TSTP Solution File: SWC315+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC315+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 11:26:24 EST 2010
% Result : Theorem 0.34s
% Output : CNFRefutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 10
% Syntax : Number of formulae : 138 ( 13 unt; 0 def)
% Number of atoms : 576 ( 260 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 700 ( 262 ~; 319 |; 81 &)
% ( 1 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 166 ( 0 sgn 110 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpCRACSu/sel_SWC315+1.p_1',ax26) ).
fof(3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/tmp/tmpCRACSu/sel_SWC315+1.p_1',ax80) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpCRACSu/sel_SWC315+1.p_1',ax81) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpCRACSu/sel_SWC315+1.p_1',ax15) ).
fof(11,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpCRACSu/sel_SWC315+1.p_1',ax16) ).
fof(12,axiom,
ssList(nil),
file('/tmp/tmpCRACSu/sel_SWC315+1.p_1',ax17) ).
fof(15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/tmp/tmpCRACSu/sel_SWC315+1.p_1',ax27) ).
fof(17,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmpCRACSu/sel_SWC315+1.p_1',ax21) ).
fof(18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssItem(X4)
=> ( cons(X3,X1) = cons(X4,X2)
=> ( X3 = X4
& X2 = X1 ) ) ) ) ) ),
file('/tmp/tmpCRACSu/sel_SWC315+1.p_1',ax19) ).
fof(19,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X2
| app(X6,cons(X5,nil)) = X1 ) )
& ( nil != X2
| nil = X1 ) )
| ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ~ ssList(X8)
| app(cons(X7,nil),X8) != X4
| app(X8,cons(X7,nil)) != X3 ) )
& neq(X4,nil) ) ) ) ) ),
file('/tmp/tmpCRACSu/sel_SWC315+1.p_1',co1) ).
fof(20,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X2
| app(X6,cons(X5,nil)) = X1 ) )
& ( nil != X2
| nil = X1 ) )
| ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ~ ssList(X8)
| app(cons(X7,nil),X8) != X4
| app(X8,cons(X7,nil)) != X3 ) )
& neq(X4,nil) ) ) ) ) ),
inference(assume_negation,[status(cth)],[19]) ).
fof(21,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X2
| app(X6,cons(X5,nil)) = X1 ) )
& ( nil != X2
| nil = X1 ) )
| ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ~ ssList(X8)
| app(cons(X7,nil),X8) != X4
| app(X8,cons(X7,nil)) != X3 ) )
& neq(X4,nil) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[20,theory(equality)]) ).
fof(27,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(28,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[27]) ).
fof(29,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[28]) ).
cnf(30,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,X3) != app(X2,X1)
| X3 = X1 ) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(32,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(X5,X6) != app(X5,X4)
| X6 = X4 ) ) ),
inference(variable_rename,[status(thm)],[31]) ).
fof(33,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| app(X5,X6) != app(X5,X4)
| X6 = X4
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[32]) ).
cnf(34,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X3) != app(X2,X1)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[33]) ).
fof(53,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(54,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[53]) ).
fof(55,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[54]) ).
cnf(56,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[55]) ).
fof(64,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(65,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[64]) ).
fof(66,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[65]) ).
fof(67,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)],[66]) ).
cnf(68,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[67]) ).
fof(70,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(71,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[70]) ).
fof(72,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[71]) ).
cnf(73,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[72]) ).
cnf(74,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[12]) ).
fof(84,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)],[15]) ).
fof(85,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)],[84]) ).
fof(86,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)],[85]) ).
cnf(87,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[86]) ).
fof(92,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| nil != cons(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(93,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3) ) ),
inference(variable_rename,[status(thm)],[92]) ).
fof(94,plain,
! [X3,X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[93]) ).
cnf(95,plain,
( ~ ssList(X1)
| nil != cons(X2,X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[94]) ).
fof(96,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssItem(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X3,X1) != cons(X4,X2)
| ( X3 = X4
& X2 = X1 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(97,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssItem(X8)
| cons(X7,X5) != cons(X8,X6)
| ( X7 = X8
& X6 = X5 ) ) ) ) ),
inference(variable_rename,[status(thm)],[96]) ).
