%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n031.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 : 300s
% DateTime : Tue May 5 07:03:10 PM UTC 2026
% Result : Theorem 22.13s 22.39s
% Output : Proof 22.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_d_unsorted,type,
d_unsorted: $tType ).
thf(ty_irel,type,
irel: $i > $i > $o ).
thf(ty_icountersatisfiable,type,
icountersatisfiable: ( $i > $o ) > $o ).
thf(ty_mbox_s4,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(ty_itrue,type,
itrue: $i > $o ).
thf(ty_mand,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_mimplies,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ty_ixor,type,
ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ty_isatisfiable,type,
isatisfiable: ( $i > $o ) > $o ).
thf(ty_ior,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ty_inot,type,
inot: ( $i > $o ) > $i > $o ).
thf(ty_ifalse,type,
ifalse: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_iinvalid,type,
iinvalid: ( $i > $o ) > $o ).
thf(ty_d_unsorted_0,type,
d_unsorted_0: d_unsorted ).
thf(ty_iequiv,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ty_mnot,type,
mnot: ( $i > $o ) > $i > $o ).
thf(ty_d2unsorted,type,
d2unsorted: d_unsorted > $i ).
thf(ty_iatom,type,
iatom: ( $i > $o ) > $i > $o ).
thf(ty_iand,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ty_iimplied,type,
iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ty_iimplies,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ty_mor,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_ivalid,type,
ivalid: ( $i > $o ) > $o ).
thf(sP1,plain,
( sP1
<=> ( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( mbox_s4 @ eigen__0 )
= ( ^ [X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( eigen__0 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( mbox_s4 @ eigen__0 @ X1 )
= ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( eigen__0 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( mor @ ( mbox_s4 @ eigen__0 ) @ ( mbox_s4 @ eigen__1 ) )
= ( ^ [X1: $i] :
( ~ ( mbox_s4 @ eigen__0 @ X1 )
=> ( mbox_s4 @ eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( mbox_s4 @ eigen__1 )
= ( ^ [X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( eigen__1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i > $o] :
( ( mor @ ( mbox_s4 @ eigen__0 ) @ X1 )
= ( ^ [X2: $i] :
( ~ ( mbox_s4 @ eigen__0 @ X2 )
=> ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i > $o] :
( ( mbox_s4 @ X1 )
= ( ^ [X2: $i] :
! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( mbox_s4 @ eigen__1 @ X1 )
= ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( eigen__1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( ior @ eigen__0 )
= ( ^ [X1: $i > $o,X2: $i] :
( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( eigen__0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( mbox_s4 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( mor @ ( mbox_s4 @ eigen__0 ) @ ( mbox_s4 @ eigen__1 ) @ X1 )
= ( ~ ( mbox_s4 @ eigen__0 @ X1 )
=> ( mbox_s4 @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i > $o] :
( ( ior @ eigen__0 @ X1 )
= ( ^ [X2: $i] :
( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( eigen__0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( mor @ ( mbox_s4 @ eigen__0 ) @ ( mbox_s4 @ eigen__1 ) @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i > $o] :
( ( mor @ X1 )
= ( ^ [X2: $i > $o,X3: $i] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( eigen__0 @ X1 ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( mbox_s4 @ eigen__0 @ eigen__2 )
= ( ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ ( mbox_s4 @ eigen__0 @ eigen__2 )
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ior
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ior @ eigen__0 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP11 = sP2 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
( ( ior @ eigen__0 @ eigen__1 @ X1 )
= ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( eigen__0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( eigen__1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( mbox_s4 @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP21 = sP14 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i > $o] :
( ( ior @ X1 )
= ( ^ [X2: $i > $o,X3: $i] :
( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( ior @ eigen__0 @ eigen__1 )
= ( ^ [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( eigen__0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( eigen__1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP14 = sP18 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( mor @ ( mbox_s4 @ eigen__0 ) )
= ( ^ [X1: $i > $o,X2: $i] :
( ~ ( mbox_s4 @ eigen__0 @ X2 )
=> ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP21 = sP16 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(ior,conjecture,
( ior
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(h0,negated_conjecture,
( ior
!= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ),
inference(assume_negation,[status(cth)],[ior]) ).
