TSTP Solution File: SWC005+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC005+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 10:04:03 EST 2010
% Result : Theorem 0.49s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 16
% Syntax : Number of formulae : 179 ( 15 unt; 0 def)
% Number of atoms : 761 ( 290 equ)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 998 ( 416 ~; 453 |; 87 &)
% ( 2 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 263 ( 0 sgn 131 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmphdwd2p/sel_SWC005+1.p_1',ax84) ).
fof(4,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmphdwd2p/sel_SWC005+1.p_1',ax83) ).
fof(5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/tmp/tmphdwd2p/sel_SWC005+1.p_1',ax82) ).
fof(6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmphdwd2p/sel_SWC005+1.p_1',ax81) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmphdwd2p/sel_SWC005+1.p_1',ax28) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/tmp/tmphdwd2p/sel_SWC005+1.p_1',ax24) ).
fof(11,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/tmp/tmphdwd2p/sel_SWC005+1.p_1',ax27) ).
fof(12,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmphdwd2p/sel_SWC005+1.p_1',ax26) ).
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmphdwd2p/sel_SWC005+1.p_1',ax21) ).
fof(15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/tmp/tmphdwd2p/sel_SWC005+1.p_1',ax23) ).
fof(16,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/tmp/tmphdwd2p/sel_SWC005+1.p_1',ax22) ).
fof(22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/tmp/tmphdwd2p/sel_SWC005+1.p_1',ax78) ).
fof(24,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmphdwd2p/sel_SWC005+1.p_1',ax15) ).
fof(25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmphdwd2p/sel_SWC005+1.p_1',ax16) ).
fof(26,axiom,
ssList(nil),
file('/tmp/tmphdwd2p/sel_SWC005+1.p_1',ax17) ).
fof(29,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X5,X6),X7) = X2
& app(X5,X7) = X1
& neq(X6,nil) ) ) )
| ? [X8] :
( ssList(X8)
& X3 != X8
& tl(X4) = X8
& neq(nil,X4) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/tmp/tmphdwd2p/sel_SWC005+1.p_1',co1) ).
fof(30,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X5,X6),X7) = X2
& app(X5,X7) = X1
& neq(X6,nil) ) ) )
| ? [X8] :
( ssList(X8)
& X3 != X8
& tl(X4) = X8
& neq(nil,X4) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[29]) ).
fof(31,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X5,X6),X7) = X2
& app(X5,X7) = X1
& neq(X6,nil) ) ) )
| ? [X8] :
( ssList(X8)
& X3 != X8
& tl(X4) = X8
& neq(nil,X4) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[30,theory(equality)]) ).
fof(40,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[3]) ).
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)],[4]) ).
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(47,plain,
( nil = app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| nil != X1
| nil != 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)],[5]) ).
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)],[6]) ).
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(62,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(63,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[62]) ).
cnf(64,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[63]) ).
fof(69,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(70,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| ssList(tl(X2)) ),
inference(variable_rename,[status(thm)],[69]) ).
cnf(71,plain,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[70]) ).
fof(72,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)],[11]) ).
fof(73,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)],[72]) ).
fof(74,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)],[73]) ).
cnf(75,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[74]) ).
fof(76,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(77,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[76]) ).
fof(78,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[77]) ).
cnf(79,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[78]) ).
fof(80,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| nil != cons(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(81,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3) ) ),
inference(variable_rename,[status(thm)],[80]) ).
fof(82,plain,
! [X3,X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[81]) ).
cnf(83,plain,
( ~ ssList(X1)
| nil != cons(X2,X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[82]) ).
fof(91,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| hd(cons(X2,X1)) = X2 ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(92,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| hd(cons(X4,X3)) = X4 ) ),
inference(variable_rename,[status(thm)],[91]) ).
fof(93,plain,
! [X3,X4] :
( ~ ssItem(X4)
| hd(cons(X4,X3)) = X4
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[92]) ).
cnf(94,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[93]) ).
