%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC382+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 11:40:51 EST 2010
% Result : Theorem 12.74s
% Output : CNFRefutation 12.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 20
% Syntax : Number of formulae : 253 ( 16 unt; 0 def)
% Number of atoms : 1078 ( 333 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 1386 ( 561 ~; 651 |; 122 &)
% ( 5 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 360 ( 6 sgn 172 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/tmp/tmpGpnzs0/sel_SWC382+1.p_1',ax85) ).
fof(2,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmpGpnzs0/sel_SWC382+1.p_1',ax84) ).
fof(3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmpGpnzs0/sel_SWC382+1.p_1',ax83) ).
fof(5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpGpnzs0/sel_SWC382+1.p_1',ax81) ).
fof(7,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpGpnzs0/sel_SWC382+1.p_1',ax28) ).
fof(8,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/tmp/tmpGpnzs0/sel_SWC382+1.p_1',ax27) ).
fof(9,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpGpnzs0/sel_SWC382+1.p_1',ax26) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmpGpnzs0/sel_SWC382+1.p_1',ax21) ).
fof(11,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/tmp/tmpGpnzs0/sel_SWC382+1.p_1',ax20) ).
fof(12,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/tmp/tmpGpnzs0/sel_SWC382+1.p_1',ax23) ).
fof(13,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/tmp/tmpGpnzs0/sel_SWC382+1.p_1',ax22) ).
fof(16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/tmp/tmpGpnzs0/sel_SWC382+1.p_1',ax7) ).
fof(17,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
file('/tmp/tmpGpnzs0/sel_SWC382+1.p_1',ax4) ).
fof(22,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/tmp/tmpGpnzs0/sel_SWC382+1.p_1',ax58) ).
fof(23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpGpnzs0/sel_SWC382+1.p_1',ax15) ).
fof(24,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpGpnzs0/sel_SWC382+1.p_1',ax16) ).
fof(25,axiom,
ssList(nil),
file('/tmp/tmpGpnzs0/sel_SWC382+1.p_1',ax17) ).
fof(28,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/tmp/tmpGpnzs0/sel_SWC382+1.p_1',ax55) ).
fof(29,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/tmpGpnzs0/sel_SWC382+1.p_1',ax56) ).
fof(32,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X3 != X5
& ? [X6] :
( ssItem(X6)
& cons(X6,nil) = X5
& hd(X4) = X6
& neq(nil,X4) ) )
| ( singletonP(X1)
& segmentP(X2,X1) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/tmp/tmpGpnzs0/sel_SWC382+1.p_1',co1) ).
fof(33,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X3 != X5
& ? [X6] :
( ssItem(X6)
& cons(X6,nil) = X5
& hd(X4) = X6
& neq(nil,X4) ) )
| ( singletonP(X1)
& segmentP(X2,X1) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[32]) ).
fof(35,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X3 != X5
& ? [X6] :
( ssItem(X6)
& cons(X6,nil) = X5
& hd(X4) = X6
& neq(nil,X4) ) )
| ( singletonP(X1)
& segmentP(X2,X1) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[33,theory(equality)]) ).
fof(36,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| nil = X1
| hd(app(X1,X2)) = hd(X1) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(37,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| nil = X3
| hd(app(X3,X4)) = hd(X3) ) ),
inference(variable_rename,[status(thm)],[36]) ).
fof(38,plain,
! [X3,X4] :
( ~ ssList(X4)
| nil = X3
| hd(app(X3,X4)) = hd(X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[37]) ).
cnf(39,plain,
( hd(app(X1,X2)) = hd(X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[38]) ).
fof(40,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(41,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[40]) ).
cnf(42,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(43,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)],[3]) ).
fof(44,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)],[43]) ).
fof(45,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)],[44]) ).
fof(46,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)],[45]) ).
cnf(47,plain,
( nil = app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| nil != X1
| nil != X2 ),
inference(split_conjunct,[status(thm)],[46]) ).
fof(54,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(55,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[54]) ).
fof(56,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[55]) ).
cnf(57,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[56]) ).
fof(62,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(63,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[62]) ).
cnf(64,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[63]) ).
fof(65,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssItem(X3)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(66,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssItem(X6)
| cons(X6,app(X5,X4)) = app(cons(X6,X5),X4) ) ) ),
inference(variable_rename,[status(thm)],[65]) ).
fof(67,plain,
! [X4,X5,X6] :
( ~ ssItem(X6)
| cons(X6,app(X5,X4)) = app(cons(X6,X5),X4)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[66]) ).
cnf(68,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[67]) ).
fof(69,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(70,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[69]) ).
fof(71,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[70]) ).
cnf(72,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[71]) ).
fof(73,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| nil != cons(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(74,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3) ) ),
inference(variable_rename,[status(thm)],[73]) ).