thf(h1,assumption,
~ ! [X1: $i > $o] :
( ( ior @ X1 )
= ( ^ [X2: $i > $o] : ( mor @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ( ior @ eigen__0 )
!= ( ^ [X1: $i > $o] : ( mor @ ( mbox_s4 @ eigen__0 ) @ ( mbox_s4 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i > $o] :
( ( ior @ eigen__0 @ X1 )
= ( mor @ ( mbox_s4 @ eigen__0 ) @ ( mbox_s4 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ( ior @ eigen__0 @ eigen__1 )
!= ( mor @ ( mbox_s4 @ eigen__0 ) @ ( mbox_s4 @ eigen__1 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ( ior @ eigen__0 @ eigen__1 @ X1 )
= ( mor @ ( mbox_s4 @ eigen__0 ) @ ( mbox_s4 @ eigen__1 ) @ X1 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP25,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ sP1 )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ~ sP19 )
=> ( iatom
!= ( ^ [X1: $i > $o] : X1 ) ) )
=> ( inot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) )
=> ( iand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ~ sP20 )
=> ( iimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ( iimplied
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ) )
=> ( iequiv
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X1 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ~ ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X2 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X1 @ X5 ) ) ) ) ) )
=> ( ixor
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ! [X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ( ~ ( ( irel @ X4 @ X5 )
=> ~ ! [X9: $i] :
( ( irel @ X5 @ X9 )
=> ( X1 @ X9 ) ) )
=> ~ ( irel @ X5 @ X6 ) )
=> ( X2 @ X6 ) )
=> ~ ( ~ ( ~ ( ( irel @ X4 @ X7 )
=> ~ ! [X9: $i] :
( ( irel @ X7 @ X9 )
=> ( X2 @ X9 ) ) )
=> ~ ( irel @ X7 @ X8 ) )
=> ( X1 @ X8 ) ) ) ) ) ) )
=> ( ivalid
!= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) )
=> ( isatisfiable
!= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ( icountersatisfiable
!= ( ^ [X1: $i > $o] :
~ ! [X2: $i] : ( X1 @ X2 ) ) ) )
=> ( iinvalid
!= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) )
=> ~ ( itrue @ ( d2unsorted @ d_unsorted_0 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ifalse @ ( d2unsorted @ d_unsorted_0 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ sP1 )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ~ sP19 )
=> ( iatom
!= ( ^ [X1: $i > $o] : X1 ) ) )
=> ( inot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) )
=> ( iand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ~ sP20 )
=> ( iimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ( iimplied
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ) )
=> ( iequiv
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X1 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ~ ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X2 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X1 @ X5 ) ) ) ) ) )
=> ( ixor
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ! [X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ( ~ ( ( irel @ X4 @ X5 )
=> ~ ! [X9: $i] :
( ( irel @ X5 @ X9 )
=> ( X1 @ X9 ) ) )
=> ~ ( irel @ X5 @ X6 ) )
=> ( X2 @ X6 ) )
=> ~ ( ~ ( ~ ( ( irel @ X4 @ X7 )
=> ~ ! [X9: $i] :
( ( irel @ X7 @ X9 )
=> ( X2 @ X9 ) ) )
=> ~ ( irel @ X7 @ X8 ) )
=> ( X1 @ X8 ) ) ) ) ) ) )
=> ( ivalid
!= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) )
=> ( isatisfiable
!= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ( icountersatisfiable
!= ( ^ [X1: $i > $o] :
~ ! [X2: $i] : ( X1 @ X2 ) ) ) )
=> ( iinvalid
!= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
itrue @ ( d2unsorted @ d_unsorted_0 ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ sP1 )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ~ sP19 )
=> ( iatom
!= ( ^ [X1: $i > $o] : X1 ) ) )
=> ( inot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) )
=> ( iand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ~ sP20 )
=> ( iimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ( iimplied
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ) )
=> ( iequiv
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X1 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ~ ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X2 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X1 @ X5 ) ) ) ) ) )
=> ( ixor
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ! [X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ( ~ ( ( irel @ X4 @ X5 )
=> ~ ! [X9: $i] :
( ( irel @ X5 @ X9 )
=> ( X1 @ X9 ) ) )
=> ~ ( irel @ X5 @ X6 ) )
=> ( X2 @ X6 ) )
=> ~ ( ~ ( ~ ( ( irel @ X4 @ X7 )
=> ~ ! [X9: $i] :
( ( irel @ X7 @ X9 )
=> ( X2 @ X9 ) ) )
=> ~ ( irel @ X7 @ X8 ) )
=> ( X1 @ X8 ) ) ) ) ) ) )
=> ( ivalid
!= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) )
=> ( isatisfiable
!= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ( icountersatisfiable
!= ( ^ [X1: $i > $o] :
~ ! [X2: $i] : ( X1 @ X2 ) ) ) )
=> ( iinvalid
!= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ sP1 )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ~ sP19 )
=> ( iatom
!= ( ^ [X1: $i > $o] : X1 ) ) )
=> ( inot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) )
=> ( iand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ~ sP20 )
=> ( iimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ( iimplied
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ) )
=> ( iequiv
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X1 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ~ ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X2 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X1 @ X5 ) ) ) ) ) )
=> ( ixor
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ! [X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ( ~ ( ( irel @ X4 @ X5 )
=> ~ ! [X9: $i] :
( ( irel @ X5 @ X9 )
=> ( X1 @ X9 ) ) )
=> ~ ( irel @ X5 @ X6 ) )
=> ( X2 @ X6 ) )
=> ~ ( ~ ( ~ ( ( irel @ X4 @ X7 )
=> ~ ! [X9: $i] :
( ( irel @ X7 @ X9 )
=> ( X2 @ X9 ) ) )
=> ~ ( irel @ X7 @ X8 ) )
=> ( X1 @ X8 ) ) ) ) ) ) )
=> ( ivalid
!= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) )
=> ( isatisfiable
!= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ( icountersatisfiable
!= ( ^ [X1: $i > $o] :
~ ! [X2: $i] : ( X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
( iinvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ sP1 )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ~ sP19 )
=> ( iatom
!= ( ^ [X1: $i > $o] : X1 ) ) )
=> ( inot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) )
=> ( iand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ~ sP20 )
=> ( iimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ( iimplied
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ) )
=> ( iequiv
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X1 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ~ ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X2 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X1 @ X5 ) ) ) ) ) )
=> ( ixor
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ! [X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ( ~ ( ( irel @ X4 @ X5 )
=> ~ ! [X9: $i] :
( ( irel @ X5 @ X9 )
=> ( X1 @ X9 ) ) )
=> ~ ( irel @ X5 @ X6 ) )
=> ( X2 @ X6 ) )
=> ~ ( ~ ( ~ ( ( irel @ X4 @ X7 )
=> ~ ! [X9: $i] :
( ( irel @ X7 @ X9 )
=> ( X2 @ X9 ) ) )
=> ~ ( irel @ X7 @ X8 ) )
=> ( X1 @ X8 ) ) ) ) ) ) )
=> ( ivalid
!= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) )
=> ( isatisfiable
!= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
( icountersatisfiable
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] : ( X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ sP1 )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ~ sP19 )
=> ( iatom
!= ( ^ [X1: $i > $o] : X1 ) ) )
=> ( inot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) )
=> ( iand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ~ sP20 )
=> ( iimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ( iimplied
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ) )
=> ( iequiv
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X1 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ~ ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X2 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X1 @ X5 ) ) ) ) ) )
=> ( ixor
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ! [X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ( ~ ( ( irel @ X4 @ X5 )
=> ~ ! [X9: $i] :
( ( irel @ X5 @ X9 )
=> ( X1 @ X9 ) ) )
=> ~ ( irel @ X5 @ X6 ) )
=> ( X2 @ X6 ) )
=> ~ ( ~ ( ~ ( ( irel @ X4 @ X7 )
=> ~ ! [X9: $i] :
( ( irel @ X7 @ X9 )
=> ( X2 @ X9 ) ) )
=> ~ ( irel @ X7 @ X8 ) )
=> ( X1 @ X8 ) ) ) ) ) ) )
=> ( ivalid
!= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
( isatisfiable
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ sP1 )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ~ sP19 )
=> ( iatom
!= ( ^ [X1: $i > $o] : X1 ) ) )
=> ( inot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) )
=> ( iand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ~ sP20 )
=> ( iimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ( iimplied
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ) )
=> ( iequiv
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X1 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ~ ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X2 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X1 @ X5 ) ) ) ) ) )
=> ( ixor
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ! [X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ( ~ ( ( irel @ X4 @ X5 )
=> ~ ! [X9: $i] :
( ( irel @ X5 @ X9 )
=> ( X1 @ X9 ) ) )
=> ~ ( irel @ X5 @ X6 ) )
=> ( X2 @ X6 ) )
=> ~ ( ~ ( ~ ( ( irel @ X4 @ X7 )
=> ~ ! [X9: $i] :
( ( irel @ X7 @ X9 )
=> ( X2 @ X9 ) ) )
=> ~ ( irel @ X7 @ X8 ) )
=> ( X1 @ X8 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
( ivalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ sP1 )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ~ sP19 )
=> ( iatom
!= ( ^ [X1: $i > $o] : X1 ) ) )
=> ( inot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) )
=> ( iand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ~ sP20 )
=> ( iimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ( iimplied
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ) )
=> ( iequiv
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X1 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ~ ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X2 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X1 @ X5 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
( ixor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ! [X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ( ~ ( ( irel @ X4 @ X5 )
=> ~ ! [X9: $i] :
( ( irel @ X5 @ X9 )
=> ( X1 @ X9 ) ) )
=> ~ ( irel @ X5 @ X6 ) )
=> ( X2 @ X6 ) )
=> ~ ( ~ ( ~ ( ( irel @ X4 @ X7 )
=> ~ ! [X9: $i] :
( ( irel @ X7 @ X9 )
=> ( X2 @ X9 ) ) )
=> ~ ( irel @ X7 @ X8 ) )
=> ( X1 @ X8 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ sP1 )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ~ sP19 )
=> ( iatom
!= ( ^ [X1: $i > $o] : X1 ) ) )
=> ( inot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) )
=> ( iand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ~ sP20 )
=> ( iimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ( iimplied
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
( iequiv
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X1 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ~ ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X2 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X1 @ X5 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ sP1 )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ~ sP19 )
=> ( iatom
!= ( ^ [X1: $i > $o] : X1 ) ) )
=> ( inot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) )
=> ( iand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ~ sP20 )
=> ( iimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h26,assumption,
( iimplied
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ sP1 )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ~ sP19 )
=> ( iatom
!= ( ^ [X1: $i > $o] : X1 ) ) )
=> ( inot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) )
=> ( iand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ~ sP20 ),
introduced(assumption,[]) ).
thf(h28,assumption,
( iimplies
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h29,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ sP1 )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ~ sP19 )
=> ( iatom
!= ( ^ [X1: $i > $o] : X1 ) ) )
=> ( inot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) )
=> ( iand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h30,assumption,
sP20,
introduced(assumption,[]) ).
thf(h31,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ sP1 )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ~ sP19 )
=> ( iatom
!= ( ^ [X1: $i > $o] : X1 ) ) )
=> ( inot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h32,assumption,
( iand
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h33,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ sP1 )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ~ sP19 )
=> ( iatom
!= ( ^ [X1: $i > $o] : X1 ) ) ),
introduced(assumption,[]) ).
thf(h34,assumption,
( inot
= ( ^ [X1: $i > $o,X2: $i] :
~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h35,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ sP1 )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ~ sP19 ),
introduced(assumption,[]) ).
thf(h36,assumption,
( iatom
= ( ^ [X1: $i > $o] : X1 ) ),
introduced(assumption,[]) ).
thf(h37,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ sP1 )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h38,assumption,
sP19,
introduced(assumption,[]) ).
thf(h39,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ sP1 )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h40,assumption,
( mimplies
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h41,assumption,
~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h42,assumption,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h43,assumption,
~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h44,assumption,
sP1,
introduced(assumption,[]) ).
thf(h45,assumption,
~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h46,assumption,
( mnot
= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h47,assumption,
~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) ),
introduced(assumption,[]) ).
thf(h48,assumption,
! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h49,assumption,
! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) ),
introduced(assumption,[]) ).
thf(h50,assumption,
! [X1: d_unsorted] : ( X1 = d_unsorted_0 ),
introduced(assumption,[]) ).