fof(98,plain,
! [X5,X6,X7,X8] :
( ~ ssItem(X8)
| cons(X7,X5) != cons(X8,X6)
| ( X7 = X8
& X6 = X5 )
| ~ ssItem(X7)
| ~ ssList(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[97]) ).
fof(99,plain,
! [X5,X6,X7,X8] :
( ( X7 = X8
| cons(X7,X5) != cons(X8,X6)
| ~ ssItem(X8)
| ~ ssItem(X7)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( X6 = X5
| cons(X7,X5) != cons(X8,X6)
| ~ ssItem(X8)
| ~ ssItem(X7)
| ~ ssList(X6)
| ~ ssList(X5) ) ),
inference(distribute,[status(thm)],[98]) ).
cnf(101,plain,
( X3 = X4
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3)
| ~ ssItem(X4)
| cons(X3,X1) != cons(X4,X2) ),
inference(split_conjunct,[status(thm)],[99]) ).
fof(102,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ( nil = X3
| nil != X4 )
& ( ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X2
& app(X6,cons(X5,nil)) != X1 ) )
| ( nil = X2
& nil != X1 ) )
& ( ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(cons(X7,nil),X8) = X4
& app(X8,cons(X7,nil)) = X3 ) )
| ~ neq(X4,nil) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(103,negated_conjecture,
? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& X10 = X12
& X9 = X11
& ( nil = X11
| nil != X12 )
& ( ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssList(X14)
& app(cons(X13,nil),X14) = X10
& app(X14,cons(X13,nil)) != X9 ) )
| ( nil = X10
& nil != X9 ) )
& ( ? [X15] :
( ssItem(X15)
& ? [X16] :
( ssList(X16)
& app(cons(X15,nil),X16) = X12
& app(X16,cons(X15,nil)) = X11 ) )
| ~ neq(X12,nil) ) ) ) ) ),
inference(variable_rename,[status(thm)],[102]) ).
fof(104,negated_conjecture,
( ssList(esk5_0)
& ssList(esk6_0)
& ssList(esk7_0)
& ssList(esk8_0)
& esk6_0 = esk8_0
& esk5_0 = esk7_0
& ( nil = esk7_0
| nil != esk8_0 )
& ( ( ssItem(esk9_0)
& ssList(esk10_0)
& app(cons(esk9_0,nil),esk10_0) = esk6_0
& app(esk10_0,cons(esk9_0,nil)) != esk5_0 )
| ( nil = esk6_0
& nil != esk5_0 ) )
& ( ( ssItem(esk11_0)
& ssList(esk12_0)
& app(cons(esk11_0,nil),esk12_0) = esk8_0
& app(esk12_0,cons(esk11_0,nil)) = esk7_0 )
| ~ neq(esk8_0,nil) ) ),
inference(skolemize,[status(esa)],[103]) ).
fof(105,negated_conjecture,
( ssList(esk5_0)
& ssList(esk6_0)
& ssList(esk7_0)
& ssList(esk8_0)
& esk6_0 = esk8_0
& esk5_0 = esk7_0
& ( nil = esk7_0
| nil != esk8_0 )
& ( nil = esk6_0
| ssItem(esk9_0) )
& ( nil != esk5_0
| ssItem(esk9_0) )
& ( nil = esk6_0
| ssList(esk10_0) )
& ( nil != esk5_0
| ssList(esk10_0) )
& ( nil = esk6_0
| app(cons(esk9_0,nil),esk10_0) = esk6_0 )
& ( nil != esk5_0
| app(cons(esk9_0,nil),esk10_0) = esk6_0 )
& ( nil = esk6_0
| app(esk10_0,cons(esk9_0,nil)) != esk5_0 )
& ( nil != esk5_0
| app(esk10_0,cons(esk9_0,nil)) != esk5_0 )
& ( ssItem(esk11_0)
| ~ neq(esk8_0,nil) )
& ( ssList(esk12_0)
| ~ neq(esk8_0,nil) )
& ( app(cons(esk11_0,nil),esk12_0) = esk8_0
| ~ neq(esk8_0,nil) )
& ( app(esk12_0,cons(esk11_0,nil)) = esk7_0
| ~ neq(esk8_0,nil) ) ),
inference(distribute,[status(thm)],[104]) ).
