%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC374+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 11:40:04 EST 2010
% Result : Theorem 14.53s
% Output : CNFRefutation 14.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 21
% Syntax : Number of formulae : 316 ( 18 unt; 0 def)
% Number of atoms : 1351 ( 432 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 1704 ( 669 ~; 861 |; 111 &)
% ( 5 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 414 ( 0 sgn 203 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmpiVmkZq/sel_SWC374+1.p_1',ax84) ).
fof(2,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmpiVmkZq/sel_SWC374+1.p_1',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/tmpiVmkZq/sel_SWC374+1.p_1',ax82) ).
fof(4,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpiVmkZq/sel_SWC374+1.p_1',ax81) ).
fof(6,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpiVmkZq/sel_SWC374+1.p_1',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/tmpiVmkZq/sel_SWC374+1.p_1',ax27) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpiVmkZq/sel_SWC374+1.p_1',ax26) ).
fof(9,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmpiVmkZq/sel_SWC374+1.p_1',ax21) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/tmp/tmpiVmkZq/sel_SWC374+1.p_1',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/tmpiVmkZq/sel_SWC374+1.p_1',ax3) ).
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/tmp/tmpiVmkZq/sel_SWC374+1.p_1',ax7) ).
fof(14,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X1) )
=> X1 = X2 ) ) ),
file('/tmp/tmpiVmkZq/sel_SWC374+1.p_1',ax54) ).
fof(17,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/tmp/tmpiVmkZq/sel_SWC374+1.p_1',ax58) ).
fof(18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpiVmkZq/sel_SWC374+1.p_1',ax16) ).
fof(19,axiom,
ssList(nil),
file('/tmp/tmpiVmkZq/sel_SWC374+1.p_1',ax17) ).
fof(21,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( X1 = X2
| memberP(X3,X1) ) ) ) ) ),
file('/tmp/tmpiVmkZq/sel_SWC374+1.p_1',ax37) ).
fof(22,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/tmp/tmpiVmkZq/sel_SWC374+1.p_1',ax38) ).
fof(23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X3) )
=> segmentP(X1,X3) ) ) ) ),
file('/tmp/tmpiVmkZq/sel_SWC374+1.p_1',ax53) ).
fof(24,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/tmp/tmpiVmkZq/sel_SWC374+1.p_1',ax18) ).
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/tmpiVmkZq/sel_SWC374+1.p_1',ax56) ).
fof(28,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| segmentP(X2,X1)
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X3
| ~ memberP(X4,X5) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
file('/tmp/tmpiVmkZq/sel_SWC374+1.p_1',co1) ).
fof(29,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| segmentP(X2,X1)
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X3
| ~ memberP(X4,X5) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[28]) ).
fof(30,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[22,theory(equality)]) ).
fof(31,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| segmentP(X2,X1)
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X3
| ~ memberP(X4,X5) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
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(86,plain,
( app(esk5_2(X1,X2),cons(X2,esk6_2(X1,X2))) = X1
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2) ),
inference(split_conjunct,[status(thm)],[85]) ).
cnf(87,plain,
( ssList(esk6_2(X1,X2))
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2) ),
inference(split_conjunct,[status(thm)],[85]) ).
cnf(88,plain,
( ssList(esk5_2(X1,X2))
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2) ),
inference(split_conjunct,[status(thm)],[85]) ).
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(90,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ segmentP(X1,X2)
| ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) )
& ( ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| app(app(X3,X2),X4) != X1 ) )
| segmentP(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(91,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ segmentP(X5,X6)
| ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& app(app(X7,X6),X8) = X5 ) ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X9,X6),X10) != X5 ) )
| segmentP(X5,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[90]) ).
fof(92,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ segmentP(X5,X6)
| ( ssList(esk7_2(X5,X6))
& ssList(esk8_2(X5,X6))
& app(app(esk7_2(X5,X6),X6),esk8_2(X5,X6)) = X5 ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X9,X6),X10) != X5 ) )
| segmentP(X5,X6) ) ) ) ),
inference(skolemize,[status(esa)],[91]) ).
fof(93,plain,
! [X5,X6,X9,X10] :
( ( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6) )
& ( ~ segmentP(X5,X6)
| ( ssList(esk7_2(X5,X6))
& ssList(esk8_2(X5,X6))
& app(app(esk7_2(X5,X6),X6),esk8_2(X5,X6)) = X5 ) ) )
| ~ ssList(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[92]) ).
fof(94,plain,
! [X5,X6,X9,X10] :
( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk7_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk8_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( app(app(esk7_2(X5,X6),X6),esk8_2(X5,X6)) = X5
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) ) ),
inference(distribute,[status(thm)],[93]) ).
cnf(98,plain,
( segmentP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[94]) ).
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(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(113,plain,
( segmentP(nil,X1)
| ~ ssList(X1)
| 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(127,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)],[21]) ).
fof(128,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)],[127]) ).
fof(129,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)],[128]) ).
fof(130,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)],[129]) ).
cnf(133,plain,
( memberP(X3,X1)
| X1 = X2
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ memberP(cons(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[130]) ).
fof(134,plain,
! [X1] :
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(fof_nnf,[status(thm)],[30]) ).
fof(135,plain,
! [X2] :
( ~ ssItem(X2)
| ~ memberP(nil,X2) ),
inference(variable_rename,[status(thm)],[134]) ).
cnf(136,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[135]) ).
