TSTP Solution File: SWC409+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC409+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 11:49:21 EST 2010
% Result : Theorem 0.95s
% Output : CNFRefutation 0.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 14
% Syntax : Number of formulae : 207 ( 24 unt; 0 def)
% Number of atoms : 873 ( 238 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 1095 ( 429 ~; 519 |; 104 &)
% ( 4 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 279 ( 0 sgn 136 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax3) ).
fof(3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax26) ).
fof(6,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax84) ).
fof(7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax83) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax82) ).
fof(9,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax81) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax20) ).
fof(11,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax38) ).
fof(12,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax16) ).
fof(13,axiom,
ssList(nil),
file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax17) ).
fof(14,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X2,X1)
| memberP(X3,X1) ) ) ) ) ),
file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax36) ).
fof(15,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax28) ).
fof(20,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( X1 = X2
| memberP(X3,X1) ) ) ) ) ),
file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax37) ).
fof(21,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) != X3
& app(cons(X5,nil),X6) = X4 ) )
| ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X2,X7)
| memberP(X1,X7) ) )
| ( nil != X3
& nil = X4 ) ) ) ) ) ),
file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',co1) ).
fof(22,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) != X3
& app(cons(X5,nil),X6) = X4 ) )
| ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X2,X7)
| memberP(X1,X7) ) )
| ( nil != X3
& nil = X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[21]) ).
fof(23,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).
fof(24,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) != X3
& app(cons(X5,nil),X6) = X4 ) )
| ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X2,X7)
| memberP(X1,X7) ) )
| ( nil != X3
& nil = X4 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[22,theory(equality)]) ).
fof(30,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)],[2]) ).
fof(31,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)],[30]) ).
fof(32,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssItem(X6)
| ( ( ~ memberP(X5,X6)
| ( ssList(esk3_2(X5,X6))
& ssList(esk4_2(X5,X6))
& app(esk3_2(X5,X6),cons(X6,esk4_2(X5,X6))) = X5 ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(X9,cons(X6,X10)) != X5 ) )
| memberP(X5,X6) ) ) ) ),
inference(skolemize,[status(esa)],[31]) ).
fof(33,plain,
! [X5,X6,X9,X10] :
( ( ( ~ ssList(X10)
| app(X9,cons(X6,X10)) != X5
| ~ ssList(X9)
| memberP(X5,X6) )
& ( ~ memberP(X5,X6)
| ( ssList(esk3_2(X5,X6))
& ssList(esk4_2(X5,X6))
& app(esk3_2(X5,X6),cons(X6,esk4_2(X5,X6))) = X5 ) ) )
| ~ ssItem(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[32]) ).
fof(34,plain,
! [X5,X6,X9,X10] :
( ( ~ ssList(X10)
| app(X9,cons(X6,X10)) != X5
| ~ ssList(X9)
| memberP(X5,X6)
| ~ ssItem(X6)
| ~ ssList(X5) )
& ( ssList(esk3_2(X5,X6))
| ~ memberP(X5,X6)
| ~ ssItem(X6)
| ~ ssList(X5) )
& ( ssList(esk4_2(X5,X6))
| ~ memberP(X5,X6)
| ~ ssItem(X6)
| ~ ssList(X5) )
& ( app(esk3_2(X5,X6),cons(X6,esk4_2(X5,X6))) = X5
| ~ memberP(X5,X6)
| ~ ssItem(X6)
| ~ ssList(X5) ) ),
inference(distribute,[status(thm)],[33]) ).
cnf(35,plain,
( app(esk3_2(X1,X2),cons(X2,esk4_2(X1,X2))) = X1
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2) ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(36,plain,
( ssList(esk4_2(X1,X2))
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2) ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(37,plain,
( ssList(esk3_2(X1,X2))
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2) ),
inference(split_conjunct,[status(thm)],[34]) ).
fof(39,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(40,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[39]) ).
fof(41,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[40]) ).
cnf(42,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(51,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(52,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[51]) ).
cnf(53,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[52]) ).
fof(54,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)],[7]) ).
fof(55,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)],[54]) ).
fof(56,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)],[55]) ).
fof(57,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)],[56]) ).
