%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC285+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 11:14:03 EST 2010
% Result : Theorem 2.34s
% Output : CNFRefutation 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 17
% Syntax : Number of formulae : 217 ( 24 unt; 0 def)
% Number of atoms : 1070 ( 210 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 1467 ( 614 ~; 663 |; 128 &)
% ( 7 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 274 ( 0 sgn 169 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmpQe6OOG/sel_SWC285+1.p_1',ax84) ).
fof(2,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmpQe6OOG/sel_SWC285+1.p_1',ax83) ).
fof(3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/tmp/tmpQe6OOG/sel_SWC285+1.p_1',ax82) ).
fof(4,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpQe6OOG/sel_SWC285+1.p_1',ax81) ).
fof(9,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpQe6OOG/sel_SWC285+1.p_1',ax26) ).
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
file('/tmp/tmpQe6OOG/sel_SWC285+1.p_1',ax3) ).
fof(16,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
file('/tmp/tmpQe6OOG/sel_SWC285+1.p_1',ax4) ).
fof(20,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/tmp/tmpQe6OOG/sel_SWC285+1.p_1',ax58) ).
fof(21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpQe6OOG/sel_SWC285+1.p_1',ax15) ).
fof(22,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpQe6OOG/sel_SWC285+1.p_1',ax16) ).
fof(23,axiom,
ssList(nil),
file('/tmp/tmpQe6OOG/sel_SWC285+1.p_1',ax17) ).
fof(24,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X2,X1)
| memberP(X3,X1) ) ) ) ) ),
file('/tmp/tmpQe6OOG/sel_SWC285+1.p_1',ax36) ).
fof(25,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( X1 = X2
| memberP(X3,X1) ) ) ) ) ),
file('/tmp/tmpQe6OOG/sel_SWC285+1.p_1',ax37) ).
fof(26,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/tmp/tmpQe6OOG/sel_SWC285+1.p_1',ax38) ).
fof(27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X3) )
=> segmentP(X1,X3) ) ) ) ),
file('/tmp/tmpQe6OOG/sel_SWC285+1.p_1',ax53) ).
fof(33,axiom,
! [X1] :
( ssItem(X1)
=> leq(X1,X1) ),
file('/tmp/tmpQe6OOG/sel_SWC285+1.p_1',ax31) ).
fof(35,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ segmentP(X4,X3)
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(app(X6,cons(X5,nil)),X7) != X1
| ! [X8] :
( ssItem(X8)
=> ( ( ~ memberP(X6,X8)
| leq(X8,X5) )
& ( ~ memberP(X7,X8)
| leq(X5,X8) ) ) ) ) ) ) )
| ( ~ singletonP(X3)
& neq(X4,nil) ) ) ) ) ) ),
file('/tmp/tmpQe6OOG/sel_SWC285+1.p_1',co1) ).
fof(36,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ segmentP(X4,X3)
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(app(X6,cons(X5,nil)),X7) != X1
| ! [X8] :
( ssItem(X8)
=> ( ( ~ memberP(X6,X8)
| leq(X8,X5) )
& ( ~ memberP(X7,X8)
| leq(X5,X8) ) ) ) ) ) ) )
| ( ~ singletonP(X3)
& neq(X4,nil) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[35]) ).
fof(38,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[26,theory(equality)]) ).
fof(39,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ segmentP(X4,X3)
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(app(X6,cons(X5,nil)),X7) != X1
| ! [X8] :
( ssItem(X8)
=> ( ( ~ memberP(X6,X8)
| leq(X8,X5) )
& ( ~ memberP(X7,X8)
| leq(X5,X8) ) ) ) ) ) ) )
| ( ~ singletonP(X3)
& neq(X4,nil) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[36,theory(equality)]) ).
fof(40,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(41,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[40]) ).
cnf(42,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(43,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(44,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)],[43]) ).
fof(45,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)],[44]) ).
fof(46,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)],[45]) ).
cnf(48,plain,
( nil = X1
| ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[46]) ).
cnf(49,plain,
( nil = X2
| ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[46]) ).
fof(50,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(51,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)],[50]) ).
fof(52,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)],[51]) ).
cnf(53,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[52]) ).
fof(54,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(55,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[54]) ).
fof(56,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[55]) ).
cnf(57,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[56]) ).
fof(73,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(74,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[73]) ).
fof(75,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[74]) ).
cnf(76,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[75]) ).
fof(93,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)],[13]) ).
fof(94,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)],[93]) ).
fof(95,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)],[94]) ).
fof(96,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)],[95]) ).
fof(97,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)],[96]) ).
cnf(101,plain,
( memberP(X1,X2)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(X3,cons(X2,X4)) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[97]) ).
fof(112,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ singletonP(X1)
| ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) )
& ( ! [X2] :
( ~ ssItem(X2)
| cons(X2,nil) != X1 )
| singletonP(X1) ) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(113,plain,
! [X3] :
( ~ ssList(X3)
| ( ( ~ singletonP(X3)
| ? [X4] :
( ssItem(X4)
& cons(X4,nil) = X3 ) )
& ( ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X3 )
| singletonP(X3) ) ) ),
inference(variable_rename,[status(thm)],[112]) ).