fof(75,plain,
! [X3,X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[74]) ).
cnf(76,plain,
( ~ ssList(X1)
| nil != cons(X2,X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[75]) ).
fof(77,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(78,plain,
! [X4] :
( ~ ssList(X4)
| nil = X4
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssItem(X6)
& cons(X6,X5) = X4 ) ) ),
inference(variable_rename,[status(thm)],[77]) ).
fof(79,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)],[78]) ).
fof(80,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)],[79]) ).
cnf(81,plain,
( nil = X1
| cons(esk2_1(X1),esk1_1(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[80]) ).
cnf(82,plain,
( nil = X1
| ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[80]) ).
cnf(83,plain,
( nil = X1
| ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[80]) ).
fof(84,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| hd(cons(X2,X1)) = X2 ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(85,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| hd(cons(X4,X3)) = X4 ) ),
inference(variable_rename,[status(thm)],[84]) ).
fof(86,plain,
! [X3,X4] :
( ~ ssItem(X4)
| hd(cons(X4,X3)) = X4
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[85]) ).
cnf(87,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[86]) ).
fof(88,plain,
! [X1] :
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(89,plain,
! [X2] :
( ~ ssList(X2)
| nil = X2
| ssItem(hd(X2)) ),
inference(variable_rename,[status(thm)],[88]) ).
cnf(90,plain,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[89]) ).
fof(97,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)],[16]) ).
fof(98,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)],[97]) ).
fof(99,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ segmentP(X5,X6)
| ( ssList(esk5_2(X5,X6))
& ssList(esk6_2(X5,X6))
& app(app(esk5_2(X5,X6),X6),esk6_2(X5,X6)) = X5 ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X9,X6),X10) != X5 ) )
| segmentP(X5,X6) ) ) ) ),
inference(skolemize,[status(esa)],[98]) ).
fof(100,plain,
! [X5,X6,X9,X10] :
( ( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6) )
& ( ~ segmentP(X5,X6)
| ( ssList(esk5_2(X5,X6))
& ssList(esk6_2(X5,X6))
& app(app(esk5_2(X5,X6),X6),esk6_2(X5,X6)) = X5 ) ) )
| ~ ssList(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[99]) ).
fof(101,plain,
! [X5,X6,X9,X10] :
( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk5_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk6_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( app(app(esk5_2(X5,X6),X6),esk6_2(X5,X6)) = X5
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) ) ),
inference(distribute,[status(thm)],[100]) ).
cnf(104,plain,
( ssList(esk5_2(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2) ),
inference(split_conjunct,[status(thm)],[101]) ).
fof(106,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ singletonP(X1)
| ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) )
& ( ! [X2] :
( ~ ssItem(X2)
| cons(X2,nil) != X1 )
| singletonP(X1) ) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(107,plain,
! [X3] :
( ~ ssList(X3)
| ( ( ~ singletonP(X3)
| ? [X4] :
( ssItem(X4)
& cons(X4,nil) = X3 ) )
& ( ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X3 )
| singletonP(X3) ) ) ),
inference(variable_rename,[status(thm)],[106]) ).
fof(108,plain,
! [X3] :
( ~ ssList(X3)
| ( ( ~ singletonP(X3)
| ( ssItem(esk7_1(X3))
& cons(esk7_1(X3),nil) = X3 ) )
& ( ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X3 )
| singletonP(X3) ) ) ),
inference(skolemize,[status(esa)],[107]) ).
fof(109,plain,
! [X3,X5] :
( ( ( ~ ssItem(X5)
| cons(X5,nil) != X3
| singletonP(X3) )
& ( ~ singletonP(X3)
| ( ssItem(esk7_1(X3))
& cons(esk7_1(X3),nil) = X3 ) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[108]) ).
fof(110,plain,
! [X3,X5] :
( ( ~ ssItem(X5)
| cons(X5,nil) != X3
| singletonP(X3)
| ~ ssList(X3) )
& ( ssItem(esk7_1(X3))
| ~ singletonP(X3)
| ~ ssList(X3) )
& ( cons(esk7_1(X3),nil) = X3
| ~ singletonP(X3)
| ~ ssList(X3) ) ),
inference(distribute,[status(thm)],[109]) ).
cnf(111,plain,
( cons(esk7_1(X1),nil) = X1
| ~ ssList(X1)
| ~ singletonP(X1) ),
inference(split_conjunct,[status(thm)],[110]) ).
cnf(112,plain,
( ssItem(esk7_1(X1))
| ~ ssList(X1)
| ~ singletonP(X1) ),
inference(split_conjunct,[status(thm)],[110]) ).
cnf(113,plain,
( singletonP(X1)
| ~ ssList(X1)
| cons(X2,nil) != X1
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[110]) ).
