TSTP Solution File: MSC007^1.003.004 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : MSC007^1.003.004 : TPTP v8.1.0. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 22:57:24 EDT 2022
% Result : Theorem 64.96s 64.78s
% Output : Proof 64.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 61
% Syntax : Number of formulae : 278 ( 71 unt; 0 typ; 0 def)
% Number of atoms : 3341 ( 784 equ; 0 cnn)
% Maximal formula atoms : 48 ( 12 avg)
% Number of connectives : 2196 ( 553 ~; 720 |; 70 &; 757 @)
% ( 0 <=>; 85 =>; 11 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 48 usr; 49 con; 0-2 aty)
% Number of variables : 49 ( 0 ^ 49 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(sharing_a_hole,conjecture,
~ ! [X1: pigeon,X2: pigeon] :
( ( ( pigeon_hole @ X1 )
= ( pigeon_hole @ X2 ) )
=> ( X1 = X2 ) ) ).
thf(h0,negated_conjecture,
! [X1: pigeon,X2: pigeon] :
( ( ( pigeon_hole @ X1 )
= ( pigeon_hole @ X2 ) )
=> ( X1 = X2 ) ),
inference(assume_negation,[status(cth)],[sharing_a_hole]) ).
thf(ax1619,axiom,
( ~ p8
| p21 ),
file('<stdin>',ax1619) ).
thf(pax958,axiom,
( p958
=> ( ~ ( ~ ( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
=> ( fhole1 = fhole3 ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
=> ( fhole2 = fhole3 ) ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
=> ( fhole3 = fhole3 ) ) )
=> ! [X1: hole] :
( ( ( fpigeon_hole @ fpigeon1 )
= X1 )
=> ( X1 = fhole3 ) ) ) ),
file('<stdin>',pax958) ).
thf(ax42,axiom,
( ~ p1
| p958 ),
file('<stdin>',ax42) ).
thf(ax420,axiom,
( ~ p1
| p580 ),
file('<stdin>',ax420) ).
thf(ax284,axiom,
( ~ p1
| p716 ),
file('<stdin>',ax284) ).
thf(ax148,axiom,
( ~ p1
| p852 ),
file('<stdin>',ax148) ).
thf(ax419,axiom,
( ~ p1
| p581 ),
file('<stdin>',ax419) ).
thf(ax283,axiom,
( ~ p1
| p717 ),
file('<stdin>',ax283) ).
thf(ax147,axiom,
( ~ p1
| p853 ),
file('<stdin>',ax147) ).
thf(ax1629,axiom,
( ~ p10
| p13 ),
file('<stdin>',ax1629) ).
thf(ax1538,axiom,
( ~ p21
| p65 ),
file('<stdin>',ax1538) ).
thf(ax1634,axiom,
p8,
file('<stdin>',ax1634) ).
thf(pax8,axiom,
( p8
=> ! [X3: pigeon,X4: pigeon] :
( ( ( fpigeon_hole @ X3 )
= ( fpigeon_hole @ X4 ) )
=> ( X3 = X4 ) ) ),
file('<stdin>',pax8) ).
thf(ax1641,axiom,
p1,
file('<stdin>',ax1641) ).
thf(pax580,axiom,
( p580
=> ( ~ ( ~ ( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
=> ( fhole1
!= ( fpigeon_hole @ fpigeon4 ) ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
=> ( fhole2
!= ( fpigeon_hole @ fpigeon4 ) ) ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
=> ( fhole3
!= ( fpigeon_hole @ fpigeon4 ) ) ) )
=> ! [X1: hole] :
( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
=> ( X1
!= ( fpigeon_hole @ fpigeon4 ) ) ) ) ),
file('<stdin>',pax580) ).
thf(pax716,axiom,
( p716
=> ( ~ ( ~ ( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
=> ( fhole1
!= ( fpigeon_hole @ fpigeon4 ) ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
=> ( fhole2
!= ( fpigeon_hole @ fpigeon4 ) ) ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
=> ( fhole3
!= ( fpigeon_hole @ fpigeon4 ) ) ) )
=> ! [X1: hole] :
( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
=> ( X1
!= ( fpigeon_hole @ fpigeon4 ) ) ) ) ),
file('<stdin>',pax716) ).
thf(pax852,axiom,
( p852
=> ( ~ ( ~ ( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
=> ( fhole1
!= ( fpigeon_hole @ fpigeon4 ) ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
=> ( fhole2
!= ( fpigeon_hole @ fpigeon4 ) ) ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
=> ( fhole3
!= ( fpigeon_hole @ fpigeon4 ) ) ) )
=> ! [X1: hole] :
( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
=> ( X1
!= ( fpigeon_hole @ fpigeon4 ) ) ) ) ),
file('<stdin>',pax852) ).
thf(ax418,axiom,
( ~ p1
| p582 ),
file('<stdin>',ax418) ).
thf(ax282,axiom,
( ~ p1
| p718 ),
file('<stdin>',ax282) ).
thf(ax146,axiom,
( ~ p1
| p854 ),
file('<stdin>',ax146) ).
thf(ax1539,axiom,
( ~ p21
| p64 ),
file('<stdin>',ax1539) ).
thf(pax581,axiom,
( p581
=> ( ~ ( ~ ( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
=> ( fhole1
!= ( fpigeon_hole @ fpigeon3 ) ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
=> ( fhole2
!= ( fpigeon_hole @ fpigeon3 ) ) ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
=> ( fhole3
!= ( fpigeon_hole @ fpigeon3 ) ) ) )
=> ! [X1: hole] :
( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
=> ( X1
!= ( fpigeon_hole @ fpigeon3 ) ) ) ) ),
file('<stdin>',pax581) ).