fof(114,plain,
! [X3] :
( ~ ssList(X3)
| ( ( ~ singletonP(X3)
| ( ssItem(esk9_1(X3))
& cons(esk9_1(X3),nil) = X3 ) )
& ( ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X3 )
| singletonP(X3) ) ) ),
inference(skolemize,[status(esa)],[113]) ).
fof(115,plain,
! [X3,X5] :
( ( ( ~ ssItem(X5)
| cons(X5,nil) != X3
| singletonP(X3) )
& ( ~ singletonP(X3)
| ( ssItem(esk9_1(X3))
& cons(esk9_1(X3),nil) = X3 ) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[114]) ).
fof(116,plain,
! [X3,X5] :
( ( ~ ssItem(X5)
| cons(X5,nil) != X3
| singletonP(X3)
| ~ ssList(X3) )
& ( ssItem(esk9_1(X3))
| ~ singletonP(X3)
| ~ ssList(X3) )
& ( cons(esk9_1(X3),nil) = X3
| ~ singletonP(X3)
| ~ ssList(X3) ) ),
inference(distribute,[status(thm)],[115]) ).
cnf(117,plain,
( cons(esk9_1(X1),nil) = X1
| ~ ssList(X1)
| ~ singletonP(X1) ),
inference(split_conjunct,[status(thm)],[116]) ).
cnf(118,plain,
( ssItem(esk9_1(X1))
| ~ ssList(X1)
| ~ singletonP(X1) ),
inference(split_conjunct,[status(thm)],[116]) ).
fof(134,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(nil,X1)
| nil = X1 )
& ( nil != X1
| segmentP(nil,X1) ) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(135,plain,
! [X2] :
( ~ ssList(X2)
| ( ( ~ segmentP(nil,X2)
| nil = X2 )
& ( nil != X2
| segmentP(nil,X2) ) ) ),
inference(variable_rename,[status(thm)],[134]) ).
fof(136,plain,
! [X2] :
( ( ~ segmentP(nil,X2)
| nil = X2
| ~ ssList(X2) )
& ( nil != X2
| segmentP(nil,X2)
| ~ ssList(X2) ) ),
inference(distribute,[status(thm)],[135]) ).
cnf(137,plain,
( segmentP(nil,X1)
| ~ ssList(X1)
| nil != X1 ),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(138,plain,
( nil = X1
| ~ ssList(X1)
| ~ segmentP(nil,X1) ),
inference(split_conjunct,[status(thm)],[136]) ).
fof(139,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(140,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[139]) ).
fof(141,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[140]) ).
fof(142,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)],[141]) ).
cnf(143,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[142]) ).
fof(145,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(146,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[145]) ).
fof(147,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[146]) ).
cnf(148,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[147]) ).
cnf(149,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[23]) ).
fof(150,plain,
! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ( ( ~ memberP(app(X2,X3),X1)
| memberP(X2,X1)
| memberP(X3,X1) )
& ( ( ~ memberP(X2,X1)
& ~ memberP(X3,X1) )
| memberP(app(X2,X3),X1) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(151,plain,
! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ memberP(app(X5,X6),X4)
| memberP(X5,X4)
| memberP(X6,X4) )
& ( ( ~ memberP(X5,X4)
& ~ memberP(X6,X4) )
| memberP(app(X5,X6),X4) ) ) ) ) ),
inference(variable_rename,[status(thm)],[150]) ).
fof(152,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ( ( ~ memberP(app(X5,X6),X4)
| memberP(X5,X4)
| memberP(X6,X4) )
& ( ( ~ memberP(X5,X4)
& ~ memberP(X6,X4) )
| memberP(app(X5,X6),X4) ) )
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(shift_quantors,[status(thm)],[151]) ).
fof(153,plain,
! [X4,X5,X6] :
( ( ~ memberP(app(X5,X6),X4)
| memberP(X5,X4)
| memberP(X6,X4)
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) )
& ( ~ memberP(X5,X4)
| memberP(app(X5,X6),X4)
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) )
& ( ~ memberP(X6,X4)
| memberP(app(X5,X6),X4)
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ) ),
inference(distribute,[status(thm)],[152]) ).
cnf(154,plain,
( memberP(app(X2,X3),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(X3,X1) ),
inference(split_conjunct,[status(thm)],[153]) ).
cnf(155,plain,
( memberP(app(X2,X3),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(X2,X1) ),
inference(split_conjunct,[status(thm)],[153]) ).
fof(157,plain,
! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssItem(X2)
| ! [X3] :
( ~ ssList(X3)
| ( ( ~ memberP(cons(X2,X3),X1)
| X1 = X2
| memberP(X3,X1) )
& ( ( X1 != X2
& ~ memberP(X3,X1) )
| memberP(cons(X2,X3),X1) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(158,plain,
! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ memberP(cons(X5,X6),X4)
| X4 = X5
| memberP(X6,X4) )
& ( ( X4 != X5
& ~ memberP(X6,X4) )
| memberP(cons(X5,X6),X4) ) ) ) ) ),
inference(variable_rename,[status(thm)],[157]) ).
