TSTP Solution File: SWC045+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC045+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 10:13:03 EST 2010
% Result : Theorem 99.12s
% Output : CNFRefutation 99.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 20
% Syntax : Number of formulae : 255 ( 20 unt; 0 def)
% Number of atoms : 1095 ( 269 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 1464 ( 624 ~; 672 |; 108 &)
% ( 3 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 463 ( 0 sgn 195 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmp4nWpsS/sel_SWC045+1.p_2',ax84) ).
fof(2,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmp4nWpsS/sel_SWC045+1.p_2',ax83) ).
fof(3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/tmp/tmp4nWpsS/sel_SWC045+1.p_2',ax82) ).
fof(4,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmp4nWpsS/sel_SWC045+1.p_2',ax81) ).
fof(6,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmp4nWpsS/sel_SWC045+1.p_2',ax28) ).
fof(7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/tmp/tmp4nWpsS/sel_SWC045+1.p_2',ax27) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmp4nWpsS/sel_SWC045+1.p_2',ax26) ).
fof(9,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmp4nWpsS/sel_SWC045+1.p_2',ax21) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/tmp/tmp4nWpsS/sel_SWC045+1.p_2',ax20) ).
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/tmp4nWpsS/sel_SWC045+1.p_2',ax3) ).
fof(14,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X1) )
=> X1 = X2 ) ) ),
file('/tmp/tmp4nWpsS/sel_SWC045+1.p_2',ax54) ).
fof(15,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/tmp/tmp4nWpsS/sel_SWC045+1.p_2',ax55) ).
fof(17,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/tmp/tmp4nWpsS/sel_SWC045+1.p_2',ax58) ).
fof(18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmp4nWpsS/sel_SWC045+1.p_2',ax16) ).
fof(19,axiom,
ssList(nil),
file('/tmp/tmp4nWpsS/sel_SWC045+1.p_2',ax17) ).
fof(23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X3) )
=> segmentP(X1,X3) ) ) ) ),
file('/tmp/tmp4nWpsS/sel_SWC045+1.p_2',ax53) ).
fof(24,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/tmp/tmp4nWpsS/sel_SWC045+1.p_2',ax18) ).
fof(25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssItem(X4)
=> ( cons(X3,X1) = cons(X4,X2)
=> ( X3 = X4
& X2 = X1 ) ) ) ) ) ),
file('/tmp/tmp4nWpsS/sel_SWC045+1.p_2',ax19) ).
fof(26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( segmentP(X1,X2)
=> segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
file('/tmp/tmp4nWpsS/sel_SWC045+1.p_2',ax56) ).
fof(28,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( nil != X2
| X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ( ( ~ memberP(X3,X5)
& ? [X6] :
( ssList(X6)
& segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) ) )
| ( ! [X6] :
( ssList(X6)
=> ~ segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) )
& memberP(X3,X5) ) ) ) ) ) ) ) ),
file('/tmp/tmp4nWpsS/sel_SWC045+1.p_2',co1) ).
fof(29,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( nil != X2
| X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ( ( ~ memberP(X3,X5)
& ? [X6] :
( ssList(X6)
& segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) ) )
| ( ! [X6] :
( ssList(X6)
=> ~ segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) )
& memberP(X3,X5) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[28]) ).
fof(31,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( nil != X2
| X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ( ( ~ memberP(X3,X5)
& ? [X6] :
( ssList(X6)
& segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) ) )
| ( ! [X6] :
( ssList(X6)
=> ~ segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) )
& memberP(X3,X5) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[29,theory(equality)]) ).
fof(32,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(33,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[32]) ).
cnf(34,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[33]) ).
fof(35,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(36,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)],[35]) ).
fof(37,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)],[36]) ).
fof(38,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)],[37]) ).
cnf(39,plain,
( nil = app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| nil != X1
| nil != X2 ),
inference(split_conjunct,[status(thm)],[38]) ).
fof(42,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(43,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)],[42]) ).
fof(44,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)],[43]) ).
cnf(45,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[44]) ).
fof(46,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(47,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[46]) ).
fof(48,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[47]) ).
cnf(49,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[48]) ).
fof(54,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(55,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[54]) ).
cnf(56,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[55]) ).
fof(57,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(58,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)],[57]) ).
fof(59,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)],[58]) ).
cnf(60,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[59]) ).
fof(61,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(62,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[61]) ).
fof(63,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[62]) ).
cnf(64,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[63]) ).
fof(65,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| nil != cons(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(66,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3) ) ),
inference(variable_rename,[status(thm)],[65]) ).
fof(67,plain,
! [X3,X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[66]) ).
cnf(68,plain,
( ~ ssList(X1)
| nil != cons(X2,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(esk1_1(X4))
& ssItem(esk2_1(X4))
& cons(esk2_1(X4),esk1_1(X4)) = X4 ) ),
inference(skolemize,[status(esa)],[70]) ).
