TSTP Solution File: SWC111+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC111+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 10:18:10 EST 2010
% Result : Theorem 114.02s
% Output : CNFRefutation 114.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 16
% Syntax : Number of formulae : 160 ( 18 unt; 0 def)
% Number of atoms : 778 ( 210 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 1047 ( 429 ~; 445 |; 132 &)
% ( 4 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 243 ( 0 sgn 136 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( totalorderedP(cons(X1,X2))
<=> ( nil = X2
| ( nil != X2
& totalorderedP(X2)
& leq(X1,hd(X2)) ) ) ) ) ),
file('/tmp/tmpbLiYsM/sel_SWC111+1.p_3',ax67) ).
fof(3,axiom,
totalorderedP(nil),
file('/tmp/tmpbLiYsM/sel_SWC111+1.p_3',ax66) ).
fof(6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmpbLiYsM/sel_SWC111+1.p_3',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/tmpbLiYsM/sel_SWC111+1.p_3',ax82) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpbLiYsM/sel_SWC111+1.p_3',ax81) ).
fof(11,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpbLiYsM/sel_SWC111+1.p_3',ax28) ).
fof(12,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/tmp/tmpbLiYsM/sel_SWC111+1.p_3',ax27) ).
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpbLiYsM/sel_SWC111+1.p_3',ax26) ).
fof(14,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmpbLiYsM/sel_SWC111+1.p_3',ax21) ).
fof(15,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/tmp/tmpbLiYsM/sel_SWC111+1.p_3',ax20) ).
fof(20,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/tmp/tmpbLiYsM/sel_SWC111+1.p_3',ax7) ).
fof(31,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpbLiYsM/sel_SWC111+1.p_3',ax16) ).
fof(32,axiom,
ssList(nil),
file('/tmp/tmpbLiYsM/sel_SWC111+1.p_3',ax17) ).
fof(39,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/tmp/tmpbLiYsM/sel_SWC111+1.p_3',ax57) ).
fof(40,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpbLiYsM/sel_SWC111+1.p_3',ax15) ).
fof(43,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ segmentP(X4,X3)
| ~ totalorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& segmentP(X4,X5)
& segmentP(X5,X3)
& totalorderedP(X5) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) ) ) ) ) ) ),
file('/tmp/tmpbLiYsM/sel_SWC111+1.p_3',co1) ).
fof(44,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ segmentP(X4,X3)
| ~ totalorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& segmentP(X4,X5)
& segmentP(X5,X3)
& totalorderedP(X5) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[43]) ).
fof(47,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ segmentP(X4,X3)
| ~ totalorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& segmentP(X4,X5)
& segmentP(X5,X3)
& totalorderedP(X5) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[44,theory(equality)]) ).
fof(51,plain,
! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ totalorderedP(cons(X1,X2))
| nil = X2
| ( nil != X2
& totalorderedP(X2)
& leq(X1,hd(X2)) ) )
& ( ( nil != X2
& ( nil = X2
| ~ totalorderedP(X2)
| ~ leq(X1,hd(X2)) ) )
| totalorderedP(cons(X1,X2)) ) ) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(52,plain,
! [X3] :
( ~ ssItem(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ totalorderedP(cons(X3,X4))
| nil = X4
| ( nil != X4
& totalorderedP(X4)
& leq(X3,hd(X4)) ) )
& ( ( nil != X4
& ( nil = X4
| ~ totalorderedP(X4)
| ~ leq(X3,hd(X4)) ) )
| totalorderedP(cons(X3,X4)) ) ) ) ),
inference(variable_rename,[status(thm)],[51]) ).
fof(53,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ totalorderedP(cons(X3,X4))
| nil = X4
| ( nil != X4
& totalorderedP(X4)
& leq(X3,hd(X4)) ) )
& ( ( nil != X4
& ( nil = X4
| ~ totalorderedP(X4)
| ~ leq(X3,hd(X4)) ) )
| totalorderedP(cons(X3,X4)) ) )
| ~ ssItem(X3) ),
inference(shift_quantors,[status(thm)],[52]) ).
