%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC377+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 11:40:23 EST 2010
% Result : Theorem 10.67s
% Output : CNFRefutation 10.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 12
% Syntax : Number of formulae : 187 ( 15 unt; 0 def)
% Number of atoms : 910 ( 274 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 1139 ( 416 ~; 564 |; 110 &)
% ( 5 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 234 ( 0 sgn 133 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmpsMoIcJ/sel_SWC377+1.p_1',ax83) ).
fof(4,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpsMoIcJ/sel_SWC377+1.p_1',ax81) ).
fof(7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/tmp/tmpsMoIcJ/sel_SWC377+1.p_1',ax27) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpsMoIcJ/sel_SWC377+1.p_1',ax26) ).
fof(12,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
file('/tmp/tmpsMoIcJ/sel_SWC377+1.p_1',ax3) ).
fof(15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpsMoIcJ/sel_SWC377+1.p_1',ax15) ).
fof(16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpsMoIcJ/sel_SWC377+1.p_1',ax16) ).
fof(17,axiom,
ssList(nil),
file('/tmp/tmpsMoIcJ/sel_SWC377+1.p_1',ax17) ).
fof(18,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X2,X1)
| memberP(X3,X1) ) ) ) ) ),
file('/tmp/tmpsMoIcJ/sel_SWC377+1.p_1',ax36) ).
fof(19,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( X1 = X2
| memberP(X3,X1) ) ) ) ) ),
file('/tmp/tmpsMoIcJ/sel_SWC377+1.p_1',ax37) ).
fof(20,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/tmp/tmpsMoIcJ/sel_SWC377+1.p_1',ax38) ).
fof(23,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ( ( ~ memberP(X2,X5)
& ~ memberP(X1,X5) )
| ( memberP(X2,X5)
& memberP(X1,X5) ) ) )
| ( nil != X3
& nil = X4 )
| ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) != X4 ) ) )
& neq(X4,nil) ) ) ) ) ) ),
file('/tmp/tmpsMoIcJ/sel_SWC377+1.p_1',co1) ).
fof(24,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ( ( ~ memberP(X2,X5)
& ~ memberP(X1,X5) )
| ( memberP(X2,X5)
& memberP(X1,X5) ) ) )
| ( nil != X3
& nil = X4 )
| ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) != X4 ) ) )
& neq(X4,nil) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[23]) ).
fof(25,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[20,theory(equality)]) ).
fof(26,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ( ( ~ memberP(X2,X5)
& ~ memberP(X1,X5) )
| ( memberP(X2,X5)
& memberP(X1,X5) ) ) )
| ( nil != X3
& nil = X4 )
| ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) != X4 ) ) )
& neq(X4,nil) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[24,theory(equality)]) ).
fof(30,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(31,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)],[30]) ).
fof(32,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)],[31]) ).
fof(33,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)],[32]) ).
cnf(34,plain,
( nil = app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| nil != X1
| nil != X2 ),
inference(split_conjunct,[status(thm)],[33]) ).
fof(41,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(42,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[41]) ).
fof(43,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[42]) ).
cnf(44,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(52,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssItem(X3)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(53,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)],[52]) ).
fof(54,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)],[53]) ).
cnf(55,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[54]) ).
fof(56,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(57,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[56]) ).
fof(58,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[57]) ).
cnf(59,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[58]) ).
fof(76,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ( ( ~ memberP(X1,X2)
| ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) )
& ( ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| app(X3,cons(X2,X4)) != X1 ) )
| memberP(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(77,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)],[76]) ).
fof(78,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)],[77]) ).
fof(79,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)],[78]) ).
fof(80,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)],[79]) ).
cnf(84,plain,
( memberP(X1,X2)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(X3,cons(X2,X4)) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[80]) ).
fof(95,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(96,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[95]) ).
fof(97,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[96]) ).
fof(98,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)],[97]) ).
cnf(99,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[98]) ).
fof(101,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(102,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[101]) ).
fof(103,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[102]) ).