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(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)
& X2 = X4
& X1 = X3
& ~ segmentP(X2,X1)
& ( ? [X5] :
( ssItem(X5)
& cons(X5,nil) = X3
& memberP(X4,X5) )
| ( nil = X4
& nil = X3 ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(159,negated_conjecture,
? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& X7 = X9
& X6 = X8
& ~ segmentP(X7,X6)
& ( ? [X10] :
( ssItem(X10)
& cons(X10,nil) = X8
& memberP(X9,X10) )
| ( nil = X9
& nil = X8 ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[158]) ).
fof(160,negated_conjecture,
( ssList(esk9_0)
& ssList(esk10_0)
& ssList(esk11_0)
& ssList(esk12_0)
& esk10_0 = esk12_0
& esk9_0 = esk11_0
& ~ segmentP(esk10_0,esk9_0)
& ( ( ssItem(esk13_0)
& cons(esk13_0,nil) = esk11_0
& memberP(esk12_0,esk13_0) )
| ( nil = esk12_0
& nil = esk11_0 ) ) ),
inference(skolemize,[status(esa)],[159]) ).
fof(161,negated_conjecture,
( ssList(esk9_0)
& ssList(esk10_0)
& ssList(esk11_0)
& ssList(esk12_0)
& esk10_0 = esk12_0
& esk9_0 = esk11_0
& ~ segmentP(esk10_0,esk9_0)
& ( nil = esk12_0
| ssItem(esk13_0) )
& ( nil = esk11_0
| ssItem(esk13_0) )
& ( nil = esk12_0
| cons(esk13_0,nil) = esk11_0 )
& ( nil = esk11_0
| cons(esk13_0,nil) = esk11_0 )
& ( nil = esk12_0
| memberP(esk12_0,esk13_0) )
& ( nil = esk11_0
| memberP(esk12_0,esk13_0) ) ),
inference(distribute,[status(thm)],[160]) ).
cnf(162,negated_conjecture,
( memberP(esk12_0,esk13_0)
| nil = esk11_0 ),
inference(split_conjunct,[status(thm)],[161]) ).
cnf(164,negated_conjecture,
( cons(esk13_0,nil) = esk11_0
| nil = esk11_0 ),
inference(split_conjunct,[status(thm)],[161]) ).
cnf(165,negated_conjecture,
( cons(esk13_0,nil) = esk11_0
| nil = esk12_0 ),
inference(split_conjunct,[status(thm)],[161]) ).
cnf(166,negated_conjecture,
( ssItem(esk13_0)
| nil = esk11_0 ),
inference(split_conjunct,[status(thm)],[161]) ).
cnf(167,negated_conjecture,
( ssItem(esk13_0)
| nil = esk12_0 ),
inference(split_conjunct,[status(thm)],[161]) ).
cnf(168,negated_conjecture,
~ segmentP(esk10_0,esk9_0),
inference(split_conjunct,[status(thm)],[161]) ).
cnf(169,negated_conjecture,
esk9_0 = esk11_0,
inference(split_conjunct,[status(thm)],[161]) ).
cnf(170,negated_conjecture,
esk10_0 = esk12_0,
inference(split_conjunct,[status(thm)],[161]) ).
cnf(173,negated_conjecture,
ssList(esk10_0),
inference(split_conjunct,[status(thm)],[161]) ).
cnf(174,negated_conjecture,
ssList(esk9_0),
inference(split_conjunct,[status(thm)],[161]) ).
cnf(175,negated_conjecture,
ssList(esk11_0),
inference(rw,[status(thm)],[174,169,theory(equality)]) ).
cnf(176,negated_conjecture,
ssList(esk12_0),
inference(rw,[status(thm)],[173,170,theory(equality)]) ).
cnf(177,negated_conjecture,
~ segmentP(esk12_0,esk11_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[168,170,theory(equality)]),169,theory(equality)]) ).
cnf(178,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(er,[status(thm)],[113,theory(equality)]) ).
cnf(179,plain,
( segmentP(nil,nil)
| $false ),
inference(rw,[status(thm)],[178,119,theory(equality)]) ).
cnf(180,plain,
segmentP(nil,nil),
inference(cn,[status(thm)],[179,theory(equality)]) ).
cnf(188,negated_conjecture,
( esk12_0 = nil
| esk11_0 != nil
| ~ ssItem(esk13_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[68,165,theory(equality)]) ).
cnf(191,negated_conjecture,
( esk12_0 = nil
| esk11_0 != nil
| ~ ssItem(esk13_0)
| $false ),
inference(rw,[status(thm)],[188,119,theory(equality)]) ).
cnf(192,negated_conjecture,
( esk12_0 = nil
| esk11_0 != nil
| ~ ssItem(esk13_0) ),
inference(cn,[status(thm)],[191,theory(equality)]) ).
cnf(214,negated_conjecture,
( ssList(esk5_2(esk12_0,esk13_0))
| esk11_0 = nil
| ~ ssItem(esk13_0)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[88,162,theory(equality)]) ).
cnf(216,negated_conjecture,
( ssList(esk6_2(esk12_0,esk13_0))
| esk11_0 = nil
| ~ ssItem(esk13_0)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[87,162,theory(equality)]) ).
cnf(218,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(er,[status(thm)],[39,theory(equality)]) ).
cnf(219,plain,
( app(X1,nil) = nil
| nil != X1
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[218,119,theory(equality)]) ).
cnf(220,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[219,theory(equality)]) ).
cnf(236,negated_conjecture,
( app(esk11_0,X1) = cons(esk13_0,X1)
| esk11_0 = nil
| ~ ssItem(esk13_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[49,164,theory(equality)]) ).
cnf(237,negated_conjecture,
( app(esk11_0,X1) = cons(esk13_0,X1)
| esk12_0 = nil
| ~ ssItem(esk13_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[49,165,theory(equality)]) ).
cnf(263,negated_conjecture,
( X1 = esk13_0
| memberP(nil,X1)
| esk11_0 = nil
| ~ memberP(esk11_0,X1)
| ~ ssItem(esk13_0)
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[133,164,theory(equality)]) ).
