated_conjecture,
( ~ neq(esk16_0,nil)
| ~ segmentP(esk15_0,esk14_0) ),
inference(rw,[status(thm)],[278,282,theory(equality)]) ).
cnf(289,negated_conjecture,
( ~ neq(esk16_0,nil)
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[288,283,theory(equality)]),282,theory(equality)]),280,theory(equality)]) ).
cnf(290,negated_conjecture,
~ neq(esk16_0,nil),
inference(cn,[status(thm)],[289,theory(equality)]) ).
cnf(293,negated_conjecture,
( esk16_0 = nil
| ~ ssList(nil)
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[290,261,theory(equality)]) ).
cnf(294,negated_conjecture,
( esk16_0 = nil
| $false
| ~ ssList(esk16_0) ),
inference(rw,[status(thm)],[293,222,theory(equality)]) ).
cnf(295,negated_conjecture,
( esk16_0 = nil
| ~ ssList(esk16_0) ),
inference(cn,[status(thm)],[294,theory(equality)]) ).
cnf(396,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[147,94,theory(equality)]) ).
cnf(403,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[396,222,theory(equality)]) ).
cnf(404,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[403,theory(equality)]) ).
cnf(446,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[79,94,theory(equality)]) ).
cnf(469,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[446,222,theory(equality)]) ).
cnf(470,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[469,theory(equality)]) ).
cnf(511,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssList(app(X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[221,105,theory(equality)]) ).
cnf(571,negated_conjecture,
( esk16_0 = nil
| $false ),
inference(rw,[status(thm)],[295,285,theory(equality)]) ).
cnf(572,negated_conjecture,
esk16_0 = nil,
inference(cn,[status(thm)],[571,theory(equality)]) ).
cnf(580,negated_conjecture,
~ neq(nil,nil),
inference(rw,[status(thm)],[290,572,theory(equality)]) ).
cnf(581,negated_conjecture,
( ~ segmentP(X1,nil)
| ~ segmentP(esk17_0,X1)
| ~ neq(esk16_0,X1)
| ~ ssList(X1)
| ~ strictorderedP(X1) ),
inference(rw,[status(thm)],[284,572,theory(equality)]) ).
cnf(582,negated_conjecture,
( ~ segmentP(X1,nil)
| ~ segmentP(esk17_0,X1)
| ~ neq(nil,X1)
| ~ ssList(X1)
| ~ strictorderedP(X1) ),
inference(rw,[status(thm)],[581,572,theory(equality)]) ).
cnf(603,negated_conjecture,
( ~ segmentP(esk17_0,X1)
| ~ neq(nil,X1)
| ~ ssList(X1)
| ~ strictorderedP(X1) ),
inference(csr,[status(thm)],[582,256]) ).
cnf(604,negated_conjecture,
( nil = X1
| ~ segmentP(esk17_0,X1)
| ~ ssList(X1)
| ~ strictorderedP(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[603,261,theory(equality)]) ).
cnf(606,negated_conjecture,
( nil = X1
| ~ segmentP(esk17_0,X1)
| ~ ssList(X1)
| ~ strictorderedP(X1)
| $false ),
inference(rw,[status(thm)],[604,222,theory(equality)]) ).
cnf(607,negated_conjecture,
( nil = X1
| ~ segmentP(esk17_0,X1)
| ~ ssList(X1)
| ~ strictorderedP(X1) ),
inference(cn,[status(thm)],[606,theory(equality)]) ).
cnf(609,negated_conjecture,
( nil = cons(X1,X2)
| ~ segmentP(esk17_0,cons(X1,X2))
| ~ ssList(cons(X1,X2))
| nil != X2
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[607,190,theory(equality)]) ).
cnf(828,negated_conjecture,
( cons(X1,X2) = nil
| nil != X2
| ~ segmentP(esk17_0,cons(X1,X2))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[609,221]) ).
cnf(829,negated_conjecture,
( nil != X2
| ~ segmentP(esk17_0,cons(X1,X2))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[828,113]) ).
cnf(982,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(er,[status(thm)],[404,theory(equality)]) ).
cnf(1016,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[982,109]) ).
cnf(1022,plain,
( segmentP(cons(X1,X2),cons(X1,nil))
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[1016,83,theory(equality)]) ).