cnf(58,plain,
( nil = app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| nil != X1
| nil != X2 ),
inference(split_conjunct,[status(thm)],[57]) ).
fof(61,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)],[8]) ).
fof(62,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)],[61]) ).
fof(63,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)],[62]) ).
cnf(64,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[63]) ).
fof(65,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(66,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[65]) ).
fof(67,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[66]) ).
cnf(68,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[67]) ).
fof(69,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(70,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssItem(X6)
& cons(X6,X5) = X4 ) ) ),
inference(variable_rename,[status(thm)],[69]) ).
fof(71,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ( ssList(esk5_1(X4))
& ssItem(esk6_1(X4))
& cons(esk6_1(X4),esk5_1(X4)) = X4 ) ),
inference(skolemize,[status(esa)],[70]) ).
fof(72,plain,
! [X4] :
( ( ssList(esk5_1(X4))
| nil = X4
| ~ ssList(X4) )
& ( ssItem(esk6_1(X4))
| nil = X4
| ~ ssList(X4) )
& ( cons(esk6_1(X4),esk5_1(X4)) = X4
| nil = X4
| ~ ssList(X4) ) ),
inference(distribute,[status(thm)],[71]) ).
cnf(73,plain,
( nil = X1
| cons(esk6_1(X1),esk5_1(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[72]) ).
cnf(74,plain,
( nil = X1
| ssItem(esk6_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[72]) ).
cnf(75,plain,
( nil = X1
| ssList(esk5_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[72]) ).
fof(76,plain,
! [X1] :
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(77,plain,
! [X2] :
( ~ ssItem(X2)
| ~ memberP(nil,X2) ),
inference(variable_rename,[status(thm)],[76]) ).
cnf(78,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[77]) ).
fof(79,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(80,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[79]) ).
fof(81,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[80]) ).
cnf(82,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[81]) ).
cnf(83,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[13]) ).
fof(84,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)],[14]) ).
fof(85,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)],[84]) ).
fof(86,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)],[85]) ).
fof(87,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)],[86]) ).
cnf(88,plain,
( memberP(app(X2,X3),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(X3,X1) ),
inference(split_conjunct,[status(thm)],[87]) ).
cnf(89,plain,
( memberP(app(X2,X3),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ memberP(X2,X1) ),
inference(split_conjunct,[status(thm)],[87]) ).
fof(91,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(92,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[91]) ).
cnf(93,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[92]) ).
fof(112,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)],[20]) ).
fof(113,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)],[112]) ).
fof(114,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)],[113]) ).
fof(115,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)],[114]) ).
cnf(117,plain,
( memberP(cons(X2,X3),X1)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[115]) ).
cnf(118,plain,
( memberP(X3,X1)
| X1 = X2
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ memberP(cons(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[115]) ).
fof(119,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(X6,cons(X5,nil)) = X3
| app(cons(X5,nil),X6) != X4 ) )
& ? [X7] :
( ssItem(X7)
& memberP(X2,X7)
& ~ memberP(X1,X7) )
& ( nil = X3
| nil != X4 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(120,negated_conjecture,
? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& X9 = X11
& X8 = X10
& ! [X12] :
( ~ ssItem(X12)
| ! [X13] :
( ~ ssList(X13)
| app(X13,cons(X12,nil)) = X10
| app(cons(X12,nil),X13) != X11 ) )
& ? [X14] :
( ssItem(X14)
& memberP(X9,X14)
& ~ memberP(X8,X14) )
& ( nil = X10
| nil != X11 ) ) ) ) ),
inference(variable_rename,[status(thm)],[119]) ).
fof(121,negated_conjecture,
( ssList(esk7_0)
& ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ! [X12] :
( ~ ssItem(X12)
| ! [X13] :
( ~ ssList(X13)
| app(X13,cons(X12,nil)) = esk9_0
| app(cons(X12,nil),X13) != esk10_0 ) )
& ssItem(esk11_0)
& memberP(esk8_0,esk11_0)
& ~ memberP(esk7_0,esk11_0)
& ( nil = esk9_0
| nil != esk10_0 ) ),
inference(skolemize,[status(esa)],[120]) ).
