TSTP Solution File: SWC239+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC239+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 11:03:27 EST 2010
% Result : Theorem 0.68s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 10
% Syntax : Number of formulae : 114 ( 12 unt; 0 def)
% Number of atoms : 563 ( 171 equ)
% Maximal formula atoms : 54 ( 4 avg)
% Number of connectives : 737 ( 288 ~; 305 |; 107 &)
% ( 0 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 202 ( 0 sgn 105 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',ax82) ).
fof(4,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',ax81) ).
fof(5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',ax80) ).
fof(7,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',ax28) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',ax27) ).
fof(9,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',ax26) ).
fof(20,axiom,
ssList(nil),
file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',ax17) ).
fof(24,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',ax38) ).
fof(28,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',ax16) ).
fof(30,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ lt(X5,X8)
| leq(X5,X8) ) ) ) ) )
| ( ! [X9] :
( ssItem(X9)
=> ( cons(X9,nil) != X3
| ~ memberP(X4,X9)
| ? [X10] :
( ssItem(X10)
& X9 != X10
& memberP(X4,X10)
& leq(X9,X10) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',co1) ).
fof(31,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ lt(X5,X8)
| leq(X5,X8) ) ) ) ) )
| ( ! [X9] :
( ssItem(X9)
=> ( cons(X9,nil) != X3
| ~ memberP(X4,X9)
| ? [X10] :
( ssItem(X10)
& X9 != X10
& memberP(X4,X10)
& leq(X9,X10) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[30]) ).
fof(34,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[24,theory(equality)]) ).
fof(35,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ lt(X5,X8)
| leq(X5,X8) ) ) ) ) )
| ( ! [X9] :
( ssItem(X9)
=> ( cons(X9,nil) != X3
| ~ memberP(X4,X9)
| ? [X10] :
( ssItem(X10)
& X9 != X10
& memberP(X4,X10)
& leq(X9,X10) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[31,theory(equality)]) ).
fof(46,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(47,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)],[46]) ).
fof(48,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)],[47]) ).
cnf(49,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[48]) ).
fof(50,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(51,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[50]) ).
fof(52,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[51]) ).
cnf(53,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[52]) ).
fof(54,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,X3) != app(X2,X1)
| X3 = X1 ) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(55,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(X5,X6) != app(X5,X4)
| X6 = X4 ) ) ),
inference(variable_rename,[status(thm)],[54]) ).
fof(56,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| app(X5,X6) != app(X5,X4)
| X6 = X4
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[55]) ).
cnf(57,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X3) != app(X2,X1)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[56]) ).
fof(62,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[7]) ).
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(65,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)],[8]) ).
fof(66,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)],[65]) ).
fof(67,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)],[66]) ).
cnf(68,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[67]) ).
fof(69,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(70,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[69]) ).
fof(71,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[70]) ).
cnf(72,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[71]) ).
cnf(121,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[20]) ).
fof(140,plain,
! [X1] :
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(141,plain,
! [X2] :
( ~ ssItem(X2)
| ~ memberP(nil,X2) ),
inference(variable_rename,[status(thm)],[140]) ).
cnf(142,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[141]) ).
fof(160,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(161,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[160]) ).
fof(162,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[161]) ).
cnf(163,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[162]) ).
fof(167,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& nil != X1
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssList(X7)
| app(app(X6,cons(X5,nil)),X7) != X1
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& memberP(X7,X8)
& lt(X5,X8)
& ~ leq(X5,X8) ) ) ) )
& ( ? [X9] :
( ssItem(X9)
& cons(X9,nil) = X3
& memberP(X4,X9)
& ! [X10] :
( ~ ssItem(X10)
| X9 = X10
| ~ memberP(X4,X10)
| ~ leq(X9,X10) ) )
| ( nil = X4
& nil = X3 ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[35]) ).
fof(168,negated_conjecture,
? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& ? [X13] :
( ssList(X13)
& ? [X14] :
( ssList(X14)
& X12 = X14
& X11 = X13
& nil != X11
& ! [X15] :
( ~ ssItem(X15)
| ! [X16] :
( ~ ssList(X16)
| ! [X17] :
( ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != X11
| ? [X18] :
( ssItem(X18)
& memberP(X16,X18)
& memberP(X17,X18)
& lt(X15,X18)
& ~ leq(X15,X18) ) ) ) )
& ( ? [X19] :
( ssItem(X19)
& cons(X19,nil) = X13
& memberP(X14,X19)
& ! [X20] :
( ~ ssItem(X20)
| X19 = X20
| ~ memberP(X14,X20)
| ~ leq(X19,X20) ) )
| ( nil = X14
& nil = X13 ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[167]) ).