cnf(104,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(105,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[17]) ).
fof(106,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)],[18]) ).
fof(107,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)],[106]) ).
fof(108,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)],[107]) ).
fof(109,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)],[108]) ).
cnf(110,plain,
( memberP(app(X2,X3),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(X3,X1) ),
inference(split_conjunct,[status(thm)],[109]) ).
cnf(111,plain,
( memberP(app(X2,X3),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(X2,X1) ),
inference(split_conjunct,[status(thm)],[109]) ).
cnf(112,plain,
( memberP(X3,X1)
| memberP(X2,X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(app(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[109]) ).
fof(113,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)],[19]) ).
fof(114,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)],[113]) ).
fof(115,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)],[114]) ).
fof(116,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)],[115]) ).
cnf(118,plain,
( memberP(cons(X2,X3),X1)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[116]) ).
cnf(119,plain,
( memberP(X3,X1)
| X1 = X2
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ memberP(cons(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[116]) ).
fof(120,plain,
! [X1] :
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(121,plain,
! [X2] :
( ~ ssItem(X2)
| ~ memberP(nil,X2) ),
inference(variable_rename,[status(thm)],[120]) ).
cnf(122,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[121]) ).
fof(133,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ? [X5] :
( ssItem(X5)
& ( memberP(X2,X5)
| memberP(X1,X5) )
& ( ~ memberP(X2,X5)
| ~ memberP(X1,X5) ) )
& ( nil = X3
| nil != X4 )
& ( ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X3
& app(X7,cons(X6,nil)) = X4 ) )
| ~ neq(X4,nil) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(134,negated_conjecture,
? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& X9 = X11
& X8 = X10
& ? [X12] :
( ssItem(X12)
& ( memberP(X9,X12)
| memberP(X8,X12) )
& ( ~ memberP(X9,X12)
| ~ memberP(X8,X12) ) )
& ( nil = X10
| nil != X11 )
& ( ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssList(X14)
& app(cons(X13,nil),X14) = X10
& app(X14,cons(X13,nil)) = X11 ) )
| ~ neq(X11,nil) ) ) ) ) ),
inference(variable_rename,[status(thm)],[133]) ).
fof(135,negated_conjecture,
( ssList(esk7_0)
& ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ssItem(esk11_0)
& ( memberP(esk8_0,esk11_0)
| memberP(esk7_0,esk11_0) )
& ( ~ memberP(esk8_0,esk11_0)
| ~ memberP(esk7_0,esk11_0) )
& ( nil = esk9_0
| nil != esk10_0 )
& ( ( ssItem(esk12_0)
& ssList(esk13_0)
& app(cons(esk12_0,nil),esk13_0) = esk9_0
& app(esk13_0,cons(esk12_0,nil)) = esk10_0 )
| ~ neq(esk10_0,nil) ) ),
inference(skolemize,[status(esa)],[134]) ).
fof(136,negated_conjecture,
( ssList(esk7_0)
& ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ssItem(esk11_0)
& ( memberP(esk8_0,esk11_0)
| memberP(esk7_0,esk11_0) )
& ( ~ memberP(esk8_0,esk11_0)
| ~ memberP(esk7_0,esk11_0) )
& ( nil = esk9_0
| nil != esk10_0 )
& ( ssItem(esk12_0)
| ~ neq(esk10_0,nil) )
& ( ssList(esk13_0)
| ~ neq(esk10_0,nil) )
& ( app(cons(esk12_0,nil),esk13_0) = esk9_0
| ~ neq(esk10_0,nil) )
& ( app(esk13_0,cons(esk12_0,nil)) = esk10_0
| ~ neq(esk10_0,nil) ) ),
inference(distribute,[status(thm)],[135]) ).