cnf(106,negated_conjecture,
( app(esk12_0,cons(esk11_0,nil)) = esk7_0
| ~ neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(107,negated_conjecture,
( app(cons(esk11_0,nil),esk12_0) = esk8_0
| ~ neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(108,negated_conjecture,
( ssList(esk12_0)
| ~ neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(109,negated_conjecture,
( ssItem(esk11_0)
| ~ neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(111,negated_conjecture,
( nil = esk6_0
| app(esk10_0,cons(esk9_0,nil)) != esk5_0 ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(112,negated_conjecture,
( app(cons(esk9_0,nil),esk10_0) = esk6_0
| nil != esk5_0 ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(113,negated_conjecture,
( app(cons(esk9_0,nil),esk10_0) = esk6_0
| nil = esk6_0 ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(114,negated_conjecture,
( ssList(esk10_0)
| nil != esk5_0 ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(115,negated_conjecture,
( ssList(esk10_0)
| nil = esk6_0 ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(116,negated_conjecture,
( ssItem(esk9_0)
| nil != esk5_0 ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(117,negated_conjecture,
( ssItem(esk9_0)
| nil = esk6_0 ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(118,negated_conjecture,
( nil = esk7_0
| nil != esk8_0 ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(119,negated_conjecture,
esk5_0 = esk7_0,
inference(split_conjunct,[status(thm)],[105]) ).
cnf(120,negated_conjecture,
esk6_0 = esk8_0,
inference(split_conjunct,[status(thm)],[105]) ).
cnf(123,negated_conjecture,
ssList(esk6_0),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(127,negated_conjecture,
ssList(esk8_0),
inference(rw,[status(thm)],[123,120,theory(equality)]) ).
cnf(128,negated_conjecture,
( esk8_0 = nil
| ssItem(esk9_0) ),
inference(rw,[status(thm)],[117,120,theory(equality)]) ).
cnf(129,negated_conjecture,
( esk8_0 = nil
| ssList(esk10_0) ),
inference(rw,[status(thm)],[115,120,theory(equality)]) ).
cnf(130,negated_conjecture,
( esk5_0 = nil
| esk8_0 != nil ),
inference(rw,[status(thm)],[118,119,theory(equality)]) ).
cnf(137,negated_conjecture,
( esk8_0 = nil
| app(cons(esk9_0,nil),esk10_0) = esk6_0 ),
inference(rw,[status(thm)],[113,120,theory(equality)]) ).
cnf(138,negated_conjecture,
( esk8_0 = nil
| app(cons(esk9_0,nil),esk10_0) = esk8_0 ),
inference(rw,[status(thm)],[137,120,theory(equality)]) ).
cnf(140,negated_conjecture,
( app(cons(esk9_0,nil),esk10_0) = esk8_0
| esk5_0 != nil ),
inference(rw,[status(thm)],[112,120,theory(equality)]) ).
cnf(141,negated_conjecture,
( esk8_0 = nil
| app(esk10_0,cons(esk9_0,nil)) != esk5_0 ),
inference(rw,[status(thm)],[111,120,theory(equality)]) ).
cnf(144,negated_conjecture,
( ssItem(esk11_0)
| esk8_0 = nil
| ~ ssList(nil)
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[109,68,theory(equality)]) ).
cnf(145,negated_conjecture,
( ssList(esk12_0)
| esk8_0 = nil
| ~ ssList(nil)
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[108,68,theory(equality)]) ).
cnf(146,negated_conjecture,
( ssItem(esk11_0)
| esk8_0 = nil
| $false
| ~ ssList(esk8_0) ),
inference(rw,[status(thm)],[144,74,theory(equality)]) ).
cnf(147,negated_conjecture,
( ssItem(esk11_0)
| esk8_0 = nil
| ~ ssList(esk8_0) ),
inference(cn,[status(thm)],[146,theory(equality)]) ).