cnf(266,negated_conjecture,
( X1 = esk13_0
| memberP(nil,X1)
| esk11_0 = nil
| ~ memberP(esk11_0,X1)
| ~ ssItem(esk13_0)
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[263,119,theory(equality)]) ).
cnf(267,negated_conjecture,
( X1 = esk13_0
| memberP(nil,X1)
| esk11_0 = nil
| ~ memberP(esk11_0,X1)
| ~ ssItem(esk13_0)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[266,theory(equality)]) ).
cnf(312,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(337,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(355,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(359,plain,
( app(cons(X1,X2),X3) != app(X2,X3)
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[144,60,theory(equality)]) ).
cnf(375,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[98,56,theory(equality)]) ).
cnf(383,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[375,119,theory(equality)]) ).
cnf(384,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[383,theory(equality)]) ).
cnf(389,negated_conjecture,
( app(esk5_2(esk12_0,esk13_0),cons(esk13_0,esk6_2(esk12_0,esk13_0))) = esk12_0
| esk11_0 = nil
| ~ ssItem(esk13_0)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[86,162,theory(equality)]) ).
cnf(413,negated_conjecture,
( esk12_0 = nil
| esk11_0 != nil ),
inference(csr,[status(thm)],[192,167]) ).
cnf(433,negated_conjecture,
( ssList(esk5_2(esk12_0,esk13_0))
| esk11_0 = nil
| ~ ssItem(esk13_0)
| $false ),
inference(rw,[status(thm)],[214,176,theory(equality)]) ).
cnf(434,negated_conjecture,
( ssList(esk5_2(esk12_0,esk13_0))
| esk11_0 = nil
| ~ ssItem(esk13_0) ),
inference(cn,[status(thm)],[433,theory(equality)]) ).
cnf(435,negated_conjecture,
( esk11_0 = nil
| ssList(esk5_2(esk12_0,esk13_0)) ),
inference(csr,[status(thm)],[434,166]) ).
cnf(449,negated_conjecture,
( ssList(esk6_2(esk12_0,esk13_0))
| esk11_0 = nil
| ~ ssItem(esk13_0)
| $false ),
inference(rw,[status(thm)],[216,176,theory(equality)]) ).
cnf(450,negated_conjecture,
( ssList(esk6_2(esk12_0,esk13_0))
| esk11_0 = nil
| ~ ssItem(esk13_0) ),
inference(cn,[status(thm)],[449,theory(equality)]) ).
cnf(451,negated_conjecture,
( esk11_0 = nil
| ssList(esk6_2(esk12_0,esk13_0)) ),
inference(csr,[status(thm)],[450,166]) ).
cnf(458,plain,
( app(cons(X1,X2),X3) != app(X2,X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[359,64]) ).
cnf(495,plain,
( app(nil,nil) = nil
| ~ ssList(nil) ),
inference(er,[status(thm)],[220,theory(equality)]) ).
cnf(496,plain,
( app(nil,nil) = nil
| $false ),
inference(rw,[status(thm)],[495,119,theory(equality)]) ).
cnf(497,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[496,theory(equality)]) ).
cnf(516,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[60,497,theory(equality)]) ).
cnf(535,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[516,119,theory(equality)]) ).
cnf(536,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[535,theory(equality)]) ).
cnf(664,negated_conjecture,
( cons(esk13_0,X1) = app(esk11_0,X1)
| esk11_0 = nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[236,166]) ).
cnf(665,negated_conjecture,
( app(esk11_0,nil) = esk11_0
| esk11_0 = nil
| ~ ssList(nil) ),
inference(spm,[status(thm)],[164,664,theory(equality)]) ).
cnf(670,negated_conjecture,
( app(app(esk11_0,nil),X1) = cons(esk13_0,X1)
| esk11_0 = nil
| ~ ssItem(esk13_0)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[49,664,theory(equality)]) ).
cnf(686,negated_conjecture,
( app(esk11_0,nil) = esk11_0
| esk11_0 = nil
| $false ),
inference(rw,[status(thm)],[665,119,theory(equality)]) ).
cnf(687,negated_conjecture,
( app(esk11_0,nil) = esk11_0
| esk11_0 = nil ),
inference(cn,[status(thm)],[686,theory(equality)]) ).
cnf(690,negated_conjecture,
( app(app(esk11_0,nil),X1) = cons(esk13_0,X1)
| esk11_0 = nil
| ~ ssItem(esk13_0)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[670,119,theory(equality)]) ).
cnf(691,negated_conjecture,
( app(app(esk11_0,nil),X1) = cons(esk13_0,X1)
| esk11_0 = nil
| ~ ssItem(esk13_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[690,theory(equality)]) ).
cnf(777,negated_conjecture,
( cons(esk13_0,X1) = app(esk11_0,X1)
| esk12_0 = nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[237,167]) ).
cnf(779,negated_conjecture,
( app(esk11_0,nil) = esk11_0
| esk12_0 = nil
| ~ ssList(nil) ),
inference(spm,[status(thm)],[165,777,theory(equality)]) ).
cnf(783,negated_conjecture,
( app(app(esk11_0,nil),X1) = cons(esk13_0,X1)
| esk12_0 = nil
| ~ ssItem(esk13_0)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[49,777,theory(equality)]) ).
cnf(792,negated_conjecture,
( esk12_0 = nil
| app(app(esk11_0,X1),X2) != app(X1,X2)
| ~ ssItem(esk13_0)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[458,777,theory(equality)]) ).
cnf(802,negated_conjecture,
( app(esk11_0,nil) = esk11_0
| esk12_0 = nil
| $false ),
inference(rw,[status(thm)],[779,119,theory(equality)]) ).