thf(pax717,axiom,
( p717
=> ( ~ ( ~ ( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
=> ( fhole1
!= ( fpigeon_hole @ fpigeon3 ) ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
=> ( fhole2
!= ( fpigeon_hole @ fpigeon3 ) ) ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
=> ( fhole3
!= ( fpigeon_hole @ fpigeon3 ) ) ) )
=> ! [X1: hole] :
( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
=> ( X1
!= ( fpigeon_hole @ fpigeon3 ) ) ) ) ),
file('<stdin>',pax717) ).
thf(pax853,axiom,
( p853
=> ( ~ ( ~ ( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
=> ( fhole1
!= ( fpigeon_hole @ fpigeon3 ) ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
=> ( fhole2
!= ( fpigeon_hole @ fpigeon3 ) ) ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
=> ( fhole3
!= ( fpigeon_hole @ fpigeon3 ) ) ) )
=> ! [X1: hole] :
( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
=> ( X1
!= ( fpigeon_hole @ fpigeon3 ) ) ) ) ),
file('<stdin>',pax853) ).
thf(ax1625,axiom,
( ~ p8
| p16 ),
file('<stdin>',ax1625) ).
thf(ax1628,axiom,
( ~ p13
| p14 ),
file('<stdin>',ax1628) ).
thf(ax1633,axiom,
p10,
file('<stdin>',ax1633) ).
thf(ax1537,axiom,
( ~ p65
| ~ p66
| p6 ),
file('<stdin>',ax1537) ).
thf(ax1636,axiom,
~ p6,
file('<stdin>',ax1636) ).
thf(nax5,axiom,
( p5
<= ( fpigeon1 = fpigeon4 ) ),
file('<stdin>',nax5) ).
thf(ax1637,axiom,
~ p5,
file('<stdin>',ax1637) ).
thf(pax582,axiom,
( p582
=> ( ~ ( ~ ( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
=> ( fhole1
!= ( fpigeon_hole @ fpigeon2 ) ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
=> ( fhole2
!= ( fpigeon_hole @ fpigeon2 ) ) ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
=> ( fhole3
!= ( fpigeon_hole @ fpigeon2 ) ) ) )
=> ! [X1: hole] :
( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
=> ( X1
!= ( fpigeon_hole @ fpigeon2 ) ) ) ) ),
file('<stdin>',pax582) ).
thf(pax718,axiom,
( p718
=> ( ~ ( ~ ( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
=> ( fhole1
!= ( fpigeon_hole @ fpigeon2 ) ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
=> ( fhole2
!= ( fpigeon_hole @ fpigeon2 ) ) ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
=> ( fhole3
!= ( fpigeon_hole @ fpigeon2 ) ) ) )
=> ! [X1: hole] :
( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
=> ( X1
!= ( fpigeon_hole @ fpigeon2 ) ) ) ) ),
file('<stdin>',pax718) ).
thf(pax854,axiom,
( p854
=> ( ~ ( ~ ( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
=> ( fhole1
!= ( fpigeon_hole @ fpigeon2 ) ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
=> ( fhole2
!= ( fpigeon_hole @ fpigeon2 ) ) ) )
=> ~ ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
=> ( fhole3
!= ( fpigeon_hole @ fpigeon2 ) ) ) )
=> ! [X1: hole] :
( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
=> ( X1
!= ( fpigeon_hole @ fpigeon2 ) ) ) ) ),
file('<stdin>',pax854) ).
thf(ax1523,axiom,
( ~ p64
| ~ p70
| p4 ),
file('<stdin>',ax1523) ).
thf(ax1638,axiom,
~ p4,
file('<stdin>',ax1638) ).
thf(nax3,axiom,
( p3
<= ( fpigeon1 = fpigeon3 ) ),
file('<stdin>',nax3) ).
thf(ax1639,axiom,
~ p3,
file('<stdin>',ax1639) ).
thf(ax1493,axiom,
( ~ p16
| p77 ),
file('<stdin>',ax1493) ).
thf(ax1627,axiom,
( ~ p14
| ~ p9
| p7 ),
file('<stdin>',ax1627) ).
thf(ax1635,axiom,
~ p7,
file('<stdin>',ax1635) ).
thf(nax66,axiom,
( p66
<= ( ( fpigeon_hole @ fpigeon2 )
= ( fpigeon_hole @ fpigeon4 ) ) ),
file('<stdin>',nax66) ).
thf(nax2,axiom,
( p2
<= ( fpigeon1 = fpigeon2 ) ),
file('<stdin>',nax2) ).
thf(ax1640,axiom,
~ p2,
file('<stdin>',ax1640) ).
thf(nax70,axiom,
( p70
<= ( ( fpigeon_hole @ fpigeon2 )
= ( fpigeon_hole @ fpigeon3 ) ) ),
file('<stdin>',nax70) ).
thf(ax1487,axiom,
( ~ p77
| ~ p80
| p9 ),
file('<stdin>',ax1487) ).
thf(ax1613,axiom,
( ~ p8
| p26 ),
file('<stdin>',ax1613) ).
thf(nax80,axiom,
( p80
<= ( ( fpigeon_hole @ fpigeon4 )
= ( fpigeon_hole @ fpigeon3 ) ) ),
file('<stdin>',nax80) ).
thf(ax1597,axiom,
( ~ p26
| p39 ),
file('<stdin>',ax1597) ).
thf(ax1598,axiom,
( ~ p26
| p38 ),
file('<stdin>',ax1598) ).
thf(ax1596,axiom,
( ~ p39
| ~ p40
| p5 ),
file('<stdin>',ax1596) ).
thf(nax6,axiom,
( p6
<= ( fpigeon2 = fpigeon4 ) ),
file('<stdin>',nax6) ).
thf(ax1577,axiom,
( ~ p38
| ~ p49
| p3 ),
file('<stdin>',ax1577) ).