fof(72,plain,
! [X4] :
( ( ssList(esk1_1(X4))
| nil = X4
| ~ ssList(X4) )
& ( ssItem(esk2_1(X4))
| nil = X4
| ~ ssList(X4) )
& ( cons(esk2_1(X4),esk1_1(X4)) = X4
| nil = X4
| ~ ssList(X4) ) ),
inference(distribute,[status(thm)],[71]) ).
cnf(73,plain,
( nil = X1
| cons(esk2_1(X1),esk1_1(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[72]) ).
cnf(74,plain,
( nil = X1
| ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[72]) ).
cnf(75,plain,
( nil = X1
| ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[72]) ).
fof(81,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(82,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)],[81]) ).
fof(83,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)],[82]) ).
fof(84,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)],[83]) ).
fof(85,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)],[84]) ).
cnf(89,plain,
( memberP(X1,X2)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| app(X3,cons(X2,X4)) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[85]) ).
fof(99,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(100,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ~ segmentP(X3,X4)
| ~ segmentP(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[99]) ).
fof(101,plain,
! [X3,X4] :
( ~ ssList(X4)
| ~ segmentP(X3,X4)
| ~ segmentP(X4,X3)
| X3 = X4
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[100]) ).
cnf(102,plain,
( X1 = X2
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[101]) ).
fof(103,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(104,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,X2) ),
inference(variable_rename,[status(thm)],[103]) ).
cnf(105,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[104]) ).
fof(110,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(nil,X1)
| nil = X1 )
& ( nil != X1
| segmentP(nil,X1) ) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(111,plain,
! [X2] :
( ~ ssList(X2)
| ( ( ~ segmentP(nil,X2)
| nil = X2 )
& ( nil != X2
| segmentP(nil,X2) ) ) ),
inference(variable_rename,[status(thm)],[110]) ).
fof(112,plain,
! [X2] :
( ( ~ segmentP(nil,X2)
| nil = X2
| ~ ssList(X2) )
& ( nil != X2
| segmentP(nil,X2)
| ~ ssList(X2) ) ),
inference(distribute,[status(thm)],[111]) ).
cnf(114,plain,
( nil = X1
| ~ ssList(X1)
| ~ segmentP(nil,X1) ),
inference(split_conjunct,[status(thm)],[112]) ).
fof(115,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(116,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[115]) ).
fof(117,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[116]) ).
cnf(118,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[117]) ).
cnf(119,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[19]) ).
fof(137,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X3)
| segmentP(X1,X3) ) ) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(138,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ~ segmentP(X4,X5)
| ~ segmentP(X5,X6)
| segmentP(X4,X6) ) ) ),
inference(variable_rename,[status(thm)],[137]) ).
fof(139,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ~ segmentP(X4,X5)
| ~ segmentP(X5,X6)
| segmentP(X4,X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[138]) ).
cnf(140,plain,
( segmentP(X1,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[139]) ).
fof(141,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) != X1 ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(142,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) != X3 ) ),
inference(variable_rename,[status(thm)],[141]) ).
fof(143,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) != X3
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[142]) ).
cnf(144,plain,
( ~ ssList(X1)
| cons(X2,X1) != X1
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[143]) ).
fof(145,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssItem(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X3,X1) != cons(X4,X2)
| ( X3 = X4
& X2 = X1 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(146,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssItem(X8)
| cons(X7,X5) != cons(X8,X6)
| ( X7 = X8
& X6 = X5 ) ) ) ) ),
inference(variable_rename,[status(thm)],[145]) ).
fof(147,plain,
! [X5,X6,X7,X8] :
( ~ ssItem(X8)
| cons(X7,X5) != cons(X8,X6)
| ( X7 = X8
& X6 = X5 )
| ~ ssItem(X7)
| ~ ssList(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[146]) ).
fof(148,plain,
! [X5,X6,X7,X8] :
( ( X7 = X8
| cons(X7,X5) != cons(X8,X6)
| ~ ssItem(X8)
| ~ ssItem(X7)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( X6 = X5
| cons(X7,X5) != cons(X8,X6)
| ~ ssItem(X8)
| ~ ssItem(X7)
| ~ ssList(X6)
| ~ ssList(X5) ) ),
inference(distribute,[status(thm)],[147]) ).
cnf(149,plain,
( X2 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3)
| ~ ssItem(X4)
| cons(X3,X1) != cons(X4,X2) ),
inference(split_conjunct,[status(thm)],[148]) ).
cnf(150,plain,
( X3 = X4
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3)
| ~ ssItem(X4)
| cons(X3,X1) != cons(X4,X2) ),
inference(split_conjunct,[status(thm)],[148]) ).
fof(151,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ~ segmentP(X1,X2)
| segmentP(app(app(X3,X1),X4),X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(152,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| ~ segmentP(X5,X6)
| segmentP(app(app(X7,X5),X8),X6) ) ) ) ),
inference(variable_rename,[status(thm)],[151]) ).