cnf(803,negated_conjecture,
( app(esk11_0,nil) = esk11_0
| esk12_0 = nil ),
inference(cn,[status(thm)],[802,theory(equality)]) ).
cnf(804,negated_conjecture,
( app(app(esk11_0,nil),X1) = cons(esk13_0,X1)
| esk12_0 = nil
| ~ ssItem(esk13_0)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[783,119,theory(equality)]) ).
cnf(805,negated_conjecture,
( app(app(esk11_0,nil),X1) = cons(esk13_0,X1)
| esk12_0 = nil
| ~ ssItem(esk13_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[804,theory(equality)]) ).
cnf(1545,negated_conjecture,
( esk11_0 = nil
| X1 = esk13_0
| memberP(nil,X1)
| ~ memberP(esk11_0,X1)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[267,166]) ).
cnf(1546,negated_conjecture,
( esk11_0 = nil
| X1 = esk13_0
| ~ memberP(esk11_0,X1)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[1545,136]) ).
cnf(2479,negated_conjecture,
( esk12_0 = nil
| app(app(esk11_0,X1),X2) != app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[792,167]) ).
cnf(2482,negated_conjecture,
( esk12_0 = nil
| app(esk11_0,app(X1,X2)) != app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[2479,45,theory(equality)]) ).
cnf(2490,negated_conjecture,
( esk12_0 = nil
| app(esk11_0,app(X1,X2)) != app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[2482,175,theory(equality)]) ).
cnf(2491,negated_conjecture,
( esk12_0 = nil
| app(esk11_0,app(X1,X2)) != app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[2490,theory(equality)]) ).
cnf(2557,negated_conjecture,
( esk12_0 = nil
| app(esk11_0,esk11_0) != esk11_0
| ~ ssList(esk11_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[2491,803,theory(equality)]) ).
cnf(2569,negated_conjecture,
( esk12_0 = nil
| app(esk11_0,esk11_0) != esk11_0
| $false
| ~ ssList(nil) ),
inference(rw,[status(thm)],[2557,175,theory(equality)]) ).
cnf(2570,negated_conjecture,
( esk12_0 = nil
| app(esk11_0,esk11_0) != esk11_0
| $false
| $false ),
inference(rw,[status(thm)],[2569,119,theory(equality)]) ).
cnf(2571,negated_conjecture,
( esk12_0 = nil
| app(esk11_0,esk11_0) != esk11_0 ),
inference(cn,[status(thm)],[2570,theory(equality)]) ).
cnf(2661,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)],[312,75]) ).
cnf(2662,plain,
( nil = X2
| memberP(X1,esk2_1(X2))
| app(X3,X2) != X1
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[2661,74]) ).
cnf(2664,plain,
( nil = X1
| memberP(X2,esk2_1(X1))
| X1 != X2
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[2662,56,theory(equality)]) ).
cnf(2668,plain,
( nil = X1
| memberP(X2,esk2_1(X1))
| X1 != X2
| $false
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[2664,119,theory(equality)]) ).
cnf(2669,plain,
( nil = X1
| memberP(X2,esk2_1(X1))
| X1 != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[2668,theory(equality)]) ).
cnf(2670,plain,
( nil = X1
| memberP(X1,esk2_1(X1))
| ~ ssList(X1) ),
inference(er,[status(thm)],[2669,theory(equality)]) ).
cnf(2689,negated_conjecture,
( esk11_0 = nil
| esk2_1(esk11_0) = esk13_0
| ~ ssItem(esk2_1(esk11_0))
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[1546,2670,theory(equality)]) ).
cnf(2693,negated_conjecture,
( esk11_0 = nil
| esk2_1(esk11_0) = esk13_0
| ~ ssItem(esk2_1(esk11_0))
| $false ),
inference(rw,[status(thm)],[2689,175,theory(equality)]) ).
cnf(2694,negated_conjecture,
( esk11_0 = nil
| esk2_1(esk11_0) = esk13_0
| ~ ssItem(esk2_1(esk11_0)) ),
inference(cn,[status(thm)],[2693,theory(equality)]) ).
cnf(2697,negated_conjecture,
( esk2_1(esk11_0) = esk13_0
| esk11_0 = nil
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[2694,74,theory(equality)]) ).
cnf(2698,negated_conjecture,
( esk2_1(esk11_0) = esk13_0
| esk11_0 = nil
| $false ),
inference(rw,[status(thm)],[2697,175,theory(equality)]) ).
cnf(2699,negated_conjecture,
( esk2_1(esk11_0) = esk13_0
| esk11_0 = nil ),
inference(cn,[status(thm)],[2698,theory(equality)]) ).
cnf(2701,negated_conjecture,
( cons(esk13_0,esk1_1(esk11_0)) = esk11_0
| nil = esk11_0
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[73,2699,theory(equality)]) ).
cnf(2705,negated_conjecture,
( cons(esk13_0,esk1_1(esk11_0)) = esk11_0
| nil = esk11_0
| $false ),
inference(rw,[status(thm)],[2701,175,theory(equality)]) ).
cnf(2706,negated_conjecture,
( cons(esk13_0,esk1_1(esk11_0)) = esk11_0
| nil = esk11_0 ),
inference(cn,[status(thm)],[2705,theory(equality)]) ).
cnf(2740,negated_conjecture,
( esk11_0 = app(esk11_0,esk1_1(esk11_0))
| esk11_0 = nil
| ~ ssList(esk1_1(esk11_0)) ),
inference(spm,[status(thm)],[664,2706,theory(equality)]) ).
cnf(3489,plain,
( ssList(app(X1,app(X2,X3)))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[337,64]) ).