fof(95,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(96,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| ssItem(hd(X2)) ),
inference(variable_rename,[status(thm)],[95]) ).
cnf(97,plain,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[96]) ).
fof(125,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(126,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| cons(hd(X2),tl(X2)) = X2 ),
inference(variable_rename,[status(thm)],[125]) ).
cnf(127,plain,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[126]) ).
fof(132,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(133,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[132]) ).
fof(134,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[133]) ).
fof(135,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)],[134]) ).
cnf(136,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[135]) ).
cnf(137,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[135]) ).
fof(138,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(139,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[138]) ).
fof(140,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[139]) ).
cnf(141,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[140]) ).
cnf(142,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[26]) ).
fof(153,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ( ( neq(X2,nil)
& ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssList(X7)
| app(app(X5,X6),X7) != X2
| app(X5,X7) != X1
| ~ neq(X6,nil) ) ) )
& ! [X8] :
( ~ ssList(X8)
| X3 = X8
| tl(X4) != X8
| ~ neq(nil,X4) ) )
| ( neq(X2,nil)
& ~ neq(X4,nil) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(154,negated_conjecture,
? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& X10 = X12
& X9 = X11
& ( ( neq(X10,nil)
& ! [X13] :
( ~ ssList(X13)
| ! [X14] :
( ~ ssList(X14)
| ! [X15] :
( ~ ssList(X15)
| app(app(X13,X14),X15) != X10
| app(X13,X15) != X9
| ~ neq(X14,nil) ) ) )
& ! [X16] :
( ~ ssList(X16)
| X11 = X16
| tl(X12) != X16
| ~ neq(nil,X12) ) )
| ( neq(X10,nil)
& ~ neq(X12,nil) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[153]) ).
fof(155,negated_conjecture,
( ssList(esk7_0)
& ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ( ( neq(esk8_0,nil)
& ! [X13] :
( ~ ssList(X13)
| ! [X14] :
( ~ ssList(X14)
| ! [X15] :
( ~ ssList(X15)
| app(app(X13,X14),X15) != esk8_0
| app(X13,X15) != esk7_0
| ~ neq(X14,nil) ) ) )
& ! [X16] :
( ~ ssList(X16)
| esk9_0 = X16
| tl(esk10_0) != X16
| ~ neq(nil,esk10_0) ) )
| ( neq(esk8_0,nil)
& ~ neq(esk10_0,nil) ) ) ),
inference(skolemize,[status(esa)],[154]) ).
fof(156,negated_conjecture,
! [X13,X14,X15,X16] :
( ( ( ( ~ ssList(X16)
| esk9_0 = X16
| tl(esk10_0) != X16
| ~ neq(nil,esk10_0) )
& ( ~ ssList(X15)
| app(app(X13,X14),X15) != esk8_0
| app(X13,X15) != esk7_0
| ~ neq(X14,nil)
| ~ ssList(X14)
| ~ ssList(X13) )
& neq(esk8_0,nil) )
| ( neq(esk8_0,nil)
& ~ neq(esk10_0,nil) ) )
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(shift_quantors,[status(thm)],[155]) ).
fof(157,negated_conjecture,
! [X13,X14,X15,X16] :
( ( neq(esk8_0,nil)
| ~ ssList(X16)
| esk9_0 = X16
| tl(esk10_0) != X16
| ~ neq(nil,esk10_0) )
& ( ~ neq(esk10_0,nil)
| ~ ssList(X16)
| esk9_0 = X16
| tl(esk10_0) != X16
| ~ neq(nil,esk10_0) )
& ( neq(esk8_0,nil)
| ~ ssList(X15)
| app(app(X13,X14),X15) != esk8_0
| app(X13,X15) != esk7_0
| ~ neq(X14,nil)
| ~ ssList(X14)
| ~ ssList(X13) )
& ( ~ neq(esk10_0,nil)
| ~ ssList(X15)
| app(app(X13,X14),X15) != esk8_0
| app(X13,X15) != esk7_0
| ~ neq(X14,nil)
| ~ ssList(X14)
| ~ ssList(X13) )
& ( neq(esk8_0,nil)
| neq(esk8_0,nil) )
& ( ~ neq(esk10_0,nil)
| neq(esk8_0,nil) )
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(distribute,[status(thm)],[156]) ).