thf(nax40,axiom,
( p40
<= ( ( fpigeon_hole @ fpigeon1 )
= ( fpigeon_hole @ fpigeon4 ) ) ),
file('<stdin>',nax40) ).
thf(nax4,axiom,
( p4
<= ( fpigeon2 = fpigeon3 ) ),
file('<stdin>',nax4) ).
thf(nax49,axiom,
( p49
<= ( ( fpigeon_hole @ fpigeon1 )
= ( fpigeon_hole @ fpigeon3 ) ) ),
file('<stdin>',nax49) ).
thf(ax1599,axiom,
( ~ p26
| p37 ),
file('<stdin>',ax1599) ).
thf(ax1561,axiom,
( ~ p37
| ~ p55
| p2 ),
file('<stdin>',ax1561) ).
thf(nax55,axiom,
( p55
<= ( ( fpigeon_hole @ fpigeon1 )
= ( fpigeon_hole @ fpigeon2 ) ) ),
file('<stdin>',nax55) ).
thf(c_0_59,plain,
( ~ p8
| p21 ),
inference(fof_simplification,[status(thm)],[ax1619]) ).
thf(c_0_60,plain,
! [X91: hole] :
( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= X91 )
| ( X91 = fhole3 )
| ~ p958 )
& ( ( fhole3 != fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= X91 )
| ( X91 = fhole3 )
| ~ p958 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( fhole2 != fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= X91 )
| ( X91 = fhole3 )
| ~ p958 )
& ( ( fhole3 != fhole3 )
| ( fhole2 != fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= X91 )
| ( X91 = fhole3 )
| ~ p958 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( fhole1 != fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
!= X91 )
| ( X91 = fhole3 )
| ~ p958 )
& ( ( fhole3 != fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( fhole1 != fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
!= X91 )
| ( X91 = fhole3 )
| ~ p958 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( fhole2 != fhole3 )
| ( fhole1 != fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
!= X91 )
| ( X91 = fhole3 )
| ~ p958 )
& ( ( fhole3 != fhole3 )
| ( fhole2 != fhole3 )
| ( fhole1 != fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
!= X91 )
| ( X91 = fhole3 )
| ~ p958 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax958])])])]) ).
thf(c_0_61,plain,
( ~ p1
| p958 ),
inference(fof_simplification,[status(thm)],[ax42]) ).
thf(c_0_62,plain,
( ~ p1
| p580 ),
inference(fof_simplification,[status(thm)],[ax420]) ).
thf(c_0_63,plain,
( ~ p1
| p716 ),
inference(fof_simplification,[status(thm)],[ax284]) ).
thf(c_0_64,plain,
( ~ p1
| p852 ),
inference(fof_simplification,[status(thm)],[ax148]) ).
thf(c_0_65,plain,
( ~ p1
| p581 ),
inference(fof_simplification,[status(thm)],[ax419]) ).
thf(c_0_66,plain,
( ~ p1
| p717 ),
inference(fof_simplification,[status(thm)],[ax283]) ).
thf(c_0_67,plain,
( ~ p1
| p853 ),
inference(fof_simplification,[status(thm)],[ax147]) ).
thf(c_0_68,plain,
( ~ p10
| p13 ),
inference(fof_simplification,[status(thm)],[ax1629]) ).
thf(c_0_69,plain,
( ~ p21
| p65 ),
inference(fof_simplification,[status(thm)],[ax1538]) ).
thf(c_0_70,plain,
( p21
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
thf(c_0_71,plain,
p8,
inference(split_conjunct,[status(thm)],[ax1634]) ).
thf(c_0_72,plain,
! [X565: pigeon,X566: pigeon] :
( ~ p8
| ( ( fpigeon_hole @ X565 )
!= ( fpigeon_hole @ X566 ) )
| ( X565 = X566 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax8])])]) ).
thf(c_0_73,plain,
! [X1: hole] :
( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( X1 = fhole3 )
| ( fhole3 != fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
!= X1 )
| ~ p958 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
thf(c_0_74,plain,
( p958
| ~ p1 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_75,plain,
p1,
inference(split_conjunct,[status(thm)],[ax1641]) ).
thf(c_0_76,plain,
! [X329: hole] :
( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X329
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p580 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X329
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p580 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( fhole2
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X329
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p580 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon4 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X329
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p580 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( fhole1
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X329
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p580 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( fhole1
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X329
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p580 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( fhole2
= ( fpigeon_hole @ fpigeon4 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X329
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p580 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon4 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon4 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X329
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p580 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax580])])])])]) ).
thf(c_0_77,plain,
( p580
| ~ p1 ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_78,plain,
! [X273: hole] :
( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X273
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p716 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X273
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p716 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( fhole2
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X273
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p716 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon4 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X273
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p716 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( fhole1
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X273
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p716 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( fhole1
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X273
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p716 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( fhole2
= ( fpigeon_hole @ fpigeon4 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X273
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p716 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon4 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon4 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X273
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p716 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax716])])])])]) ).
thf(c_0_79,plain,
( p716
| ~ p1 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_80,plain,
! [X217: hole] :
( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X217
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p852 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X217
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p852 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( fhole2
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X217
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p852 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon4 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X217
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p852 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( fhole1
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X217
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p852 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( fhole1
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X217
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p852 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( fhole2
= ( fpigeon_hole @ fpigeon4 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X217
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p852 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon4 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon4 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X217
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p852 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax852])])])])]) ).
thf(c_0_81,plain,
( p852
| ~ p1 ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
thf(c_0_82,plain,
( ~ p1
| p582 ),
inference(fof_simplification,[status(thm)],[ax418]) ).
thf(c_0_83,plain,
( ~ p1
| p718 ),
inference(fof_simplification,[status(thm)],[ax282]) ).