cnf(3490,plain,
( ssList(app(X1,nil))
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[3489,497,theory(equality)]) ).
cnf(3498,negated_conjecture,
( ssList(app(X1,esk11_0))
| esk11_0 = nil
| ~ ssList(nil)
| ~ ssList(esk11_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[3489,687,theory(equality)]) ).
cnf(3499,negated_conjecture,
( ssList(app(X1,esk11_0))
| esk12_0 = nil
| ~ ssList(nil)
| ~ ssList(esk11_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[3489,803,theory(equality)]) ).
cnf(3510,plain,
( ssList(app(X1,nil))
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[3490,119,theory(equality)]) ).
cnf(3511,plain,
( ssList(app(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[3510,theory(equality)]) ).
cnf(3518,negated_conjecture,
( ssList(app(X1,esk11_0))
| esk11_0 = nil
| $false
| ~ ssList(esk11_0)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[3498,119,theory(equality)]) ).
cnf(3519,negated_conjecture,
( ssList(app(X1,esk11_0))
| esk11_0 = nil
| $false
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[3518,175,theory(equality)]) ).
cnf(3520,negated_conjecture,
( ssList(app(X1,esk11_0))
| esk11_0 = nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[3519,theory(equality)]) ).
cnf(3521,negated_conjecture,
( ssList(app(X1,esk11_0))
| esk12_0 = nil
| $false
| ~ ssList(esk11_0)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[3499,119,theory(equality)]) ).
cnf(3522,negated_conjecture,
( ssList(app(X1,esk11_0))
| esk12_0 = nil
| $false
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[3521,175,theory(equality)]) ).
cnf(3523,negated_conjecture,
( ssList(app(X1,esk11_0))
| esk12_0 = nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[3522,theory(equality)]) ).
cnf(3939,negated_conjecture,
( esk11_0 = nil
| ssList(cons(X1,esk11_0))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[3520,49,theory(equality)]) ).
cnf(3947,negated_conjecture,
( esk11_0 = nil
| ssList(cons(X1,esk11_0))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[3939,175,theory(equality)]) ).
cnf(3948,negated_conjecture,
( esk11_0 = nil
| ssList(cons(X1,esk11_0))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[3947,theory(equality)]) ).
cnf(3957,negated_conjecture,
( esk11_0 = nil
| ssList(cons(esk13_0,esk11_0))
| ~ ssItem(esk13_0)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[3948,164,theory(equality)]) ).
cnf(3963,negated_conjecture,
( esk11_0 = nil
| ssList(cons(esk13_0,esk11_0))
| ~ ssItem(esk13_0)
| $false ),
inference(rw,[status(thm)],[3957,175,theory(equality)]) ).
cnf(3964,negated_conjecture,
( esk11_0 = nil
| ssList(cons(esk13_0,esk11_0))
| ~ ssItem(esk13_0) ),
inference(cn,[status(thm)],[3963,theory(equality)]) ).
cnf(3975,negated_conjecture,
( esk11_0 = nil
| ssList(cons(esk13_0,esk11_0)) ),
inference(csr,[status(thm)],[3964,166]) ).
cnf(4115,negated_conjecture,
( esk12_0 = nil
| ssList(cons(X1,esk11_0))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[3523,49,theory(equality)]) ).
cnf(4123,negated_conjecture,
( esk12_0 = nil
| ssList(cons(X1,esk11_0))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[4115,175,theory(equality)]) ).
cnf(4124,negated_conjecture,
( esk12_0 = nil
| ssList(cons(X1,esk11_0))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[4123,theory(equality)]) ).
cnf(4212,negated_conjecture,
( esk12_0 = nil
| ssList(cons(esk13_0,esk11_0))
| ~ ssItem(esk13_0)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[4124,165,theory(equality)]) ).
cnf(4219,negated_conjecture,
( esk12_0 = nil
| ssList(cons(esk13_0,esk11_0))
| ~ ssItem(esk13_0)
| $false ),
inference(rw,[status(thm)],[4212,175,theory(equality)]) ).
cnf(4220,negated_conjecture,
( esk12_0 = nil
| ssList(cons(esk13_0,esk11_0))
| ~ ssItem(esk13_0) ),
inference(cn,[status(thm)],[4219,theory(equality)]) ).
cnf(4229,negated_conjecture,
( esk12_0 = nil
| ssList(cons(esk13_0,esk11_0)) ),
inference(csr,[status(thm)],[4220,167]) ).
cnf(4439,negated_conjecture,
( app(esk11_0,esk1_1(esk11_0)) = esk11_0
| esk11_0 = nil
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[2740,75,theory(equality)]) ).
cnf(4442,negated_conjecture,
( app(esk11_0,esk1_1(esk11_0)) = esk11_0
| esk11_0 = nil
| $false ),
inference(rw,[status(thm)],[4439,175,theory(equality)]) ).
cnf(4443,negated_conjecture,
( app(esk11_0,esk1_1(esk11_0)) = esk11_0
| esk11_0 = nil ),
inference(cn,[status(thm)],[4442,theory(equality)]) ).
cnf(4561,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[355,64]) ).
cnf(4570,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[4561,536,theory(equality)]) ).
cnf(4584,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[4570,119,theory(equality)]) ).
cnf(4585,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[4584,theory(equality)]) ).
cnf(4592,negated_conjecture,
( ssList(app(esk11_0,nil))
| esk11_0 = nil
| ~ ssItem(esk13_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[4585,664,theory(equality)]) ).
cnf(4593,negated_conjecture,
( ssList(app(esk11_0,nil))
| esk12_0 = nil
| ~ ssItem(esk13_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[4585,777,theory(equality)]) ).