fof(122,negated_conjecture,
! [X12,X13] :
( ( ~ ssList(X13)
| app(X13,cons(X12,nil)) = esk9_0
| app(cons(X12,nil),X13) != esk10_0
| ~ ssItem(X12) )
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ssItem(esk11_0)
& memberP(esk8_0,esk11_0)
& ~ memberP(esk7_0,esk11_0)
& ( nil = esk9_0
| nil != esk10_0 )
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(shift_quantors,[status(thm)],[121]) ).
cnf(124,negated_conjecture,
ssList(esk8_0),
inference(split_conjunct,[status(thm)],[122]) ).
cnf(128,negated_conjecture,
~ memberP(esk7_0,esk11_0),
inference(split_conjunct,[status(thm)],[122]) ).
cnf(129,negated_conjecture,
memberP(esk8_0,esk11_0),
inference(split_conjunct,[status(thm)],[122]) ).
cnf(130,negated_conjecture,
ssItem(esk11_0),
inference(split_conjunct,[status(thm)],[122]) ).
cnf(131,negated_conjecture,
esk7_0 = esk9_0,
inference(split_conjunct,[status(thm)],[122]) ).
cnf(132,negated_conjecture,
esk8_0 = esk10_0,
inference(split_conjunct,[status(thm)],[122]) ).
cnf(133,negated_conjecture,
( app(X2,cons(X1,nil)) = esk9_0
| ~ ssItem(X1)
| app(cons(X1,nil),X2) != esk10_0
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[122]) ).
cnf(135,negated_conjecture,
ssList(esk10_0),
inference(rw,[status(thm)],[124,132,theory(equality)]) ).
cnf(136,negated_conjecture,
memberP(esk10_0,esk11_0),
inference(rw,[status(thm)],[129,132,theory(equality)]) ).
cnf(137,negated_conjecture,
~ memberP(esk9_0,esk11_0),
inference(rw,[status(thm)],[128,131,theory(equality)]) ).
cnf(150,negated_conjecture,
( ssList(esk3_2(esk10_0,esk11_0))
| ~ ssList(esk10_0)
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[37,136,theory(equality)]) ).
cnf(151,negated_conjecture,
( ssList(esk3_2(esk10_0,esk11_0))
| ~ ssList(esk10_0)
| $false ),
inference(rw,[status(thm)],[150,130,theory(equality)]) ).
cnf(152,negated_conjecture,
( ssList(esk3_2(esk10_0,esk11_0))
| ~ ssList(esk10_0) ),
inference(cn,[status(thm)],[151,theory(equality)]) ).
cnf(153,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(er,[status(thm)],[58,theory(equality)]) ).
cnf(154,plain,
( app(X1,nil) = nil
| nil != X1
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[153,83,theory(equality)]) ).
cnf(155,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[154,theory(equality)]) ).
cnf(156,negated_conjecture,
( ssList(esk4_2(esk10_0,esk11_0))
| ~ ssList(esk10_0)
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[36,136,theory(equality)]) ).
cnf(157,negated_conjecture,
( ssList(esk4_2(esk10_0,esk11_0))
| ~ ssList(esk10_0)
| $false ),
inference(rw,[status(thm)],[156,130,theory(equality)]) ).
cnf(158,negated_conjecture,
( ssList(esk4_2(esk10_0,esk11_0))
| ~ ssList(esk10_0) ),
inference(cn,[status(thm)],[157,theory(equality)]) ).
cnf(159,plain,
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[117,theory(equality)]) ).
cnf(169,negated_conjecture,
( memberP(app(X1,esk10_0),esk11_0)
| ~ ssList(esk10_0)
| ~ ssList(X1)
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[88,136,theory(equality)]) ).
cnf(170,negated_conjecture,
( memberP(app(X1,esk10_0),esk11_0)
| ~ ssList(esk10_0)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[169,130,theory(equality)]) ).
cnf(171,negated_conjecture,
( memberP(app(X1,esk10_0),esk11_0)
| ~ ssList(esk10_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[170,theory(equality)]) ).