thf(c_0_84,plain,
( ~ p1
| p854 ),
inference(fof_simplification,[status(thm)],[ax146]) ).
thf(c_0_85,plain,
( ~ p21
| p64 ),
inference(fof_simplification,[status(thm)],[ax1539]) ).
thf(c_0_86,plain,
! [X327: hole] :
( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X327
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p581 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X327
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p581 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( fhole2
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X327
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p581 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon3 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X327
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p581 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( fhole1
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X327
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p581 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( fhole1
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X327
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p581 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( fhole2
= ( fpigeon_hole @ fpigeon3 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X327
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p581 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon3 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon3 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X327
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p581 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax581])])])])]) ).
thf(c_0_87,plain,
( p581
| ~ p1 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
thf(c_0_88,plain,
! [X271: hole] :
( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X271
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p717 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X271
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p717 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( fhole2
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X271
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p717 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon3 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X271
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p717 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( fhole1
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X271
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p717 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( fhole1
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X271
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p717 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( fhole2
= ( fpigeon_hole @ fpigeon3 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X271
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p717 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon3 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon3 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X271
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p717 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax717])])])])]) ).
thf(c_0_89,plain,
( p717
| ~ p1 ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
thf(c_0_90,plain,
! [X215: hole] :
( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X215
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p853 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X215
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p853 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( fhole2
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X215
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p853 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon3 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X215
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p853 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( fhole1
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X215
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p853 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( fhole1
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X215
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p853 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( fhole2
= ( fpigeon_hole @ fpigeon3 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X215
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p853 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon3 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon3 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X215
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p853 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax853])])])])]) ).
thf(c_0_91,plain,
( p853
| ~ p1 ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_92,plain,
( ~ p8
| p16 ),
inference(fof_simplification,[status(thm)],[ax1625]) ).
thf(c_0_93,plain,
( ~ p13
| p14 ),
inference(fof_simplification,[status(thm)],[ax1628]) ).
thf(c_0_94,plain,
( p13
| ~ p10 ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
thf(c_0_95,plain,
p10,
inference(split_conjunct,[status(thm)],[ax1633]) ).
thf(c_0_96,plain,
( ~ p65
| ~ p66
| p6 ),
inference(fof_simplification,[status(thm)],[ax1537]) ).
thf(c_0_97,plain,
( p65
| ~ p21 ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
thf(c_0_98,plain,
p21,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71])]) ).
thf(c_0_99,plain,
~ p6,
inference(fof_simplification,[status(thm)],[ax1636]) ).
thf(c_0_100,plain,
! [X3: pigeon,X4: pigeon] :
( ( X3 = X4 )
| ~ p8
| ( ( fpigeon_hole @ X3 )
!= ( fpigeon_hole @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
thf(c_0_101,plain,
! [X1: hole] :
( ( X1 = fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= X1 )
| ~ p958 ),
inference(cn,[status(thm)],[c_0_73]) ).
thf(c_0_102,plain,
p958,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).
thf(c_0_103,plain,
! [X1: hole] :
( ( fhole3
= ( fpigeon_hole @ fpigeon4 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon4 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X1
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p580 ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
thf(c_0_104,plain,
p580,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_75])]) ).
thf(c_0_105,plain,
! [X1: hole] :
( ( fhole3
= ( fpigeon_hole @ fpigeon4 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon4 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X1
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p716 ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
thf(c_0_106,plain,
p716,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_75])]) ).
thf(c_0_107,plain,
! [X1: hole] :
( ( fhole3
= ( fpigeon_hole @ fpigeon4 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon4 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon4 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X1
!= ( fpigeon_hole @ fpigeon4 ) )
| ~ p852 ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
thf(c_0_108,plain,
p852,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_75])]) ).
thf(c_0_109,plain,
( ( fpigeon1 != fpigeon4 )
| p5 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax5])]) ).
thf(c_0_110,plain,
~ p5,
inference(fof_simplification,[status(thm)],[ax1637]) ).
thf(c_0_111,plain,
! [X325: hole] :
( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X325
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p582 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X325
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p582 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( fhole2
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X325
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p582 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon2 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X325
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p582 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( fhole1
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X325
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p582 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( fhole1
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X325
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p582 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( fhole2
= ( fpigeon_hole @ fpigeon2 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X325
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p582 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon2 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon2 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X325
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p582 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax582])])])])]) ).
thf(c_0_112,plain,
( p582
| ~ p1 ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
thf(c_0_113,plain,
! [X269: hole] :
( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X269
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p718 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X269
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p718 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( fhole2
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X269
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p718 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon2 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X269
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p718 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( fhole1
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X269
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p718 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( fhole1
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X269
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p718 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( fhole2
= ( fpigeon_hole @ fpigeon2 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X269
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p718 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon2 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon2 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X269
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p718 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax718])])])])]) ).
thf(c_0_114,plain,
( p718
| ~ p1 ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
thf(c_0_115,plain,
! [X213: hole] :
( ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X213
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p854 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X213
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p854 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( fhole2
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X213
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p854 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon2 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X213
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p854 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( fhole1
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X213
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p854 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( fhole1
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X213
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p854 )
& ( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( fhole2
= ( fpigeon_hole @ fpigeon2 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X213
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p854 )
& ( ( fhole3
= ( fpigeon_hole @ fpigeon2 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon2 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X213
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p854 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax854])])])])]) ).
thf(c_0_116,plain,
( p854
| ~ p1 ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
thf(c_0_117,plain,
( ~ p64
| ~ p70
| p4 ),
inference(fof_simplification,[status(thm)],[ax1523]) ).
thf(c_0_118,plain,
( p64
| ~ p21 ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
thf(c_0_119,plain,
~ p4,
inference(fof_simplification,[status(thm)],[ax1638]) ).