thf(1,plain,
( sP18
| ~ sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP18
| ~ sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP18
| sP24
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP16
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP16
| ~ sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP16
| sP31
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP28
| ~ sP14
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP28
| sP14
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP30
| ~ sP21
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP30
| sP21
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP12
| sP28 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP23
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP5
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP22
| ~ sP11
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP22
| sP11
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP17
| ~ sP24
| sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP17
| sP24
| ~ sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP27
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP7
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP9
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP4
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP13
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP29
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP6
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP3
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP10
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP15
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP8
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP8
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP26
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP1
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP19
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP20
| sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( sP25
| ~ sP21
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( sP25
| sP21
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,h44,h38,h30,h6]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h49,h50])],[h47,36,h49,h50]) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h47,h48])],[h45,37,h47,h48]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h45,h46])],[h43,38,h45,h46]) ).
thf(40,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h43,h44])],[h41,39,h43,h44]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h41,h42])],[h39,40,h41,h42]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h39,h40])],[h37,41,h39,h40]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h37,h38])],[h35,42,h37,h38]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h35,h36])],[h33,43,h35,h36]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h33,h34])],[h31,44,h33,h34]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h31,h32])],[h29,45,h31,h32]) ).
thf(47,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h29,h30])],[h27,46,h29,h30]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h27,h28])],[h25,47,h27,h28]) ).
thf(49,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h25,h26])],[h23,48,h25,h26]) ).
thf(50,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h23,h24])],[h21,49,h23,h24]) ).
thf(51,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h19,50,h21,h22]) ).
thf(52,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h17,51,h19,h20]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,52,h17,h18]) ).
thf(54,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h13,53,h15,h16]) ).
thf(55,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,54,h13,h14]) ).
thf(56,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,55,h11,h12]) ).
thf(57,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,56,h9,h10]) ).
thf(lcl696_1,axiom,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ sP1 )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ~ sP19 )
=> ( iatom
!= ( ^ [X1: $i > $o] : X1 ) ) )
=> ( inot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) )
=> ( iand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ~ sP20 )
=> ( iimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) )
=> ( iimplied
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ) )
=> ( iequiv
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X1 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ~ ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( irel @ X3 @ X4 )
=> ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( X2 @ X6 ) ) )
=> ~ ( irel @ X4 @ X5 ) )
=> ( X1 @ X5 ) ) ) ) ) )
=> ( ixor
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ! [X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ( ~ ( ( irel @ X4 @ X5 )
=> ~ ! [X9: $i] :
( ( irel @ X5 @ X9 )
=> ( X1 @ X9 ) ) )
=> ~ ( irel @ X5 @ X6 ) )
=> ( X2 @ X6 ) )
=> ~ ( ~ ( ~ ( ( irel @ X4 @ X7 )
=> ~ ! [X9: $i] :
( ( irel @ X7 @ X9 )
=> ( X2 @ X9 ) ) )
=> ~ ( irel @ X7 @ X8 ) )
=> ( X1 @ X8 ) ) ) ) ) ) )
=> ( ivalid
!= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) )
=> ( isatisfiable
!= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ( icountersatisfiable
!= ( ^ [X1: $i > $o] :
~ ! [X2: $i] : ( X1 @ X2 ) ) ) )
=> ( iinvalid
!= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ~ ( irel @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) )
=> ~ ( itrue @ ( d2unsorted @ d_unsorted_0 ) ) )
=> ( ifalse @ ( d2unsorted @ d_unsorted_0 ) ) ) ).
thf(58,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[lcl696_1,57,h7,h8]) ).
thf(59,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,58,h6]) ).
thf(60,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_fe(discharge,[h5])],[h4,59,h5]) ).
thf(61,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,60,h4]) ).
thf(62,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h2,h1,h0]),tab_fe(discharge,[h3])],[h2,61,h3]) ).
thf(63,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,62,h2]) ).
thf(64,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h0]),tab_fe(discharge,[h1])],[h0,63,h1]) ).
thf(0,theorem,
( ior
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[64,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.16/0.33 % Computer : n031.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 09:23:08 EDT 2026
% 0.16/0.33 % CPUTime :
% 22.13/22.39 % SZS status Theorem
% 22.13/22.39 % Mode: cade22grackle2x798d
% 22.13/22.39 % Steps: 17689
% 22.13/22.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------