cnf(137,negated_conjecture,
( app(esk13_0,cons(esk12_0,nil)) = esk10_0
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(138,negated_conjecture,
( app(cons(esk12_0,nil),esk13_0) = esk9_0
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(139,negated_conjecture,
( ssList(esk13_0)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(140,negated_conjecture,
( ssItem(esk12_0)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(141,negated_conjecture,
( nil = esk9_0
| nil != esk10_0 ),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(142,negated_conjecture,
( ~ memberP(esk7_0,esk11_0)
| ~ memberP(esk8_0,esk11_0) ),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(143,negated_conjecture,
( memberP(esk7_0,esk11_0)
| memberP(esk8_0,esk11_0) ),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(144,negated_conjecture,
ssItem(esk11_0),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(145,negated_conjecture,
esk7_0 = esk9_0,
inference(split_conjunct,[status(thm)],[136]) ).
cnf(146,negated_conjecture,
esk8_0 = esk10_0,
inference(split_conjunct,[status(thm)],[136]) ).
cnf(149,negated_conjecture,
ssList(esk8_0),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(153,negated_conjecture,
ssList(esk10_0),
inference(rw,[status(thm)],[149,146,theory(equality)]) ).
cnf(154,negated_conjecture,
( esk7_0 = nil
| esk10_0 != nil ),
inference(rw,[status(thm)],[141,145,theory(equality)]) ).
cnf(155,negated_conjecture,
( memberP(esk7_0,esk11_0)
| memberP(esk10_0,esk11_0) ),
inference(rw,[status(thm)],[143,146,theory(equality)]) ).
cnf(156,negated_conjecture,
( ~ memberP(esk7_0,esk11_0)
| ~ memberP(esk10_0,esk11_0) ),
inference(rw,[status(thm)],[142,146,theory(equality)]) ).
cnf(164,negated_conjecture,
( app(cons(esk12_0,nil),esk13_0) = esk7_0
| ~ neq(esk10_0,nil) ),
inference(rw,[status(thm)],[138,145,theory(equality)]) ).
cnf(165,negated_conjecture,
( ssList(esk13_0)
| esk10_0 = nil
| ~ ssList(nil)
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[139,99,theory(equality)]) ).
cnf(166,negated_conjecture,
( ssItem(esk12_0)
| esk10_0 = nil
| ~ ssList(nil)
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[140,99,theory(equality)]) ).
cnf(167,negated_conjecture,
( app(esk13_0,cons(esk12_0,nil)) = esk10_0
| esk10_0 = nil
| ~ ssList(nil)
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[137,99,theory(equality)]) ).
cnf(168,negated_conjecture,
( app(cons(esk12_0,nil),esk13_0) = esk7_0
| esk10_0 = nil
| ~ ssList(nil)
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[164,99,theory(equality)]) ).
cnf(169,negated_conjecture,
( ssList(esk13_0)
| esk10_0 = nil
| $false
| ~ ssList(esk10_0) ),
inference(rw,[status(thm)],[165,105,theory(equality)]) ).
cnf(170,negated_conjecture,
( ssList(esk13_0)
| esk10_0 = nil
| ~ ssList(esk10_0) ),
inference(cn,[status(thm)],[169,theory(equality)]) ).
cnf(171,negated_conjecture,
( ssItem(esk12_0)
| esk10_0 = nil
| $false
| ~ ssList(esk10_0) ),
inference(rw,[status(thm)],[166,105,theory(equality)]) ).
cnf(172,negated_conjecture,
( ssItem(esk12_0)
| esk10_0 = nil
| ~ ssList(esk10_0) ),
inference(cn,[status(thm)],[171,theory(equality)]) ).
cnf(173,negated_conjecture,
( app(esk13_0,cons(esk12_0,nil)) = esk10_0
| esk10_0 = nil
| $false
| ~ ssList(esk10_0) ),
inference(rw,[status(thm)],[167,105,theory(equality)]) ).
cnf(174,negated_conjecture,
( app(esk13_0,cons(esk12_0,nil)) = esk10_0
| esk10_0 = nil
| ~ ssList(esk10_0) ),
inference(cn,[status(thm)],[173,theory(equality)]) ).