thf(c_0_120,plain,
! [X1: hole] :
( ( fhole3
= ( fpigeon_hole @ fpigeon3 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon3 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X1
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p581 ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
thf(c_0_121,plain,
p581,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_75])]) ).
thf(c_0_122,plain,
! [X1: hole] :
( ( fhole3
= ( fpigeon_hole @ fpigeon3 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon3 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X1
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p717 ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
thf(c_0_123,plain,
p717,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_75])]) ).
thf(c_0_124,plain,
! [X1: hole] :
( ( fhole3
= ( fpigeon_hole @ fpigeon3 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon3 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon3 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X1
!= ( fpigeon_hole @ fpigeon3 ) )
| ~ p853 ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
thf(c_0_125,plain,
p853,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_75])]) ).
thf(c_0_126,plain,
( ( fpigeon1 != fpigeon3 )
| p3 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax3])]) ).
thf(c_0_127,plain,
~ p3,
inference(fof_simplification,[status(thm)],[ax1639]) ).
thf(c_0_128,plain,
( ~ p16
| p77 ),
inference(fof_simplification,[status(thm)],[ax1493]) ).
thf(c_0_129,plain,
( p16
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
thf(c_0_130,plain,
( ~ p14
| ~ p9
| p7 ),
inference(fof_simplification,[status(thm)],[ax1627]) ).
thf(c_0_131,plain,
( p14
| ~ p13 ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
thf(c_0_132,plain,
p13,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95])]) ).
thf(c_0_133,plain,
~ p7,
inference(fof_simplification,[status(thm)],[ax1635]) ).
thf(c_0_134,plain,
( ( ( fpigeon_hole @ fpigeon2 )
!= ( fpigeon_hole @ fpigeon4 ) )
| p66 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax66])]) ).
thf(c_0_135,plain,
( p6
| ~ p65
| ~ p66 ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
thf(c_0_136,plain,
p65,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98])]) ).
thf(c_0_137,plain,
~ p6,
inference(split_conjunct,[status(thm)],[c_0_99]) ).
thf(c_0_138,plain,
! [X3: pigeon,X4: pigeon] :
( ( X3 = X4 )
| ( ( fpigeon_hole @ X3 )
!= ( fpigeon_hole @ X4 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_71])]) ).
thf(c_0_139,plain,
( ( ( fpigeon_hole @ fpigeon1 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 ) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_102])])]) ).
thf(c_0_140,plain,
( ( ( fpigeon_hole @ fpigeon4 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 ) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_104])])]) ).
thf(c_0_141,plain,
( ( ( fpigeon_hole @ fpigeon4 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 ) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106])])]) ).
thf(c_0_142,plain,
( ( ( fpigeon_hole @ fpigeon4 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 ) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_108])])]) ).
thf(c_0_143,plain,
( p5
| ( fpigeon1 != fpigeon4 ) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
thf(c_0_144,plain,
~ p5,
inference(split_conjunct,[status(thm)],[c_0_110]) ).
thf(c_0_145,plain,
! [X1: hole] :
( ( fhole3
= ( fpigeon_hole @ fpigeon2 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon2 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 )
| ( X1
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p582 ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
thf(c_0_146,plain,
p582,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_75])]) ).
thf(c_0_147,plain,
! [X1: hole] :
( ( fhole3
= ( fpigeon_hole @ fpigeon2 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon2 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 )
| ( X1
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p718 ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
thf(c_0_148,plain,
p718,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_75])]) ).
thf(c_0_149,plain,
! [X1: hole] :
( ( fhole3
= ( fpigeon_hole @ fpigeon2 ) )
| ( fhole2
= ( fpigeon_hole @ fpigeon2 ) )
| ( fhole1
= ( fpigeon_hole @ fpigeon2 ) )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 )
| ( X1
!= ( fpigeon_hole @ fpigeon2 ) )
| ~ p854 ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
thf(c_0_150,plain,
p854,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_75])]) ).
thf(c_0_151,plain,
( ( fpigeon1 != fpigeon2 )
| p2 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax2])]) ).
thf(c_0_152,plain,
~ p2,
inference(fof_simplification,[status(thm)],[ax1640]) ).
thf(c_0_153,plain,
( ( ( fpigeon_hole @ fpigeon2 )
!= ( fpigeon_hole @ fpigeon3 ) )
| p70 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax70])]) ).
thf(c_0_154,plain,
( p4
| ~ p64
| ~ p70 ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
thf(c_0_155,plain,
p64,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_98])]) ).
thf(c_0_156,plain,
~ p4,
inference(split_conjunct,[status(thm)],[c_0_119]) ).
thf(c_0_157,plain,
( ( ( fpigeon_hole @ fpigeon3 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 ) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_121])])]) ).
thf(c_0_158,plain,
( ( ( fpigeon_hole @ fpigeon3 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 ) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_123])])]) ).
thf(c_0_159,plain,
( ( ( fpigeon_hole @ fpigeon3 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 ) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_125])])]) ).
thf(c_0_160,plain,
( p3
| ( fpigeon1 != fpigeon3 ) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
thf(c_0_161,plain,
~ p3,
inference(split_conjunct,[status(thm)],[c_0_127]) ).
thf(c_0_162,plain,
( ~ p77
| ~ p80
| p9 ),
inference(fof_simplification,[status(thm)],[ax1487]) ).
thf(c_0_163,plain,
( p77
| ~ p16 ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
thf(c_0_164,plain,
p16,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_71])]) ).
thf(c_0_165,plain,
( p7
| ~ p14
| ~ p9 ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
thf(c_0_166,plain,
p14,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_132])]) ).
thf(c_0_167,plain,
~ p7,
inference(split_conjunct,[status(thm)],[c_0_133]) ).