cnf(158,negated_conjecture,
ssList(esk7_0),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(159,negated_conjecture,
ssList(esk8_0),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(162,negated_conjecture,
esk7_0 = esk9_0,
inference(split_conjunct,[status(thm)],[157]) ).
cnf(163,negated_conjecture,
esk8_0 = esk10_0,
inference(split_conjunct,[status(thm)],[157]) ).
cnf(165,negated_conjecture,
( neq(esk8_0,nil)
| neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(166,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ neq(X2,nil)
| app(X1,X3) != esk7_0
| app(app(X1,X2),X3) != esk8_0
| ~ ssList(X3)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(168,negated_conjecture,
( esk9_0 = X1
| ~ neq(nil,esk10_0)
| tl(esk10_0) != X1
| ~ ssList(X1)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(172,negated_conjecture,
ssList(esk10_0),
inference(rw,[status(thm)],[159,163,theory(equality)]) ).
cnf(173,negated_conjecture,
neq(esk10_0,nil),
inference(rw,[status(thm)],[165,163,theory(equality)]) ).
cnf(184,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[137,theory(equality)]) ).
cnf(194,negated_conjecture,
( esk7_0 = X1
| tl(esk10_0) != X1
| ~ ssList(X1)
| ~ neq(nil,esk10_0)
| ~ neq(esk10_0,nil) ),
inference(rw,[status(thm)],[168,162,theory(equality)]) ).
cnf(195,negated_conjecture,
( esk7_0 = X1
| tl(esk10_0) != X1
| ~ ssList(X1)
| ~ neq(nil,esk10_0)
| $false ),
inference(rw,[status(thm)],[194,173,theory(equality)]) ).
cnf(196,negated_conjecture,
( esk7_0 = X1
| tl(esk10_0) != X1
| ~ ssList(X1)
| ~ neq(nil,esk10_0) ),
inference(cn,[status(thm)],[195,theory(equality)]) ).
cnf(197,negated_conjecture,
( esk7_0 = X1
| nil = esk10_0
| tl(esk10_0) != X1
| ~ ssList(X1)
| ~ ssList(esk10_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[196,136,theory(equality)]) ).
cnf(198,negated_conjecture,
( esk7_0 = X1
| nil = esk10_0
| tl(esk10_0) != X1
| ~ ssList(X1)
| ~ ssList(esk10_0)
| $false ),
inference(rw,[status(thm)],[197,142,theory(equality)]) ).
cnf(199,negated_conjecture,
( esk7_0 = X1
| nil = esk10_0
| tl(esk10_0) != X1
| ~ ssList(X1)
| ~ ssList(esk10_0) ),
inference(cn,[status(thm)],[198,theory(equality)]) ).
cnf(200,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(er,[status(thm)],[47,theory(equality)]) ).
cnf(201,plain,
( app(X1,nil) = nil
| nil != X1
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[200,142,theory(equality)]) ).
cnf(202,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[201,theory(equality)]) ).
cnf(211,plain,
( cons(X1,tl(cons(X1,X2))) = cons(X1,X2)
| nil = cons(X1,X2)
| ~ ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[127,94,theory(equality)]) ).
cnf(247,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[53,64,theory(equality)]) ).
cnf(263,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[247,142,theory(equality)]) ).
cnf(264,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[263,theory(equality)]) ).
cnf(285,plain,
( cons(X1,X2) = app(cons(X1,X2),nil)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[75,42,theory(equality)]) ).
cnf(287,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[141,75,theory(equality)]) ).
cnf(288,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[83,75,theory(equality)]) ).
cnf(294,plain,
( cons(X1,X2) = app(cons(X1,X2),nil)
| ~ ssItem(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[285,142,theory(equality)]) ).