fof(134,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(nil,X1)
| nil = X1 )
& ( nil != X1
| segmentP(nil,X1) ) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(135,plain,
! [X2] :
( ~ ssList(X2)
| ( ( ~ segmentP(nil,X2)
| nil = X2 )
& ( nil != X2
| segmentP(nil,X2) ) ) ),
inference(variable_rename,[status(thm)],[134]) ).
fof(136,plain,
! [X2] :
( ( ~ segmentP(nil,X2)
| nil = X2
| ~ ssList(X2) )
& ( nil != X2
| segmentP(nil,X2)
| ~ ssList(X2) ) ),
inference(distribute,[status(thm)],[135]) ).
cnf(137,plain,
( segmentP(nil,X1)
| ~ ssList(X1)
| nil != X1 ),
inference(split_conjunct,[status(thm)],[136]) ).
fof(139,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(140,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[139]) ).
fof(141,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[140]) ).
fof(142,plain,
! [X3,X4] :
( ( ~ neq(X3,X4)
| X3 != X4
| ~ ssList(X4)
| ~ ssList(X3) )
& ( X3 = X4
| neq(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3) ) ),
inference(distribute,[status(thm)],[141]) ).
cnf(143,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[142]) ).
cnf(144,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[142]) ).
fof(145,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(146,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[145]) ).
fof(147,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[146]) ).
cnf(148,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[147]) ).
cnf(149,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[25]) ).
fof(158,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(159,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,X2) ),
inference(variable_rename,[status(thm)],[158]) ).
cnf(160,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[159]) ).
fof(161,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)],[29]) ).
fof(162,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)],[161]) ).
fof(163,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)],[162]) ).
cnf(164,plain,
( segmentP(app(app(X3,X1),X4),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[163]) ).
fof(174,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ( ( neq(X2,nil)
& ! [X5] :
( ~ ssList(X5)
| X3 = X5
| ! [X6] :
( ~ ssItem(X6)
| cons(X6,nil) != X5
| hd(X4) != X6
| ~ neq(nil,X4) ) )
& ( ~ singletonP(X1)
| ~ segmentP(X2,X1) ) )
| ( neq(X2,nil)
& ~ neq(X4,nil) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[35]) ).
fof(175,negated_conjecture,
? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& X8 = X10
& X7 = X9
& ( ( neq(X8,nil)
& ! [X11] :
( ~ ssList(X11)
| X9 = X11
| ! [X12] :
( ~ ssItem(X12)
| cons(X12,nil) != X11
| hd(X10) != X12
| ~ neq(nil,X10) ) )
& ( ~ singletonP(X7)
| ~ segmentP(X8,X7) ) )
| ( neq(X8,nil)
& ~ neq(X10,nil) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[174]) ).
fof(176,negated_conjecture,
( ssList(esk9_0)
& ssList(esk10_0)
& ssList(esk11_0)
& ssList(esk12_0)
& esk10_0 = esk12_0
& esk9_0 = esk11_0
& ( ( neq(esk10_0,nil)
& ! [X11] :
( ~ ssList(X11)
| esk11_0 = X11
| ! [X12] :
( ~ ssItem(X12)
| cons(X12,nil) != X11
| hd(esk12_0) != X12
| ~ neq(nil,esk12_0) ) )
& ( ~ singletonP(esk9_0)
| ~ segmentP(esk10_0,esk9_0) ) )
| ( neq(esk10_0,nil)
& ~ neq(esk12_0,nil) ) ) ),
inference(skolemize,[status(esa)],[175]) ).
fof(177,negated_conjecture,
! [X11,X12] :
( ( ( ( ~ ssItem(X12)
| cons(X12,nil) != X11
| hd(esk12_0) != X12
| ~ neq(nil,esk12_0)
| ~ ssList(X11)
| esk11_0 = X11 )
& neq(esk10_0,nil)
& ( ~ singletonP(esk9_0)
| ~ segmentP(esk10_0,esk9_0) ) )
| ( neq(esk10_0,nil)
& ~ neq(esk12_0,nil) ) )
& esk10_0 = esk12_0
& esk9_0 = esk11_0
& ssList(esk12_0)
& ssList(esk11_0)
& ssList(esk10_0)
& ssList(esk9_0) ),
inference(shift_quantors,[status(thm)],[176]) ).