fof(159,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ( ( ~ memberP(cons(X5,X6),X4)
| X4 = X5
| memberP(X6,X4) )
& ( ( X4 != X5
& ~ memberP(X6,X4) )
| memberP(cons(X5,X6),X4) ) )
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(shift_quantors,[status(thm)],[158]) ).
fof(160,plain,
! [X4,X5,X6] :
( ( ~ memberP(cons(X5,X6),X4)
| X4 = X5
| memberP(X6,X4)
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) )
& ( X4 != X5
| memberP(cons(X5,X6),X4)
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) )
& ( ~ memberP(X6,X4)
| memberP(cons(X5,X6),X4)
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ) ),
inference(distribute,[status(thm)],[159]) ).
cnf(163,plain,
( memberP(X3,X1)
| X1 = X2
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ memberP(cons(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[160]) ).
fof(164,plain,
! [X1] :
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(fof_nnf,[status(thm)],[38]) ).
fof(165,plain,
! [X2] :
( ~ ssItem(X2)
| ~ memberP(nil,X2) ),
inference(variable_rename,[status(thm)],[164]) ).
cnf(166,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[165]) ).
fof(167,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X3)
| segmentP(X1,X3) ) ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(168,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ~ segmentP(X4,X5)
| ~ segmentP(X5,X6)
| segmentP(X4,X6) ) ) ),
inference(variable_rename,[status(thm)],[167]) ).
fof(169,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ~ segmentP(X4,X5)
| ~ segmentP(X5,X6)
| segmentP(X4,X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[168]) ).
cnf(170,plain,
( segmentP(X1,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[169]) ).
fof(189,plain,
! [X1] :
( ~ ssItem(X1)
| leq(X1,X1) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(190,plain,
! [X2] :
( ~ ssItem(X2)
| leq(X2,X2) ),
inference(variable_rename,[status(thm)],[189]) ).
cnf(191,plain,
( leq(X1,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[190]) ).
fof(198,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& segmentP(X4,X3)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ? [X8] :
( ssItem(X8)
& ( ( memberP(X6,X8)
& ~ leq(X8,X5) )
| ( memberP(X7,X8)
& ~ leq(X5,X8) ) ) ) ) ) )
& ( singletonP(X3)
| ~ neq(X4,nil) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(199,negated_conjecture,
? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& X10 = X12
& X9 = X11
& segmentP(X12,X11)
& ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssList(X14)
& ? [X15] :
( ssList(X15)
& app(app(X14,cons(X13,nil)),X15) = X9
& ? [X16] :
( ssItem(X16)
& ( ( memberP(X14,X16)
& ~ leq(X16,X13) )
| ( memberP(X15,X16)
& ~ leq(X13,X16) ) ) ) ) ) )
& ( singletonP(X11)
| ~ neq(X12,nil) ) ) ) ) ),
inference(variable_rename,[status(thm)],[198]) ).
fof(200,negated_conjecture,
( ssList(esk10_0)
& ssList(esk11_0)
& ssList(esk12_0)
& ssList(esk13_0)
& esk11_0 = esk13_0
& esk10_0 = esk12_0
& segmentP(esk13_0,esk12_0)
& ssItem(esk14_0)
& ssList(esk15_0)
& ssList(esk16_0)
& app(app(esk15_0,cons(esk14_0,nil)),esk16_0) = esk10_0
& ssItem(esk17_0)
& ( ( memberP(esk15_0,esk17_0)
& ~ leq(esk17_0,esk14_0) )
| ( memberP(esk16_0,esk17_0)
& ~ leq(esk14_0,esk17_0) ) )
& ( singletonP(esk12_0)
| ~ neq(esk13_0,nil) ) ),
inference(skolemize,[status(esa)],[199]) ).
fof(201,negated_conjecture,
( ssList(esk10_0)
& ssList(esk11_0)
& ssList(esk12_0)
& ssList(esk13_0)
& esk11_0 = esk13_0
& esk10_0 = esk12_0
& segmentP(esk13_0,esk12_0)
& ssItem(esk14_0)
& ssList(esk15_0)
& ssList(esk16_0)
& app(app(esk15_0,cons(esk14_0,nil)),esk16_0) = esk10_0
& ssItem(esk17_0)
& ( memberP(esk16_0,esk17_0)
| memberP(esk15_0,esk17_0) )
& ( ~ leq(esk14_0,esk17_0)
| memberP(esk15_0,esk17_0) )
& ( memberP(esk16_0,esk17_0)
| ~ leq(esk17_0,esk14_0) )
& ( ~ leq(esk14_0,esk17_0)
| ~ leq(esk17_0,esk14_0) )
& ( singletonP(esk12_0)
| ~ neq(esk13_0,nil) ) ),
inference(distribute,[status(thm)],[200]) ).