cnf(175,negated_conjecture,
( app(cons(esk12_0,nil),esk13_0) = esk7_0
| esk10_0 = nil
| $false
| ~ ssList(esk10_0) ),
inference(rw,[status(thm)],[168,105,theory(equality)]) ).
cnf(176,negated_conjecture,
( app(cons(esk12_0,nil),esk13_0) = esk7_0
| esk10_0 = nil
| ~ ssList(esk10_0) ),
inference(cn,[status(thm)],[175,theory(equality)]) ).
cnf(189,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(er,[status(thm)],[34,theory(equality)]) ).
cnf(190,plain,
( app(X1,nil) = nil
| nil != X1
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[189,105,theory(equality)]) ).
cnf(191,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[190,theory(equality)]) ).
cnf(203,plain,
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(er,[status(thm)],[118,theory(equality)]) ).
cnf(298,plain,
( X1 = X2
| memberP(app(X3,X4),X1)
| ~ memberP(app(cons(X2,X3),X4),X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(app(X3,X4))
| ~ ssList(X3)
| ~ ssList(X4) ),
inference(spm,[status(thm)],[119,55,theory(equality)]) ).
cnf(312,negated_conjecture,
( ssList(esk13_0)
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[170,153,theory(equality)]) ).
cnf(313,negated_conjecture,
( ssList(esk13_0)
| esk10_0 = nil ),
inference(cn,[status(thm)],[312,theory(equality)]) ).
cnf(329,negated_conjecture,
( ssItem(esk12_0)
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[172,153,theory(equality)]) ).
cnf(330,negated_conjecture,
( ssItem(esk12_0)
| esk10_0 = nil ),
inference(cn,[status(thm)],[329,theory(equality)]) ).
cnf(335,negated_conjecture,
( app(esk13_0,cons(esk12_0,nil)) = esk10_0
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[174,153,theory(equality)]) ).
cnf(336,negated_conjecture,
( app(esk13_0,cons(esk12_0,nil)) = esk10_0
| esk10_0 = nil ),
inference(cn,[status(thm)],[335,theory(equality)]) ).
cnf(344,negated_conjecture,
( memberP(esk13_0,X1)
| memberP(cons(esk12_0,nil),X1)
| esk10_0 = nil
| ~ memberP(esk10_0,X1)
| ~ ssItem(X1)
| ~ ssList(cons(esk12_0,nil))
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[112,336,theory(equality)]) ).
cnf(345,negated_conjecture,
( memberP(X1,esk12_0)
| esk10_0 = nil
| esk10_0 != X1
| ~ ssItem(esk12_0)
| ~ ssList(nil)
| ~ ssList(esk13_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[84,336,theory(equality)]) ).
cnf(349,negated_conjecture,
( memberP(X1,esk12_0)
| esk10_0 = nil
| esk10_0 != X1
| ~ ssItem(esk12_0)
| $false
| ~ ssList(esk13_0)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[345,105,theory(equality)]) ).
cnf(350,negated_conjecture,
( memberP(X1,esk12_0)
| esk10_0 = nil
| esk10_0 != X1
| ~ ssItem(esk12_0)
| ~ ssList(esk13_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[349,theory(equality)]) ).
cnf(363,negated_conjecture,
( app(cons(esk12_0,nil),esk13_0) = esk7_0
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[176,153,theory(equality)]) ).
cnf(364,negated_conjecture,
( app(cons(esk12_0,nil),esk13_0) = esk7_0
| esk10_0 = nil ),
inference(cn,[status(thm)],[363,theory(equality)]) ).
cnf(368,negated_conjecture,
( esk7_0 = cons(esk12_0,esk13_0)
| esk10_0 = nil
| ~ ssItem(esk12_0)
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[44,364,theory(equality)]) ).
cnf(404,negated_conjecture,
( cons(esk12_0,esk13_0) = esk7_0
| esk10_0 = nil
| ~ ssItem(esk12_0) ),
inference(csr,[status(thm)],[368,313]) ).