fof(178,negated_conjecture,
! [X11,X12] :
( ( neq(esk10_0,nil)
| ~ ssItem(X12)
| cons(X12,nil) != X11
| hd(esk12_0) != X12
| ~ neq(nil,esk12_0)
| ~ ssList(X11)
| esk11_0 = X11 )
& ( ~ neq(esk12_0,nil)
| ~ ssItem(X12)
| cons(X12,nil) != X11
| hd(esk12_0) != X12
| ~ neq(nil,esk12_0)
| ~ ssList(X11)
| esk11_0 = X11 )
& ( neq(esk10_0,nil)
| neq(esk10_0,nil) )
& ( ~ neq(esk12_0,nil)
| neq(esk10_0,nil) )
& ( neq(esk10_0,nil)
| ~ singletonP(esk9_0)
| ~ segmentP(esk10_0,esk9_0) )
& ( ~ neq(esk12_0,nil)
| ~ singletonP(esk9_0)
| ~ segmentP(esk10_0,esk9_0) )
& esk10_0 = esk12_0
& esk9_0 = esk11_0
& ssList(esk12_0)
& ssList(esk11_0)
& ssList(esk10_0)
& ssList(esk9_0) ),
inference(distribute,[status(thm)],[177]) ).
cnf(179,negated_conjecture,
ssList(esk9_0),
inference(split_conjunct,[status(thm)],[178]) ).
cnf(180,negated_conjecture,
ssList(esk10_0),
inference(split_conjunct,[status(thm)],[178]) ).
cnf(183,negated_conjecture,
esk9_0 = esk11_0,
inference(split_conjunct,[status(thm)],[178]) ).
cnf(184,negated_conjecture,
esk10_0 = esk12_0,
inference(split_conjunct,[status(thm)],[178]) ).
cnf(185,negated_conjecture,
( ~ segmentP(esk10_0,esk9_0)
| ~ singletonP(esk9_0)
| ~ neq(esk12_0,nil) ),
inference(split_conjunct,[status(thm)],[178]) ).
cnf(188,negated_conjecture,
( neq(esk10_0,nil)
| neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[178]) ).
cnf(189,negated_conjecture,
( esk11_0 = X1
| ~ ssList(X1)
| ~ neq(nil,esk12_0)
| hd(esk12_0) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| ~ neq(esk12_0,nil) ),
inference(split_conjunct,[status(thm)],[178]) ).
cnf(193,negated_conjecture,
ssList(esk12_0),
inference(rw,[status(thm)],[180,184,theory(equality)]) ).
cnf(194,negated_conjecture,
neq(esk12_0,nil),
inference(rw,[status(thm)],[188,184,theory(equality)]) ).
cnf(200,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(er,[status(thm)],[137,theory(equality)]) ).
cnf(201,plain,
( segmentP(nil,nil)
| $false ),
inference(rw,[status(thm)],[200,149,theory(equality)]) ).
cnf(202,plain,
segmentP(nil,nil),
inference(cn,[status(thm)],[201,theory(equality)]) ).
cnf(204,negated_conjecture,
( ~ singletonP(esk9_0)
| ~ segmentP(esk12_0,esk9_0)
| ~ neq(esk12_0,nil) ),
inference(rw,[status(thm)],[185,184,theory(equality)]) ).
cnf(205,negated_conjecture,
( ~ singletonP(esk9_0)
| ~ segmentP(esk12_0,esk9_0)
| $false ),
inference(rw,[status(thm)],[204,194,theory(equality)]) ).
cnf(206,negated_conjecture,
( ~ singletonP(esk9_0)
| ~ segmentP(esk12_0,esk9_0) ),
inference(cn,[status(thm)],[205,theory(equality)]) ).
cnf(208,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(er,[status(thm)],[113,theory(equality)]) ).
cnf(215,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(er,[status(thm)],[47,theory(equality)]) ).
cnf(216,plain,
( app(X1,nil) = nil
| nil != X1
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[215,149,theory(equality)]) ).
cnf(217,plain,
( app(X1,nil) = nil
| nil != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[216,theory(equality)]) ).
cnf(218,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[144,theory(equality)]) ).
cnf(223,plain,
( hd(X1) = esk7_1(X1)
| ~ ssItem(esk7_1(X1))
| ~ ssList(nil)
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[87,111,theory(equality)]) ).
cnf(231,plain,
( hd(X1) = esk7_1(X1)
| ~ ssItem(esk7_1(X1))
| $false
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[223,149,theory(equality)]) ).
cnf(232,plain,
( hd(X1) = esk7_1(X1)
| ~ ssItem(esk7_1(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[231,theory(equality)]) ).
cnf(254,plain,
( hd(X1) = esk2_1(X1)
| nil = X1
| ~ ssItem(esk2_1(X1))
| ~ ssList(esk1_1(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[87,81,theory(equality)]) ).
cnf(264,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| nil = cons(X1,nil)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[39,57,theory(equality)]) ).
cnf(276,negated_conjecture,
( esk9_0 = X1
| hd(esk12_0) != X2
| cons(X2,nil) != X1
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ neq(nil,esk12_0)
| ~ neq(esk12_0,nil) ),
inference(rw,[status(thm)],[189,183,theory(equality)]) ).