cnf(205,plain,
( X1 = esk6_1(X2)
| memberP(esk5_1(X2),X1)
| nil = X2
| ~ memberP(X2,X1)
| ~ ssList(esk5_1(X2))
| ~ ssItem(esk6_1(X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[118,73,theory(equality)]) ).
cnf(220,negated_conjecture,
( app(X1,cons(X2,nil)) = esk9_0
| cons(X2,X1) != esk10_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(spm,[status(thm)],[133,68,theory(equality)]) ).
cnf(238,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[53,64,theory(equality)]) ).
cnf(240,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[64,93,theory(equality)]) ).
cnf(241,plain,
( ssList(app(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[42,64,theory(equality)]) ).
cnf(253,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[238,83,theory(equality)]) ).
cnf(254,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[253,theory(equality)]) ).
cnf(257,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[240,83,theory(equality)]) ).
cnf(258,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[257,theory(equality)]) ).
cnf(267,negated_conjecture,
( app(esk3_2(esk10_0,esk11_0),cons(esk11_0,esk4_2(esk10_0,esk11_0))) = esk10_0
| ~ ssList(esk10_0)
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[35,136,theory(equality)]) ).
cnf(268,negated_conjecture,
( app(esk3_2(esk10_0,esk11_0),cons(esk11_0,esk4_2(esk10_0,esk11_0))) = esk10_0
| ~ ssList(esk10_0)
| $false ),
inference(rw,[status(thm)],[267,130,theory(equality)]) ).
cnf(269,negated_conjecture,
( app(esk3_2(esk10_0,esk11_0),cons(esk11_0,esk4_2(esk10_0,esk11_0))) = esk10_0
| ~ ssList(esk10_0) ),
inference(cn,[status(thm)],[268,theory(equality)]) ).
cnf(284,negated_conjecture,
( ssList(esk3_2(esk10_0,esk11_0))
| $false ),
inference(rw,[status(thm)],[152,135,theory(equality)]) ).
cnf(285,negated_conjecture,
ssList(esk3_2(esk10_0,esk11_0)),
inference(cn,[status(thm)],[284,theory(equality)]) ).
cnf(286,negated_conjecture,
( ssList(esk4_2(esk10_0,esk11_0))
| $false ),
inference(rw,[status(thm)],[158,135,theory(equality)]) ).
cnf(287,negated_conjecture,
ssList(esk4_2(esk10_0,esk11_0)),
inference(cn,[status(thm)],[286,theory(equality)]) ).
cnf(288,plain,
( app(nil,nil) = nil
| ~ ssList(nil) ),
inference(er,[status(thm)],[155,theory(equality)]) ).
cnf(289,plain,
( app(nil,nil) = nil
| $false ),
inference(rw,[status(thm)],[288,83,theory(equality)]) ).
cnf(290,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[289,theory(equality)]) ).
cnf(357,negated_conjecture,
( memberP(app(X1,esk10_0),esk11_0)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[171,135,theory(equality)]) ).
cnf(358,negated_conjecture,
( memberP(app(X1,esk10_0),esk11_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[357,theory(equality)]) ).
cnf(364,negated_conjecture,
( memberP(app(X1,app(X2,esk10_0)),esk11_0)
| ~ ssList(app(X2,esk10_0))
| ~ ssList(X1)
| ~ ssItem(esk11_0)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[88,358,theory(equality)]) ).
cnf(381,negated_conjecture,
( memberP(app(X1,app(X2,esk10_0)),esk11_0)
| ~ ssList(app(X2,esk10_0))
| ~ ssList(X1)
| $false
| ~ ssList(X2) ),
inference(rw,[status(thm)],[364,130,theory(equality)]) ).
cnf(382,negated_conjecture,
( memberP(app(X1,app(X2,esk10_0)),esk11_0)
| ~ ssList(app(X2,esk10_0))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[381,theory(equality)]) ).
cnf(397,plain,
( memberP(app(X1,cons(X2,X3)),X2)
| ~ ssList(cons(X2,X3))
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[88,159,theory(equality)]) ).
cnf(813,negated_conjecture,
( app(esk3_2(esk10_0,esk11_0),cons(esk11_0,esk4_2(esk10_0,esk11_0))) = esk10_0
| $false ),
inference(rw,[status(thm)],[269,135,theory(equality)]) ).