cnf(405,negated_conjecture,
( cons(esk12_0,esk13_0) = esk7_0
| esk10_0 = nil ),
inference(csr,[status(thm)],[404,330]) ).
cnf(411,negated_conjecture,
( X1 = esk12_0
| memberP(esk13_0,X1)
| esk10_0 = nil
| ~ memberP(esk7_0,X1)
| ~ ssItem(esk12_0)
| ~ ssItem(X1)
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[119,405,theory(equality)]) ).
cnf(418,negated_conjecture,
( memberP(esk7_0,esk12_0)
| esk10_0 = nil
| ~ ssItem(esk12_0)
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[203,405,theory(equality)]) ).
cnf(425,plain,
( app(nil,nil) = nil
| ~ ssList(nil) ),
inference(er,[status(thm)],[191,theory(equality)]) ).
cnf(426,plain,
( app(nil,nil) = nil
| $false ),
inference(rw,[status(thm)],[425,105,theory(equality)]) ).
cnf(427,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[426,theory(equality)]) ).
cnf(449,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[55,427,theory(equality)]) ).
cnf(465,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[449,105,theory(equality)]) ).
cnf(466,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[465,theory(equality)]) ).
cnf(467,negated_conjecture,
( esk10_0 = nil
| memberP(esk7_0,esk12_0)
| ~ ssItem(esk12_0) ),
inference(csr,[status(thm)],[418,313]) ).
cnf(468,negated_conjecture,
( esk10_0 = nil
| memberP(esk7_0,esk12_0) ),
inference(csr,[status(thm)],[467,330]) ).
cnf(921,negated_conjecture,
( esk10_0 = nil
| memberP(X1,esk12_0)
| esk10_0 != X1
| ~ ssItem(esk12_0)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[350,313]) ).
cnf(922,negated_conjecture,
( esk10_0 = nil
| memberP(X1,esk12_0)
| esk10_0 != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[921,330]) ).
cnf(923,negated_conjecture,
( esk10_0 = nil
| memberP(esk10_0,esk12_0)
| ~ ssList(esk10_0) ),
inference(er,[status(thm)],[922,theory(equality)]) ).
cnf(924,negated_conjecture,
( esk10_0 = nil
| memberP(esk10_0,esk12_0)
| $false ),
inference(rw,[status(thm)],[923,153,theory(equality)]) ).
cnf(925,negated_conjecture,
( esk10_0 = nil
| memberP(esk10_0,esk12_0) ),
inference(cn,[status(thm)],[924,theory(equality)]) ).
cnf(3279,plain,
( X1 = X2
| memberP(app(X3,X4),X1)
| ~ memberP(app(cons(X2,X3),X4),X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X4) ),
inference(csr,[status(thm)],[298,59]) ).
cnf(3287,plain,
( X1 = X2
| memberP(app(nil,nil),X1)
| ~ memberP(cons(X2,nil),X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[3279,466,theory(equality)]) ).
cnf(3305,plain,
( X1 = X2
| memberP(nil,X1)
| ~ memberP(cons(X2,nil),X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(rw,[status(thm)],[3287,427,theory(equality)]) ).
cnf(3306,plain,
( X1 = X2
| memberP(nil,X1)
| ~ memberP(cons(X2,nil),X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[3305,105,theory(equality)]) ).
cnf(3307,plain,
( X1 = X2
| memberP(nil,X1)
| ~ memberP(cons(X2,nil),X1)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[3306,theory(equality)]) ).
cnf(3975,negated_conjecture,
( esk10_0 = nil
| memberP(cons(esk12_0,nil),X1)
| memberP(esk13_0,X1)
| ~ memberP(esk10_0,X1)
| ~ ssItem(X1)
| ~ ssList(cons(esk12_0,nil)) ),
inference(csr,[status(thm)],[344,313]) ).