cnf(277,negated_conjecture,
( esk9_0 = X1
| hd(esk12_0) != X2
| cons(X2,nil) != X1
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ neq(nil,esk12_0)
| $false ),
inference(rw,[status(thm)],[276,194,theory(equality)]) ).
cnf(278,negated_conjecture,
( esk9_0 = X1
| hd(esk12_0) != X2
| cons(X2,nil) != X1
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ neq(nil,esk12_0) ),
inference(cn,[status(thm)],[277,theory(equality)]) ).
cnf(279,negated_conjecture,
( esk9_0 = X1
| nil = esk12_0
| cons(X2,nil) != X1
| hd(esk12_0) != X2
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(esk12_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[278,143,theory(equality)]) ).
cnf(281,negated_conjecture,
( esk9_0 = X1
| nil = esk12_0
| cons(X2,nil) != X1
| hd(esk12_0) != X2
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(esk12_0)
| $false ),
inference(rw,[status(thm)],[279,149,theory(equality)]) ).
cnf(282,negated_conjecture,
( esk9_0 = X1
| nil = esk12_0
| cons(X2,nil) != X1
| hd(esk12_0) != X2
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(esk12_0) ),
inference(cn,[status(thm)],[281,theory(equality)]) ).
cnf(334,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[148,68,theory(equality)]) ).
cnf(336,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssItem(X1)
| ~ ssList(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[76,68,theory(equality)]) ).
cnf(349,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[164,160,theory(equality)]) ).
cnf(383,plain,
( segmentP(app(app(X1,nil),X2),nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[164,202,theory(equality)]) ).
cnf(391,plain,
( segmentP(app(app(X1,nil),X2),nil)
| ~ ssList(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[383,149,theory(equality)]) ).
cnf(392,plain,
( segmentP(app(app(X1,nil),X2),nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[391,theory(equality)]) ).
cnf(403,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[208,148,theory(equality)]) ).
cnf(405,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[403,149,theory(equality)]) ).
cnf(406,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[405,theory(equality)]) ).
cnf(407,plain,
( app(nil,nil) = nil
| ~ ssList(nil) ),
inference(er,[status(thm)],[217,theory(equality)]) ).
cnf(408,plain,
( app(nil,nil) = nil
| $false ),
inference(rw,[status(thm)],[407,149,theory(equality)]) ).
cnf(409,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[408,theory(equality)]) ).
cnf(413,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[336,72]) ).
cnf(431,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[68,409,theory(equality)]) ).
cnf(446,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[431,149,theory(equality)]) ).
cnf(447,plain,
( cons(X1,nil) = app(cons(X1,nil),nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[446,theory(equality)]) ).
cnf(451,plain,
( esk7_1(X1) = hd(X1)
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[232,112]) ).
cnf(452,plain,
( ssItem(hd(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[112,451,theory(equality)]) ).
cnf(453,plain,
( cons(hd(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[111,451,theory(equality)]) ).
cnf(499,plain,
( esk2_1(X1) = hd(X1)
| nil = X1
| ~ ssItem(esk2_1(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[254,83]) ).
cnf(500,plain,
( esk2_1(X1) = hd(X1)
| nil = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[499,82]) ).
cnf(502,plain,
( cons(hd(X1),esk1_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[81,500,theory(equality)]) ).
cnf(603,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[413,447,theory(equality)]) ).
cnf(627,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[603,149,theory(equality)]) ).
cnf(628,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[627,theory(equality)]) ).
cnf(697,plain,
( segmentP(app(X1,X2),nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[392,42,theory(equality)]) ).
cnf(734,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2) ),
inference(csr,[status(thm)],[264,628]) ).
cnf(735,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[734,148,theory(equality)]) ).
cnf(739,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[735,149,theory(equality)]) ).
cnf(740,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[739,theory(equality)]) ).
cnf(746,plain,
( hd(cons(X1,nil)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[87,740,theory(equality)]) ).
cnf(753,plain,
( ssItem(hd(cons(X1,X2)))
| ~ singletonP(cons(X1,nil))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[452,740,theory(equality)]) ).
cnf(826,plain,
( segmentP(cons(X1,X2),nil)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[697,57,theory(equality)]) ).
cnf(873,plain,
( segmentP(cons(X1,X2),nil)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[826,148,theory(equality)]) ).
cnf(877,plain,
( segmentP(cons(X1,X2),nil)
| ~ ssItem(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[873,149,theory(equality)]) ).
cnf(878,plain,
( segmentP(cons(X1,X2),nil)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[877,theory(equality)]) ).
cnf(1000,plain,
( ssItem(hd(cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2) ),
inference(csr,[status(thm)],[753,406]) ).
cnf(1001,plain,
( ssItem(hd(cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1000,148,theory(equality)]) ).