cnf(814,negated_conjecture,
app(esk3_2(esk10_0,esk11_0),cons(esk11_0,esk4_2(esk10_0,esk11_0))) = esk10_0,
inference(cn,[status(thm)],[813,theory(equality)]) ).
cnf(928,plain,
( X1 = esk6_1(X2)
| nil = X2
| memberP(esk5_1(X2),X1)
| ~ memberP(X2,X1)
| ~ ssList(esk5_1(X2))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[205,74]) ).
cnf(929,plain,
( X1 = esk6_1(X2)
| nil = X2
| memberP(esk5_1(X2),X1)
| ~ memberP(X2,X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[928,75]) ).
cnf(930,negated_conjecture,
( esk11_0 = esk6_1(esk10_0)
| nil = esk10_0
| memberP(esk5_1(esk10_0),esk11_0)
| ~ ssList(esk10_0)
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[929,136,theory(equality)]) ).
cnf(935,negated_conjecture,
( esk11_0 = esk6_1(esk10_0)
| nil = esk10_0
| memberP(esk5_1(esk10_0),esk11_0)
| $false
| ~ ssItem(esk11_0) ),
inference(rw,[status(thm)],[930,135,theory(equality)]) ).
cnf(936,negated_conjecture,
( esk11_0 = esk6_1(esk10_0)
| nil = esk10_0
| memberP(esk5_1(esk10_0),esk11_0)
| $false
| $false ),
inference(rw,[status(thm)],[935,130,theory(equality)]) ).
cnf(937,negated_conjecture,
( esk11_0 = esk6_1(esk10_0)
| nil = esk10_0
| memberP(esk5_1(esk10_0),esk11_0) ),
inference(cn,[status(thm)],[936,theory(equality)]) ).
cnf(950,negated_conjecture,
( memberP(app(esk5_1(esk10_0),X1),esk11_0)
| esk6_1(esk10_0) = esk11_0
| esk10_0 = nil
| ~ ssList(X1)
| ~ ssList(esk5_1(esk10_0))
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[89,937,theory(equality)]) ).
cnf(961,negated_conjecture,
( memberP(app(esk5_1(esk10_0),X1),esk11_0)
| esk6_1(esk10_0) = esk11_0
| esk10_0 = nil
| ~ ssList(X1)
| ~ ssList(esk5_1(esk10_0))
| $false ),
inference(rw,[status(thm)],[950,130,theory(equality)]) ).
cnf(962,negated_conjecture,
( memberP(app(esk5_1(esk10_0),X1),esk11_0)
| esk6_1(esk10_0) = esk11_0
| esk10_0 = nil
| ~ ssList(X1)
| ~ ssList(esk5_1(esk10_0)) ),
inference(cn,[status(thm)],[961,theory(equality)]) ).
cnf(1053,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| ~ ssList(cons(esk11_0,esk4_2(esk10_0,esk11_0)))
| ~ ssList(esk3_2(esk10_0,esk11_0)) ),
inference(spm,[status(thm)],[258,814,theory(equality)]) ).
cnf(1084,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| ~ ssList(cons(esk11_0,esk4_2(esk10_0,esk11_0)))
| $false ),
inference(rw,[status(thm)],[1053,285,theory(equality)]) ).
cnf(1085,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| ~ ssList(cons(esk11_0,esk4_2(esk10_0,esk11_0))) ),
inference(cn,[status(thm)],[1084,theory(equality)]) ).
cnf(1130,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| ~ ssList(esk4_2(esk10_0,esk11_0))
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[1085,82,theory(equality)]) ).
cnf(1131,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| $false
| ~ ssItem(esk11_0) ),
inference(rw,[status(thm)],[1130,287,theory(equality)]) ).
cnf(1132,negated_conjecture,
( app(nil,esk10_0) = esk10_0
| $false
| $false ),
inference(rw,[status(thm)],[1131,130,theory(equality)]) ).
cnf(1133,negated_conjecture,
app(nil,esk10_0) = esk10_0,
inference(cn,[status(thm)],[1132,theory(equality)]) ).
