TSTP Solution File: LCL602^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL602^1 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n017.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 : Thu Aug 31 08:03:45 EDT 2023
% Result : Theorem 86.61s 86.94s
% Output : Proof 86.61s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__16,type,
eigen__16: $i ).
thf(ty_eigen__17,type,
eigen__17: $i ).
thf(ty_eigen__13,type,
eigen__13: $i ).
thf(ty_eigen__15,type,
eigen__15: $i ).
thf(ty_eigen__12,type,
eigen__12: $i > $o ).
thf(ty_eigen__10,type,
eigen__10: $i ).
thf(sP1,plain,
( sP1
<=> ( @+[X1: $i > $i > $o] :
( ( ! [X2: $i > $o] :
~ ( ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X2 @ X5 ) ) ) )
=> ~ ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) )
!= ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
@ eigen__1
@ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ! [X1: $i] :
( ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__1
@ X1 )
=> ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__0
@ X1 ) )
=> ! [X1: $i] :
( ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__1
@ X1 )
=> ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 )
=> ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ eigen__0
@ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__12 @ eigen__17 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__12 @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__2
@ X1 )
=> ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__0
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__0
@ X1 )
=> ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 )
=> ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ eigen__0
@ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__15
@ X1 )
=> ( eigen__12 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( @+[X1: $i > $i > $o] :
( ( ! [X2: $i > $o] :
~ ( ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X2 @ X5 ) ) ) )
=> ~ ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) )
!= ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
@ eigen__0
@ eigen__1 )
=> ! [X1: $i] :
( ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__1
@ X1 )
=> ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__0
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( @+[X1: $i > $i > $o] :
( ( ! [X2: $i > $o] :
~ ( ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X2 @ X5 ) ) ) )
=> ~ ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) )
!= ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
@ eigen__15
@ eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 )
=> ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ eigen__10
@ X2 ) )
=> ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__10
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ~ ( sP9
=> ~ ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__16
@ X1 ) )
=> ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__15
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( @+[X1: $i > $i > $o] :
( ( ! [X2: $i > $o] :
~ ( ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X2 @ X5 ) ) ) )
=> ~ ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) )
!= ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
@ eigen__16
@ eigen__17 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i] :
( ~ ( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ eigen__15
@ X1 )
=> ~ ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 ) )
=> ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ eigen__15
@ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( @+[X1: $i > $i > $o] :
( ( ! [X2: $i > $o] :
~ ( ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X2 @ X5 ) ) ) )
=> ~ ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) )
!= ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
@ eigen__15
@ eigen__17 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP14
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 )
=> ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ eigen__0
@ X2 ) )
=> ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__0
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( @+[X1: $i > $i > $o] :
( ( ! [X2: $i > $o] :
~ ( ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X2 @ X5 ) ) ) )
=> ~ ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) )
!= ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
@ eigen__0
@ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP9
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( @+[X1: $i > $i > $o] :
( ( ! [X2: $i > $o] :
~ ( ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X2 @ X5 ) ) ) )
=> ~ ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) )
!= ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
@ eigen__0
@ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__13
@ X1 )
=> ( eigen__12 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ! [X1: $i] :
( ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 )
=> ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ eigen__0
@ X2 ) )
=> ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 )
=> ! [X3: $i] :
( ( @+[X4: $i > $i > $o] :
( ( ! [X5: $i > $o] :
~ ( ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ( X5 @ X8 ) ) ) )
=> ~ ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) ) )
!= ( ~ ( ! [X5: $i] : ( X4 @ X5 @ X5 )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) ) ) )
@ X2
@ X3 )
=> ( @+[X4: $i > $i > $o] :
( ( ! [X5: $i > $o] :
~ ( ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ( X5 @ X8 ) ) ) )
=> ~ ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) ) )
!= ( ~ ( ! [X5: $i] : ( X4 @ X5 @ X5 )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) ) ) )
@ eigen__0
@ X3 ) ) ) )
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ sP18
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( @+[X1: $i > $i > $o] :
( ( ! [X2: $i > $o] :
~ ( ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X2 @ X5 ) ) ) )
=> ~ ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) )
!= ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
@ eigen__10
@ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
( ( ! [X5: $i > $o] :
~ ( ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ( X5 @ X8 ) ) ) )
=> ~ ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) ) )
!= ( ~ ( ! [X5: $i] : ( X4 @ X5 @ X5 )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) ) ) )
@ X1
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
( ( ! [X5: $i > $o] :
~ ( ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ( X5 @ X8 ) ) ) )
=> ~ ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) ) )
!= ( ~ ( ! [X5: $i] : ( X4 @ X5 @ X5 )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) ) ) )
@ X2
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
( ( ! [X5: $i > $o] :
~ ( ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ( X5 @ X8 ) ) ) )
=> ~ ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) ) )
!= ( ~ ( ! [X5: $i] : ( X4 @ X5 @ X5 )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) ) ) )
@ X1
@ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ X1
@ X1 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( @+[X1: $i > $i > $o] :
( ( ! [X2: $i > $o] :
~ ( ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X2 @ X5 ) ) ) )
=> ~ ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) )
!= ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
@ eigen__13
@ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP26
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP5
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP1
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i > $o] :
~ ( ! [X2: $i] :
( ! [X3: $i] :
( ( @+[X4: $i > $i > $o] :
( ( ! [X5: $i > $o] :
~ ( ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ( X5 @ X8 ) ) ) )
=> ~ ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) ) )
!= ( ~ ( ! [X5: $i] : ( X4 @ X5 @ X5 )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) ) ) )
@ X2
@ X3 )
=> ( X1 @ X3 ) )
=> ! [X3: $i] :
( ( @+[X4: $i > $i > $o] :
( ( ! [X5: $i > $o] :
~ ( ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ( X5 @ X8 ) ) ) )
=> ~ ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) ) )
!= ( ~ ( ! [X5: $i] : ( X4 @ X5 @ X5 )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) ) ) )
@ X2
@ X3 )
=> ! [X4: $i] :
( ( @+[X5: $i > $i > $o] :
( ( ! [X6: $i > $o] :
~ ( ! [X7: $i] :
( ! [X8: $i] :
( ( X5 @ X7 @ X8 )
=> ( X6 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X7 @ X8 )
=> ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ( X6 @ X9 ) ) ) )
=> ~ ! [X7: $i] :
( ! [X8: $i] :
( ( X5 @ X7 @ X8 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) ) )
!= ( ~ ( ! [X6: $i] : ( X5 @ X6 @ X6 )
=> ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) ) ) )
@ X3
@ X4 )
=> ( X1 @ X4 ) ) ) )
=> ~ ! [X2: $i] :
( ! [X3: $i] :
( ( @+[X4: $i > $i > $o] :
( ( ! [X5: $i > $o] :
~ ( ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ( X5 @ X8 ) ) ) )
=> ~ ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) ) )
!= ( ~ ( ! [X5: $i] : ( X4 @ X5 @ X5 )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) ) ) )
@ X2
@ X3 )
=> ( X1 @ X3 ) )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__1
@ X1 )
=> ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__0
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 )
=> ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ eigen__0
@ X2 ) )
=> ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 )
=> ! [X3: $i] :
( ( @+[X4: $i > $i > $o] :
( ( ! [X5: $i > $o] :
~ ( ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ( X5 @ X8 ) ) ) )
=> ~ ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) ) )
!= ( ~ ( ! [X5: $i] : ( X4 @ X5 @ X5 )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) ) ) )
@ X2
@ X3 )
=> ( @+[X4: $i > $i > $o] :
( ( ! [X5: $i > $o] :
~ ( ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ( X5 @ X8 ) ) ) )
=> ~ ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) ) )
!= ( ~ ( ! [X5: $i] : ( X4 @ X5 @ X5 )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) ) ) )
@ eigen__0
@ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__1
@ X1 )
=> ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 )
=> ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ eigen__0
@ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ! [X1: $i] :
( ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 )
=> ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ eigen__10
@ X2 ) )
=> ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 )
=> ! [X3: $i] :
( ( @+[X4: $i > $i > $o] :
( ( ! [X5: $i > $o] :
~ ( ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ( X5 @ X8 ) ) ) )
=> ~ ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) ) )
!= ( ~ ( ! [X5: $i] : ( X4 @ X5 @ X5 )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) ) ) )
@ X2
@ X3 )
=> ( @+[X4: $i > $i > $o] :
( ( ! [X5: $i > $o] :
~ ( ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ( X5 @ X8 ) ) ) )
=> ~ ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) ) )
!= ( ~ ( ! [X5: $i] : ( X4 @ X5 @ X5 )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) ) ) )
@ eigen__10
@ X3 ) ) ) )
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(def_mfalse,definition,
( mfalse
= ( ^ [X1: $i] : $false ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : $true ) ) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_mimpl,definition,
( mimpl
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_miff,definition,
( miff
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimpl @ X1 @ X2 ) @ ( mimpl @ X2 @ X1 ) ) ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X3 @ X4 )
@ ( X2 @ X4 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
? [X4: $i] :
( ( X1 @ X3 @ X4 )
& ( X2 @ X4 ) ) ) ) ).