cnf(1005,plain,
( ssItem(hd(cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(X2)
| $false ),
inference(rw,[status(thm)],[1001,149,theory(equality)]) ).
cnf(1006,plain,
( ssItem(hd(cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[1005,theory(equality)]) ).
cnf(1109,negated_conjecture,
( esk9_0 = X1
| esk12_0 = nil
| cons(X2,nil) != X1
| hd(esk12_0) != X2
| ~ ssItem(X2)
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[282,193,theory(equality)]) ).
cnf(1110,negated_conjecture,
( esk9_0 = X1
| esk12_0 = nil
| cons(X2,nil) != X1
| hd(esk12_0) != X2
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1109,theory(equality)]) ).
cnf(1111,negated_conjecture,
( esk12_0 = nil
| esk9_0 = X1
| cons(hd(esk12_0),nil) != X1
| ~ ssItem(hd(esk12_0))
| ~ ssList(X1) ),
inference(er,[status(thm)],[1110,theory(equality)]) ).
cnf(1298,negated_conjecture,
( esk12_0 = nil
| esk9_0 = X1
| cons(hd(esk12_0),nil) != X1
| ~ ssList(X1)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[1111,90,theory(equality)]) ).
cnf(1300,negated_conjecture,
( esk12_0 = nil
| esk9_0 = X1
| cons(hd(esk12_0),nil) != X1
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[1298,193,theory(equality)]) ).
cnf(1301,negated_conjecture,
( esk12_0 = nil
| esk9_0 = X1
| cons(hd(esk12_0),nil) != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1300,theory(equality)]) ).
cnf(1304,negated_conjecture,
( esk12_0 = nil
| esk9_0 = cons(hd(esk12_0),nil)
| ~ ssList(cons(hd(esk12_0),nil)) ),
inference(er,[status(thm)],[1301,theory(equality)]) ).
cnf(1363,negated_conjecture,
( cons(hd(esk12_0),nil) = esk9_0
| esk12_0 = nil
| ~ ssItem(hd(esk12_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1304,148,theory(equality)]) ).
cnf(1365,negated_conjecture,
( cons(hd(esk12_0),nil) = esk9_0
| esk12_0 = nil
| ~ ssItem(hd(esk12_0))
| $false ),
inference(rw,[status(thm)],[1363,149,theory(equality)]) ).
cnf(1366,negated_conjecture,
( cons(hd(esk12_0),nil) = esk9_0
| esk12_0 = nil
| ~ ssItem(hd(esk12_0)) ),
inference(cn,[status(thm)],[1365,theory(equality)]) ).
cnf(1471,negated_conjecture,
( cons(hd(esk12_0),nil) = esk9_0
| esk12_0 = nil
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[1366,90,theory(equality)]) ).
cnf(1473,negated_conjecture,
( cons(hd(esk12_0),nil) = esk9_0
| esk12_0 = nil
| $false ),
inference(rw,[status(thm)],[1471,193,theory(equality)]) ).
cnf(1474,negated_conjecture,
( cons(hd(esk12_0),nil) = esk9_0
| esk12_0 = nil ),
inference(cn,[status(thm)],[1473,theory(equality)]) ).
cnf(1488,negated_conjecture,
( singletonP(esk9_0)
| esk12_0 = nil
| ~ ssItem(hd(esk12_0)) ),
inference(spm,[status(thm)],[406,1474,theory(equality)]) ).
cnf(1495,negated_conjecture,
( hd(esk9_0) = hd(cons(hd(esk12_0),nil))
| esk12_0 = nil
| ~ ssItem(hd(esk12_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[740,1474,theory(equality)]) ).
cnf(1497,negated_conjecture,
( hd(esk9_0) = hd(esk12_0)
| esk12_0 = nil
| ~ ssItem(hd(esk12_0))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[746,1474,theory(equality)]) ).
cnf(1499,negated_conjecture,
( segmentP(esk9_0,nil)
| esk12_0 = nil
| ~ ssItem(hd(esk12_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[878,1474,theory(equality)]) ).
cnf(1501,negated_conjecture,
( ssItem(hd(esk9_0))
| esk12_0 = nil
| ~ ssItem(hd(esk12_0))
| ~ ssList(nil) ),
inference(spm,[status(thm)],[1006,1474,theory(equality)]) ).
cnf(1536,negated_conjecture,
( hd(esk9_0) = hd(cons(hd(esk12_0),nil))
| esk12_0 = nil
| ~ ssItem(hd(esk12_0))
| $false ),
inference(rw,[status(thm)],[1495,149,theory(equality)]) ).
cnf(1537,negated_conjecture,
( hd(esk9_0) = hd(cons(hd(esk12_0),nil))
| esk12_0 = nil
| ~ ssItem(hd(esk12_0)) ),
inference(cn,[status(thm)],[1536,theory(equality)]) ).