cnf(295,plain,
( cons(X1,X2) = app(cons(X1,X2),nil)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[294,theory(equality)]) ).
cnf(300,negated_conjecture,
( app(X1,X3) != esk7_0
| app(app(X1,X2),X3) != esk10_0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(X2,nil)
| ~ neq(esk10_0,nil) ),
inference(rw,[status(thm)],[166,163,theory(equality)]) ).
cnf(301,negated_conjecture,
( app(X1,X3) != esk7_0
| app(app(X1,X2),X3) != esk10_0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(X2,nil)
| $false ),
inference(rw,[status(thm)],[300,173,theory(equality)]) ).
cnf(302,negated_conjecture,
( app(X1,X3) != esk7_0
| app(app(X1,X2),X3) != esk10_0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(X2,nil) ),
inference(cn,[status(thm)],[301,theory(equality)]) ).
cnf(304,negated_conjecture,
( app(app(nil,X1),X2) != esk10_0
| X2 != esk7_0
| ~ neq(X1,nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[302,64,theory(equality)]) ).
cnf(309,negated_conjecture,
( app(app(nil,X1),X2) != esk10_0
| X2 != esk7_0
| ~ neq(X1,nil)
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[304,142,theory(equality)]) ).
cnf(310,negated_conjecture,
( app(app(nil,X1),X2) != esk10_0
| X2 != esk7_0
| ~ neq(X1,nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[309,theory(equality)]) ).
cnf(346,plain,
( app(nil,nil) = nil
| ~ ssList(nil) ),
inference(er,[status(thm)],[202,theory(equality)]) ).
cnf(347,plain,
( app(nil,nil) = nil
| $false ),
inference(rw,[status(thm)],[346,142,theory(equality)]) ).
cnf(348,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[347,theory(equality)]) ).
cnf(355,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[75,348,theory(equality)]) ).
cnf(370,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[355,142,theory(equality)]) ).
cnf(371,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[370,theory(equality)]) ).
cnf(397,negated_conjecture,
( esk7_0 = X1
| esk10_0 = nil
| tl(esk10_0) != X1
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[199,172,theory(equality)]) ).
cnf(398,negated_conjecture,
( esk7_0 = X1
| esk10_0 = nil
| tl(esk10_0) != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[397,theory(equality)]) ).
cnf(399,negated_conjecture,
( esk10_0 = nil
| esk7_0 = tl(esk10_0)
| ~ ssList(tl(esk10_0)) ),
inference(er,[status(thm)],[398,theory(equality)]) ).
cnf(401,negated_conjecture,
( app(app(nil,X1),esk7_0) != esk10_0
| ~ neq(X1,nil)
| ~ ssList(esk7_0)
| ~ ssList(X1) ),
inference(er,[status(thm)],[310,theory(equality)]) ).
cnf(402,negated_conjecture,
( app(app(nil,X1),esk7_0) != esk10_0
| ~ neq(X1,nil)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[401,158,theory(equality)]) ).
cnf(403,negated_conjecture,
( app(app(nil,X1),esk7_0) != esk10_0
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[402,theory(equality)]) ).
cnf(405,negated_conjecture,
( X1 = nil
| app(app(nil,X1),esk7_0) != esk10_0
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[403,136,theory(equality)]) ).
cnf(409,negated_conjecture,
( X1 = nil
| app(app(nil,X1),esk7_0) != esk10_0
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[405,142,theory(equality)]) ).
cnf(410,negated_conjecture,
( X1 = nil
| app(app(nil,X1),esk7_0) != esk10_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[409,theory(equality)]) ).
cnf(411,negated_conjecture,
( tl(esk10_0) = esk7_0
| esk10_0 = nil
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[399,71,theory(equality)]) ).
cnf(412,negated_conjecture,
( tl(esk10_0) = esk7_0
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[411,172,theory(equality)]) ).
cnf(413,negated_conjecture,
( tl(esk10_0) = esk7_0
| esk10_0 = nil ),
inference(cn,[status(thm)],[412,theory(equality)]) ).