cnf(1142,negated_conjecture,
( app(esk10_0,X1) = app(nil,app(esk10_0,X1))
| ~ ssList(X1)
| ~ ssList(esk10_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[64,1133,theory(equality)]) ).
cnf(1179,negated_conjecture,
( app(esk10_0,X1) = app(nil,app(esk10_0,X1))
| ~ ssList(X1)
| $false
| ~ ssList(nil) ),
inference(rw,[status(thm)],[1142,135,theory(equality)]) ).
cnf(1180,negated_conjecture,
( app(esk10_0,X1) = app(nil,app(esk10_0,X1))
| ~ ssList(X1)
| $false
| $false ),
inference(rw,[status(thm)],[1179,83,theory(equality)]) ).
cnf(1181,negated_conjecture,
( app(esk10_0,X1) = app(nil,app(esk10_0,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1180,theory(equality)]) ).
cnf(1437,negated_conjecture,
( app(esk5_1(X1),cons(esk6_1(X1),nil)) = esk9_0
| nil = X1
| X1 != esk10_0
| ~ ssList(esk5_1(X1))
| ~ ssItem(esk6_1(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[220,73,theory(equality)]) ).
cnf(1847,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[254,42]) ).
cnf(1886,plain,
( app(nil,X1) = app(X1,nil)
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[258,1847,theory(equality)]) ).
cnf(1926,plain,
( app(nil,X1) = app(X1,nil)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[1886,83,theory(equality)]) ).
cnf(1927,plain,
( app(nil,X1) = app(X1,nil)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1926,theory(equality)]) ).
cnf(2031,plain,
( ssList(app(X1,app(X2,X3)))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[241,42]) ).
cnf(2034,negated_conjecture,
( ssList(app(X1,esk10_0))
| ~ ssList(esk10_0)
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[2031,1133,theory(equality)]) ).
cnf(2063,negated_conjecture,
( ssList(app(X1,esk10_0))
| $false
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[2034,135,theory(equality)]) ).
cnf(2064,negated_conjecture,
( ssList(app(X1,esk10_0))
| $false
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[2063,83,theory(equality)]) ).
cnf(2065,negated_conjecture,
( ssList(app(X1,esk10_0))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[2064,theory(equality)]) ).
cnf(4606,negated_conjecture,
( memberP(app(X1,app(X2,esk10_0)),esk11_0)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[382,2065]) ).
cnf(4626,negated_conjecture,
( memberP(app(esk10_0,esk10_0),esk11_0)
| ~ ssList(nil)
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[4606,1181,theory(equality)]) ).
cnf(4672,negated_conjecture,
( memberP(app(esk10_0,esk10_0),esk11_0)
| $false
| ~ ssList(esk10_0) ),
inference(rw,[status(thm)],[4626,83,theory(equality)]) ).
cnf(4673,negated_conjecture,
( memberP(app(esk10_0,esk10_0),esk11_0)
| $false
| $false ),
inference(rw,[status(thm)],[4672,135,theory(equality)]) ).
cnf(4674,negated_conjecture,
memberP(app(esk10_0,esk10_0),esk11_0),
inference(cn,[status(thm)],[4673,theory(equality)]) ).
cnf(4695,negated_conjecture,
( memberP(app(app(esk10_0,esk10_0),X1),esk11_0)
| ~ ssList(X1)
| ~ ssList(app(esk10_0,esk10_0))
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[89,4674,theory(equality)]) ).
cnf(4707,negated_conjecture,
( memberP(app(app(esk10_0,esk10_0),X1),esk11_0)
| ~ ssList(X1)
| ~ ssList(app(esk10_0,esk10_0))
| $false ),
inference(rw,[status(thm)],[4695,130,theory(equality)]) ).
cnf(4708,negated_conjecture,
( memberP(app(app(esk10_0,esk10_0),X1),esk11_0)
| ~ ssList(X1)
| ~ ssList(app(esk10_0,esk10_0)) ),
inference(cn,[status(thm)],[4707,theory(equality)]) ).
cnf(5107,plain,
( memberP(app(X1,cons(X2,X3)),X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[397,82]) ).
cnf(5991,negated_conjecture,
( memberP(app(app(esk10_0,esk10_0),X1),esk11_0)
| ~ ssList(X1)
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[4708,42,theory(equality)]) ).