cnf(4599,negated_conjecture,
( ssList(app(esk11_0,nil))
| esk11_0 = nil
| ~ ssItem(esk13_0)
| $false ),
inference(rw,[status(thm)],[4592,119,theory(equality)]) ).
cnf(4600,negated_conjecture,
( ssList(app(esk11_0,nil))
| esk11_0 = nil
| ~ ssItem(esk13_0) ),
inference(cn,[status(thm)],[4599,theory(equality)]) ).
cnf(4601,negated_conjecture,
( ssList(app(esk11_0,nil))
| esk12_0 = nil
| ~ ssItem(esk13_0)
| $false ),
inference(rw,[status(thm)],[4593,119,theory(equality)]) ).
cnf(4602,negated_conjecture,
( ssList(app(esk11_0,nil))
| esk12_0 = nil
| ~ ssItem(esk13_0) ),
inference(cn,[status(thm)],[4601,theory(equality)]) ).
cnf(4604,negated_conjecture,
( esk11_0 = nil
| ssList(app(esk11_0,nil)) ),
inference(csr,[status(thm)],[4600,166]) ).
cnf(5334,negated_conjecture,
( esk12_0 = nil
| ssList(app(esk11_0,nil)) ),
inference(csr,[status(thm)],[4602,167]) ).
cnf(5954,plain,
( segmentP(X1,cons(X2,nil))
| cons(X2,X3) != X1
| ~ ssList(X3)
| ~ ssList(cons(X2,nil))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(spm,[status(thm)],[384,49,theory(equality)]) ).
cnf(5966,negated_conjecture,
( segmentP(X1,esk11_0)
| esk11_0 = nil
| esk11_0 != X1
| ~ ssList(esk1_1(esk11_0))
| ~ ssList(esk11_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[384,4443,theory(equality)]) ).
cnf(5997,negated_conjecture,
( segmentP(X1,esk11_0)
| esk11_0 = nil
| esk11_0 != X1
| ~ ssList(esk1_1(esk11_0))
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[5966,175,theory(equality)]) ).
cnf(5998,negated_conjecture,
( segmentP(X1,esk11_0)
| esk11_0 = nil
| esk11_0 != X1
| ~ ssList(esk1_1(esk11_0))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[5997,theory(equality)]) ).
cnf(6006,negated_conjecture,
( esk11_0 = nil
| segmentP(X1,esk11_0)
| esk11_0 != X1
| ~ ssList(X1)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[5998,75,theory(equality)]) ).
cnf(6009,negated_conjecture,
( esk11_0 = nil
| segmentP(X1,esk11_0)
| esk11_0 != X1
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[6006,175,theory(equality)]) ).
cnf(6010,negated_conjecture,
( esk11_0 = nil
| segmentP(X1,esk11_0)
| esk11_0 != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[6009,theory(equality)]) ).
cnf(6051,negated_conjecture,
( esk11_0 = nil
| segmentP(esk11_0,esk11_0)
| ~ ssList(esk11_0) ),
inference(er,[status(thm)],[6010,theory(equality)]) ).
cnf(6052,negated_conjecture,
( esk11_0 = nil
| segmentP(esk11_0,esk11_0)
| $false ),
inference(rw,[status(thm)],[6051,175,theory(equality)]) ).
cnf(6053,negated_conjecture,
( esk11_0 = nil
| segmentP(esk11_0,esk11_0) ),
inference(cn,[status(thm)],[6052,theory(equality)]) ).
cnf(6057,negated_conjecture,
( segmentP(app(app(X1,esk11_0),X2),esk11_0)
| esk11_0 = nil
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[154,6053,theory(equality)]) ).
cnf(6065,negated_conjecture,
( segmentP(app(app(X1,esk11_0),X2),esk11_0)
| esk11_0 = nil
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[6057,175,theory(equality)]) ).
cnf(6066,negated_conjecture,
( segmentP(app(app(X1,esk11_0),X2),esk11_0)
| esk11_0 = nil
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[6065,theory(equality)]) ).
cnf(6460,negated_conjecture,
( app(esk5_2(esk12_0,esk13_0),cons(esk13_0,esk6_2(esk12_0,esk13_0))) = esk12_0
| esk11_0 = nil
| ~ ssItem(esk13_0)
| $false ),
inference(rw,[status(thm)],[389,176,theory(equality)]) ).
cnf(6461,negated_conjecture,
( app(esk5_2(esk12_0,esk13_0),cons(esk13_0,esk6_2(esk12_0,esk13_0))) = esk12_0
| esk11_0 = nil
| ~ ssItem(esk13_0) ),
inference(cn,[status(thm)],[6460,theory(equality)]) ).
cnf(6462,negated_conjecture,
( app(esk5_2(esk12_0,esk13_0),cons(esk13_0,esk6_2(esk12_0,esk13_0))) = esk12_0
| esk11_0 = nil ),
inference(csr,[status(thm)],[6461,166]) ).
cnf(6475,negated_conjecture,
( app(esk5_2(esk12_0,esk13_0),app(esk11_0,esk6_2(esk12_0,esk13_0))) = esk12_0
| esk11_0 = nil
| ~ ssList(esk6_2(esk12_0,esk13_0)) ),
inference(spm,[status(thm)],[6462,664,theory(equality)]) ).
cnf(8598,negated_conjecture,
( app(app(esk11_0,nil),X1) = cons(esk13_0,X1)
| esk11_0 = nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[691,166]) ).
cnf(10493,negated_conjecture,
( app(app(esk11_0,nil),X1) = cons(esk13_0,X1)
| esk12_0 = nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[805,167]) ).
cnf(10547,negated_conjecture,
( ssList(cons(esk13_0,nil))
| esk12_0 = nil
| ~ ssList(app(esk11_0,nil))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[3511,10493,theory(equality)]) ).