cnf(415,negated_conjecture,
( cons(hd(esk10_0),esk7_0) = esk10_0
| nil = esk10_0
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[127,413,theory(equality)]) ).
cnf(422,negated_conjecture,
( cons(hd(esk10_0),esk7_0) = esk10_0
| nil = esk10_0
| $false ),
inference(rw,[status(thm)],[415,172,theory(equality)]) ).
cnf(423,negated_conjecture,
( cons(hd(esk10_0),esk7_0) = esk10_0
| nil = esk10_0 ),
inference(cn,[status(thm)],[422,theory(equality)]) ).
cnf(479,negated_conjecture,
( X1 = nil
| app(nil,app(X1,esk7_0)) != esk10_0
| ~ ssList(X1)
| ~ ssList(esk7_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[410,53,theory(equality)]) ).
cnf(481,negated_conjecture,
( X1 = nil
| app(nil,app(X1,esk7_0)) != esk10_0
| ~ ssList(X1)
| $false
| ~ ssList(nil) ),
inference(rw,[status(thm)],[479,158,theory(equality)]) ).
cnf(482,negated_conjecture,
( X1 = nil
| app(nil,app(X1,esk7_0)) != esk10_0
| ~ ssList(X1)
| $false
| $false ),
inference(rw,[status(thm)],[481,142,theory(equality)]) ).
cnf(483,negated_conjecture,
( X1 = nil
| app(nil,app(X1,esk7_0)) != esk10_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[482,theory(equality)]) ).
cnf(492,negated_conjecture,
( cons(X1,nil) = nil
| app(nil,cons(X1,esk7_0)) != esk10_0
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(esk7_0) ),
inference(spm,[status(thm)],[483,57,theory(equality)]) ).
cnf(495,negated_conjecture,
( cons(X1,nil) = nil
| app(nil,cons(X1,esk7_0)) != esk10_0
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[492,158,theory(equality)]) ).
cnf(496,negated_conjecture,
( cons(X1,nil) = nil
| app(nil,cons(X1,esk7_0)) != esk10_0
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[495,theory(equality)]) ).
cnf(712,plain,
( cons(X1,tl(cons(X1,X2))) = cons(X1,X2)
| cons(X1,X2) = nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[211,141]) ).
cnf(713,plain,
( cons(X1,tl(cons(X1,X2))) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[712,83]) ).
cnf(725,negated_conjecture,
( cons(hd(esk10_0),tl(esk10_0)) = esk10_0
| esk10_0 = nil
| ~ ssItem(hd(esk10_0))
| ~ ssList(esk7_0) ),
inference(spm,[status(thm)],[713,423,theory(equality)]) ).
cnf(730,negated_conjecture,
( cons(hd(esk10_0),tl(esk10_0)) = esk10_0
| esk10_0 = nil
| ~ ssItem(hd(esk10_0))
| $false ),
inference(rw,[status(thm)],[725,158,theory(equality)]) ).
cnf(731,negated_conjecture,
( cons(hd(esk10_0),tl(esk10_0)) = esk10_0
| esk10_0 = nil
| ~ ssItem(hd(esk10_0)) ),
inference(cn,[status(thm)],[730,theory(equality)]) ).
cnf(855,negated_conjecture,
( cons(hd(esk10_0),tl(esk10_0)) = esk10_0
| esk10_0 = nil
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[731,97,theory(equality)]) ).
cnf(856,negated_conjecture,
( cons(hd(esk10_0),tl(esk10_0)) = esk10_0
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[855,172,theory(equality)]) ).
cnf(857,negated_conjecture,
( cons(hd(esk10_0),tl(esk10_0)) = esk10_0
| esk10_0 = nil ),
inference(cn,[status(thm)],[856,theory(equality)]) ).
cnf(1135,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[288,79]) ).
cnf(1143,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1135,371,theory(equality)]) ).
cnf(1153,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[1143,142,theory(equality)]) ).