cnf(202,negated_conjecture,
( singletonP(esk12_0)
| ~ neq(esk13_0,nil) ),
inference(split_conjunct,[status(thm)],[201]) ).
cnf(203,negated_conjecture,
( ~ leq(esk17_0,esk14_0)
| ~ leq(esk14_0,esk17_0) ),
inference(split_conjunct,[status(thm)],[201]) ).
cnf(206,negated_conjecture,
( memberP(esk15_0,esk17_0)
| memberP(esk16_0,esk17_0) ),
inference(split_conjunct,[status(thm)],[201]) ).
cnf(207,negated_conjecture,
ssItem(esk17_0),
inference(split_conjunct,[status(thm)],[201]) ).
cnf(208,negated_conjecture,
app(app(esk15_0,cons(esk14_0,nil)),esk16_0) = esk10_0,
inference(split_conjunct,[status(thm)],[201]) ).
cnf(209,negated_conjecture,
ssList(esk16_0),
inference(split_conjunct,[status(thm)],[201]) ).
cnf(210,negated_conjecture,
ssList(esk15_0),
inference(split_conjunct,[status(thm)],[201]) ).
cnf(211,negated_conjecture,
ssItem(esk14_0),
inference(split_conjunct,[status(thm)],[201]) ).
cnf(212,negated_conjecture,
segmentP(esk13_0,esk12_0),
inference(split_conjunct,[status(thm)],[201]) ).
cnf(213,negated_conjecture,
esk10_0 = esk12_0,
inference(split_conjunct,[status(thm)],[201]) ).
cnf(214,negated_conjecture,
esk11_0 = esk13_0,
inference(split_conjunct,[status(thm)],[201]) ).
cnf(217,negated_conjecture,
ssList(esk11_0),
inference(split_conjunct,[status(thm)],[201]) ).
cnf(218,negated_conjecture,
ssList(esk10_0),
inference(split_conjunct,[status(thm)],[201]) ).
cnf(219,negated_conjecture,
ssList(esk12_0),
inference(rw,[status(thm)],[218,213,theory(equality)]) ).
cnf(220,negated_conjecture,
ssList(esk13_0),
inference(rw,[status(thm)],[217,214,theory(equality)]) ).
cnf(222,negated_conjecture,
app(app(esk15_0,cons(esk14_0,nil)),esk16_0) = esk12_0,
inference(rw,[status(thm)],[208,213,theory(equality)]) ).
cnf(230,negated_conjecture,
( singletonP(esk12_0)
| esk13_0 = nil
| ~ ssList(nil)
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[202,143,theory(equality)]) ).
cnf(231,negated_conjecture,
( singletonP(esk12_0)
| esk13_0 = nil
| $false
| ~ ssList(esk13_0) ),
inference(rw,[status(thm)],[230,149,theory(equality)]) ).
cnf(232,negated_conjecture,
( singletonP(esk12_0)
| esk13_0 = nil
| ~ ssList(esk13_0) ),
inference(cn,[status(thm)],[231,theory(equality)]) ).
cnf(236,negated_conjecture,
( nil = esk16_0
| esk12_0 != nil
| ~ ssList(esk16_0)
| ~ ssList(app(esk15_0,cons(esk14_0,nil))) ),
inference(spm,[status(thm)],[49,222,theory(equality)]) ).
cnf(284,negated_conjecture,
( memberP(esk12_0,X1)
| ~ memberP(esk16_0,X1)
| ~ ssItem(X1)
| ~ ssList(esk16_0)
| ~ ssList(app(esk15_0,cons(esk14_0,nil))) ),
inference(spm,[status(thm)],[154,222,theory(equality)]) ).
cnf(307,negated_conjecture,
( segmentP(X1,esk12_0)
| ~ segmentP(X1,esk13_0)
| ~ ssList(esk12_0)
| ~ ssList(esk13_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[170,212,theory(equality)]) ).
cnf(362,plain,
( X1 = esk9_1(X2)
| memberP(nil,X1)
| ~ memberP(X2,X1)
| ~ ssItem(esk9_1(X2))
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ singletonP(X2)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[163,117,theory(equality)]) ).
cnf(365,plain,
( X1 = esk9_1(X2)
| memberP(nil,X1)
| ~ memberP(X2,X1)
| ~ ssItem(esk9_1(X2))
| ~ ssItem(X1)
| $false
| ~ singletonP(X2)
| ~ ssList(X2) ),
inference(rw,[status(thm)],[362,149,theory(equality)]) ).
cnf(366,plain,
( X1 = esk9_1(X2)
| memberP(nil,X1)
| ~ memberP(X2,X1)
| ~ ssItem(esk9_1(X2))
| ~ ssItem(X1)
| ~ singletonP(X2)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[365,theory(equality)]) ).
cnf(387,plain,
( memberP(app(X1,cons(X2,X3)),X2)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(app(X1,cons(X2,X3))) ),
inference(er,[status(thm)],[101,theory(equality)]) ).