fof(153,plain,
! [X5,X6,X7,X8] :
( ~ ssList(X8)
| ~ segmentP(X5,X6)
| segmentP(app(app(X7,X5),X8),X6)
| ~ ssList(X7)
| ~ ssList(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[152]) ).
cnf(154,plain,
( segmentP(app(app(X3,X1),X4),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[153]) ).
fof(158,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& nil = X2
& X2 = X4
& X1 = X3
& nil != X1
& ! [X5] :
( ~ ssItem(X5)
| ( ( memberP(X3,X5)
| ! [X6] :
( ~ ssList(X6)
| ~ segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) ) )
& ( ? [X6] :
( ssList(X6)
& segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) )
| ~ memberP(X3,X5) ) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(159,negated_conjecture,
? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& nil = X8
& X8 = X10
& X7 = X9
& nil != X7
& ! [X11] :
( ~ ssItem(X11)
| ( ( memberP(X9,X11)
| ! [X12] :
( ~ ssList(X12)
| ~ segmentP(X10,app(app(cons(X11,nil),X12),cons(X11,nil))) ) )
& ( ? [X13] :
( ssList(X13)
& segmentP(X10,app(app(cons(X11,nil),X13),cons(X11,nil))) )
| ~ memberP(X9,X11) ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[158]) ).
fof(160,negated_conjecture,
( ssList(esk9_0)
& ssList(esk10_0)
& ssList(esk11_0)
& ssList(esk12_0)
& nil = esk10_0
& esk10_0 = esk12_0
& esk9_0 = esk11_0
& nil != esk9_0
& ! [X11] :
( ~ ssItem(X11)
| ( ( memberP(esk11_0,X11)
| ! [X12] :
( ~ ssList(X12)
| ~ segmentP(esk12_0,app(app(cons(X11,nil),X12),cons(X11,nil))) ) )
& ( ( ssList(esk13_1(X11))
& segmentP(esk12_0,app(app(cons(X11,nil),esk13_1(X11)),cons(X11,nil))) )
| ~ memberP(esk11_0,X11) ) ) ) ),
inference(skolemize,[status(esa)],[159]) ).
fof(161,negated_conjecture,
! [X11,X12] :
( ( ( ( ~ ssList(X12)
| ~ segmentP(esk12_0,app(app(cons(X11,nil),X12),cons(X11,nil)))
| memberP(esk11_0,X11) )
& ( ( ssList(esk13_1(X11))
& segmentP(esk12_0,app(app(cons(X11,nil),esk13_1(X11)),cons(X11,nil))) )
| ~ memberP(esk11_0,X11) ) )
| ~ ssItem(X11) )
& nil = esk10_0
& esk10_0 = esk12_0
& esk9_0 = esk11_0
& nil != esk9_0
& ssList(esk12_0)
& ssList(esk11_0)
& ssList(esk10_0)
& ssList(esk9_0) ),
inference(shift_quantors,[status(thm)],[160]) ).
fof(162,negated_conjecture,
! [X11,X12] :
( ( ~ ssList(X12)
| ~ segmentP(esk12_0,app(app(cons(X11,nil),X12),cons(X11,nil)))
| memberP(esk11_0,X11)
| ~ ssItem(X11) )
& ( ssList(esk13_1(X11))
| ~ memberP(esk11_0,X11)
| ~ ssItem(X11) )
& ( segmentP(esk12_0,app(app(cons(X11,nil),esk13_1(X11)),cons(X11,nil)))
| ~ memberP(esk11_0,X11)
| ~ ssItem(X11) )
& nil = esk10_0
& esk10_0 = esk12_0
& esk9_0 = esk11_0
& nil != esk9_0
& ssList(esk12_0)
& ssList(esk11_0)
& ssList(esk10_0)
& ssList(esk9_0) ),
inference(distribute,[status(thm)],[161]) ).
cnf(163,negated_conjecture,
ssList(esk9_0),
inference(split_conjunct,[status(thm)],[162]) ).
cnf(167,negated_conjecture,
nil != esk9_0,
inference(split_conjunct,[status(thm)],[162]) ).
cnf(168,negated_conjecture,
esk9_0 = esk11_0,
inference(split_conjunct,[status(thm)],[162]) ).
cnf(169,negated_conjecture,
esk10_0 = esk12_0,
inference(split_conjunct,[status(thm)],[162]) ).
cnf(170,negated_conjecture,
nil = esk10_0,
inference(split_conjunct,[status(thm)],[162]) ).
cnf(171,negated_conjecture,
( segmentP(esk12_0,app(app(cons(X1,nil),esk13_1(X1)),cons(X1,nil)))
| ~ ssItem(X1)
| ~ memberP(esk11_0,X1) ),
inference(split_conjunct,[status(thm)],[162]) ).