fof(169,negated_conjecture,
( ssList(esk7_0)
& ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& nil != esk7_0
& ! [X15] :
( ~ ssItem(X15)
| ! [X16] :
( ~ ssList(X16)
| ! [X17] :
( ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ( ssItem(esk11_3(X15,X16,X17))
& memberP(X16,esk11_3(X15,X16,X17))
& memberP(X17,esk11_3(X15,X16,X17))
& lt(X15,esk11_3(X15,X16,X17))
& ~ leq(X15,esk11_3(X15,X16,X17)) ) ) ) )
& ( ( ssItem(esk12_0)
& cons(esk12_0,nil) = esk9_0
& memberP(esk10_0,esk12_0)
& ! [X20] :
( ~ ssItem(X20)
| esk12_0 = X20
| ~ memberP(esk10_0,X20)
| ~ leq(esk12_0,X20) ) )
| ( nil = esk10_0
& nil = esk9_0 ) ) ),
inference(skolemize,[status(esa)],[168]) ).
fof(170,negated_conjecture,
! [X15,X16,X17,X20] :
( ( ( ( ~ ssItem(X20)
| esk12_0 = X20
| ~ memberP(esk10_0,X20)
| ~ leq(esk12_0,X20) )
& cons(esk12_0,nil) = esk9_0
& memberP(esk10_0,esk12_0)
& ssItem(esk12_0) )
| ( nil = esk10_0
& nil = esk9_0 ) )
& ( ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ( ssItem(esk11_3(X15,X16,X17))
& memberP(X16,esk11_3(X15,X16,X17))
& memberP(X17,esk11_3(X15,X16,X17))
& lt(X15,esk11_3(X15,X16,X17))
& ~ leq(X15,esk11_3(X15,X16,X17)) )
| ~ ssList(X16)
| ~ ssItem(X15) )
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& nil != esk7_0
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(shift_quantors,[status(thm)],[169]) ).
fof(171,negated_conjecture,
! [X15,X16,X17,X20] :
( ( nil = esk10_0
| ~ ssItem(X20)
| esk12_0 = X20
| ~ memberP(esk10_0,X20)
| ~ leq(esk12_0,X20) )
& ( nil = esk9_0
| ~ ssItem(X20)
| esk12_0 = X20
| ~ memberP(esk10_0,X20)
| ~ leq(esk12_0,X20) )
& ( nil = esk10_0
| cons(esk12_0,nil) = esk9_0 )
& ( nil = esk9_0
| cons(esk12_0,nil) = esk9_0 )
& ( nil = esk10_0
| memberP(esk10_0,esk12_0) )
& ( nil = esk9_0
| memberP(esk10_0,esk12_0) )
& ( nil = esk10_0
| ssItem(esk12_0) )
& ( nil = esk9_0
| ssItem(esk12_0) )
& ( ssItem(esk11_3(X15,X16,X17))
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( memberP(X16,esk11_3(X15,X16,X17))
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( memberP(X17,esk11_3(X15,X16,X17))
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( lt(X15,esk11_3(X15,X16,X17))
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& ( ~ leq(X15,esk11_3(X15,X16,X17))
| ~ ssList(X17)
| app(app(X16,cons(X15,nil)),X17) != esk7_0
| ~ ssList(X16)
| ~ ssItem(X15) )
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& nil != esk7_0
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(distribute,[status(thm)],[170]) ).
cnf(172,negated_conjecture,
ssList(esk7_0),
inference(split_conjunct,[status(thm)],[171]) ).
cnf(176,negated_conjecture,
nil != esk7_0,
inference(split_conjunct,[status(thm)],[171]) ).
cnf(177,negated_conjecture,
esk7_0 = esk9_0,
inference(split_conjunct,[status(thm)],[171]) ).
cnf(181,negated_conjecture,
( memberP(X3,esk11_3(X1,X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk7_0
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[171]) ).
cnf(183,negated_conjecture,
( ssItem(esk11_3(X1,X2,X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(X2,cons(X1,nil)),X3) != esk7_0
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[171]) ).
cnf(184,negated_conjecture,
( ssItem(esk12_0)
| nil = esk9_0 ),
inference(split_conjunct,[status(thm)],[171]) ).
cnf(188,negated_conjecture,
( cons(esk12_0,nil) = esk9_0
| nil = esk9_0 ),
inference(split_conjunct,[status(thm)],[171]) ).
cnf(195,negated_conjecture,
( esk7_0 = nil
| ssItem(esk12_0) ),
inference(rw,[status(thm)],[184,177,theory(equality)]) ).
cnf(196,negated_conjecture,
ssItem(esk12_0),
inference(sr,[status(thm)],[195,176,theory(equality)]) ).
cnf(198,negated_conjecture,
( esk7_0 = nil
| cons(esk12_0,nil) = esk9_0 ),
inference(rw,[status(thm)],[188,177,theory(equality)]) ).