cnf(397,negated_conjecture,
( app(esk15_0,app(cons(esk14_0,nil),esk16_0)) = esk12_0
| ~ ssList(esk16_0)
| ~ ssList(cons(esk14_0,nil))
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[222,53,theory(equality)]) ).
cnf(409,plain,
( memberP(app(X1,app(X2,X3)),X4)
| ~ memberP(app(X1,X2),X4)
| ~ ssItem(X4)
| ~ ssList(X3)
| ~ ssList(app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[155,53,theory(equality)]) ).
cnf(526,negated_conjecture,
( singletonP(esk12_0)
| esk13_0 = nil
| $false ),
inference(rw,[status(thm)],[232,220,theory(equality)]) ).
cnf(527,negated_conjecture,
( singletonP(esk12_0)
| esk13_0 = nil ),
inference(cn,[status(thm)],[526,theory(equality)]) ).
cnf(567,negated_conjecture,
( segmentP(X1,esk12_0)
| ~ segmentP(X1,esk13_0)
| $false
| ~ ssList(esk13_0)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[307,219,theory(equality)]) ).
cnf(568,negated_conjecture,
( segmentP(X1,esk12_0)
| ~ segmentP(X1,esk13_0)
| $false
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[567,220,theory(equality)]) ).
cnf(569,negated_conjecture,
( segmentP(X1,esk12_0)
| ~ segmentP(X1,esk13_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[568,theory(equality)]) ).
cnf(570,negated_conjecture,
( nil = esk12_0
| ~ ssList(esk12_0)
| ~ segmentP(nil,esk13_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[138,569,theory(equality)]) ).
cnf(573,negated_conjecture,
( nil = esk12_0
| $false
| ~ segmentP(nil,esk13_0)
| ~ ssList(nil) ),
inference(rw,[status(thm)],[570,219,theory(equality)]) ).
cnf(574,negated_conjecture,
( nil = esk12_0
| $false
| ~ segmentP(nil,esk13_0)
| $false ),
inference(rw,[status(thm)],[573,149,theory(equality)]) ).
cnf(575,negated_conjecture,
( nil = esk12_0
| ~ segmentP(nil,esk13_0) ),
inference(cn,[status(thm)],[574,theory(equality)]) ).
cnf(580,negated_conjecture,
( esk12_0 = nil
| nil != esk13_0
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[575,137,theory(equality)]) ).
cnf(581,negated_conjecture,
( esk12_0 = nil
| nil != esk13_0
| $false ),
inference(rw,[status(thm)],[580,220,theory(equality)]) ).
cnf(582,negated_conjecture,
( esk12_0 = nil
| nil != esk13_0 ),
inference(cn,[status(thm)],[581,theory(equality)]) ).
cnf(598,negated_conjecture,
( esk16_0 = nil
| esk12_0 != nil
| ~ ssList(esk16_0)
| ~ ssList(cons(esk14_0,nil))
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[236,76,theory(equality)]) ).
cnf(617,negated_conjecture,
( esk16_0 = nil
| esk12_0 != nil
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| ~ ssItem(esk14_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[598,148,theory(equality)]) ).
cnf(618,negated_conjecture,
( esk16_0 = nil
| esk12_0 != nil
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| $false
| ~ ssList(nil) ),
inference(rw,[status(thm)],[617,211,theory(equality)]) ).
cnf(619,negated_conjecture,
( esk16_0 = nil
| esk12_0 != nil
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| $false
| $false ),
inference(rw,[status(thm)],[618,149,theory(equality)]) ).
cnf(620,negated_conjecture,
( esk16_0 = nil
| esk12_0 != nil
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(cn,[status(thm)],[619,theory(equality)]) ).
cnf(621,negated_conjecture,
( esk16_0 = nil
| esk12_0 != nil
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[620,209,theory(equality)]) ).
cnf(622,negated_conjecture,
( esk16_0 = nil
| esk12_0 != nil ),
inference(spm,[status(thm)],[621,210,theory(equality)]) ).
cnf(624,negated_conjecture,
( app(app(esk15_0,cons(esk14_0,nil)),nil) = esk12_0
| esk12_0 != nil ),
inference(spm,[status(thm)],[222,622,theory(equality)]) ).
cnf(625,negated_conjecture,
( memberP(nil,esk17_0)
| memberP(esk15_0,esk17_0)
| esk12_0 != nil ),
inference(spm,[status(thm)],[206,622,theory(equality)]) ).
cnf(696,negated_conjecture,
( esk12_0 = app(esk15_0,cons(esk14_0,nil))
| ~ ssList(app(esk15_0,cons(esk14_0,nil)))
| esk12_0 != nil ),
inference(spm,[status(thm)],[42,624,theory(equality)]) ).
cnf(791,negated_conjecture,
( app(esk15_0,cons(esk14_0,nil)) = esk12_0
| esk12_0 != nil
| ~ ssList(cons(esk14_0,nil))
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[696,76,theory(equality)]) ).
