TSTP Solution File: SWC363+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC363+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 11:38:42 EST 2010
% Result : Theorem 2.15s
% Output : CNFRefutation 2.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 14
% Syntax : Number of formulae : 155 ( 23 unt; 0 def)
% Number of atoms : 666 ( 134 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 866 ( 355 ~; 372 |; 94 &)
% ( 3 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 254 ( 0 sgn 142 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmpBx3TNc/sel_SWC363+1.p_1',ax84) ).
fof(2,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmpBx3TNc/sel_SWC363+1.p_1',ax83) ).
fof(4,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpBx3TNc/sel_SWC363+1.p_1',ax81) ).
fof(6,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpBx3TNc/sel_SWC363+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/tmpBx3TNc/sel_SWC363+1.p_1',ax27) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpBx3TNc/sel_SWC363+1.p_1',ax26) ).
fof(12,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
file('/tmp/tmpBx3TNc/sel_SWC363+1.p_1',ax3) ).
fof(14,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/tmp/tmpBx3TNc/sel_SWC363+1.p_1',ax7) ).
fof(20,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpBx3TNc/sel_SWC363+1.p_1',ax16) ).
fof(21,axiom,
ssList(nil),
file('/tmp/tmpBx3TNc/sel_SWC363+1.p_1',ax17) ).
fof(25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X3) )
=> segmentP(X1,X3) ) ) ) ),
file('/tmp/tmpBx3TNc/sel_SWC363+1.p_1',ax53) ).
fof(27,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/tmp/tmpBx3TNc/sel_SWC363+1.p_1',ax55) ).
fof(28,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/tmpBx3TNc/sel_SWC363+1.p_1',ax56) ).
fof(30,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| segmentP(X2,X1)
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X3
| ~ memberP(X4,X5) ) )
& neq(X4,nil) ) ) ) ) ) ),
file('/tmp/tmpBx3TNc/sel_SWC363+1.p_1',co1) ).
fof(31,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| segmentP(X2,X1)
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X3
| ~ memberP(X4,X5) ) )
& neq(X4,nil) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[30]) ).
fof(33,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| segmentP(X2,X1)
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X3
| ~ memberP(X4,X5) ) )
& neq(X4,nil) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[31,theory(equality)]) ).
fof(34,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(35,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[34]) ).
cnf(36,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,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(38,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)],[37]) ).
fof(39,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)],[38]) ).
fof(40,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)],[39]) ).
cnf(41,plain,
( nil = app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| nil != X1
| nil != X2 ),
inference(split_conjunct,[status(thm)],[40]) ).
fof(48,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(49,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[48]) ).
fof(50,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[49]) ).
cnf(51,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[50]) ).
fof(56,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(57,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[56]) ).
cnf(58,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[57]) ).
fof(59,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(60,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)],[59]) ).
fof(61,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)],[60]) ).
cnf(62,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[61]) ).
fof(63,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(64,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[63]) ).
fof(65,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[64]) ).
cnf(66,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[65]) ).
fof(83,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ( ( ~ memberP(X1,X2)
| ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) )
& ( ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| app(X3,cons(X2,X4)) != X1 ) )
| memberP(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(84,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssItem(X6)
| ( ( ~ memberP(X5,X6)
| ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& app(X7,cons(X6,X8)) = X5 ) ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(X9,cons(X6,X10)) != X5 ) )
| memberP(X5,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[83]) ).
fof(85,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssItem(X6)
| ( ( ~ memberP(X5,X6)
| ( ssList(esk5_2(X5,X6))
& ssList(esk6_2(X5,X6))
& app(esk5_2(X5,X6),cons(X6,esk6_2(X5,X6))) = X5 ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(X9,cons(X6,X10)) != X5 ) )
| memberP(X5,X6) ) ) ) ),
inference(skolemize,[status(esa)],[84]) ).