fof(54,plain,
! [X3,X4] :
( ( nil != X4
| nil = X4
| ~ totalorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) )
& ( totalorderedP(X4)
| nil = X4
| ~ totalorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) )
& ( leq(X3,hd(X4))
| nil = X4
| ~ totalorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) )
& ( nil != X4
| totalorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) )
& ( nil = X4
| ~ totalorderedP(X4)
| ~ leq(X3,hd(X4))
| totalorderedP(cons(X3,X4))
| ~ ssList(X4)
| ~ ssItem(X3) ) ),
inference(distribute,[status(thm)],[53]) ).
cnf(56,plain,
( totalorderedP(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2)
| nil != X2 ),
inference(split_conjunct,[status(thm)],[54]) ).
cnf(60,plain,
totalorderedP(nil),
inference(split_conjunct,[status(thm)],[3]) ).
fof(68,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(69,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)],[68]) ).
fof(70,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)],[69]) ).
fof(71,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)],[70]) ).
cnf(72,plain,
( nil = app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| nil != X1
| nil != X2 ),
inference(split_conjunct,[status(thm)],[71]) ).
fof(75,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(76,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)],[75]) ).
fof(77,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)],[76]) ).
cnf(78,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[77]) ).
fof(79,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(80,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[79]) ).
fof(81,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[80]) ).
cnf(82,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[81]) ).
fof(91,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(92,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[91]) ).
cnf(93,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[92]) ).
fof(94,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)],[12]) ).
fof(95,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)],[94]) ).
fof(96,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)],[95]) ).
cnf(97,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[96]) ).
fof(98,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(99,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[98]) ).
fof(100,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[99]) ).
cnf(101,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[100]) ).
fof(102,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| nil != cons(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(103,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3) ) ),
inference(variable_rename,[status(thm)],[102]) ).
fof(104,plain,
! [X3,X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[103]) ).
cnf(105,plain,
( ~ ssList(X1)
| nil != cons(X2,X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[104]) ).
fof(106,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(107,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssItem(X6)
& cons(X6,X5) = X4 ) ) ),
inference(variable_rename,[status(thm)],[106]) ).
fof(108,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ( ssList(esk1_1(X4))
& ssItem(esk2_1(X4))
& cons(esk2_1(X4),esk1_1(X4)) = X4 ) ),
inference(skolemize,[status(esa)],[107]) ).
fof(109,plain,
! [X4] :
( ( ssList(esk1_1(X4))
| nil = X4
| ~ ssList(X4) )
& ( ssItem(esk2_1(X4))
| nil = X4
| ~ ssList(X4) )
& ( cons(esk2_1(X4),esk1_1(X4)) = X4
| nil = X4
| ~ ssList(X4) ) ),
inference(distribute,[status(thm)],[108]) ).
cnf(110,plain,
( nil = X1
| cons(esk2_1(X1),esk1_1(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[109]) ).
cnf(111,plain,
( nil = X1
| ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[109]) ).
cnf(112,plain,
( nil = X1
| ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[109]) ).
fof(131,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)],[20]) ).
fof(132,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)],[131]) ).
fof(133,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)],[132]) ).
fof(134,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)],[133]) ).
fof(135,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)],[134]) ).
cnf(139,plain,
( segmentP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[135]) ).
fof(187,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(188,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[187]) ).
fof(189,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[188]) ).
cnf(190,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[189]) ).
cnf(191,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[32]) ).
fof(224,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(225,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,nil) ),
inference(variable_rename,[status(thm)],[224]) ).
cnf(226,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[225]) ).
fof(227,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[40]) ).
fof(228,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[227]) ).
fof(229,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[228]) ).
fof(230,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)],[229]) ).
cnf(231,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[230]) ).
fof(240,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& segmentP(X4,X3)
& totalorderedP(X3)
& ! [X5] :
( ~ ssList(X5)
| ~ neq(X3,X5)
| ~ segmentP(X4,X5)
| ~ segmentP(X5,X3)
| ~ totalorderedP(X5) )
& ( ( nil = X2
& nil != X1 )
| ( neq(X2,nil)
& ( ~ neq(X1,nil)
| ~ segmentP(X2,X1) ) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[47]) ).