cnf(172,negated_conjecture,
( ssList(esk13_1(X1))
| ~ ssItem(X1)
| ~ memberP(esk11_0,X1) ),
inference(split_conjunct,[status(thm)],[162]) ).
cnf(176,negated_conjecture,
ssList(esk11_0),
inference(rw,[status(thm)],[163,168,theory(equality)]) ).
cnf(177,negated_conjecture,
esk12_0 = nil,
inference(rw,[status(thm)],[169,170,theory(equality)]) ).
cnf(180,negated_conjecture,
esk11_0 != nil,
inference(rw,[status(thm)],[167,168,theory(equality)]) ).
cnf(193,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(er,[status(thm)],[39,theory(equality)]) ).
cnf(194,plain,
( app(X1,nil) = nil
| nil != X1
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[193,119,theory(equality)]) ).
cnf(195,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[194,theory(equality)]) ).
cnf(221,negated_conjecture,
( segmentP(nil,app(app(cons(X1,nil),esk13_1(X1)),cons(X1,nil)))
| ~ ssItem(X1)
| ~ memberP(esk11_0,X1) ),
inference(rw,[status(thm)],[171,177,theory(equality)]) ).
cnf(253,plain,
( esk2_1(X1) = X2
| nil = X1
| X1 != cons(X2,X3)
| ~ ssItem(X2)
| ~ ssItem(esk2_1(X1))
| ~ ssList(X3)
| ~ ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[150,73,theory(equality)]) ).
cnf(264,plain,
( esk1_1(X1) = X2
| nil = X1
| X1 != cons(X3,X2)
| ~ ssItem(X3)
| ~ ssItem(esk2_1(X1))
| ~ ssList(X2)
| ~ ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[149,73,theory(equality)]) ).
cnf(269,plain,
( memberP(X1,esk2_1(X2))
| nil = X2
| app(X3,X2) != X1
| ~ ssItem(esk2_1(X2))
| ~ ssList(esk1_1(X2))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[89,73,theory(equality)]) ).
cnf(277,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[34,45,theory(equality)]) ).
cnf(278,plain,
( app(X1,X2) = app(X1,app(nil,X2))
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[45,34,theory(equality)]) ).
cnf(279,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[45,56,theory(equality)]) ).
cnf(280,plain,
( ssList(app(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[64,45,theory(equality)]) ).
cnf(293,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[277,119,theory(equality)]) ).
cnf(294,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[293,theory(equality)]) ).
cnf(295,plain,
( app(X1,X2) = app(X1,app(nil,X2))
| ~ ssList(X2)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[278,119,theory(equality)]) ).
cnf(296,plain,
( app(X1,X2) = app(X1,app(nil,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[295,theory(equality)]) ).
cnf(297,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[279,119,theory(equality)]) ).
cnf(298,plain,
( app(X1,X2) = app(nil,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[297,theory(equality)]) ).
cnf(301,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[118,60,theory(equality)]) ).
cnf(330,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[154,105,theory(equality)]) ).
cnf(364,plain,
( app(nil,nil) = nil
| ~ ssList(nil) ),
inference(er,[status(thm)],[195,theory(equality)]) ).
cnf(365,plain,
( app(nil,nil) = nil
| $false ),
inference(rw,[status(thm)],[364,119,theory(equality)]) ).
cnf(366,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[365,theory(equality)]) ).
cnf(385,plain,
( app(nil,X1) = app(nil,app(nil,X1))
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[45,366,theory(equality)]) ).
cnf(386,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[60,366,theory(equality)]) ).
cnf(401,plain,
( app(nil,X1) = app(nil,app(nil,X1))
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[385,119,theory(equality)]) ).
cnf(402,plain,
( app(nil,X1) = app(nil,app(nil,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[401,theory(equality)]) ).
cnf(403,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[386,119,theory(equality)]) ).
cnf(404,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[403,theory(equality)]) ).
cnf(1170,plain,
( esk2_1(X1) = X2
| nil = X1
| X1 != cons(X2,X3)
| ~ ssItem(esk2_1(X1))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[253,75]) ).
cnf(1171,plain,
( esk2_1(X1) = X2
| nil = X1
| X1 != cons(X2,X3)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[1170,74]) ).
cnf(1172,plain,
( esk2_1(cons(X1,X2)) = X1
| nil = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,X2)) ),
inference(er,[status(thm)],[1171,theory(equality)]) ).
cnf(1189,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,app(nil,X3)))
| ~ ssList(app(nil,X3))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(app(X1,X2)) ),
inference(spm,[status(thm)],[45,296,theory(equality)]) ).
cnf(1400,plain,
( esk1_1(X1) = X2
| nil = X1
| X1 != cons(X3,X2)
| ~ ssItem(esk2_1(X1))
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[264,75]) ).
cnf(1401,plain,
( esk1_1(X1) = X2
| nil = X1
| X1 != cons(X3,X2)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[1400,74]) ).