cnf(148,negated_conjecture,
( ssList(esk12_0)
| esk8_0 = nil
| $false
| ~ ssList(esk8_0) ),
inference(rw,[status(thm)],[145,74,theory(equality)]) ).
cnf(149,negated_conjecture,
( ssList(esk12_0)
| esk8_0 = nil
| ~ ssList(esk8_0) ),
inference(cn,[status(thm)],[148,theory(equality)]) ).
cnf(151,negated_conjecture,
( app(esk12_0,cons(esk11_0,nil)) = esk5_0
| ~ neq(esk8_0,nil) ),
inference(rw,[status(thm)],[106,119,theory(equality)]) ).
cnf(153,negated_conjecture,
( app(esk12_0,cons(esk11_0,nil)) = esk5_0
| esk8_0 = nil
| ~ ssList(nil)
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[151,68,theory(equality)]) ).
cnf(154,negated_conjecture,
( app(esk12_0,cons(esk11_0,nil)) = esk5_0
| esk8_0 = nil
| $false
| ~ ssList(esk8_0) ),
inference(rw,[status(thm)],[153,74,theory(equality)]) ).
cnf(155,negated_conjecture,
( app(esk12_0,cons(esk11_0,nil)) = esk5_0
| esk8_0 = nil
| ~ ssList(esk8_0) ),
inference(cn,[status(thm)],[154,theory(equality)]) ).
cnf(157,negated_conjecture,
( app(cons(esk11_0,nil),esk12_0) = esk8_0
| esk8_0 = nil
| ~ ssList(nil)
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[107,68,theory(equality)]) ).
cnf(158,negated_conjecture,
( app(cons(esk11_0,nil),esk12_0) = esk8_0
| esk8_0 = nil
| $false
| ~ ssList(esk8_0) ),
inference(rw,[status(thm)],[157,74,theory(equality)]) ).
cnf(159,negated_conjecture,
( app(cons(esk11_0,nil),esk12_0) = esk8_0
| esk8_0 = nil
| ~ ssList(esk8_0) ),
inference(cn,[status(thm)],[158,theory(equality)]) ).
cnf(173,negated_conjecture,
( cons(esk9_0,esk10_0) = esk8_0
| esk8_0 = nil
| ~ ssList(esk10_0)
| ~ ssItem(esk9_0) ),
inference(spm,[status(thm)],[138,56,theory(equality)]) ).
cnf(184,negated_conjecture,
( esk10_0 = X1
| esk8_0 = nil
| esk8_0 != app(cons(esk9_0,nil),X1)
| ~ ssList(X1)
| ~ ssList(cons(esk9_0,nil))
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[34,138,theory(equality)]) ).
cnf(237,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssList(app(X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[95,87,theory(equality)]) ).
cnf(262,negated_conjecture,
( ssItem(esk11_0)
| esk8_0 = nil
| $false ),
inference(rw,[status(thm)],[147,127,theory(equality)]) ).
cnf(263,negated_conjecture,
( ssItem(esk11_0)
| esk8_0 = nil ),
inference(cn,[status(thm)],[262,theory(equality)]) ).
cnf(264,negated_conjecture,
( ssList(esk12_0)
| esk8_0 = nil
| $false ),
inference(rw,[status(thm)],[149,127,theory(equality)]) ).
cnf(265,negated_conjecture,
( ssList(esk12_0)
| esk8_0 = nil ),
inference(cn,[status(thm)],[264,theory(equality)]) ).
cnf(269,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[237,30]) ).
cnf(334,negated_conjecture,
( cons(esk9_0,esk10_0) = esk8_0
| esk8_0 = nil
| ~ ssList(esk10_0) ),
inference(csr,[status(thm)],[173,128]) ).
cnf(335,negated_conjecture,
( cons(esk9_0,esk10_0) = esk8_0
| esk8_0 = nil ),
inference(csr,[status(thm)],[334,129]) ).