cnf(1171,plain,
( app(nil,nil) = nil
| ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| nil != X1 ),
inference(spm,[status(thm)],[470,73,theory(equality)]) ).
cnf(1314,plain,
( app(nil,nil) = nil
| nil != X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1171,222,theory(equality)]) ).
cnf(1326,plain,
app(nil,nil) = nil,
inference(spm,[status(thm)],[1314,222,theory(equality)]) ).
cnf(1375,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssList(nil)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[105,1326,theory(equality)]) ).
cnf(1403,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| $false
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[1375,222,theory(equality)]) ).
cnf(1404,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[1403,theory(equality)]) ).
cnf(2854,plain,
( segmentP(X1,cons(hd(X1),nil))
| nil = X1
| ~ ssList(cons(hd(X1),nil))
| ~ ssList(tl(X1))
| ~ ssItem(hd(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1022,225,theory(equality)]) ).
cnf(8408,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[511,109]) ).
cnf(8421,plain,
( ssList(cons(X1,nil))
| ~ ssList(nil)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[8408,1404,theory(equality)]) ).
cnf(8438,plain,
( ssList(cons(X1,nil))
| $false
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[8421,222,theory(equality)]) ).
cnf(8439,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[8438,theory(equality)]) ).
cnf(114955,plain,
( nil = X1
| segmentP(X1,cons(hd(X1),nil))
| ~ ssList(cons(hd(X1),nil))
| ~ ssList(tl(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[2854,127]) ).
cnf(114956,plain,
( nil = X1
| segmentP(X1,cons(hd(X1),nil))
| ~ ssList(cons(hd(X1),nil))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[114955,101]) ).
cnf(114965,negated_conjecture,
( nil = esk17_0
| ~ ssList(nil)
| ~ ssItem(hd(esk17_0))
| ~ ssList(cons(hd(esk17_0),nil))
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[829,114956,theory(equality)]) ).
cnf(115056,negated_conjecture,
( nil = esk17_0
| $false
| ~ ssItem(hd(esk17_0))
| ~ ssList(cons(hd(esk17_0),nil))
| ~ ssList(esk17_0) ),
inference(rw,[status(thm)],[114965,222,theory(equality)]) ).
cnf(115057,negated_conjecture,
( nil = esk17_0
| $false
| ~ ssItem(hd(esk17_0))
| ~ ssList(cons(hd(esk17_0),nil))
| $false ),
inference(rw,[status(thm)],[115056,286,theory(equality)]) ).
cnf(115058,negated_conjecture,
( nil = esk17_0
| ~ ssItem(hd(esk17_0))
| ~ ssList(cons(hd(esk17_0),nil)) ),
inference(cn,[status(thm)],[115057,theory(equality)]) ).
cnf(115719,negated_conjecture,
( esk17_0 = nil
| ~ ssItem(hd(esk17_0)) ),
inference(csr,[status(thm)],[115058,8439]) ).
cnf(115720,negated_conjecture,
( esk17_0 = nil
| ~ ssList(esk17_0) ),
inference(spm,[status(thm)],[115719,127,theory(equality)]) ).
cnf(115721,negated_conjecture,
( esk17_0 = nil
| $false ),
inference(rw,[status(thm)],[115720,286,theory(equality)]) ).
cnf(115722,negated_conjecture,
esk17_0 = nil,
inference(cn,[status(thm)],[115721,theory(equality)]) ).
cnf(115765,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[287,115722,theory(equality)]) ).
cnf(115766,negated_conjecture,
$false,
inference(sr,[status(thm)],[115765,580,theory(equality)]) ).
cnf(115767,negated_conjecture,
$false,
115766,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC125+1.p
% --creating new selector for [SWC001+0.ax]
% eprover: CPU time limit exceeded, terminating
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmp2HxPwO/sel_SWC125+1.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmp2HxPwO/sel_SWC125+1.p_2 with time limit 81
% -prover status ResourceOut
% --creating new selector for [SWC001+0.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmp2HxPwO/sel_SWC125+1.p_3 with time limit 75
% -prover status ResourceOut
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmp2HxPwO/sel_SWC125+1.p_4 with time limit 55
% -prover status Theorem
% Problem SWC125+1.p solved in phase 3.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC125+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC125+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
%
%------------------------------------------------------------------------------