cnf(1402,plain,
( esk1_1(cons(X1,X2)) = X2
| nil = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,X2)) ),
inference(er,[status(thm)],[1401,theory(equality)]) ).
cnf(1584,plain,
( segmentP(app(X1,X2),X2)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(app(X1,X2)) ),
inference(spm,[status(thm)],[330,34,theory(equality)]) ).
cnf(1590,plain,
( segmentP(X1,X2)
| ~ segmentP(X1,app(app(X3,X2),X4))
| ~ ssList(X2)
| ~ ssList(app(app(X3,X2),X4))
| ~ ssList(X1)
| ~ ssList(X4)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[140,330,theory(equality)]) ).
cnf(1605,plain,
( segmentP(app(X1,X2),X2)
| $false
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(app(X1,X2)) ),
inference(rw,[status(thm)],[1584,119,theory(equality)]) ).
cnf(1606,plain,
( segmentP(app(X1,X2),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(app(X1,X2)) ),
inference(cn,[status(thm)],[1605,theory(equality)]) ).
cnf(1653,plain,
( nil = X2
| memberP(X1,esk2_1(X2))
| app(X3,X2) != X1
| ~ ssItem(esk2_1(X2))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[269,75]) ).
cnf(1654,plain,
( nil = X2
| memberP(X1,esk2_1(X2))
| app(X3,X2) != X1
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[1653,74]) ).
cnf(1656,plain,
( nil = X1
| memberP(X2,esk2_1(X1))
| X1 != X2
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1654,56,theory(equality)]) ).
cnf(1662,plain,
( nil = X1
| memberP(X2,esk2_1(X1))
| X1 != X2
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[1656,119,theory(equality)]) ).
cnf(1663,plain,
( nil = X1
| memberP(X2,esk2_1(X1))
| X1 != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1662,theory(equality)]) ).
cnf(1664,plain,
( nil = X1
| memberP(X1,esk2_1(X1))
| ~ ssList(X1) ),
inference(er,[status(thm)],[1663,theory(equality)]) ).
cnf(1675,negated_conjecture,
( ssList(esk13_1(esk2_1(esk11_0)))
| nil = esk11_0
| ~ ssItem(esk2_1(esk11_0))
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[172,1664,theory(equality)]) ).
cnf(1681,negated_conjecture,
( segmentP(nil,app(app(cons(esk2_1(esk11_0),nil),esk13_1(esk2_1(esk11_0))),cons(esk2_1(esk11_0),nil)))
| nil = esk11_0
| ~ ssItem(esk2_1(esk11_0))
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[221,1664,theory(equality)]) ).
cnf(1687,negated_conjecture,
( ssList(esk13_1(esk2_1(esk11_0)))
| nil = esk11_0
| ~ ssItem(esk2_1(esk11_0))
| $false ),
inference(rw,[status(thm)],[1675,176,theory(equality)]) ).
cnf(1688,negated_conjecture,
( ssList(esk13_1(esk2_1(esk11_0)))
| nil = esk11_0
| ~ ssItem(esk2_1(esk11_0)) ),
inference(cn,[status(thm)],[1687,theory(equality)]) ).
cnf(1689,negated_conjecture,
( ssList(esk13_1(esk2_1(esk11_0)))
| ~ ssItem(esk2_1(esk11_0)) ),
inference(sr,[status(thm)],[1688,180,theory(equality)]) ).
cnf(1690,negated_conjecture,
( segmentP(nil,app(app(cons(esk2_1(esk11_0),nil),esk13_1(esk2_1(esk11_0))),cons(esk2_1(esk11_0),nil)))
| nil = esk11_0
| ~ ssItem(esk2_1(esk11_0))
| $false ),
inference(rw,[status(thm)],[1681,176,theory(equality)]) ).
cnf(1691,negated_conjecture,
( segmentP(nil,app(app(cons(esk2_1(esk11_0),nil),esk13_1(esk2_1(esk11_0))),cons(esk2_1(esk11_0),nil)))
| nil = esk11_0
| ~ ssItem(esk2_1(esk11_0)) ),
inference(cn,[status(thm)],[1690,theory(equality)]) ).
cnf(1692,negated_conjecture,
( segmentP(nil,app(app(cons(esk2_1(esk11_0),nil),esk13_1(esk2_1(esk11_0))),cons(esk2_1(esk11_0),nil)))
| ~ ssItem(esk2_1(esk11_0)) ),
inference(sr,[status(thm)],[1691,180,theory(equality)]) ).
cnf(1693,negated_conjecture,
( ssList(esk13_1(esk2_1(esk11_0)))
| nil = esk11_0
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[1689,74,theory(equality)]) ).
cnf(1694,negated_conjecture,
( ssList(esk13_1(esk2_1(esk11_0)))
| nil = esk11_0
| $false ),
inference(rw,[status(thm)],[1693,176,theory(equality)]) ).