fof(86,plain,
! [X5,X6,X9,X10] :
( ( ( ~ ssList(X10)
| app(X9,cons(X6,X10)) != X5
| ~ ssList(X9)
| memberP(X5,X6) )
& ( ~ memberP(X5,X6)
| ( ssList(esk5_2(X5,X6))
& ssList(esk6_2(X5,X6))
& app(esk5_2(X5,X6),cons(X6,esk6_2(X5,X6))) = X5 ) ) )
| ~ ssItem(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[85]) ).
fof(87,plain,
! [X5,X6,X9,X10] :
( ( ~ ssList(X10)
| app(X9,cons(X6,X10)) != X5
| ~ ssList(X9)
| memberP(X5,X6)
| ~ ssItem(X6)
| ~ ssList(X5) )
& ( ssList(esk5_2(X5,X6))
| ~ memberP(X5,X6)
| ~ ssItem(X6)
| ~ ssList(X5) )
& ( ssList(esk6_2(X5,X6))
| ~ memberP(X5,X6)
| ~ ssItem(X6)
| ~ ssList(X5) )
& ( app(esk5_2(X5,X6),cons(X6,esk6_2(X5,X6))) = X5
| ~ memberP(X5,X6)
| ~ ssItem(X6)
| ~ ssList(X5) ) ),
inference(distribute,[status(thm)],[86]) ).
cnf(88,plain,
( app(esk5_2(X1,X2),cons(X2,esk6_2(X1,X2))) = X1
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2) ),
inference(split_conjunct,[status(thm)],[87]) ).
cnf(89,plain,
( ssList(esk6_2(X1,X2))
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2) ),
inference(split_conjunct,[status(thm)],[87]) ).
cnf(90,plain,
( ssList(esk5_2(X1,X2))
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2) ),
inference(split_conjunct,[status(thm)],[87]) ).
fof(98,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)],[14]) ).
fof(99,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)],[98]) ).
fof(100,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ segmentP(X5,X6)
| ( ssList(esk7_2(X5,X6))
& ssList(esk8_2(X5,X6))
& app(app(esk7_2(X5,X6),X6),esk8_2(X5,X6)) = X5 ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X9,X6),X10) != X5 ) )
| segmentP(X5,X6) ) ) ) ),
inference(skolemize,[status(esa)],[99]) ).
fof(101,plain,
! [X5,X6,X9,X10] :
( ( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6) )
& ( ~ segmentP(X5,X6)
| ( ssList(esk7_2(X5,X6))
& ssList(esk8_2(X5,X6))
& app(app(esk7_2(X5,X6),X6),esk8_2(X5,X6)) = X5 ) ) )
| ~ ssList(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[100]) ).
fof(102,plain,
! [X5,X6,X9,X10] :
( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk7_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk8_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( app(app(esk7_2(X5,X6),X6),esk8_2(X5,X6)) = X5
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) ) ),
inference(distribute,[status(thm)],[101]) ).
cnf(106,plain,
( segmentP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[102]) ).
fof(132,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(133,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[132]) ).
fof(134,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[133]) ).
cnf(135,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[134]) ).
cnf(136,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[21]) ).
fof(154,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X3)
| segmentP(X1,X3) ) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(155,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ~ segmentP(X4,X5)
| ~ segmentP(X5,X6)
| segmentP(X4,X6) ) ) ),
inference(variable_rename,[status(thm)],[154]) ).
fof(156,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ~ segmentP(X4,X5)
| ~ segmentP(X5,X6)
| segmentP(X4,X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[155]) ).
cnf(157,plain,
( segmentP(X1,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[156]) ).
fof(162,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(163,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,X2) ),
inference(variable_rename,[status(thm)],[162]) ).
cnf(164,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[163]) ).
fof(165,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)],[28]) ).
fof(166,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)],[165]) ).
fof(167,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)],[166]) ).
cnf(168,plain,
( segmentP(app(app(X3,X1),X4),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[167]) ).