cnf(10647,negated_conjecture,
( ssList(cons(esk13_0,nil))
| esk12_0 = nil
| ~ ssList(app(esk11_0,nil))
| $false ),
inference(rw,[status(thm)],[10547,119,theory(equality)]) ).
cnf(10648,negated_conjecture,
( ssList(cons(esk13_0,nil))
| esk12_0 = nil
| ~ ssList(app(esk11_0,nil)) ),
inference(cn,[status(thm)],[10647,theory(equality)]) ).
cnf(10758,negated_conjecture,
( esk12_0 = nil
| ssList(cons(esk13_0,nil)) ),
inference(csr,[status(thm)],[10648,5334]) ).
cnf(19930,negated_conjecture,
( esk11_0 = nil
| segmentP(app(X1,esk11_0),esk11_0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(app(X1,esk11_0)) ),
inference(spm,[status(thm)],[6066,34,theory(equality)]) ).
cnf(19938,negated_conjecture,
( esk11_0 = nil
| segmentP(app(X1,app(esk11_0,X2)),esk11_0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[6066,45,theory(equality)]) ).
cnf(19956,negated_conjecture,
( esk11_0 = nil
| segmentP(app(X1,esk11_0),esk11_0)
| $false
| ~ ssList(X1)
| ~ ssList(app(X1,esk11_0)) ),
inference(rw,[status(thm)],[19930,119,theory(equality)]) ).
cnf(19957,negated_conjecture,
( esk11_0 = nil
| segmentP(app(X1,esk11_0),esk11_0)
| ~ ssList(X1)
| ~ ssList(app(X1,esk11_0)) ),
inference(cn,[status(thm)],[19956,theory(equality)]) ).
cnf(19973,negated_conjecture,
( esk11_0 = nil
| segmentP(app(X1,app(esk11_0,X2)),esk11_0)
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[19938,175,theory(equality)]) ).
cnf(19974,negated_conjecture,
( esk11_0 = nil
| segmentP(app(X1,app(esk11_0,X2)),esk11_0)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[19973,theory(equality)]) ).
cnf(20007,negated_conjecture,
( esk11_0 = nil
| segmentP(app(X1,esk11_0),esk11_0)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[19957,3520]) ).
cnf(20022,negated_conjecture,
( esk11_0 = nil
| segmentP(cons(esk13_0,esk11_0),esk11_0)
| ~ ssList(app(esk11_0,nil))
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[20007,8598,theory(equality)]) ).
cnf(20054,negated_conjecture,
( esk11_0 = nil
| segmentP(cons(esk13_0,esk11_0),esk11_0)
| ~ ssList(app(esk11_0,nil))
| $false ),
inference(rw,[status(thm)],[20022,175,theory(equality)]) ).
cnf(20055,negated_conjecture,
( esk11_0 = nil
| segmentP(cons(esk13_0,esk11_0),esk11_0)
| ~ ssList(app(esk11_0,nil)) ),
inference(cn,[status(thm)],[20054,theory(equality)]) ).
cnf(20092,negated_conjecture,
( esk11_0 = nil
| segmentP(cons(esk13_0,esk11_0),esk11_0) ),
inference(csr,[status(thm)],[20055,4604]) ).
cnf(229839,plain,
( segmentP(X1,cons(X2,nil))
| cons(X2,X3) != X1
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[5954,4585]) ).
cnf(229842,negated_conjecture,
( segmentP(X1,cons(esk13_0,nil))
| esk12_0 = nil
| esk11_0 != X1
| ~ ssItem(esk13_0)
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[229839,165,theory(equality)]) ).
cnf(229871,negated_conjecture,
( segmentP(X1,cons(esk13_0,nil))
| esk12_0 = nil
| esk11_0 != X1
| ~ ssItem(esk13_0)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[229842,119,theory(equality)]) ).
cnf(229872,negated_conjecture,
( segmentP(X1,cons(esk13_0,nil))
| esk12_0 = nil
| esk11_0 != X1
| ~ ssItem(esk13_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[229871,theory(equality)]) ).
cnf(232020,negated_conjecture,
( esk12_0 = nil
| segmentP(X1,cons(esk13_0,nil))
| esk11_0 != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[229872,167]) ).
cnf(232021,negated_conjecture,
( esk12_0 = nil
| segmentP(esk11_0,cons(esk13_0,nil))
| ~ ssList(esk11_0) ),
inference(er,[status(thm)],[232020,theory(equality)]) ).
cnf(232022,negated_conjecture,
( esk12_0 = nil
| segmentP(esk11_0,cons(esk13_0,nil))
| $false ),
inference(rw,[status(thm)],[232021,175,theory(equality)]) ).
cnf(232023,negated_conjecture,
( esk12_0 = nil
| segmentP(esk11_0,cons(esk13_0,nil)) ),
inference(cn,[status(thm)],[232022,theory(equality)]) ).
cnf(232029,negated_conjecture,
( segmentP(X1,cons(esk13_0,nil))
| esk12_0 = nil
| ~ segmentP(X1,esk11_0)
| ~ ssList(cons(esk13_0,nil))
| ~ ssList(esk11_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[140,232023,theory(equality)]) ).
cnf(232042,negated_conjecture,
( segmentP(X1,cons(esk13_0,nil))
| esk12_0 = nil
| ~ segmentP(X1,esk11_0)
| ~ ssList(cons(esk13_0,nil))
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[232029,175,theory(equality)]) ).
cnf(232043,negated_conjecture,
( segmentP(X1,cons(esk13_0,nil))
| esk12_0 = nil
| ~ segmentP(X1,esk11_0)
| ~ ssList(cons(esk13_0,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[232042,theory(equality)]) ).