cnf(339,negated_conjecture,
( esk9_0 = X1
| esk8_0 = nil
| esk8_0 != cons(X1,X2)
| ~ ssList(X2)
| ~ ssList(esk10_0)
| ~ ssItem(X1)
| ~ ssItem(esk9_0) ),
inference(spm,[status(thm)],[101,335,theory(equality)]) ).
cnf(351,negated_conjecture,
( app(esk12_0,cons(esk11_0,nil)) = esk5_0
| esk8_0 = nil
| $false ),
inference(rw,[status(thm)],[155,127,theory(equality)]) ).
cnf(352,negated_conjecture,
( app(esk12_0,cons(esk11_0,nil)) = esk5_0
| esk8_0 = nil ),
inference(cn,[status(thm)],[351,theory(equality)]) ).
cnf(376,negated_conjecture,
( app(cons(esk11_0,nil),esk12_0) = esk8_0
| esk8_0 = nil
| $false ),
inference(rw,[status(thm)],[159,127,theory(equality)]) ).
cnf(377,negated_conjecture,
( app(cons(esk11_0,nil),esk12_0) = esk8_0
| esk8_0 = nil ),
inference(cn,[status(thm)],[376,theory(equality)]) ).
cnf(381,negated_conjecture,
( esk8_0 = cons(esk11_0,esk12_0)
| esk8_0 = nil
| ~ ssList(esk12_0)
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[56,377,theory(equality)]) ).
cnf(413,negated_conjecture,
( cons(esk11_0,esk12_0) = esk8_0
| esk8_0 = nil
| ~ ssList(esk12_0) ),
inference(csr,[status(thm)],[381,263]) ).
cnf(414,negated_conjecture,
( cons(esk11_0,esk12_0) = esk8_0
| esk8_0 = nil ),
inference(csr,[status(thm)],[413,265]) ).
cnf(621,negated_conjecture,
( esk8_0 = nil
| esk10_0 = X1
| app(cons(esk9_0,nil),X1) != esk8_0
| ~ ssList(cons(esk9_0,nil))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[184,129]) ).
cnf(622,negated_conjecture,
( esk8_0 = nil
| esk10_0 = X1
| app(cons(esk9_0,nil),X1) != esk8_0
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(esk9_0) ),
inference(spm,[status(thm)],[621,73,theory(equality)]) ).
cnf(623,negated_conjecture,
( esk8_0 = nil
| esk10_0 = X1
| app(cons(esk9_0,nil),X1) != esk8_0
| ~ ssList(X1)
| $false
| ~ ssItem(esk9_0) ),
inference(rw,[status(thm)],[622,74,theory(equality)]) ).
cnf(624,negated_conjecture,
( esk8_0 = nil
| esk10_0 = X1
| app(cons(esk9_0,nil),X1) != esk8_0
| ~ ssList(X1)
| ~ ssItem(esk9_0) ),
inference(cn,[status(thm)],[623,theory(equality)]) ).
cnf(713,negated_conjecture,
( esk8_0 = nil
| esk10_0 = X1
| app(cons(esk9_0,nil),X1) != esk8_0
| ~ ssList(X1) ),
inference(csr,[status(thm)],[624,128]) ).
cnf(715,negated_conjecture,
( esk8_0 = nil
| esk10_0 = X1
| cons(esk9_0,X1) != esk8_0
| ~ ssList(X1)
| ~ ssItem(esk9_0) ),
inference(spm,[status(thm)],[713,56,theory(equality)]) ).
cnf(725,negated_conjecture,
( esk8_0 = nil
| esk10_0 = X1
| cons(esk9_0,X1) != esk8_0
| ~ ssList(X1) ),
inference(csr,[status(thm)],[715,128]) ).
cnf(3168,negated_conjecture,
( esk8_0 = nil
| esk9_0 = X1
| cons(X1,X2) != esk8_0
| ~ ssList(esk10_0)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[339,128]) ).
cnf(3169,negated_conjecture,
( esk8_0 = nil
| esk9_0 = X1
| cons(X1,X2) != esk8_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[3168,129]) ).
cnf(3172,negated_conjecture,
( esk8_0 = nil
| esk9_0 = esk11_0
| ~ ssList(esk12_0)
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[3169,414,theory(equality)]) ).