fof(172,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& neq(X2,nil)
& ~ segmentP(X2,X1)
& ( nil = X3
| nil != X4 )
& ( ? [X5] :
( ssItem(X5)
& cons(X5,nil) = X3
& memberP(X4,X5) )
| ~ neq(X4,nil) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(173,negated_conjecture,
? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& X7 = X9
& X6 = X8
& neq(X7,nil)
& ~ segmentP(X7,X6)
& ( nil = X8
| nil != X9 )
& ( ? [X10] :
( ssItem(X10)
& cons(X10,nil) = X8
& memberP(X9,X10) )
| ~ neq(X9,nil) ) ) ) ) ),
inference(variable_rename,[status(thm)],[172]) ).
fof(174,negated_conjecture,
( ssList(esk9_0)
& ssList(esk10_0)
& ssList(esk11_0)
& ssList(esk12_0)
& esk10_0 = esk12_0
& esk9_0 = esk11_0
& neq(esk10_0,nil)
& ~ segmentP(esk10_0,esk9_0)
& ( nil = esk11_0
| nil != esk12_0 )
& ( ( ssItem(esk13_0)
& cons(esk13_0,nil) = esk11_0
& memberP(esk12_0,esk13_0) )
| ~ neq(esk12_0,nil) ) ),
inference(skolemize,[status(esa)],[173]) ).
fof(175,negated_conjecture,
( ssList(esk9_0)
& ssList(esk10_0)
& ssList(esk11_0)
& ssList(esk12_0)
& esk10_0 = esk12_0
& esk9_0 = esk11_0
& neq(esk10_0,nil)
& ~ segmentP(esk10_0,esk9_0)
& ( nil = esk11_0
| nil != esk12_0 )
& ( ssItem(esk13_0)
| ~ neq(esk12_0,nil) )
& ( cons(esk13_0,nil) = esk11_0
| ~ neq(esk12_0,nil) )
& ( memberP(esk12_0,esk13_0)
| ~ neq(esk12_0,nil) ) ),
inference(distribute,[status(thm)],[174]) ).
cnf(176,negated_conjecture,
( memberP(esk12_0,esk13_0)
| ~ neq(esk12_0,nil) ),
inference(split_conjunct,[status(thm)],[175]) ).
cnf(177,negated_conjecture,
( cons(esk13_0,nil) = esk11_0
| ~ neq(esk12_0,nil) ),
inference(split_conjunct,[status(thm)],[175]) ).
cnf(178,negated_conjecture,
( ssItem(esk13_0)
| ~ neq(esk12_0,nil) ),
inference(split_conjunct,[status(thm)],[175]) ).
cnf(180,negated_conjecture,
~ segmentP(esk10_0,esk9_0),
inference(split_conjunct,[status(thm)],[175]) ).
cnf(181,negated_conjecture,
neq(esk10_0,nil),
inference(split_conjunct,[status(thm)],[175]) ).
cnf(182,negated_conjecture,
esk9_0 = esk11_0,
inference(split_conjunct,[status(thm)],[175]) ).
cnf(183,negated_conjecture,
esk10_0 = esk12_0,
inference(split_conjunct,[status(thm)],[175]) ).
cnf(186,negated_conjecture,
ssList(esk10_0),
inference(split_conjunct,[status(thm)],[175]) ).
cnf(187,negated_conjecture,
ssList(esk9_0),
inference(split_conjunct,[status(thm)],[175]) ).
cnf(188,negated_conjecture,
ssList(esk11_0),
inference(rw,[status(thm)],[187,182,theory(equality)]) ).
cnf(189,negated_conjecture,
ssList(esk12_0),
inference(rw,[status(thm)],[186,183,theory(equality)]) ).
cnf(190,negated_conjecture,
neq(esk12_0,nil),
inference(rw,[status(thm)],[181,183,theory(equality)]) ).