cnf(798,negated_conjecture,
( nil = esk15_0
| esk12_0 != nil
| ~ ssList(cons(esk14_0,nil))
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[48,791,theory(equality)]) ).
cnf(842,negated_conjecture,
( esk15_0 = nil
| esk12_0 != nil
| ~ ssList(esk15_0)
| ~ ssItem(esk14_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[798,148,theory(equality)]) ).
cnf(843,negated_conjecture,
( esk15_0 = nil
| esk12_0 != nil
| ~ ssList(esk15_0)
| $false
| ~ ssList(nil) ),
inference(rw,[status(thm)],[842,211,theory(equality)]) ).
cnf(844,negated_conjecture,
( esk15_0 = nil
| esk12_0 != nil
| ~ ssList(esk15_0)
| $false
| $false ),
inference(rw,[status(thm)],[843,149,theory(equality)]) ).
cnf(845,negated_conjecture,
( esk15_0 = nil
| esk12_0 != nil
| ~ ssList(esk15_0) ),
inference(cn,[status(thm)],[844,theory(equality)]) ).
cnf(846,negated_conjecture,
( esk15_0 = nil
| esk12_0 != nil ),
inference(spm,[status(thm)],[845,210,theory(equality)]) ).
cnf(850,negated_conjecture,
( memberP(nil,esk17_0)
| esk12_0 != nil ),
inference(spm,[status(thm)],[625,846,theory(equality)]) ).
cnf(859,negated_conjecture,
( ~ ssItem(esk17_0)
| esk12_0 != nil ),
inference(spm,[status(thm)],[166,850,theory(equality)]) ).
cnf(860,negated_conjecture,
( $false
| esk12_0 != nil ),
inference(rw,[status(thm)],[859,207,theory(equality)]) ).
cnf(861,negated_conjecture,
esk12_0 != nil,
inference(cn,[status(thm)],[860,theory(equality)]) ).
cnf(864,negated_conjecture,
esk13_0 != nil,
inference(spm,[status(thm)],[861,582,theory(equality)]) ).
cnf(865,negated_conjecture,
singletonP(esk12_0),
inference(sr,[status(thm)],[527,864,theory(equality)]) ).
cnf(985,negated_conjecture,
( memberP(esk12_0,X1)
| ~ memberP(esk16_0,X1)
| ~ ssItem(X1)
| ~ ssList(esk16_0)
| ~ ssList(cons(esk14_0,nil))
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[284,76,theory(equality)]) ).
cnf(1053,negated_conjecture,
( memberP(esk12_0,X1)
| ~ memberP(esk16_0,X1)
| ~ ssItem(X1)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| ~ ssItem(esk14_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[985,148,theory(equality)]) ).
cnf(1054,negated_conjecture,
( memberP(esk12_0,X1)
| ~ memberP(esk16_0,X1)
| ~ ssItem(X1)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| $false
| ~ ssList(nil) ),
inference(rw,[status(thm)],[1053,211,theory(equality)]) ).
cnf(1055,negated_conjecture,
( memberP(esk12_0,X1)
| ~ memberP(esk16_0,X1)
| ~ ssItem(X1)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| $false
| $false ),
inference(rw,[status(thm)],[1054,149,theory(equality)]) ).
cnf(1056,negated_conjecture,
( memberP(esk12_0,X1)
| ~ memberP(esk16_0,X1)
| ~ ssItem(X1)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(cn,[status(thm)],[1055,theory(equality)]) ).
cnf(1065,negated_conjecture,
( memberP(esk12_0,esk17_0)
| memberP(esk15_0,esk17_0)
| ~ ssItem(esk17_0)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[1056,206,theory(equality)]) ).
cnf(1068,negated_conjecture,
( memberP(esk12_0,esk17_0)
| memberP(esk15_0,esk17_0)
| $false
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(rw,[status(thm)],[1065,207,theory(equality)]) ).
cnf(1069,negated_conjecture,
( memberP(esk12_0,esk17_0)
| memberP(esk15_0,esk17_0)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(cn,[status(thm)],[1068,theory(equality)]) ).
cnf(1671,negated_conjecture,
( app(esk15_0,cons(esk14_0,esk16_0)) = esk12_0
| ~ ssList(cons(esk14_0,nil))
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| ~ ssItem(esk14_0) ),
inference(spm,[status(thm)],[397,57,theory(equality)]) ).
cnf(1693,negated_conjecture,
( app(esk15_0,cons(esk14_0,esk16_0)) = esk12_0
| ~ ssList(cons(esk14_0,nil))
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| $false ),
inference(rw,[status(thm)],[1671,211,theory(equality)]) ).
cnf(1694,negated_conjecture,
( app(esk15_0,cons(esk14_0,esk16_0)) = esk12_0
| ~ ssList(cons(esk14_0,nil))
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(cn,[status(thm)],[1693,theory(equality)]) ).