cnf(199,negated_conjecture,
( esk7_0 = nil
| cons(esk12_0,nil) = esk7_0 ),
inference(rw,[status(thm)],[198,177,theory(equality)]) ).
cnf(200,negated_conjecture,
cons(esk12_0,nil) = esk7_0,
inference(sr,[status(thm)],[199,176,theory(equality)]) ).
cnf(245,negated_conjecture,
( app(esk7_0,X1) = cons(esk12_0,X1)
| ~ ssItem(esk12_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[53,200,theory(equality)]) ).
cnf(250,negated_conjecture,
( app(esk7_0,X1) = cons(esk12_0,X1)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[245,196,theory(equality)]) ).
cnf(251,negated_conjecture,
( app(esk7_0,X1) = cons(esk12_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[250,theory(equality)]) ).
cnf(319,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[49,64,theory(equality)]) ).
cnf(338,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[319,121,theory(equality)]) ).
cnf(339,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[338,theory(equality)]) ).
cnf(345,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[163,68,theory(equality)]) ).
cnf(381,negated_conjecture,
( ssItem(esk11_3(X1,nil,X2))
| app(cons(X1,nil),X2) != esk7_0
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(cons(X1,nil)) ),
inference(spm,[status(thm)],[183,64,theory(equality)]) ).
cnf(391,negated_conjecture,
( ssItem(esk11_3(X1,nil,X2))
| app(cons(X1,nil),X2) != esk7_0
| ~ ssItem(X1)
| ~ ssList(X2)
| $false
| ~ ssList(cons(X1,nil)) ),
inference(rw,[status(thm)],[381,121,theory(equality)]) ).
cnf(392,negated_conjecture,
( ssItem(esk11_3(X1,nil,X2))
| app(cons(X1,nil),X2) != esk7_0
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[391,theory(equality)]) ).
cnf(424,negated_conjecture,
( ~ ssItem(esk11_3(X1,X2,nil))
| app(app(X2,cons(X1,nil)),nil) != esk7_0
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[142,181,theory(equality)]) ).
cnf(427,negated_conjecture,
( ~ ssItem(esk11_3(X1,X2,nil))
| app(app(X2,cons(X1,nil)),nil) != esk7_0
| ~ ssItem(X1)
| $false
| ~ ssList(X2) ),
inference(rw,[status(thm)],[424,121,theory(equality)]) ).
cnf(428,negated_conjecture,
( ~ ssItem(esk11_3(X1,X2,nil))
| app(app(X2,cons(X1,nil)),nil) != esk7_0
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[427,theory(equality)]) ).
cnf(452,negated_conjecture,
( app(esk7_0,nil) = esk7_0
| ~ ssList(nil) ),
inference(spm,[status(thm)],[200,251,theory(equality)]) ).
cnf(467,negated_conjecture,
( app(esk7_0,nil) = esk7_0
| $false ),
inference(rw,[status(thm)],[452,121,theory(equality)]) ).
cnf(468,negated_conjecture,
app(esk7_0,nil) = esk7_0,
inference(cn,[status(thm)],[467,theory(equality)]) ).
cnf(504,negated_conjecture,
( nil = X1
| esk7_0 != app(esk7_0,X1)
| ~ ssList(X1)
| ~ ssList(esk7_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[57,468,theory(equality)]) ).
cnf(508,negated_conjecture,
( app(esk7_0,X1) = app(esk7_0,app(nil,X1))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(esk7_0) ),
inference(spm,[status(thm)],[49,468,theory(equality)]) ).
cnf(527,negated_conjecture,
( nil = X1
| esk7_0 != app(esk7_0,X1)
| ~ ssList(X1)
| $false
| ~ ssList(nil) ),
inference(rw,[status(thm)],[504,172,theory(equality)]) ).
cnf(528,negated_conjecture,
( nil = X1
| esk7_0 != app(esk7_0,X1)
| ~ ssList(X1)
| $false
| $false ),
inference(rw,[status(thm)],[527,121,theory(equality)]) ).
cnf(529,negated_conjecture,
( nil = X1
| esk7_0 != app(esk7_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[528,theory(equality)]) ).
cnf(539,negated_conjecture,
( app(esk7_0,X1) = app(esk7_0,app(nil,X1))
| ~ ssList(X1)
| $false
| ~ ssList(esk7_0) ),
inference(rw,[status(thm)],[508,121,theory(equality)]) ).
cnf(540,negated_conjecture,
( app(esk7_0,X1) = app(esk7_0,app(nil,X1))
| ~ ssList(X1)
| $false
| $false ),
inference(rw,[status(thm)],[539,172,theory(equality)]) ).