fof(241,negated_conjecture,
? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& X7 = X9
& X6 = X8
& segmentP(X9,X8)
& totalorderedP(X8)
& ! [X10] :
( ~ ssList(X10)
| ~ neq(X8,X10)
| ~ segmentP(X9,X10)
| ~ segmentP(X10,X8)
| ~ totalorderedP(X10) )
& ( ( nil = X7
& nil != X6 )
| ( neq(X7,nil)
& ( ~ neq(X6,nil)
| ~ segmentP(X7,X6) ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[240]) ).
fof(242,negated_conjecture,
( ssList(esk13_0)
& ssList(esk14_0)
& ssList(esk15_0)
& ssList(esk16_0)
& esk14_0 = esk16_0
& esk13_0 = esk15_0
& segmentP(esk16_0,esk15_0)
& totalorderedP(esk15_0)
& ! [X10] :
( ~ ssList(X10)
| ~ neq(esk15_0,X10)
| ~ segmentP(esk16_0,X10)
| ~ segmentP(X10,esk15_0)
| ~ totalorderedP(X10) )
& ( ( nil = esk14_0
& nil != esk13_0 )
| ( neq(esk14_0,nil)
& ( ~ neq(esk13_0,nil)
| ~ segmentP(esk14_0,esk13_0) ) ) ) ),
inference(skolemize,[status(esa)],[241]) ).
fof(243,negated_conjecture,
! [X10] :
( ( ~ ssList(X10)
| ~ neq(esk15_0,X10)
| ~ segmentP(esk16_0,X10)
| ~ segmentP(X10,esk15_0)
| ~ totalorderedP(X10) )
& esk14_0 = esk16_0
& esk13_0 = esk15_0
& segmentP(esk16_0,esk15_0)
& totalorderedP(esk15_0)
& ( ( nil = esk14_0
& nil != esk13_0 )
| ( neq(esk14_0,nil)
& ( ~ neq(esk13_0,nil)
| ~ segmentP(esk14_0,esk13_0) ) ) )
& ssList(esk16_0)
& ssList(esk15_0)
& ssList(esk14_0)
& ssList(esk13_0) ),
inference(shift_quantors,[status(thm)],[242]) ).
fof(244,negated_conjecture,
! [X10] :
( ( ~ ssList(X10)
| ~ neq(esk15_0,X10)
| ~ segmentP(esk16_0,X10)
| ~ segmentP(X10,esk15_0)
| ~ totalorderedP(X10) )
& esk14_0 = esk16_0
& esk13_0 = esk15_0
& segmentP(esk16_0,esk15_0)
& totalorderedP(esk15_0)
& ( neq(esk14_0,nil)
| nil = esk14_0 )
& ( ~ neq(esk13_0,nil)
| ~ segmentP(esk14_0,esk13_0)
| nil = esk14_0 )
& ( neq(esk14_0,nil)
| nil != esk13_0 )
& ( ~ neq(esk13_0,nil)
| ~ segmentP(esk14_0,esk13_0)
| nil != esk13_0 )
& ssList(esk16_0)
& ssList(esk15_0)
& ssList(esk14_0)
& ssList(esk13_0) ),
inference(distribute,[status(thm)],[243]) ).
cnf(245,negated_conjecture,
ssList(esk13_0),
inference(split_conjunct,[status(thm)],[244]) ).
cnf(246,negated_conjecture,
ssList(esk14_0),
inference(split_conjunct,[status(thm)],[244]) ).
cnf(249,negated_conjecture,
( nil != esk13_0
| ~ segmentP(esk14_0,esk13_0)
| ~ neq(esk13_0,nil) ),
inference(split_conjunct,[status(thm)],[244]) ).
cnf(250,negated_conjecture,
( neq(esk14_0,nil)
| nil != esk13_0 ),
inference(split_conjunct,[status(thm)],[244]) ).