cnf(3976,negated_conjecture,
( esk10_0 = nil
| memberP(cons(esk12_0,nil),X1)
| memberP(esk13_0,X1)
| ~ memberP(esk10_0,X1)
| ~ ssItem(X1)
| ~ ssItem(esk12_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[3975,104,theory(equality)]) ).
cnf(3978,negated_conjecture,
( esk10_0 = nil
| memberP(cons(esk12_0,nil),X1)
| memberP(esk13_0,X1)
| ~ memberP(esk10_0,X1)
| ~ ssItem(X1)
| ~ ssItem(esk12_0)
| $false ),
inference(rw,[status(thm)],[3976,105,theory(equality)]) ).
cnf(3979,negated_conjecture,
( esk10_0 = nil
| memberP(cons(esk12_0,nil),X1)
| memberP(esk13_0,X1)
| ~ memberP(esk10_0,X1)
| ~ ssItem(X1)
| ~ ssItem(esk12_0) ),
inference(cn,[status(thm)],[3978,theory(equality)]) ).
cnf(4677,negated_conjecture,
( esk10_0 = nil
| X1 = esk12_0
| memberP(esk13_0,X1)
| ~ memberP(esk7_0,X1)
| ~ ssItem(esk12_0)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[411,313]) ).
cnf(4678,negated_conjecture,
( esk10_0 = nil
| X1 = esk12_0
| memberP(esk13_0,X1)
| ~ memberP(esk7_0,X1)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[4677,330]) ).
cnf(4679,negated_conjecture,
( esk10_0 = nil
| esk11_0 = esk12_0
| memberP(esk13_0,esk11_0)
| memberP(esk10_0,esk11_0)
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[4678,155,theory(equality)]) ).
cnf(4681,negated_conjecture,
( esk10_0 = nil
| esk11_0 = esk12_0
| memberP(esk13_0,esk11_0)
| memberP(esk10_0,esk11_0)
| $false ),
inference(rw,[status(thm)],[4679,144,theory(equality)]) ).
cnf(4682,negated_conjecture,
( esk10_0 = nil
| esk11_0 = esk12_0
| memberP(esk13_0,esk11_0)
| memberP(esk10_0,esk11_0) ),
inference(cn,[status(thm)],[4681,theory(equality)]) ).
cnf(4688,negated_conjecture,
( memberP(app(esk13_0,X1),esk11_0)
| esk12_0 = esk11_0
| esk10_0 = nil
| memberP(esk10_0,esk11_0)
| ~ ssItem(esk11_0)
| ~ ssList(X1)
| ~ ssList(esk13_0) ),
inference(spm,[status(thm)],[111,4682,theory(equality)]) ).
cnf(4698,negated_conjecture,
( memberP(app(esk13_0,X1),esk11_0)
| esk12_0 = esk11_0
| esk10_0 = nil
| memberP(esk10_0,esk11_0)
| $false
| ~ ssList(X1)
| ~ ssList(esk13_0) ),
inference(rw,[status(thm)],[4688,144,theory(equality)]) ).
cnf(4699,negated_conjecture,
( memberP(app(esk13_0,X1),esk11_0)
| esk12_0 = esk11_0
| esk10_0 = nil
| memberP(esk10_0,esk11_0)
| ~ ssList(X1)
| ~ ssList(esk13_0) ),
inference(cn,[status(thm)],[4698,theory(equality)]) ).
cnf(4822,negated_conjecture,
( esk12_0 = esk11_0
| esk10_0 = nil
| memberP(app(esk13_0,X1),esk11_0)
| memberP(esk10_0,esk11_0)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[4699,313]) ).
cnf(4831,negated_conjecture,
( esk10_0 = nil
| esk12_0 = esk11_0
| memberP(esk10_0,esk11_0)
| ~ ssList(cons(esk12_0,nil)) ),
inference(spm,[status(thm)],[4822,336,theory(equality)]) ).