cnf(541,negated_conjecture,
( app(esk7_0,X1) = app(esk7_0,app(nil,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[540,theory(equality)]) ).
cnf(602,negated_conjecture,
( nil = app(nil,X1)
| app(esk7_0,X1) != esk7_0
| ~ ssList(app(nil,X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[529,541,theory(equality)]) ).
cnf(1466,negated_conjecture,
( app(nil,X1) = nil
| app(esk7_0,X1) != esk7_0
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[602,72,theory(equality)]) ).
cnf(1467,negated_conjecture,
( app(nil,X1) = nil
| app(esk7_0,X1) != esk7_0
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[1466,121,theory(equality)]) ).
cnf(1468,negated_conjecture,
( app(nil,X1) = nil
| app(esk7_0,X1) != esk7_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1467,theory(equality)]) ).
cnf(1469,negated_conjecture,
( app(nil,nil) = nil
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1468,468,theory(equality)]) ).
cnf(1475,negated_conjecture,
( app(nil,nil) = nil
| $false ),
inference(rw,[status(thm)],[1469,121,theory(equality)]) ).
cnf(1476,negated_conjecture,
app(nil,nil) = nil,
inference(cn,[status(thm)],[1475,theory(equality)]) ).
cnf(1490,negated_conjecture,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[68,1476,theory(equality)]) ).
cnf(1516,negated_conjecture,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[1490,121,theory(equality)]) ).
cnf(1517,negated_conjecture,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[1516,theory(equality)]) ).
cnf(2575,negated_conjecture,
( app(nil,esk7_0) = esk7_0
| ~ ssList(nil)
| ~ ssList(esk7_0) ),
inference(spm,[status(thm)],[339,468,theory(equality)]) ).
cnf(2630,negated_conjecture,
( app(nil,esk7_0) = esk7_0
| $false
| ~ ssList(esk7_0) ),
inference(rw,[status(thm)],[2575,121,theory(equality)]) ).
cnf(2631,negated_conjecture,
( app(nil,esk7_0) = esk7_0
| $false
| $false ),
inference(rw,[status(thm)],[2630,172,theory(equality)]) ).
cnf(2632,negated_conjecture,
app(nil,esk7_0) = esk7_0,
inference(cn,[status(thm)],[2631,theory(equality)]) ).
cnf(7869,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[345,72]) ).
cnf(7880,negated_conjecture,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[7869,1517,theory(equality)]) ).
cnf(7907,negated_conjecture,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[7880,121,theory(equality)]) ).
cnf(7908,negated_conjecture,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[7907,theory(equality)]) ).
cnf(9882,negated_conjecture,
( ssItem(esk11_3(X1,nil,X2))
| app(cons(X1,nil),X2) != esk7_0
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[392,7908]) ).
cnf(12362,negated_conjecture,
( app(app(X1,esk7_0),nil) != esk7_0
| ~ ssItem(esk11_3(esk12_0,X1,nil))
| ~ ssItem(esk12_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[428,200,theory(equality)]) ).
cnf(12381,negated_conjecture,
( app(app(X1,esk7_0),nil) != esk7_0
| ~ ssItem(esk11_3(esk12_0,X1,nil))
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[12362,196,theory(equality)]) ).
cnf(12382,negated_conjecture,
( app(app(X1,esk7_0),nil) != esk7_0
| ~ ssItem(esk11_3(esk12_0,X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[12381,theory(equality)]) ).
cnf(12409,negated_conjecture,
( app(app(nil,esk7_0),nil) != esk7_0
| ~ ssList(nil)
| app(cons(esk12_0,nil),nil) != esk7_0
| ~ ssItem(esk12_0) ),
inference(spm,[status(thm)],[12382,9882,theory(equality)]) ).
cnf(12417,negated_conjecture,
( $false
| ~ ssList(nil)
| app(cons(esk12_0,nil),nil) != esk7_0
| ~ ssItem(esk12_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[12409,2632,theory(equality)]),468,theory(equality)]) ).
cnf(12418,negated_conjecture,
( $false
| $false
| app(cons(esk12_0,nil),nil) != esk7_0
| ~ ssItem(esk12_0) ),
inference(rw,[status(thm)],[12417,121,theory(equality)]) ).
cnf(12419,negated_conjecture,
( $false
| $false
| $false
| ~ ssItem(esk12_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[12418,200,theory(equality)]),468,theory(equality)]) ).
cnf(12420,negated_conjecture,
( $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[12419,196,theory(equality)]) ).
cnf(12421,negated_conjecture,
$false,
inference(cn,[status(thm)],[12420,theory(equality)]) ).
cnf(12422,negated_conjecture,
$false,
12421,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC239+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpXwpQ3I/sel_SWC239+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC239+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC239+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC239+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
%
%------------------------------------------------------------------------------