cnf(1154,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[1153,theory(equality)]) ).
cnf(4215,negated_conjecture,
( app(esk10_0,nil) = esk10_0
| esk10_0 = nil
| ~ ssItem(hd(esk10_0))
| ~ ssList(tl(esk10_0)) ),
inference(spm,[status(thm)],[295,857,theory(equality)]) ).
cnf(4291,negated_conjecture,
( app(esk10_0,nil) = esk10_0
| esk10_0 = nil
| ~ ssList(tl(esk10_0))
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[4215,97,theory(equality)]) ).
cnf(4292,negated_conjecture,
( app(esk10_0,nil) = esk10_0
| esk10_0 = nil
| ~ ssList(tl(esk10_0))
| $false ),
inference(rw,[status(thm)],[4291,172,theory(equality)]) ).
cnf(4293,negated_conjecture,
( app(esk10_0,nil) = esk10_0
| esk10_0 = nil
| ~ ssList(tl(esk10_0)) ),
inference(cn,[status(thm)],[4292,theory(equality)]) ).
cnf(4294,negated_conjecture,
( app(esk10_0,nil) = esk10_0
| esk10_0 = nil
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[4293,71,theory(equality)]) ).
cnf(4296,negated_conjecture,
( app(esk10_0,nil) = esk10_0
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[4294,172,theory(equality)]) ).
cnf(4297,negated_conjecture,
( app(esk10_0,nil) = esk10_0
| esk10_0 = nil ),
inference(cn,[status(thm)],[4296,theory(equality)]) ).
cnf(4319,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| esk10_0 = nil
| ~ ssList(nil)
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[264,4297,theory(equality)]) ).
cnf(4384,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| esk10_0 = nil
| $false
| ~ ssList(esk10_0) ),
inference(rw,[status(thm)],[4319,142,theory(equality)]) ).
cnf(4385,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| esk10_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[4384,172,theory(equality)]) ).
cnf(4386,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| esk10_0 = nil ),
inference(cn,[status(thm)],[4385,theory(equality)]) ).
cnf(4536,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[287,79]) ).
cnf(4544,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[4536,371,theory(equality)]) ).
cnf(4559,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[4544,142,theory(equality)]) ).
cnf(4560,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[4559,theory(equality)]) ).
cnf(7282,negated_conjecture,
( cons(X1,nil) = nil
| app(nil,cons(X1,esk7_0)) != esk10_0
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[496,4560]) ).
cnf(7283,negated_conjecture,
( app(nil,cons(X1,esk7_0)) != esk10_0
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[7282,1154]) ).
cnf(7285,negated_conjecture,
( esk10_0 = nil
| app(nil,esk10_0) != esk10_0
| ~ ssItem(hd(esk10_0)) ),
inference(spm,[status(thm)],[7283,423,theory(equality)]) ).
cnf(7289,negated_conjecture,
( esk10_0 = nil
| ~ ssItem(hd(esk10_0)) ),
inference(csr,[status(thm)],[7285,4386]) ).
cnf(7290,negated_conjecture,
( esk10_0 = nil
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[7289,97,theory(equality)]) ).
cnf(7291,negated_conjecture,
( esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[7290,172,theory(equality)]) ).
cnf(7292,negated_conjecture,
esk10_0 = nil,
inference(cn,[status(thm)],[7291,theory(equality)]) ).
cnf(7295,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[173,7292,theory(equality)]) ).
cnf(7597,negated_conjecture,
~ ssList(nil),
inference(spm,[status(thm)],[184,7295,theory(equality)]) ).
cnf(7599,negated_conjecture,
$false,
inference(rw,[status(thm)],[7597,142,theory(equality)]) ).
cnf(7600,negated_conjecture,
$false,
inference(cn,[status(thm)],[7599,theory(equality)]) ).
cnf(7601,negated_conjecture,
$false,
7600,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC005+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmphdwd2p/sel_SWC005+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC005+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC005+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC005+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
%
%------------------------------------------------------------------------------