cnf(2427,plain,
( X1 = esk9_1(X2)
| memberP(nil,X1)
| ~ singletonP(X2)
| ~ memberP(X2,X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[366,118]) ).
cnf(2428,plain,
( X1 = esk9_1(X2)
| ~ singletonP(X2)
| ~ memberP(X2,X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[2427,166]) ).
cnf(3052,negated_conjecture,
( memberP(esk12_0,esk14_0)
| ~ ssItem(esk14_0)
| ~ ssList(esk12_0)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| ~ ssList(cons(esk14_0,nil)) ),
inference(spm,[status(thm)],[387,1694,theory(equality)]) ).
cnf(3065,negated_conjecture,
( memberP(esk12_0,esk14_0)
| $false
| ~ ssList(esk12_0)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| ~ ssList(cons(esk14_0,nil)) ),
inference(rw,[status(thm)],[3052,211,theory(equality)]) ).
cnf(3066,negated_conjecture,
( memberP(esk12_0,esk14_0)
| $false
| $false
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| ~ ssList(cons(esk14_0,nil)) ),
inference(rw,[status(thm)],[3065,219,theory(equality)]) ).
cnf(3067,negated_conjecture,
( memberP(esk12_0,esk14_0)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| ~ ssList(cons(esk14_0,nil)) ),
inference(cn,[status(thm)],[3066,theory(equality)]) ).
cnf(3092,negated_conjecture,
( memberP(esk12_0,esk14_0)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| ~ ssItem(esk14_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[3067,148,theory(equality)]) ).
cnf(3093,negated_conjecture,
( memberP(esk12_0,esk14_0)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| $false
| ~ ssList(nil) ),
inference(rw,[status(thm)],[3092,211,theory(equality)]) ).
cnf(3094,negated_conjecture,
( memberP(esk12_0,esk14_0)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| $false
| $false ),
inference(rw,[status(thm)],[3093,149,theory(equality)]) ).
cnf(3095,negated_conjecture,
( memberP(esk12_0,esk14_0)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(cn,[status(thm)],[3094,theory(equality)]) ).
cnf(3098,negated_conjecture,
( esk14_0 = esk9_1(esk12_0)
| ~ singletonP(esk12_0)
| ~ ssItem(esk14_0)
| ~ ssList(esk12_0)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[2428,3095,theory(equality)]) ).
cnf(3102,negated_conjecture,
( esk14_0 = esk9_1(esk12_0)
| $false
| ~ ssItem(esk14_0)
| ~ ssList(esk12_0)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(rw,[status(thm)],[3098,865,theory(equality)]) ).
cnf(3103,negated_conjecture,
( esk14_0 = esk9_1(esk12_0)
| $false
| $false
| ~ ssList(esk12_0)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(rw,[status(thm)],[3102,211,theory(equality)]) ).
cnf(3104,negated_conjecture,
( esk14_0 = esk9_1(esk12_0)
| $false
| $false
| $false
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(rw,[status(thm)],[3103,219,theory(equality)]) ).
cnf(3105,negated_conjecture,
( esk14_0 = esk9_1(esk12_0)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(cn,[status(thm)],[3104,theory(equality)]) ).
cnf(3124,negated_conjecture,
( cons(esk14_0,nil) = esk12_0
| ~ singletonP(esk12_0)
| ~ ssList(esk12_0)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[117,3105,theory(equality)]) ).
cnf(3133,negated_conjecture,
( cons(esk14_0,nil) = esk12_0
| $false
| ~ ssList(esk12_0)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(rw,[status(thm)],[3124,865,theory(equality)]) ).
cnf(3134,negated_conjecture,
( cons(esk14_0,nil) = esk12_0
| $false
| $false
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(rw,[status(thm)],[3133,219,theory(equality)]) ).
cnf(3135,negated_conjecture,
( cons(esk14_0,nil) = esk12_0
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(cn,[status(thm)],[3134,theory(equality)]) ).
cnf(3187,negated_conjecture,
( app(esk15_0,app(esk12_0,esk16_0)) = esk12_0
| ~ ssList(esk12_0)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[397,3135,theory(equality)]) ).
cnf(3273,negated_conjecture,
( app(esk15_0,app(esk12_0,esk16_0)) = esk12_0
| $false
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(rw,[status(thm)],[3187,219,theory(equality)]) ).
cnf(3274,negated_conjecture,
( app(esk15_0,app(esk12_0,esk16_0)) = esk12_0
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(cn,[status(thm)],[3273,theory(equality)]) ).
cnf(5038,negated_conjecture,
( X1 = esk14_0
| memberP(nil,X1)
| ~ memberP(esk12_0,X1)
| ~ ssItem(esk14_0)
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[163,3135,theory(equality)]) ).
cnf(5088,negated_conjecture,
( X1 = esk14_0
| memberP(nil,X1)
| ~ memberP(esk12_0,X1)
| $false
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(rw,[status(thm)],[5038,211,theory(equality)]) ).