cnf(1695,negated_conjecture,
( ssList(esk13_1(esk2_1(esk11_0)))
| nil = esk11_0 ),
inference(cn,[status(thm)],[1694,theory(equality)]) ).
cnf(1696,negated_conjecture,
ssList(esk13_1(esk2_1(esk11_0))),
inference(sr,[status(thm)],[1695,180,theory(equality)]) ).
cnf(1854,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[294,64]) ).
cnf(1898,plain,
( app(nil,X1) = app(X1,nil)
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[298,1854,theory(equality)]) ).
cnf(1931,plain,
( app(nil,X1) = app(X1,nil)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[1898,119,theory(equality)]) ).
cnf(1932,plain,
( app(nil,X1) = app(X1,nil)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1931,theory(equality)]) ).
cnf(1939,plain,
( ssList(app(X1,app(X2,X3)))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[280,64]) ).
cnf(1949,plain,
( ssList(app(nil,X1))
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1939,402,theory(equality)]) ).
cnf(1969,plain,
( ssList(app(nil,X1))
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[1949,119,theory(equality)]) ).
cnf(1970,plain,
( ssList(app(nil,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1969,theory(equality)]) ).
cnf(2140,plain,
( segmentP(app(app(X1,nil),X2),X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[330,1932,theory(equality)]) ).
cnf(2154,plain,
( ssList(app(X1,app(nil,X2)))
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1939,1932,theory(equality)]) ).
cnf(2306,plain,
( segmentP(app(app(X1,nil),X2),X1)
| ~ ssList(X2)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[2140,119,theory(equality)]) ).
cnf(2307,plain,
( segmentP(app(app(X1,nil),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[2306,theory(equality)]) ).
cnf(2330,plain,
( ssList(app(X1,app(nil,X2)))
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[2154,119,theory(equality)]) ).
cnf(2331,plain,
( ssList(app(X1,app(nil,X2)))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[2330,theory(equality)]) ).
cnf(3002,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[301,64]) ).
cnf(3007,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[3002,404,theory(equality)]) ).
cnf(3017,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[3007,119,theory(equality)]) ).
cnf(3018,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[3017,theory(equality)]) ).
cnf(4076,plain,
( segmentP(X1,X2)
| ~ segmentP(X1,app(app(X2,nil),X3))
| ~ ssList(X2)
| ~ ssList(app(app(X2,nil),X3))
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[140,2307,theory(equality)]) ).
cnf(7148,plain,
( segmentP(app(X1,X2),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[1606,64]) ).
cnf(7153,plain,
( segmentP(cons(X1,X2),X2)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[7148,49,theory(equality)]) ).
cnf(7883,plain,
( segmentP(cons(X1,X2),X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[7153,3018]) ).
cnf(7884,plain,
( X1 = cons(X2,X1)
| ~ segmentP(X1,cons(X2,X1))
| ~ ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(spm,[status(thm)],[102,7883,theory(equality)]) ).
cnf(9707,plain,
( esk2_1(cons(X1,X2)) = X1
| cons(X1,X2) = nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[1172,118]) ).
cnf(9708,plain,
( esk2_1(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[9707,68]) ).
cnf(9710,plain,
( cons(X1,esk1_1(cons(X1,X2))) = cons(X1,X2)
| nil = cons(X1,X2)
| ~ ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[73,9708,theory(equality)]) ).
cnf(10897,plain,
( app(X1,app(X2,app(nil,X3))) = app(app(X1,X2),X3)
| ~ ssList(app(nil,X3))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[1189,64]) ).
cnf(10898,plain,
( app(X1,app(X2,app(nil,X3))) = app(app(X1,X2),X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[10897,1970]) ).
cnf(10992,plain,
( ssList(app(app(X1,nil),X2))
| ~ ssList(app(nil,X2))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[2331,10898,theory(equality)]) ).
cnf(11243,plain,
( ssList(app(app(X1,nil),X2))
| ~ ssList(app(nil,X2))
| ~ ssList(X1)
| $false
| ~ ssList(X2) ),
inference(rw,[status(thm)],[10992,119,theory(equality)]) ).
cnf(11244,plain,
( ssList(app(app(X1,nil),X2))
| ~ ssList(app(nil,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[11243,theory(equality)]) ).
cnf(15047,plain,
( ssList(app(app(X1,nil),X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[11244,1970]) ).
cnf(15103,plain,
( esk1_1(cons(X1,X2)) = X2
| cons(X1,X2) = nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[1402,118]) ).
cnf(15104,plain,
( esk1_1(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[15103,68]) ).
cnf(15107,plain,
( esk1_1(app(cons(X1,X2),X3)) = app(X2,X3)
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[15104,60,theory(equality)]) ).
cnf(17153,plain,
( segmentP(X1,X2)
| ~ segmentP(X1,app(app(X3,X2),X4))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(app(X3,X2)) ),
inference(spm,[status(thm)],[1590,64,theory(equality)]) ).