cnf(251,negated_conjecture,
( nil = esk14_0
| ~ segmentP(esk14_0,esk13_0)
| ~ neq(esk13_0,nil) ),
inference(split_conjunct,[status(thm)],[244]) ).
cnf(254,negated_conjecture,
segmentP(esk16_0,esk15_0),
inference(split_conjunct,[status(thm)],[244]) ).
cnf(255,negated_conjecture,
esk13_0 = esk15_0,
inference(split_conjunct,[status(thm)],[244]) ).
cnf(256,negated_conjecture,
esk14_0 = esk16_0,
inference(split_conjunct,[status(thm)],[244]) ).
cnf(257,negated_conjecture,
( ~ totalorderedP(X1)
| ~ segmentP(X1,esk15_0)
| ~ segmentP(esk16_0,X1)
| ~ neq(esk15_0,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[244]) ).
cnf(263,negated_conjecture,
segmentP(esk14_0,esk13_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[254,256,theory(equality)]),255,theory(equality)]) ).
cnf(265,negated_conjecture,
( esk14_0 = nil
| ~ neq(esk13_0,nil)
| $false ),
inference(rw,[status(thm)],[251,263,theory(equality)]) ).
cnf(266,negated_conjecture,
( esk14_0 = nil
| ~ neq(esk13_0,nil) ),
inference(cn,[status(thm)],[265,theory(equality)]) ).
cnf(267,negated_conjecture,
( esk13_0 != nil
| ~ neq(esk13_0,nil)
| $false ),
inference(rw,[status(thm)],[249,263,theory(equality)]) ).
cnf(268,negated_conjecture,
( esk13_0 != nil
| ~ neq(esk13_0,nil) ),
inference(cn,[status(thm)],[267,theory(equality)]) ).
cnf(269,negated_conjecture,
( esk14_0 = nil
| esk13_0 = nil
| ~ ssList(nil)
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[266,231,theory(equality)]) ).
cnf(271,negated_conjecture,
( esk14_0 = nil
| esk13_0 = nil
| $false
| ~ ssList(esk13_0) ),
inference(rw,[status(thm)],[269,191,theory(equality)]) ).
cnf(272,negated_conjecture,
( esk14_0 = nil
| esk13_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[271,245,theory(equality)]) ).
cnf(273,negated_conjecture,
( esk14_0 = nil
| esk13_0 = nil ),
inference(cn,[status(thm)],[272,theory(equality)]) ).
cnf(303,negated_conjecture,
( ~ totalorderedP(X1)
| ~ ssList(X1)
| ~ segmentP(X1,esk13_0)
| ~ neq(esk15_0,X1)
| ~ segmentP(esk16_0,X1) ),
inference(rw,[status(thm)],[257,255,theory(equality)]) ).
cnf(304,negated_conjecture,
( ~ totalorderedP(X1)
| ~ ssList(X1)
| ~ segmentP(X1,esk13_0)
| ~ neq(esk13_0,X1)
| ~ segmentP(esk16_0,X1) ),
inference(rw,[status(thm)],[303,255,theory(equality)]) ).
cnf(305,negated_conjecture,
( ~ totalorderedP(X1)
| ~ ssList(X1)
| ~ segmentP(X1,esk13_0)
| ~ neq(esk13_0,X1)
| ~ segmentP(esk14_0,X1) ),
inference(rw,[status(thm)],[304,256,theory(equality)]) ).
cnf(306,negated_conjecture,
( esk13_0 = X1
| ~ segmentP(X1,esk13_0)
| ~ segmentP(esk14_0,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1)
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[305,231,theory(equality)]) ).
cnf(308,negated_conjecture,
( esk13_0 = X1
| ~ segmentP(X1,esk13_0)
| ~ segmentP(esk14_0,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1)
| $false ),
inference(rw,[status(thm)],[306,245,theory(equality)]) ).
cnf(309,negated_conjecture,
( esk13_0 = X1
| ~ segmentP(X1,esk13_0)
| ~ segmentP(esk14_0,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1) ),
inference(cn,[status(thm)],[308,theory(equality)]) ).
cnf(388,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[139,93,theory(equality)]) ).
cnf(396,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[388,191,theory(equality)]) ).