cnf(191,negated_conjecture,
~ segmentP(esk12_0,esk11_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[180,183,theory(equality)]),182,theory(equality)]) ).
cnf(192,negated_conjecture,
( ssItem(esk13_0)
| $false ),
inference(rw,[status(thm)],[178,190,theory(equality)]) ).
cnf(193,negated_conjecture,
ssItem(esk13_0),
inference(cn,[status(thm)],[192,theory(equality)]) ).
cnf(194,negated_conjecture,
( memberP(esk12_0,esk13_0)
| $false ),
inference(rw,[status(thm)],[176,190,theory(equality)]) ).
cnf(195,negated_conjecture,
memberP(esk12_0,esk13_0),
inference(cn,[status(thm)],[194,theory(equality)]) ).
cnf(199,negated_conjecture,
( cons(esk13_0,nil) = esk11_0
| $false ),
inference(rw,[status(thm)],[177,190,theory(equality)]) ).
cnf(200,negated_conjecture,
cons(esk13_0,nil) = esk11_0,
inference(cn,[status(thm)],[199,theory(equality)]) ).
cnf(227,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(er,[status(thm)],[41,theory(equality)]) ).
cnf(228,plain,
( app(X1,nil) = nil
| nil != X1
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[227,136,theory(equality)]) ).
cnf(229,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[228,theory(equality)]) ).
cnf(233,negated_conjecture,
( ssList(esk5_2(esk12_0,esk13_0))
| ~ ssItem(esk13_0)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[90,195,theory(equality)]) ).
cnf(234,negated_conjecture,
( ssList(esk5_2(esk12_0,esk13_0))
| $false
| ~ ssList(esk12_0) ),
inference(rw,[status(thm)],[233,193,theory(equality)]) ).
cnf(235,negated_conjecture,
( ssList(esk5_2(esk12_0,esk13_0))
| ~ ssList(esk12_0) ),
inference(cn,[status(thm)],[234,theory(equality)]) ).
cnf(236,negated_conjecture,
( ssList(esk6_2(esk12_0,esk13_0))
| ~ ssItem(esk13_0)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[89,195,theory(equality)]) ).
cnf(237,negated_conjecture,
( ssList(esk6_2(esk12_0,esk13_0))
| $false
| ~ ssList(esk12_0) ),
inference(rw,[status(thm)],[236,193,theory(equality)]) ).
cnf(238,negated_conjecture,
( ssList(esk6_2(esk12_0,esk13_0))
| ~ ssList(esk12_0) ),
inference(cn,[status(thm)],[237,theory(equality)]) ).
cnf(346,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| ~ ssList(nil)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X3,X2)) ),
inference(spm,[status(thm)],[106,36,theory(equality)]) ).
cnf(351,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| $false
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X3,X2)) ),
inference(rw,[status(thm)],[346,136,theory(equality)]) ).
cnf(352,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X3,X2)) ),
inference(cn,[status(thm)],[351,theory(equality)]) ).
cnf(355,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[135,62,theory(equality)]) ).
cnf(372,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[168,164,theory(equality)]) ).
cnf(375,negated_conjecture,
( app(esk5_2(esk12_0,esk13_0),cons(esk13_0,esk6_2(esk12_0,esk13_0))) = esk12_0
| ~ ssItem(esk13_0)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[88,195,theory(equality)]) ).
cnf(376,negated_conjecture,
( app(esk5_2(esk12_0,esk13_0),cons(esk13_0,esk6_2(esk12_0,esk13_0))) = esk12_0
| $false
| ~ ssList(esk12_0) ),
inference(rw,[status(thm)],[375,193,theory(equality)]) ).
cnf(377,negated_conjecture,
( app(esk5_2(esk12_0,esk13_0),cons(esk13_0,esk6_2(esk12_0,esk13_0))) = esk12_0
| ~ ssList(esk12_0) ),
inference(cn,[status(thm)],[376,theory(equality)]) ).