cnf(5994,negated_conjecture,
( memberP(app(app(esk10_0,esk10_0),X1),esk11_0)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[5991,135,theory(equality)]) ).
cnf(5995,negated_conjecture,
( memberP(app(app(esk10_0,esk10_0),X1),esk11_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[5994,theory(equality)]) ).
cnf(6012,negated_conjecture,
( memberP(app(nil,app(esk10_0,esk10_0)),esk11_0)
| ~ ssList(nil)
| ~ ssList(app(esk10_0,esk10_0)) ),
inference(spm,[status(thm)],[5995,1927,theory(equality)]) ).
cnf(6036,negated_conjecture,
( memberP(app(nil,app(esk10_0,esk10_0)),esk11_0)
| $false
| ~ ssList(app(esk10_0,esk10_0)) ),
inference(rw,[status(thm)],[6012,83,theory(equality)]) ).
cnf(6037,negated_conjecture,
( memberP(app(nil,app(esk10_0,esk10_0)),esk11_0)
| ~ ssList(app(esk10_0,esk10_0)) ),
inference(cn,[status(thm)],[6036,theory(equality)]) ).
cnf(6133,negated_conjecture,
( memberP(app(nil,app(esk10_0,esk10_0)),esk11_0)
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[6037,42,theory(equality)]) ).
cnf(6136,negated_conjecture,
( memberP(app(nil,app(esk10_0,esk10_0)),esk11_0)
| $false ),
inference(rw,[status(thm)],[6133,135,theory(equality)]) ).
cnf(6137,negated_conjecture,
memberP(app(nil,app(esk10_0,esk10_0)),esk11_0),
inference(cn,[status(thm)],[6136,theory(equality)]) ).
cnf(10924,negated_conjecture,
( esk6_1(esk10_0) = esk11_0
| esk10_0 = nil
| memberP(app(esk5_1(esk10_0),X1),esk11_0)
| ~ ssList(X1)
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[962,75,theory(equality)]) ).
cnf(10925,negated_conjecture,
( esk6_1(esk10_0) = esk11_0
| esk10_0 = nil
| memberP(app(esk5_1(esk10_0),X1),esk11_0)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[10924,135,theory(equality)]) ).
cnf(10926,negated_conjecture,
( esk6_1(esk10_0) = esk11_0
| esk10_0 = nil
| memberP(app(esk5_1(esk10_0),X1),esk11_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[10925,theory(equality)]) ).
cnf(19201,negated_conjecture,
( app(esk5_1(X1),cons(esk6_1(X1),nil)) = esk9_0
| nil = X1
| X1 != esk10_0
| ~ ssList(esk5_1(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[1437,74]) ).
cnf(19202,negated_conjecture,
( app(esk5_1(X1),cons(esk6_1(X1),nil)) = esk9_0
| nil = X1
| X1 != esk10_0
| ~ ssList(X1) ),
inference(csr,[status(thm)],[19201,75]) ).
cnf(19203,negated_conjecture,
( app(esk5_1(esk10_0),cons(esk6_1(esk10_0),nil)) = esk9_0
| nil = esk10_0
| ~ ssList(esk10_0) ),
inference(er,[status(thm)],[19202,theory(equality)]) ).
cnf(19204,negated_conjecture,
( app(esk5_1(esk10_0),cons(esk6_1(esk10_0),nil)) = esk9_0
| nil = esk10_0
| $false ),
inference(rw,[status(thm)],[19203,135,theory(equality)]) ).
cnf(19205,negated_conjecture,
( app(esk5_1(esk10_0),cons(esk6_1(esk10_0),nil)) = esk9_0
| nil = esk10_0 ),
inference(cn,[status(thm)],[19204,theory(equality)]) ).
cnf(19256,negated_conjecture,
( esk6_1(esk10_0) = esk11_0
| esk10_0 = nil
| memberP(esk9_0,esk11_0)
| ~ ssList(cons(esk6_1(esk10_0),nil)) ),
inference(spm,[status(thm)],[10926,19205,theory(equality)]) ).