cnf(5089,negated_conjecture,
( X1 = esk14_0
| memberP(nil,X1)
| ~ memberP(esk12_0,X1)
| $false
| ~ ssItem(X1)
| $false
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(rw,[status(thm)],[5088,149,theory(equality)]) ).
cnf(5090,negated_conjecture,
( X1 = esk14_0
| memberP(nil,X1)
| ~ memberP(esk12_0,X1)
| ~ ssItem(X1)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(cn,[status(thm)],[5089,theory(equality)]) ).
cnf(6697,plain,
( memberP(app(X1,app(X2,X3)),X4)
| ~ memberP(app(X1,X2),X4)
| ~ ssItem(X4)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[409,76]) ).
cnf(13224,negated_conjecture,
( X1 = esk14_0
| ~ memberP(esk12_0,X1)
| ~ ssItem(X1)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(csr,[status(thm)],[5090,166]) ).
cnf(34434,negated_conjecture,
( memberP(esk12_0,X1)
| ~ memberP(app(esk15_0,esk12_0),X1)
| ~ ssItem(X1)
| ~ ssList(esk16_0)
| ~ ssList(esk12_0)
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[6697,3274,theory(equality)]) ).
cnf(34514,negated_conjecture,
( memberP(esk12_0,X1)
| ~ memberP(app(esk15_0,esk12_0),X1)
| ~ ssItem(X1)
| ~ ssList(esk16_0)
| $false
| ~ ssList(esk15_0) ),
inference(rw,[status(thm)],[34434,219,theory(equality)]) ).
cnf(34515,negated_conjecture,
( memberP(esk12_0,X1)
| ~ memberP(app(esk15_0,esk12_0),X1)
| ~ ssItem(X1)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(cn,[status(thm)],[34514,theory(equality)]) ).
cnf(46735,negated_conjecture,
( memberP(esk12_0,X1)
| ~ ssItem(X1)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| ~ memberP(esk15_0,X1)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[34515,155,theory(equality)]) ).
cnf(46751,negated_conjecture,
( memberP(esk12_0,X1)
| ~ ssItem(X1)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| ~ memberP(esk15_0,X1)
| $false ),
inference(rw,[status(thm)],[46735,219,theory(equality)]) ).
cnf(46752,negated_conjecture,
( memberP(esk12_0,X1)
| ~ ssItem(X1)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0)
| ~ memberP(esk15_0,X1) ),
inference(cn,[status(thm)],[46751,theory(equality)]) ).
cnf(46771,negated_conjecture,
( memberP(esk12_0,esk17_0)
| ~ ssItem(esk17_0)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[46752,1069,theory(equality)]) ).
cnf(46781,negated_conjecture,
( memberP(esk12_0,esk17_0)
| $false
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(rw,[status(thm)],[46771,207,theory(equality)]) ).
cnf(46782,negated_conjecture,
( memberP(esk12_0,esk17_0)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(cn,[status(thm)],[46781,theory(equality)]) ).
cnf(46796,negated_conjecture,
( esk17_0 = esk14_0
| ~ ssItem(esk17_0)
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[13224,46782,theory(equality)]) ).
cnf(46812,negated_conjecture,
( esk17_0 = esk14_0
| $false
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(rw,[status(thm)],[46796,207,theory(equality)]) ).
cnf(46813,negated_conjecture,
( esk17_0 = esk14_0
| ~ ssList(esk16_0)
| ~ ssList(esk15_0) ),
inference(cn,[status(thm)],[46812,theory(equality)]) ).
cnf(46814,negated_conjecture,
( esk14_0 = esk17_0
| ~ ssList(esk15_0) ),
inference(spm,[status(thm)],[46813,209,theory(equality)]) ).
cnf(46818,negated_conjecture,
esk14_0 = esk17_0,
inference(spm,[status(thm)],[46814,210,theory(equality)]) ).
cnf(46884,negated_conjecture,
( ~ leq(esk17_0,esk17_0)
| ~ leq(esk17_0,esk14_0) ),
inference(rw,[status(thm)],[203,46818,theory(equality)]) ).
cnf(46885,negated_conjecture,
( ~ leq(esk17_0,esk17_0)
| ~ leq(esk17_0,esk17_0) ),
inference(rw,[status(thm)],[46884,46818,theory(equality)]) ).
cnf(46886,negated_conjecture,
~ leq(esk17_0,esk17_0),
inference(cn,[status(thm)],[46885,theory(equality)]) ).
cnf(46889,negated_conjecture,
~ ssItem(esk17_0),
inference(spm,[status(thm)],[46886,191,theory(equality)]) ).
cnf(46890,negated_conjecture,
$false,
inference(rw,[status(thm)],[46889,207,theory(equality)]) ).
cnf(46891,negated_conjecture,
$false,
inference(cn,[status(thm)],[46890,theory(equality)]) ).
cnf(46892,negated_conjecture,
$false,
46891,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC285+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpQe6OOG/sel_SWC285+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC285+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC285+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC285+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
%
%------------------------------------------------------------------------------