cnf(237886,negated_conjecture,
( esk12_0 = nil
| segmentP(X1,cons(esk13_0,nil))
| ~ segmentP(X1,esk11_0)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[232043,10758]) ).
cnf(237905,negated_conjecture,
( esk12_0 = nil
| segmentP(cons(esk13_0,esk11_0),cons(esk13_0,nil))
| esk11_0 = nil
| ~ ssList(cons(esk13_0,esk11_0)) ),
inference(spm,[status(thm)],[237886,20092,theory(equality)]) ).
cnf(238180,negated_conjecture,
( esk12_0 = nil
| esk11_0 = nil
| segmentP(cons(esk13_0,esk11_0),cons(esk13_0,nil)) ),
inference(csr,[status(thm)],[237905,3975]) ).
cnf(238181,negated_conjecture,
( esk12_0 = nil
| segmentP(cons(esk13_0,esk11_0),cons(esk13_0,nil)) ),
inference(csr,[status(thm)],[238180,413]) ).
cnf(238183,negated_conjecture,
( esk12_0 = nil
| segmentP(cons(esk13_0,esk11_0),esk11_0) ),
inference(spm,[status(thm)],[238181,165,theory(equality)]) ).
cnf(238207,negated_conjecture,
( esk11_0 = cons(esk13_0,esk11_0)
| esk12_0 = nil
| ~ segmentP(esk11_0,cons(esk13_0,esk11_0))
| ~ ssList(cons(esk13_0,esk11_0))
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[102,238183,theory(equality)]) ).
cnf(238219,negated_conjecture,
( esk11_0 = cons(esk13_0,esk11_0)
| esk12_0 = nil
| ~ segmentP(esk11_0,cons(esk13_0,esk11_0))
| ~ ssList(cons(esk13_0,esk11_0))
| $false ),
inference(rw,[status(thm)],[238207,175,theory(equality)]) ).
cnf(238220,negated_conjecture,
( esk11_0 = cons(esk13_0,esk11_0)
| esk12_0 = nil
| ~ segmentP(esk11_0,cons(esk13_0,esk11_0))
| ~ ssList(cons(esk13_0,esk11_0)) ),
inference(cn,[status(thm)],[238219,theory(equality)]) ).
cnf(239236,negated_conjecture,
( cons(esk13_0,esk11_0) = esk11_0
| esk12_0 = nil
| ~ segmentP(esk11_0,cons(esk13_0,esk11_0)) ),
inference(csr,[status(thm)],[238220,4229]) ).
cnf(239238,negated_conjecture,
( app(esk11_0,esk11_0) = esk11_0
| esk12_0 = nil
| ~ segmentP(esk11_0,app(esk11_0,esk11_0))
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[239236,777,theory(equality)]) ).
cnf(239243,negated_conjecture,
( app(esk11_0,esk11_0) = esk11_0
| esk12_0 = nil
| ~ segmentP(esk11_0,app(esk11_0,esk11_0))
| $false ),
inference(rw,[status(thm)],[239238,175,theory(equality)]) ).
cnf(239244,negated_conjecture,
( app(esk11_0,esk11_0) = esk11_0
| esk12_0 = nil
| ~ segmentP(esk11_0,app(esk11_0,esk11_0)) ),
inference(cn,[status(thm)],[239243,theory(equality)]) ).
cnf(241241,negated_conjecture,
( esk12_0 = nil
| ~ segmentP(esk11_0,app(esk11_0,esk11_0)) ),
inference(csr,[status(thm)],[239244,2571]) ).
cnf(258906,negated_conjecture,
( app(esk5_2(esk12_0,esk13_0),app(esk11_0,esk6_2(esk12_0,esk13_0))) = esk12_0
| esk11_0 = nil ),
inference(csr,[status(thm)],[6475,451]) ).
cnf(258969,negated_conjecture,
( esk11_0 = nil
| segmentP(esk12_0,esk11_0)
| ~ ssList(esk6_2(esk12_0,esk13_0))
| ~ ssList(esk5_2(esk12_0,esk13_0)) ),
inference(spm,[status(thm)],[19974,258906,theory(equality)]) ).
cnf(259415,negated_conjecture,
( esk11_0 = nil
| ~ ssList(esk6_2(esk12_0,esk13_0))
| ~ ssList(esk5_2(esk12_0,esk13_0)) ),
inference(sr,[status(thm)],[258969,177,theory(equality)]) ).
cnf(259554,negated_conjecture,
( esk11_0 = nil
| ~ ssList(esk6_2(esk12_0,esk13_0)) ),
inference(csr,[status(thm)],[259415,435]) ).
cnf(259555,negated_conjecture,
esk11_0 = nil,
inference(csr,[status(thm)],[259554,451]) ).
cnf(259560,negated_conjecture,
~ segmentP(esk12_0,nil),
inference(rw,[status(thm)],[177,259555,theory(equality)]) ).
cnf(259743,negated_conjecture,
( esk12_0 = nil
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[241241,259555,theory(equality)]),259555,theory(equality)]),259555,theory(equality)]),497,theory(equality)]),180,theory(equality)]) ).
cnf(259744,negated_conjecture,
esk12_0 = nil,
inference(cn,[status(thm)],[259743,theory(equality)]) ).
cnf(262205,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[259560,259744,theory(equality)]),180,theory(equality)]) ).
cnf(262206,negated_conjecture,
$false,
inference(cn,[status(thm)],[262205,theory(equality)]) ).
cnf(262207,negated_conjecture,
$false,
262206,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC374+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpiVmkZq/sel_SWC374+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC374+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC374+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC374+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
%
%------------------------------------------------------------------------------