cnf(397,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[396,theory(equality)]) ).
cnf(422,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[78,93,theory(equality)]) ).
cnf(444,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[422,191,theory(equality)]) ).
cnf(445,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[444,theory(equality)]) ).
cnf(476,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssList(app(X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[190,97,theory(equality)]) ).
cnf(535,negated_conjecture,
( esk13_0 = nil
| ~ segmentP(nil,esk13_0)
| ~ segmentP(esk14_0,nil)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[309,60,theory(equality)]) ).
cnf(538,negated_conjecture,
( esk13_0 = nil
| ~ segmentP(nil,esk13_0)
| ~ segmentP(esk14_0,nil)
| $false ),
inference(rw,[status(thm)],[535,191,theory(equality)]) ).
cnf(539,negated_conjecture,
( esk13_0 = nil
| ~ segmentP(nil,esk13_0)
| ~ segmentP(esk14_0,nil) ),
inference(cn,[status(thm)],[538,theory(equality)]) ).
cnf(541,negated_conjecture,
( segmentP(nil,esk13_0)
| esk13_0 = nil ),
inference(spm,[status(thm)],[263,273,theory(equality)]) ).
cnf(556,negated_conjecture,
( esk13_0 = nil
| ~ segmentP(esk14_0,nil) ),
inference(csr,[status(thm)],[539,541]) ).
cnf(557,negated_conjecture,
( esk13_0 = nil
| ~ ssList(esk14_0) ),
inference(spm,[status(thm)],[556,226,theory(equality)]) ).
cnf(559,negated_conjecture,
( esk13_0 = nil
| $false ),
inference(rw,[status(thm)],[557,246,theory(equality)]) ).
cnf(560,negated_conjecture,
esk13_0 = nil,
inference(cn,[status(thm)],[559,theory(equality)]) ).
cnf(574,negated_conjecture,
( nil = X1
| ~ segmentP(X1,esk13_0)
| ~ segmentP(esk14_0,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1) ),
inference(rw,[status(thm)],[309,560,theory(equality)]) ).
cnf(575,negated_conjecture,
( nil = X1
| ~ segmentP(X1,nil)
| ~ segmentP(esk14_0,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1) ),
inference(rw,[status(thm)],[574,560,theory(equality)]) ).
cnf(578,negated_conjecture,
( $false
| ~ neq(esk13_0,nil) ),
inference(rw,[status(thm)],[268,560,theory(equality)]) ).
cnf(579,negated_conjecture,
( $false
| ~ neq(nil,nil) ),
inference(rw,[status(thm)],[578,560,theory(equality)]) ).
cnf(580,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[579,theory(equality)]) ).
cnf(582,negated_conjecture,
( neq(esk14_0,nil)
| $false ),
inference(rw,[status(thm)],[250,560,theory(equality)]) ).
cnf(583,negated_conjecture,
neq(esk14_0,nil),
inference(cn,[status(thm)],[582,theory(equality)]) ).
cnf(600,negated_conjecture,
( nil = X1
| ~ segmentP(esk14_0,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1) ),
inference(csr,[status(thm)],[575,226]) ).
cnf(602,negated_conjecture,
( nil = cons(X1,X2)
| ~ segmentP(esk14_0,cons(X1,X2))
| ~ ssList(cons(X1,X2))
| nil != X2
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[600,56,theory(equality)]) ).
cnf(667,negated_conjecture,
( cons(X1,X2) = nil
| nil != X2
| ~ segmentP(esk14_0,cons(X1,X2))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[602,190]) ).
cnf(668,negated_conjecture,
( nil != X2
| ~ segmentP(esk14_0,cons(X1,X2))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[667,105]) ).
cnf(966,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(er,[status(thm)],[397,theory(equality)]) ).
cnf(1009,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[966,101]) ).
cnf(1015,plain,
( segmentP(cons(X1,X2),cons(X1,nil))
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[1009,82,theory(equality)]) ).
cnf(1119,plain,
( app(nil,nil) = nil
| ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| nil != X1 ),
inference(spm,[status(thm)],[445,72,theory(equality)]) ).