cnf(428,plain,
( app(nil,nil) = nil
| ~ ssList(nil) ),
inference(er,[status(thm)],[229,theory(equality)]) ).
cnf(429,plain,
( app(nil,nil) = nil
| $false ),
inference(rw,[status(thm)],[428,136,theory(equality)]) ).
cnf(430,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[429,theory(equality)]) ).
cnf(457,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[62,430,theory(equality)]) ).
cnf(474,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[457,136,theory(equality)]) ).
cnf(475,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[474,theory(equality)]) ).
cnf(478,negated_conjecture,
( ssList(esk5_2(esk12_0,esk13_0))
| $false ),
inference(rw,[status(thm)],[235,189,theory(equality)]) ).
cnf(479,negated_conjecture,
ssList(esk5_2(esk12_0,esk13_0)),
inference(cn,[status(thm)],[478,theory(equality)]) ).
cnf(480,negated_conjecture,
( ssList(esk6_2(esk12_0,esk13_0))
| $false ),
inference(rw,[status(thm)],[238,189,theory(equality)]) ).
cnf(481,negated_conjecture,
ssList(esk6_2(esk12_0,esk13_0)),
inference(cn,[status(thm)],[480,theory(equality)]) ).
cnf(2669,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[352,66]) ).
cnf(2670,plain,
( segmentP(app(X1,X2),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(app(X1,X2)) ),
inference(er,[status(thm)],[2669,theory(equality)]) ).
cnf(2842,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[355,66]) ).
cnf(2849,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[2842,475,theory(equality)]) ).
cnf(2861,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[2849,136,theory(equality)]) ).
cnf(2862,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[2861,theory(equality)]) ).
cnf(3844,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[372,58,theory(equality)]) ).
cnf(3883,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[3844,136,theory(equality)]) ).
cnf(3884,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[3883,theory(equality)]) ).
cnf(3934,negated_conjecture,
( app(esk5_2(esk12_0,esk13_0),cons(esk13_0,esk6_2(esk12_0,esk13_0))) = esk12_0
| $false ),
inference(rw,[status(thm)],[377,189,theory(equality)]) ).
cnf(3935,negated_conjecture,
app(esk5_2(esk12_0,esk13_0),cons(esk13_0,esk6_2(esk12_0,esk13_0))) = esk12_0,
inference(cn,[status(thm)],[3934,theory(equality)]) ).
cnf(6549,plain,
( segmentP(cons(X1,X2),cons(X1,nil))
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[3884,51,theory(equality)]) ).
cnf(25196,plain,
( segmentP(cons(X1,X2),cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[6549,2862]) ).
cnf(25198,negated_conjecture,
( segmentP(cons(esk13_0,X1),esk11_0)
| ~ ssItem(esk13_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[25196,200,theory(equality)]) ).
cnf(25216,negated_conjecture,
( segmentP(cons(esk13_0,X1),esk11_0)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[25198,193,theory(equality)]) ).
cnf(25217,negated_conjecture,
( segmentP(cons(esk13_0,X1),esk11_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[25216,theory(equality)]) ).
cnf(25239,negated_conjecture,
( segmentP(X1,esk11_0)
| ~ segmentP(X1,cons(esk13_0,X2))
| ~ ssList(esk11_0)
| ~ ssList(cons(esk13_0,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[157,25217,theory(equality)]) ).
cnf(25261,negated_conjecture,
( segmentP(X1,esk11_0)
| ~ segmentP(X1,cons(esk13_0,X2))
| $false
| ~ ssList(cons(esk13_0,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(rw,[status(thm)],[25239,188,theory(equality)]) ).
cnf(25262,negated_conjecture,
( segmentP(X1,esk11_0)
| ~ segmentP(X1,cons(esk13_0,X2))
| ~ ssList(cons(esk13_0,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[25261,theory(equality)]) ).