thf(c_0_168,plain,
( p66
| ( ( fpigeon_hole @ fpigeon2 )
!= ( fpigeon_hole @ fpigeon4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
thf(c_0_169,plain,
~ p66,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_135,c_0_136])]),c_0_137]) ).
thf(c_0_170,plain,
! [X3: pigeon] :
( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( fpigeon1 = X3 )
| ( ( fpigeon_hole @ X3 )
!= fhole3 ) ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
thf(c_0_171,plain,
( ( ( fpigeon_hole @ fpigeon4 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole1 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_139]),c_0_141]),c_0_142]) ).
thf(c_0_172,plain,
fpigeon4 != fpigeon1,
inference(sr,[status(thm)],[c_0_143,c_0_144]) ).
thf(c_0_173,plain,
( ( ( fpigeon_hole @ fpigeon2 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole3 ) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_145,c_0_146])])]) ).
thf(c_0_174,plain,
( ( ( fpigeon_hole @ fpigeon2 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 ) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_148])])]) ).
thf(c_0_175,plain,
( ( ( fpigeon_hole @ fpigeon2 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 ) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_150])])]) ).
thf(c_0_176,plain,
( p2
| ( fpigeon1 != fpigeon2 ) ),
inference(split_conjunct,[status(thm)],[c_0_151]) ).
thf(c_0_177,plain,
~ p2,
inference(split_conjunct,[status(thm)],[c_0_152]) ).
thf(c_0_178,plain,
( p70
| ( ( fpigeon_hole @ fpigeon2 )
!= ( fpigeon_hole @ fpigeon3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_153]) ).
thf(c_0_179,plain,
~ p70,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_154,c_0_155])]),c_0_156]) ).
thf(c_0_180,plain,
( ( ( fpigeon_hole @ fpigeon3 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole1 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_139]),c_0_158]),c_0_159]) ).
thf(c_0_181,plain,
fpigeon3 != fpigeon1,
inference(sr,[status(thm)],[c_0_160,c_0_161]) ).
thf(c_0_182,plain,
( ~ p8
| p26 ),
inference(fof_simplification,[status(thm)],[ax1613]) ).
thf(c_0_183,plain,
( ( ( fpigeon_hole @ fpigeon4 )
!= ( fpigeon_hole @ fpigeon3 ) )
| p80 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax80])]) ).
thf(c_0_184,plain,
( p9
| ~ p77
| ~ p80 ),
inference(split_conjunct,[status(thm)],[c_0_162]) ).
thf(c_0_185,plain,
p77,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_163,c_0_164])]) ).
thf(c_0_186,plain,
~ p9,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_165,c_0_166])]),c_0_167]) ).
thf(c_0_187,plain,
( fpigeon_hole @ fpigeon4 )
!= ( fpigeon_hole @ fpigeon2 ),
inference(sr,[status(thm)],[c_0_168,c_0_169]) ).
thf(c_0_188,plain,
( ( ( fpigeon_hole @ fpigeon4 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_172]) ).
thf(c_0_189,plain,
( ( ( fpigeon_hole @ fpigeon2 )
= fhole3 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole1 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_139]),c_0_174]),c_0_175]) ).
thf(c_0_190,plain,
fpigeon2 != fpigeon1,
inference(sr,[status(thm)],[c_0_176,c_0_177]) ).
thf(c_0_191,plain,
( fpigeon_hole @ fpigeon3 )
!= ( fpigeon_hole @ fpigeon2 ),
inference(sr,[status(thm)],[c_0_178,c_0_179]) ).
thf(c_0_192,plain,
( ( ( fpigeon_hole @ fpigeon3 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_180]),c_0_181]) ).
thf(c_0_193,plain,
( ~ p26
| p39 ),
inference(fof_simplification,[status(thm)],[ax1597]) ).
thf(c_0_194,plain,
( p26
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_182]) ).
thf(c_0_195,plain,
( p80
| ( ( fpigeon_hole @ fpigeon4 )
!= ( fpigeon_hole @ fpigeon3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_183]) ).
thf(c_0_196,plain,
~ p80,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_184,c_0_185])]),c_0_186]) ).
thf(c_0_197,plain,
( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon2 )
!= fhole2 ) ),
inference(spm,[status(thm)],[c_0_187,c_0_188]) ).
thf(c_0_198,plain,
( ( ( fpigeon_hole @ fpigeon2 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_189]),c_0_190]) ).
thf(c_0_199,plain,
( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon2 )
!= fhole2 ) ),
inference(spm,[status(thm)],[c_0_191,c_0_192]) ).
thf(c_0_200,plain,
( ~ p26
| p38 ),
inference(fof_simplification,[status(thm)],[ax1598]) ).
thf(c_0_201,plain,
( ~ p39
| ~ p40
| p5 ),
inference(fof_simplification,[status(thm)],[ax1596]) ).
thf(c_0_202,plain,
( p39
| ~ p26 ),
inference(split_conjunct,[status(thm)],[c_0_193]) ).
thf(c_0_203,plain,
p26,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_194,c_0_71])]) ).
thf(c_0_204,plain,
( fpigeon_hole @ fpigeon4 )
!= ( fpigeon_hole @ fpigeon3 ),
inference(sr,[status(thm)],[c_0_195,c_0_196]) ).
thf(c_0_205,plain,
( ( ( fpigeon_hole @ fpigeon2 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 ) ),
inference(spm,[status(thm)],[c_0_197,c_0_198]) ).
thf(c_0_206,plain,
( ( ( fpigeon_hole @ fpigeon2 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 ) ),
inference(spm,[status(thm)],[c_0_199,c_0_198]) ).
thf(c_0_207,plain,
( ( fpigeon2 != fpigeon4 )
| p6 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax6])]) ).