cnf(1540,negated_conjecture,
( segmentP(esk9_0,nil)
| esk12_0 = nil
| ~ ssItem(hd(esk12_0))
| $false ),
inference(rw,[status(thm)],[1499,149,theory(equality)]) ).
cnf(1541,negated_conjecture,
( segmentP(esk9_0,nil)
| esk12_0 = nil
| ~ ssItem(hd(esk12_0)) ),
inference(cn,[status(thm)],[1540,theory(equality)]) ).
cnf(1544,negated_conjecture,
( ssItem(hd(esk9_0))
| esk12_0 = nil
| ~ ssItem(hd(esk12_0))
| $false ),
inference(rw,[status(thm)],[1501,149,theory(equality)]) ).
cnf(1545,negated_conjecture,
( ssItem(hd(esk9_0))
| esk12_0 = nil
| ~ ssItem(hd(esk12_0)) ),
inference(cn,[status(thm)],[1544,theory(equality)]) ).
cnf(1554,negated_conjecture,
( esk12_0 = nil
| singletonP(esk9_0)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[1488,90,theory(equality)]) ).
cnf(1556,negated_conjecture,
( esk12_0 = nil
| singletonP(esk9_0)
| $false ),
inference(rw,[status(thm)],[1554,193,theory(equality)]) ).
cnf(1557,negated_conjecture,
( esk12_0 = nil
| singletonP(esk9_0) ),
inference(cn,[status(thm)],[1556,theory(equality)]) ).
cnf(1560,negated_conjecture,
( esk12_0 = nil
| ~ segmentP(esk12_0,esk9_0) ),
inference(spm,[status(thm)],[206,1557,theory(equality)]) ).
cnf(1570,negated_conjecture,
( esk12_0 = nil
| ssItem(hd(esk9_0))
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[1545,90,theory(equality)]) ).
cnf(1572,negated_conjecture,
( esk12_0 = nil
| ssItem(hd(esk9_0))
| $false ),
inference(rw,[status(thm)],[1570,193,theory(equality)]) ).
cnf(1573,negated_conjecture,
( esk12_0 = nil
| ssItem(hd(esk9_0)) ),
inference(cn,[status(thm)],[1572,theory(equality)]) ).
cnf(1578,negated_conjecture,
( esk12_0 = nil
| segmentP(esk9_0,nil)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[1541,90,theory(equality)]) ).
cnf(1580,negated_conjecture,
( esk12_0 = nil
| segmentP(esk9_0,nil)
| $false ),
inference(rw,[status(thm)],[1578,193,theory(equality)]) ).
cnf(1581,negated_conjecture,
( esk12_0 = nil
| segmentP(esk9_0,nil) ),
inference(cn,[status(thm)],[1580,theory(equality)]) ).
cnf(1585,negated_conjecture,
( ssList(esk5_2(esk9_0,nil))
| esk12_0 = nil
| ~ ssList(nil)
| ~ ssList(esk9_0) ),
inference(spm,[status(thm)],[104,1581,theory(equality)]) ).
cnf(1593,negated_conjecture,
( ssList(esk5_2(esk9_0,nil))
| esk12_0 = nil
| $false
| ~ ssList(esk9_0) ),
inference(rw,[status(thm)],[1585,149,theory(equality)]) ).
cnf(1594,negated_conjecture,
( ssList(esk5_2(esk9_0,nil))
| esk12_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[1593,179,theory(equality)]) ).
cnf(1595,negated_conjecture,
( ssList(esk5_2(esk9_0,nil))
| esk12_0 = nil ),
inference(cn,[status(thm)],[1594,theory(equality)]) ).
cnf(1608,negated_conjecture,
( hd(esk9_0) = hd(esk12_0)
| esk12_0 = nil
| ~ ssList(X1)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[1497,90,theory(equality)]) ).
cnf(1610,negated_conjecture,
( hd(esk9_0) = hd(esk12_0)
| esk12_0 = nil
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[1608,193,theory(equality)]) ).
cnf(1611,negated_conjecture,
( hd(esk9_0) = hd(esk12_0)
| esk12_0 = nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[1610,theory(equality)]) ).
cnf(1624,negated_conjecture,
( esk12_0 = nil
| ssItem(hd(esk12_0))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[1573,1611,theory(equality)]) ).
cnf(1638,negated_conjecture,
( hd(esk9_0) = hd(esk12_0)
| esk12_0 = nil ),
inference(spm,[status(thm)],[1611,1595,theory(equality)]) ).
cnf(1639,negated_conjecture,
( esk12_0 = nil
| ssItem(hd(esk12_0)) ),
inference(spm,[status(thm)],[1624,1595,theory(equality)]) ).