cnf(25975,negated_conjecture,
( segmentP(X1,esk11_0)
| ~ segmentP(X1,cons(esk13_0,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(esk13_0) ),
inference(spm,[status(thm)],[25262,135,theory(equality)]) ).
cnf(25997,negated_conjecture,
( segmentP(X1,esk11_0)
| ~ segmentP(X1,cons(esk13_0,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[25975,193,theory(equality)]) ).
cnf(25998,negated_conjecture,
( segmentP(X1,esk11_0)
| ~ segmentP(X1,cons(esk13_0,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[25997,theory(equality)]) ).
cnf(35080,plain,
( segmentP(app(X1,X2),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[2670,66]) ).
cnf(35085,negated_conjecture,
( segmentP(esk12_0,cons(esk13_0,esk6_2(esk12_0,esk13_0)))
| ~ ssList(esk5_2(esk12_0,esk13_0))
| ~ ssList(cons(esk13_0,esk6_2(esk12_0,esk13_0))) ),
inference(spm,[status(thm)],[35080,3935,theory(equality)]) ).
cnf(35177,negated_conjecture,
( segmentP(esk12_0,cons(esk13_0,esk6_2(esk12_0,esk13_0)))
| $false
| ~ ssList(cons(esk13_0,esk6_2(esk12_0,esk13_0))) ),
inference(rw,[status(thm)],[35085,479,theory(equality)]) ).
cnf(35178,negated_conjecture,
( segmentP(esk12_0,cons(esk13_0,esk6_2(esk12_0,esk13_0)))
| ~ ssList(cons(esk13_0,esk6_2(esk12_0,esk13_0))) ),
inference(cn,[status(thm)],[35177,theory(equality)]) ).
cnf(43053,negated_conjecture,
( segmentP(esk12_0,cons(esk13_0,esk6_2(esk12_0,esk13_0)))
| ~ ssItem(esk13_0)
| ~ ssList(esk6_2(esk12_0,esk13_0)) ),
inference(spm,[status(thm)],[35178,135,theory(equality)]) ).
cnf(43055,negated_conjecture,
( segmentP(esk12_0,cons(esk13_0,esk6_2(esk12_0,esk13_0)))
| $false
| ~ ssList(esk6_2(esk12_0,esk13_0)) ),
inference(rw,[status(thm)],[43053,193,theory(equality)]) ).
cnf(43056,negated_conjecture,
( segmentP(esk12_0,cons(esk13_0,esk6_2(esk12_0,esk13_0)))
| $false
| $false ),
inference(rw,[status(thm)],[43055,481,theory(equality)]) ).
cnf(43057,negated_conjecture,
segmentP(esk12_0,cons(esk13_0,esk6_2(esk12_0,esk13_0))),
inference(cn,[status(thm)],[43056,theory(equality)]) ).
cnf(43067,negated_conjecture,
( segmentP(esk12_0,esk11_0)
| ~ ssList(esk12_0)
| ~ ssList(esk6_2(esk12_0,esk13_0)) ),
inference(spm,[status(thm)],[25998,43057,theory(equality)]) ).
cnf(43083,negated_conjecture,
( segmentP(esk12_0,esk11_0)
| $false
| ~ ssList(esk6_2(esk12_0,esk13_0)) ),
inference(rw,[status(thm)],[43067,189,theory(equality)]) ).
cnf(43084,negated_conjecture,
( segmentP(esk12_0,esk11_0)
| $false
| $false ),
inference(rw,[status(thm)],[43083,481,theory(equality)]) ).
cnf(43085,negated_conjecture,
segmentP(esk12_0,esk11_0),
inference(cn,[status(thm)],[43084,theory(equality)]) ).
cnf(43086,negated_conjecture,
$false,
inference(sr,[status(thm)],[43085,191,theory(equality)]) ).
cnf(43087,negated_conjecture,
$false,
43086,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC363+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpBx3TNc/sel_SWC363+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC363+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC363+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC363+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
%
%------------------------------------------------------------------------------