thf(c_0_208,plain,
( ~ p38
| ~ p49
| p3 ),
inference(fof_simplification,[status(thm)],[ax1577]) ).
thf(c_0_209,plain,
( p38
| ~ p26 ),
inference(split_conjunct,[status(thm)],[c_0_200]) ).
thf(c_0_210,plain,
( ( ( fpigeon_hole @ fpigeon4 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon2 )
!= fhole3 ) ),
inference(spm,[status(thm)],[c_0_187,c_0_171]) ).
thf(c_0_211,plain,
( ( ( fpigeon_hole @ fpigeon1 )
!= ( fpigeon_hole @ fpigeon4 ) )
| p40 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax40])]) ).
thf(c_0_212,plain,
( p5
| ~ p39
| ~ p40 ),
inference(split_conjunct,[status(thm)],[c_0_201]) ).
thf(c_0_213,plain,
p39,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_202,c_0_203])]) ).
thf(c_0_214,plain,
( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_205]),c_0_206]) ).
thf(c_0_215,plain,
( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon3 )
!= fhole2 ) ),
inference(spm,[status(thm)],[c_0_204,c_0_188]) ).
thf(c_0_216,plain,
( p6
| ( fpigeon2 != fpigeon4 ) ),
inference(split_conjunct,[status(thm)],[c_0_207]) ).
thf(c_0_217,plain,
( ( fpigeon2 != fpigeon3 )
| p4 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax4])]) ).
thf(c_0_218,plain,
( ( ( fpigeon_hole @ fpigeon1 )
!= ( fpigeon_hole @ fpigeon3 ) )
| p49 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax49])]) ).
thf(c_0_219,plain,
( p3
| ~ p38
| ~ p49 ),
inference(split_conjunct,[status(thm)],[c_0_208]) ).
thf(c_0_220,plain,
p38,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_209,c_0_203])]) ).
thf(c_0_221,plain,
( ( ( fpigeon_hole @ fpigeon2 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole1 ) ),
inference(spm,[status(thm)],[c_0_210,c_0_189]) ).
thf(c_0_222,plain,
( ( ( fpigeon_hole @ fpigeon3 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon2 )
!= fhole3 ) ),
inference(spm,[status(thm)],[c_0_191,c_0_180]) ).
thf(c_0_223,plain,
( p40
| ( ( fpigeon_hole @ fpigeon1 )
!= ( fpigeon_hole @ fpigeon4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_211]) ).
thf(c_0_224,plain,
~ p40,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_212,c_0_213])]),c_0_144]) ).
thf(c_0_225,plain,
! [X3: pigeon] :
( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( fpigeon2 = X3 )
| ( ( fpigeon_hole @ X3 )
!= fhole1 ) ),
inference(spm,[status(thm)],[c_0_138,c_0_214]) ).
thf(c_0_226,plain,
( ( ( fpigeon_hole @ fpigeon3 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 ) ),
inference(spm,[status(thm)],[c_0_215,c_0_192]) ).
thf(c_0_227,plain,
fpigeon4 != fpigeon2,
inference(sr,[status(thm)],[c_0_216,c_0_137]) ).
thf(c_0_228,plain,
( p4
| ( fpigeon2 != fpigeon3 ) ),
inference(split_conjunct,[status(thm)],[c_0_217]) ).
thf(c_0_229,plain,
( p49
| ( ( fpigeon_hole @ fpigeon1 )
!= ( fpigeon_hole @ fpigeon3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_218]) ).
thf(c_0_230,plain,
~ p49,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_219,c_0_220])]),c_0_161]) ).
thf(c_0_231,plain,
( ( ( fpigeon_hole @ fpigeon4 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon3 )
!= fhole2 ) ),
inference(spm,[status(thm)],[c_0_204,c_0_221]) ).
thf(c_0_232,plain,
( ( ( fpigeon_hole @ fpigeon2 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole1 ) ),
inference(spm,[status(thm)],[c_0_222,c_0_189]) ).
thf(c_0_233,plain,
( fpigeon_hole @ fpigeon4 )
!= ( fpigeon_hole @ fpigeon1 ),
inference(sr,[status(thm)],[c_0_223,c_0_224]) ).
thf(c_0_234,plain,
( ( ( fpigeon_hole @ fpigeon3 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_226]),c_0_227]) ).
thf(c_0_235,plain,
fpigeon3 != fpigeon2,
inference(sr,[status(thm)],[c_0_228,c_0_156]) ).
thf(c_0_236,plain,
( fpigeon_hole @ fpigeon3 )
!= ( fpigeon_hole @ fpigeon1 ),
inference(sr,[status(thm)],[c_0_229,c_0_230]) ).
thf(c_0_237,plain,
( ( ( fpigeon_hole @ fpigeon3 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole1 ) ),
inference(spm,[status(thm)],[c_0_231,c_0_232]) ).
thf(c_0_238,plain,
( ( ( fpigeon_hole @ fpigeon4 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon3 )
!= fhole3 ) ),
inference(spm,[status(thm)],[c_0_204,c_0_171]) ).
thf(c_0_239,plain,
( ( ( fpigeon_hole @ fpigeon4 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 ) ),
inference(spm,[status(thm)],[c_0_233,c_0_221]) ).
thf(c_0_240,plain,
( ( ( fpigeon_hole @ fpigeon1 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_234]),c_0_235]) ).
thf(c_0_241,plain,
( ( ( fpigeon_hole @ fpigeon3 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 ) ),
inference(spm,[status(thm)],[c_0_236,c_0_232]) ).
thf(c_0_242,plain,
( ( ( fpigeon_hole @ fpigeon2 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 ) ),
inference(spm,[status(thm)],[c_0_233,c_0_237]) ).
thf(c_0_243,plain,
( ( ( fpigeon_hole @ fpigeon3 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole1 ) ),
inference(spm,[status(thm)],[c_0_238,c_0_180]) ).