cnf(20310,negated_conjecture,
( segmentP(nil,app(app(cons(esk2_1(esk11_0),nil),esk13_1(esk2_1(esk11_0))),cons(esk2_1(esk11_0),nil)))
| nil = esk11_0
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[1692,74,theory(equality)]) ).
cnf(20311,negated_conjecture,
( segmentP(nil,app(app(cons(esk2_1(esk11_0),nil),esk13_1(esk2_1(esk11_0))),cons(esk2_1(esk11_0),nil)))
| nil = esk11_0
| $false ),
inference(rw,[status(thm)],[20310,176,theory(equality)]) ).
cnf(20312,negated_conjecture,
( segmentP(nil,app(app(cons(esk2_1(esk11_0),nil),esk13_1(esk2_1(esk11_0))),cons(esk2_1(esk11_0),nil)))
| nil = esk11_0 ),
inference(cn,[status(thm)],[20311,theory(equality)]) ).
cnf(20313,negated_conjecture,
segmentP(nil,app(app(cons(esk2_1(esk11_0),nil),esk13_1(esk2_1(esk11_0))),cons(esk2_1(esk11_0),nil))),
inference(sr,[status(thm)],[20312,180,theory(equality)]) ).
cnf(176748,plain,
( segmentP(X1,X2)
| ~ segmentP(X1,app(app(X2,nil),X3))
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[4076,15047]) ).
cnf(379918,plain,
( cons(X2,X1) = X1
| ~ segmentP(X1,cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[7884,118]) ).
cnf(379919,plain,
( ~ segmentP(X1,cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[379918,144]) ).
cnf(470885,plain,
( cons(X1,esk1_1(cons(X1,X2))) = cons(X1,X2)
| cons(X1,X2) = nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[9710,118]) ).
cnf(470886,plain,
( cons(X1,esk1_1(cons(X1,X2))) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[470885,68]) ).
cnf(1284134,plain,
( esk1_1(app(cons(X1,X2),X3)) = app(X2,X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[15107,64]) ).
cnf(1284137,plain,
( esk1_1(cons(X1,X2)) = app(nil,X2)
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[1284134,49,theory(equality)]) ).
cnf(1284289,plain,
( esk1_1(cons(X1,X2)) = app(nil,X2)
| ~ ssItem(X1)
| $false
| ~ ssList(X2) ),
inference(rw,[status(thm)],[1284137,119,theory(equality)]) ).
cnf(1284290,plain,
( esk1_1(cons(X1,X2)) = app(nil,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[1284289,theory(equality)]) ).
cnf(1284959,plain,
( cons(X1,app(nil,X2)) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[470886,1284290,theory(equality)]) ).
cnf(1285842,plain,
( ~ segmentP(app(nil,X1),cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(app(nil,X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[379919,1284959,theory(equality)]) ).
cnf(1309664,plain,
( ~ segmentP(app(nil,X1),cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[1285842,1970]) ).
cnf(1309665,plain,
( ~ segmentP(nil,cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1309664,366,theory(equality)]) ).
cnf(1309764,plain,
( ~ segmentP(nil,cons(X1,nil))
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[1309665,119,theory(equality)]) ).
cnf(1309765,plain,
( ~ segmentP(nil,cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[1309764,theory(equality)]) ).
cnf(1412374,plain,
( segmentP(X1,X2)
| ~ segmentP(X1,app(app(X3,X2),X4))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X4)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[17153,64]) ).
cnf(1412376,negated_conjecture,
( segmentP(nil,esk13_1(esk2_1(esk11_0)))
| ~ ssList(esk13_1(esk2_1(esk11_0)))
| ~ ssList(nil)
| ~ ssList(cons(esk2_1(esk11_0),nil)) ),
inference(spm,[status(thm)],[1412374,20313,theory(equality)]) ).
cnf(1412929,negated_conjecture,
( segmentP(nil,esk13_1(esk2_1(esk11_0)))
| $false
| ~ ssList(nil)
| ~ ssList(cons(esk2_1(esk11_0),nil)) ),
inference(rw,[status(thm)],[1412376,1696,theory(equality)]) ).
cnf(1412930,negated_conjecture,
( segmentP(nil,esk13_1(esk2_1(esk11_0)))
| $false
| $false
| ~ ssList(cons(esk2_1(esk11_0),nil)) ),
inference(rw,[status(thm)],[1412929,119,theory(equality)]) ).
cnf(1412931,negated_conjecture,
( segmentP(nil,esk13_1(esk2_1(esk11_0)))
| ~ ssList(cons(esk2_1(esk11_0),nil)) ),
inference(cn,[status(thm)],[1412930,theory(equality)]) ).
cnf(1413312,negated_conjecture,
( segmentP(nil,esk13_1(esk2_1(esk11_0)))
| ~ ssItem(esk2_1(esk11_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1412931,118,theory(equality)]) ).