cnf(4860,negated_conjecture,
( esk12_0 = esk11_0
| esk10_0 = nil
| memberP(esk10_0,esk11_0)
| ~ ssItem(esk12_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[4831,104,theory(equality)]) ).
cnf(4862,negated_conjecture,
( esk12_0 = esk11_0
| esk10_0 = nil
| memberP(esk10_0,esk11_0)
| ~ ssItem(esk12_0)
| $false ),
inference(rw,[status(thm)],[4860,105,theory(equality)]) ).
cnf(4863,negated_conjecture,
( esk12_0 = esk11_0
| esk10_0 = nil
| memberP(esk10_0,esk11_0)
| ~ ssItem(esk12_0) ),
inference(cn,[status(thm)],[4862,theory(equality)]) ).
cnf(4864,negated_conjecture,
( esk12_0 = esk11_0
| esk10_0 = nil
| memberP(esk10_0,esk11_0) ),
inference(csr,[status(thm)],[4863,330]) ).
cnf(139114,plain,
( X1 = X2
| ~ memberP(cons(X2,nil),X1)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[3307,122]) ).
cnf(205912,negated_conjecture,
( esk10_0 = nil
| memberP(cons(esk12_0,nil),X1)
| memberP(esk13_0,X1)
| ~ memberP(esk10_0,X1)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[3979,330]) ).
cnf(205916,negated_conjecture,
( esk10_0 = nil
| memberP(cons(esk12_0,nil),esk11_0)
| memberP(esk13_0,esk11_0)
| esk12_0 = esk11_0
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[205912,4864,theory(equality)]) ).
cnf(205919,negated_conjecture,
( esk10_0 = nil
| memberP(cons(esk12_0,nil),esk11_0)
| memberP(esk13_0,esk11_0)
| esk12_0 = esk11_0
| $false ),
inference(rw,[status(thm)],[205916,144,theory(equality)]) ).
cnf(205920,negated_conjecture,
( esk10_0 = nil
| memberP(cons(esk12_0,nil),esk11_0)
| memberP(esk13_0,esk11_0)
| esk12_0 = esk11_0 ),
inference(cn,[status(thm)],[205919,theory(equality)]) ).
cnf(205934,negated_conjecture,
( esk11_0 = esk12_0
| esk10_0 = nil
| memberP(esk13_0,esk11_0)
| ~ ssItem(esk12_0)
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[139114,205920,theory(equality)]) ).
cnf(205964,negated_conjecture,
( esk11_0 = esk12_0
| esk10_0 = nil
| memberP(esk13_0,esk11_0)
| ~ ssItem(esk12_0)
| $false ),
inference(rw,[status(thm)],[205934,144,theory(equality)]) ).
cnf(205965,negated_conjecture,
( esk11_0 = esk12_0
| esk10_0 = nil
| memberP(esk13_0,esk11_0)
| ~ ssItem(esk12_0) ),
inference(cn,[status(thm)],[205964,theory(equality)]) ).
cnf(205968,negated_conjecture,
( esk12_0 = esk11_0
| esk10_0 = nil
| memberP(esk13_0,esk11_0) ),
inference(csr,[status(thm)],[205965,330]) ).
cnf(205971,negated_conjecture,
( memberP(app(X1,esk13_0),esk11_0)
| esk10_0 = nil
| esk12_0 = esk11_0
| ~ ssItem(esk11_0)
| ~ ssList(esk13_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[110,205968,theory(equality)]) ).
cnf(205981,negated_conjecture,
( memberP(app(X1,esk13_0),esk11_0)
| esk10_0 = nil
| esk12_0 = esk11_0
| $false
| ~ ssList(esk13_0)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[205971,144,theory(equality)]) ).
cnf(205982,negated_conjecture,
( memberP(app(X1,esk13_0),esk11_0)
| esk10_0 = nil
| esk12_0 = esk11_0
| ~ ssList(esk13_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[205981,theory(equality)]) ).