cnf(19285,negated_conjecture,
( esk6_1(esk10_0) = esk11_0
| esk10_0 = nil
| ~ ssList(cons(esk6_1(esk10_0),nil)) ),
inference(sr,[status(thm)],[19256,137,theory(equality)]) ).
cnf(19286,negated_conjecture,
( esk6_1(esk10_0) = esk11_0
| esk10_0 = nil
| ~ ssList(nil)
| ~ ssItem(esk6_1(esk10_0)) ),
inference(spm,[status(thm)],[19285,82,theory(equality)]) ).
cnf(19288,negated_conjecture,
( esk6_1(esk10_0) = esk11_0
| esk10_0 = nil
| $false
| ~ ssItem(esk6_1(esk10_0)) ),
inference(rw,[status(thm)],[19286,83,theory(equality)]) ).
cnf(19289,negated_conjecture,
( esk6_1(esk10_0) = esk11_0
| esk10_0 = nil
| ~ ssItem(esk6_1(esk10_0)) ),
inference(cn,[status(thm)],[19288,theory(equality)]) ).
cnf(19290,negated_conjecture,
( esk6_1(esk10_0) = esk11_0
| esk10_0 = nil
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[19289,74,theory(equality)]) ).
cnf(19291,negated_conjecture,
( esk6_1(esk10_0) = esk11_0
| esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[19290,135,theory(equality)]) ).
cnf(19292,negated_conjecture,
( esk6_1(esk10_0) = esk11_0
| esk10_0 = nil ),
inference(cn,[status(thm)],[19291,theory(equality)]) ).
cnf(19305,negated_conjecture,
( app(esk5_1(esk10_0),cons(esk11_0,nil)) = esk9_0
| esk10_0 = nil ),
inference(spm,[status(thm)],[19205,19292,theory(equality)]) ).
cnf(19686,negated_conjecture,
( memberP(esk9_0,esk11_0)
| esk10_0 = nil
| ~ ssList(esk5_1(esk10_0))
| ~ ssList(nil)
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[5107,19305,theory(equality)]) ).
cnf(19727,negated_conjecture,
( memberP(esk9_0,esk11_0)
| esk10_0 = nil
| ~ ssList(esk5_1(esk10_0))
| $false
| ~ ssItem(esk11_0) ),
inference(rw,[status(thm)],[19686,83,theory(equality)]) ).
cnf(19728,negated_conjecture,
( memberP(esk9_0,esk11_0)
| esk10_0 = nil
| ~ ssList(esk5_1(esk10_0))
| $false
| $false ),
inference(rw,[status(thm)],[19727,130,theory(equality)]) ).
cnf(19729,negated_conjecture,
( memberP(esk9_0,esk11_0)
| esk10_0 = nil
| ~ ssList(esk5_1(esk10_0)) ),
inference(cn,[status(thm)],[19728,theory(equality)]) ).
cnf(19730,negated_conjecture,
( esk10_0 = nil
| ~ ssList(esk5_1(esk10_0)) ),
inference(sr,[status(thm)],[19729,137,theory(equality)]) ).
cnf(19738,negated_conjecture,
( esk10_0 = nil
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[19730,75,theory(equality)]) ).
cnf(19739,negated_conjecture,
( esk10_0 = nil
| $false ),
inference(rw,[status(thm)],[19738,135,theory(equality)]) ).
cnf(19740,negated_conjecture,
esk10_0 = nil,
inference(cn,[status(thm)],[19739,theory(equality)]) ).
cnf(19745,negated_conjecture,
memberP(nil,esk11_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[6137,19740,theory(equality)]),19740,theory(equality)]),290,theory(equality)]),290,theory(equality)]) ).
cnf(20078,negated_conjecture,
~ ssItem(esk11_0),
inference(spm,[status(thm)],[78,19745,theory(equality)]) ).
cnf(20085,negated_conjecture,
$false,
inference(rw,[status(thm)],[20078,130,theory(equality)]) ).
cnf(20086,negated_conjecture,
$false,
inference(cn,[status(thm)],[20085,theory(equality)]) ).
cnf(20087,negated_conjecture,
$false,
20086,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC409+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpekl4Yt/sel_SWC409+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC409+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC409+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC409+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
%
%------------------------------------------------------------------------------