cnf(1413314,negated_conjecture,
( segmentP(nil,esk13_1(esk2_1(esk11_0)))
| ~ ssItem(esk2_1(esk11_0))
| $false ),
inference(rw,[status(thm)],[1413312,119,theory(equality)]) ).
cnf(1413315,negated_conjecture,
( segmentP(nil,esk13_1(esk2_1(esk11_0)))
| ~ ssItem(esk2_1(esk11_0)) ),
inference(cn,[status(thm)],[1413314,theory(equality)]) ).
cnf(1413316,negated_conjecture,
( segmentP(nil,esk13_1(esk2_1(esk11_0)))
| nil = esk11_0
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[1413315,74,theory(equality)]) ).
cnf(1413317,negated_conjecture,
( segmentP(nil,esk13_1(esk2_1(esk11_0)))
| nil = esk11_0
| $false ),
inference(rw,[status(thm)],[1413316,176,theory(equality)]) ).
cnf(1413318,negated_conjecture,
( segmentP(nil,esk13_1(esk2_1(esk11_0)))
| nil = esk11_0 ),
inference(cn,[status(thm)],[1413317,theory(equality)]) ).
cnf(1413319,negated_conjecture,
segmentP(nil,esk13_1(esk2_1(esk11_0))),
inference(sr,[status(thm)],[1413318,180,theory(equality)]) ).
cnf(1413320,negated_conjecture,
( nil = esk13_1(esk2_1(esk11_0))
| ~ ssList(esk13_1(esk2_1(esk11_0))) ),
inference(spm,[status(thm)],[114,1413319,theory(equality)]) ).
cnf(1413331,negated_conjecture,
( nil = esk13_1(esk2_1(esk11_0))
| $false ),
inference(rw,[status(thm)],[1413320,1696,theory(equality)]) ).
cnf(1413332,negated_conjecture,
nil = esk13_1(esk2_1(esk11_0)),
inference(cn,[status(thm)],[1413331,theory(equality)]) ).
cnf(1413359,negated_conjecture,
segmentP(nil,app(app(cons(esk2_1(esk11_0),nil),nil),cons(esk2_1(esk11_0),nil))),
inference(rw,[status(thm)],[20313,1413332,theory(equality)]) ).
cnf(1413380,negated_conjecture,
( segmentP(nil,cons(esk2_1(esk11_0),nil))
| ~ ssList(cons(esk2_1(esk11_0),nil))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[176748,1413359,theory(equality)]) ).
cnf(1413416,negated_conjecture,
( segmentP(nil,cons(esk2_1(esk11_0),nil))
| ~ ssList(cons(esk2_1(esk11_0),nil))
| $false ),
inference(rw,[status(thm)],[1413380,119,theory(equality)]) ).
cnf(1413417,negated_conjecture,
( segmentP(nil,cons(esk2_1(esk11_0),nil))
| ~ ssList(cons(esk2_1(esk11_0),nil)) ),
inference(cn,[status(thm)],[1413416,theory(equality)]) ).
cnf(1413454,negated_conjecture,
( segmentP(nil,cons(esk2_1(esk11_0),nil))
| ~ ssItem(esk2_1(esk11_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1413417,118,theory(equality)]) ).
cnf(1413456,negated_conjecture,
( segmentP(nil,cons(esk2_1(esk11_0),nil))
| ~ ssItem(esk2_1(esk11_0))
| $false ),
inference(rw,[status(thm)],[1413454,119,theory(equality)]) ).
cnf(1413457,negated_conjecture,
( segmentP(nil,cons(esk2_1(esk11_0),nil))
| ~ ssItem(esk2_1(esk11_0)) ),
inference(cn,[status(thm)],[1413456,theory(equality)]) ).
cnf(1413458,negated_conjecture,
~ ssItem(esk2_1(esk11_0)),
inference(csr,[status(thm)],[1413457,1309765]) ).
cnf(1413459,negated_conjecture,
( nil = esk11_0
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[1413458,74,theory(equality)]) ).
cnf(1413460,negated_conjecture,
( nil = esk11_0
| $false ),
inference(rw,[status(thm)],[1413459,176,theory(equality)]) ).
cnf(1413461,negated_conjecture,
nil = esk11_0,
inference(cn,[status(thm)],[1413460,theory(equality)]) ).
cnf(1413462,negated_conjecture,
$false,
inference(sr,[status(thm)],[1413461,180,theory(equality)]) ).
cnf(1413463,negated_conjecture,
$false,
1413462,
[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/SWC045+1.p
% --creating new selector for [SWC001+0.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmp4nWpsS/sel_SWC045+1.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmp4nWpsS/sel_SWC045+1.p_2 with time limit 81
% -prover status Theorem
% Problem SWC045+1.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC045+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC045+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
%
%------------------------------------------------------------------------------