cnf(206730,negated_conjecture,
( esk10_0 = nil
| esk12_0 = esk11_0
| memberP(app(X1,esk13_0),esk11_0)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[205982,313]) ).
cnf(206741,negated_conjecture,
( esk12_0 = esk11_0
| esk10_0 = nil
| memberP(esk7_0,esk11_0)
| ~ ssList(cons(esk12_0,nil)) ),
inference(spm,[status(thm)],[206730,364,theory(equality)]) ).
cnf(206831,negated_conjecture,
( esk10_0 = nil
| esk12_0 = esk11_0
| memberP(esk7_0,esk11_0)
| ~ ssItem(esk12_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[206741,104,theory(equality)]) ).
cnf(206833,negated_conjecture,
( esk10_0 = nil
| esk12_0 = esk11_0
| memberP(esk7_0,esk11_0)
| ~ ssItem(esk12_0)
| $false ),
inference(rw,[status(thm)],[206831,105,theory(equality)]) ).
cnf(206834,negated_conjecture,
( esk10_0 = nil
| esk12_0 = esk11_0
| memberP(esk7_0,esk11_0)
| ~ ssItem(esk12_0) ),
inference(cn,[status(thm)],[206833,theory(equality)]) ).
cnf(206835,negated_conjecture,
( esk10_0 = nil
| esk12_0 = esk11_0
| memberP(esk7_0,esk11_0) ),
inference(csr,[status(thm)],[206834,330]) ).
cnf(206836,negated_conjecture,
( esk12_0 = esk11_0
| esk10_0 = nil
| ~ memberP(esk10_0,esk11_0) ),
inference(spm,[status(thm)],[156,206835,theory(equality)]) ).
cnf(206884,negated_conjecture,
( esk12_0 = esk11_0
| esk10_0 = nil ),
inference(csr,[status(thm)],[206836,4864]) ).
cnf(206889,negated_conjecture,
( esk10_0 = nil
| memberP(esk7_0,esk11_0) ),
inference(spm,[status(thm)],[468,206884,theory(equality)]) ).
cnf(206897,negated_conjecture,
( esk10_0 = nil
| memberP(esk10_0,esk11_0) ),
inference(spm,[status(thm)],[925,206884,theory(equality)]) ).
cnf(207659,negated_conjecture,
( esk10_0 = nil
| ~ memberP(esk10_0,esk11_0) ),
inference(spm,[status(thm)],[156,206889,theory(equality)]) ).
cnf(207745,negated_conjecture,
esk10_0 = nil,
inference(csr,[status(thm)],[207659,206897]) ).
cnf(208819,negated_conjecture,
( memberP(nil,esk11_0)
| memberP(esk7_0,esk11_0) ),
inference(rw,[status(thm)],[155,207745,theory(equality)]) ).
cnf(208820,negated_conjecture,
( esk7_0 = nil
| $false ),
inference(rw,[status(thm)],[154,207745,theory(equality)]) ).
cnf(208821,negated_conjecture,
esk7_0 = nil,
inference(cn,[status(thm)],[208820,theory(equality)]) ).
cnf(209318,negated_conjecture,
( memberP(nil,esk11_0)
| memberP(nil,esk11_0) ),
inference(rw,[status(thm)],[208819,208821,theory(equality)]) ).
cnf(209319,negated_conjecture,
memberP(nil,esk11_0),
inference(cn,[status(thm)],[209318,theory(equality)]) ).
cnf(209320,negated_conjecture,
~ ssItem(esk11_0),
inference(spm,[status(thm)],[122,209319,theory(equality)]) ).
cnf(209328,negated_conjecture,
$false,
inference(rw,[status(thm)],[209320,144,theory(equality)]) ).
cnf(209329,negated_conjecture,
$false,
inference(cn,[status(thm)],[209328,theory(equality)]) ).
cnf(209330,negated_conjecture,
$false,
209329,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC377+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpsMoIcJ/sel_SWC377+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC377+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC377+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC377+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
%
%------------------------------------------------------------------------------