thf(c_0_244,plain,
( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole1 ) ),
inference(spm,[status(thm)],[c_0_239,c_0_240]) ).
thf(c_0_245,plain,
( ( ( fpigeon_hole @ fpigeon2 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_240]),c_0_242]) ).
thf(c_0_246,plain,
( ( ( fpigeon_hole @ fpigeon4 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole2 ) ),
inference(spm,[status(thm)],[c_0_233,c_0_243]) ).
thf(c_0_247,plain,
( ( ( fpigeon_hole @ fpigeon2 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon3 )
!= fhole1 ) ),
inference(spm,[status(thm)],[c_0_204,c_0_244]) ).
thf(c_0_248,plain,
( ( ( fpigeon_hole @ fpigeon2 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
!= fhole1 ) ),
inference(spm,[status(thm)],[c_0_236,c_0_245]) ).
thf(c_0_249,plain,
( ~ p26
| p37 ),
inference(fof_simplification,[status(thm)],[ax1599]) ).
thf(c_0_250,plain,
( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon4 )
= fhole1 ) ),
inference(spm,[status(thm)],[c_0_246,c_0_240]) ).
thf(c_0_251,plain,
! [X3: pigeon] :
( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( fpigeon1 = X3 )
| ( ( fpigeon_hole @ X3 )
!= fhole2 ) ),
inference(spm,[status(thm)],[c_0_138,c_0_240]) ).
thf(c_0_252,plain,
( ( ( fpigeon_hole @ fpigeon2 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon2 )
= fhole2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_245]),c_0_248]) ).
thf(c_0_253,plain,
( ~ p37
| ~ p55
| p2 ),
inference(fof_simplification,[status(thm)],[ax1561]) ).
thf(c_0_254,plain,
( p37
| ~ p26 ),
inference(split_conjunct,[status(thm)],[c_0_249]) ).
thf(c_0_255,plain,
( ( ( fpigeon_hole @ fpigeon3 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon2 )
!= fhole1 ) ),
inference(spm,[status(thm)],[c_0_187,c_0_250]) ).
thf(c_0_256,plain,
( ( ( fpigeon_hole @ fpigeon2 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_251,c_0_252]),c_0_190]) ).
thf(c_0_257,plain,
( ( ( fpigeon_hole @ fpigeon1 )
!= ( fpigeon_hole @ fpigeon2 ) )
| p55 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax55])]) ).
thf(c_0_258,plain,
( p2
| ~ p37
| ~ p55 ),
inference(split_conjunct,[status(thm)],[c_0_253]) ).
thf(c_0_259,plain,
p37,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_254,c_0_203])]) ).
thf(c_0_260,plain,
( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole2 ) ),
inference(spm,[status(thm)],[c_0_255,c_0_256]) ).
thf(c_0_261,plain,
( p55
| ( ( fpigeon_hole @ fpigeon1 )
!= ( fpigeon_hole @ fpigeon2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_257]) ).
thf(c_0_262,plain,
~ p55,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_258,c_0_259])]),c_0_177]) ).
thf(c_0_263,plain,
! [X3: pigeon] :
( ( ( fpigeon_hole @ fpigeon1 )
= fhole1 )
| ( fpigeon2 = X3 )
| ( ( fpigeon_hole @ X3 )
!= fhole1 ) ),
inference(spm,[status(thm)],[c_0_138,c_0_256]) ).
thf(c_0_264,plain,
( ( ( fpigeon_hole @ fpigeon3 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon1 )
= fhole1 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_251,c_0_260]),c_0_181]) ).
thf(c_0_265,plain,
( fpigeon_hole @ fpigeon2 )
!= ( fpigeon_hole @ fpigeon1 ),
inference(sr,[status(thm)],[c_0_261,c_0_262]) ).
thf(c_0_266,plain,
( ( fpigeon_hole @ fpigeon1 )
= fhole1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_263,c_0_264]),c_0_235]) ).
thf(c_0_267,plain,
( fpigeon_hole @ fpigeon2 )
!= fhole1,
inference(rw,[status(thm)],[c_0_265,c_0_266]) ).
thf(c_0_268,plain,
( ( ( fpigeon_hole @ fpigeon4 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole2 )
| ( ( fpigeon_hole @ fpigeon3 )
= fhole1 )
| ( ( fpigeon_hole @ fpigeon2 )
!= fhole2 ) ),
inference(spm,[status(thm)],[c_0_187,c_0_243]) ).
thf(c_0_269,plain,
( ( fpigeon_hole @ fpigeon2 )
= fhole2 ),
inference(sr,[status(thm)],[c_0_252,c_0_267]) ).
thf(c_0_270,plain,
( fpigeon_hole @ fpigeon4 )
!= fhole1,
inference(rw,[status(thm)],[c_0_233,c_0_266]) ).
thf(c_0_271,plain,
( fpigeon_hole @ fpigeon3 )
!= fhole1,
inference(rw,[status(thm)],[c_0_236,c_0_266]) ).
thf(c_0_272,plain,
( ( fpigeon_hole @ fpigeon3 )
= fhole2 ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_268,c_0_269])]),c_0_270]),c_0_271]) ).
thf(c_0_273,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_191,c_0_269]),c_0_272])]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
~ ! [X1: pigeon,X2: pigeon] :
( ( ( pigeon_hole @ X1 )
= ( pigeon_hole @ X2 ) )
=> ( X1 = X2 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MSC007^1.003.004 : TPTP v8.1.0. Released v5.4.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 1 15:56:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 64.96/64.78 % SZS status Theorem
% 64.96/64.78 % Mode: mode453
% 64.96/64.78 % Inferences: 937
% 64.96/64.78 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------