cnf(1806,negated_conjecture,
( hd(cons(hd(esk12_0),nil)) = hd(esk9_0)
| esk12_0 = nil ),
inference(csr,[status(thm)],[1537,1639]) ).
cnf(1810,negated_conjecture,
( cons(hd(esk9_0),nil) = cons(hd(esk12_0),nil)
| esk12_0 = nil
| ~ singletonP(cons(hd(esk12_0),nil))
| ~ ssList(cons(hd(esk12_0),nil)) ),
inference(spm,[status(thm)],[453,1806,theory(equality)]) ).
cnf(2157,negated_conjecture,
( cons(hd(esk9_0),nil) = esk9_0
| esk12_0 = nil
| ~ singletonP(esk9_0)
| ~ ssList(esk9_0) ),
inference(spm,[status(thm)],[1810,1474,theory(equality)]) ).
cnf(2160,negated_conjecture,
( cons(hd(esk9_0),nil) = esk9_0
| esk12_0 = nil
| ~ singletonP(esk9_0)
| $false ),
inference(rw,[status(thm)],[2157,179,theory(equality)]) ).
cnf(2161,negated_conjecture,
( cons(hd(esk9_0),nil) = esk9_0
| esk12_0 = nil
| ~ singletonP(esk9_0) ),
inference(cn,[status(thm)],[2160,theory(equality)]) ).
cnf(2251,negated_conjecture,
( cons(hd(esk9_0),nil) = esk9_0
| esk12_0 = nil ),
inference(csr,[status(thm)],[2161,1557]) ).
cnf(2338,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[334,72]) ).
cnf(2346,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[2338,447,theory(equality)]) ).
cnf(2361,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1)
| $false ),
inference(rw,[status(thm)],[2346,149,theory(equality)]) ).
cnf(2362,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[2361,theory(equality)]) ).
cnf(3008,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[349,64,theory(equality)]) ).
cnf(3029,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[3008,149,theory(equality)]) ).
cnf(3030,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[3029,theory(equality)]) ).
cnf(4703,plain,
( segmentP(cons(X1,X2),cons(X1,nil))
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[3030,57,theory(equality)]) ).
cnf(221495,plain,
( segmentP(cons(X1,X2),cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[4703,2362]) ).
cnf(221515,negated_conjecture,
( segmentP(cons(hd(esk9_0),X1),esk9_0)
| esk12_0 = nil
| ~ ssItem(hd(esk9_0))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[221495,2251,theory(equality)]) ).
cnf(222123,negated_conjecture,
( esk12_0 = nil
| segmentP(cons(hd(esk9_0),X1),esk9_0)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[221515,1573]) ).
cnf(222132,negated_conjecture,
( esk12_0 = nil
| segmentP(cons(hd(esk12_0),X1),esk9_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[222123,1638,theory(equality)]) ).
cnf(222778,negated_conjecture,
( esk12_0 = nil
| segmentP(esk12_0,esk9_0)
| ~ ssList(esk1_1(esk12_0))
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[222132,502,theory(equality)]) ).
cnf(222821,negated_conjecture,
( esk12_0 = nil
| segmentP(esk12_0,esk9_0)
| ~ ssList(esk1_1(esk12_0))
| $false ),
inference(rw,[status(thm)],[222778,193,theory(equality)]) ).
cnf(222822,negated_conjecture,
( esk12_0 = nil
| segmentP(esk12_0,esk9_0)
| ~ ssList(esk1_1(esk12_0)) ),
inference(cn,[status(thm)],[222821,theory(equality)]) ).
cnf(223543,negated_conjecture,
( esk12_0 = nil
| ~ ssList(esk1_1(esk12_0)) ),
inference(csr,[status(thm)],[222822,1560]) ).
cnf(223544,negated_conjecture,
( esk12_0 = nil
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[223543,83,theory(equality)]) ).
cnf(223546,negated_conjecture,
( esk12_0 = nil
| $false ),
inference(rw,[status(thm)],[223544,193,theory(equality)]) ).
cnf(223547,negated_conjecture,
esk12_0 = nil,
inference(cn,[status(thm)],[223546,theory(equality)]) ).
cnf(223553,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[194,223547,theory(equality)]) ).
cnf(224431,negated_conjecture,
~ ssList(nil),
inference(spm,[status(thm)],[218,223553,theory(equality)]) ).
cnf(224433,negated_conjecture,
$false,
inference(rw,[status(thm)],[224431,149,theory(equality)]) ).
cnf(224434,negated_conjecture,
$false,
inference(cn,[status(thm)],[224433,theory(equality)]) ).
cnf(224435,negated_conjecture,
$false,
224434,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC382+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpGpnzs0/sel_SWC382+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC382+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC382+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC382+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
%
%------------------------------------------------------------------------------