cnf(3185,negated_conjecture,
( esk8_0 = nil
| esk11_0 = esk9_0
| ~ ssList(esk12_0) ),
inference(csr,[status(thm)],[3172,263]) ).
cnf(3186,negated_conjecture,
( esk8_0 = nil
| esk11_0 = esk9_0 ),
inference(csr,[status(thm)],[3185,265]) ).
cnf(3188,negated_conjecture,
( app(esk12_0,cons(esk9_0,nil)) = esk5_0
| esk8_0 = nil ),
inference(spm,[status(thm)],[352,3186,theory(equality)]) ).
cnf(3190,negated_conjecture,
( cons(esk9_0,esk12_0) = esk8_0
| esk8_0 = nil ),
inference(spm,[status(thm)],[414,3186,theory(equality)]) ).
cnf(3207,negated_conjecture,
( esk8_0 = nil
| esk10_0 = esk12_0
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[725,3190,theory(equality)]) ).
cnf(3223,negated_conjecture,
( esk8_0 = nil
| esk12_0 = esk10_0 ),
inference(csr,[status(thm)],[3207,265]) ).
cnf(3332,negated_conjecture,
( app(esk10_0,cons(esk9_0,nil)) = esk5_0
| esk8_0 = nil ),
inference(spm,[status(thm)],[3188,3223,theory(equality)]) ).
cnf(3486,negated_conjecture,
esk8_0 = nil,
inference(csr,[status(thm)],[3332,141]) ).
cnf(3670,negated_conjecture,
( app(cons(esk9_0,nil),esk10_0) = nil
| esk5_0 != nil ),
inference(rw,[status(thm)],[140,3486,theory(equality)]) ).
cnf(3673,negated_conjecture,
( esk5_0 = nil
| $false ),
inference(rw,[status(thm)],[130,3486,theory(equality)]) ).
cnf(3674,negated_conjecture,
esk5_0 = nil,
inference(cn,[status(thm)],[3673,theory(equality)]) ).
cnf(3712,negated_conjecture,
( ssList(esk10_0)
| $false ),
inference(rw,[status(thm)],[114,3674,theory(equality)]) ).
cnf(3713,negated_conjecture,
ssList(esk10_0),
inference(cn,[status(thm)],[3712,theory(equality)]) ).
cnf(3714,negated_conjecture,
( ssItem(esk9_0)
| $false ),
inference(rw,[status(thm)],[116,3674,theory(equality)]) ).
cnf(3715,negated_conjecture,
ssItem(esk9_0),
inference(cn,[status(thm)],[3714,theory(equality)]) ).
cnf(3731,negated_conjecture,
( app(cons(esk9_0,nil),esk10_0) = nil
| $false ),
inference(rw,[status(thm)],[3670,3674,theory(equality)]) ).
cnf(3732,negated_conjecture,
app(cons(esk9_0,nil),esk10_0) = nil,
inference(cn,[status(thm)],[3731,theory(equality)]) ).
cnf(3743,negated_conjecture,
( ~ ssList(nil)
| ~ ssList(esk10_0)
| ~ ssItem(esk9_0) ),
inference(spm,[status(thm)],[269,3732,theory(equality)]) ).
cnf(3790,negated_conjecture,
( $false
| ~ ssList(esk10_0)
| ~ ssItem(esk9_0) ),
inference(rw,[status(thm)],[3743,74,theory(equality)]) ).
cnf(3791,negated_conjecture,
( $false
| $false
| ~ ssItem(esk9_0) ),
inference(rw,[status(thm)],[3790,3713,theory(equality)]) ).
cnf(3792,negated_conjecture,
( $false
| $false
| $false ),
inference(rw,[status(thm)],[3791,3715,theory(equality)]) ).
cnf(3793,negated_conjecture,
$false,
inference(cn,[status(thm)],[3792,theory(equality)]) ).
cnf(3794,negated_conjecture,
$false,
3793,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC315+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpCRACSu/sel_SWC315+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC315+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC315+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC315+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
%
%------------------------------------------------------------------------------