cnf(1263,plain,
( app(nil,nil) = nil
| nil != X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1119,191,theory(equality)]) ).
cnf(1273,plain,
app(nil,nil) = nil,
inference(spm,[status(thm)],[1263,191,theory(equality)]) ).
cnf(1291,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssList(nil)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[97,1273,theory(equality)]) ).
cnf(1319,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| $false
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[1291,191,theory(equality)]) ).
cnf(1320,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[1319,theory(equality)]) ).
cnf(2374,plain,
( segmentP(X1,cons(esk2_1(X1),nil))
| nil = X1
| ~ ssList(cons(esk2_1(X1),nil))
| ~ ssList(esk1_1(X1))
| ~ ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1015,110,theory(equality)]) ).
cnf(6580,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[476,101]) ).
cnf(6589,plain,
( ssList(cons(X1,nil))
| ~ ssList(nil)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[6580,1320,theory(equality)]) ).
cnf(6603,plain,
( ssList(cons(X1,nil))
| $false
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[6589,191,theory(equality)]) ).
cnf(6604,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[6603,theory(equality)]) ).
cnf(73276,plain,
( nil = X1
| segmentP(X1,cons(esk2_1(X1),nil))
| ~ ssList(cons(esk2_1(X1),nil))
| ~ ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[2374,111]) ).
cnf(73277,plain,
( nil = X1
| segmentP(X1,cons(esk2_1(X1),nil))
| ~ ssList(cons(esk2_1(X1),nil))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[73276,112]) ).
cnf(73282,negated_conjecture,
( nil = esk14_0
| ~ ssList(nil)
| ~ ssItem(esk2_1(esk14_0))
| ~ ssList(cons(esk2_1(esk14_0),nil))
| ~ ssList(esk14_0) ),
inference(spm,[status(thm)],[668,73277,theory(equality)]) ).
cnf(73347,negated_conjecture,
( nil = esk14_0
| $false
| ~ ssItem(esk2_1(esk14_0))
| ~ ssList(cons(esk2_1(esk14_0),nil))
| ~ ssList(esk14_0) ),
inference(rw,[status(thm)],[73282,191,theory(equality)]) ).
cnf(73348,negated_conjecture,
( nil = esk14_0
| $false
| ~ ssItem(esk2_1(esk14_0))
| ~ ssList(cons(esk2_1(esk14_0),nil))
| $false ),
inference(rw,[status(thm)],[73347,246,theory(equality)]) ).
cnf(73349,negated_conjecture,
( nil = esk14_0
| ~ ssItem(esk2_1(esk14_0))
| ~ ssList(cons(esk2_1(esk14_0),nil)) ),
inference(cn,[status(thm)],[73348,theory(equality)]) ).
cnf(73712,negated_conjecture,
( esk14_0 = nil
| ~ ssItem(esk2_1(esk14_0)) ),
inference(csr,[status(thm)],[73349,6604]) ).
cnf(73713,negated_conjecture,
( esk14_0 = nil
| ~ ssList(esk14_0) ),
inference(spm,[status(thm)],[73712,111,theory(equality)]) ).
cnf(73715,negated_conjecture,
( esk14_0 = nil
| $false ),
inference(rw,[status(thm)],[73713,246,theory(equality)]) ).
cnf(73716,negated_conjecture,
esk14_0 = nil,
inference(cn,[status(thm)],[73715,theory(equality)]) ).
cnf(73725,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[583,73716,theory(equality)]) ).
cnf(73726,negated_conjecture,
$false,
inference(sr,[status(thm)],[73725,580,theory(equality)]) ).
cnf(73727,negated_conjecture,
$false,
73726,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC111+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/tmpbLiYsM/sel_SWC111+1.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpbLiYsM/sel_SWC111+1.p_2 with time limit 81
% -prover status ResourceOut
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpbLiYsM/sel_SWC111+1.p_3 with time limit 74
% -prover status Theorem
% Problem SWC111+1.p solved in phase 2.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC111+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC111+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
%
%------------------------------------------------------------------------------