thf(def_mall,definition,
( mall
= ( ^ [X1: individuals > $i > $o,X2: $i] :
! [X3: individuals] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists,definition,
( mexists
= ( ^ [X1: individuals > $i > $o,X2: $i] :
? [X3: individuals] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mvalid,definition,
( mvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_msatisfiable,definition,
( msatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_minvalid,definition,
( minvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_cartesian_product,definition,
( cartesian_product
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i,X4: $i] :
( ( X1 @ X3 )
& ( X2 @ X4 ) ) ) ) ).
thf(def_pair_rel,definition,
( pair_rel
= ( ^ [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = X1 )
| ( X4 = X2 ) ) ) ) ).
thf(def_id_rel,definition,
( id_rel
= ( ^ [X1: $i > $o,X2: $i,X3: $i] :
( ( X1 @ X2 )
& ( X2 = X3 ) ) ) ) ).
thf(def_sub_rel,definition,
( sub_rel
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X3 @ X4 )
@ ( X2 @ X3 @ X4 ) ) ) ) ).
thf(def_is_rel_on,definition,
( is_rel_on
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i > $o] :
! [X4: $i,X5: $i] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( X1 @ X4 @ X5 )
@ ( ( X2 @ X4 )
& ( X3 @ X5 ) ) ) ) ) ).
thf(def_restrict_rel_domain,definition,
( restrict_rel_domain
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 )
& ( X1 @ X3 @ X4 ) ) ) ) ).
thf(def_rel_diagonal,definition,
( rel_diagonal
= ( ^ [X1: $i,X2: $i] : ( X1 = X2 ) ) ) ).
thf(def_rel_composition,definition,
( rel_composition
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o,X3: $i,X4: $i] :
? [X5: $i] :
( ( X1 @ X3 @ X5 )
& ( X2 @ X5 @ X4 ) ) ) ) ).
thf(def_reflexive,definition,
( reflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_irreflexive,definition,
( irreflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 @ X2 ) ) ) ) ).
thf(def_symmetric,definition,
( symmetric
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X2 @ X3 )
@ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_transitive,definition,
( transitive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X3 @ X4 ) )
@ ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_equiv_rel,definition,
( equiv_rel
= ( ^ [X1: $i > $i > $o] :
( ( reflexive @ X1 )
& ( symmetric @ X1 )
& ( transitive @ X1 ) ) ) ) ).
thf(def_rel_codomain,definition,
( rel_codomain
= ( ^ [X1: $i > $i > $o,X2: $i] :
? [X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_rel_domain,definition,
( rel_domain
= ( ^ [X1: $i > $i > $o,X2: $i] :
? [X3: $i] : ( X1 @ X2 @ X3 ) ) ) ).
thf(def_rel_inverse,definition,
( rel_inverse
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_equiv_classes,definition,
( equiv_classes
= ( ^ [X1: $i > $i > $o,X2: $i > $o] :
? [X3: $i] :
( ( X2 @ X3 )
& ! [X4: $i] :
( ( X2 @ X4 )
<=> ( X1 @ X3 @ X4 ) ) ) ) ) ).
thf(def_restrict_rel_codomain,definition,
( restrict_rel_codomain
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i,X4: $i] :
( ( X2 @ X4 )
& ( X1 @ X3 @ X4 ) ) ) ) ).
thf(def_rel_field,definition,
( rel_field
= ( ^ [X1: $i > $i > $o,X2: $i] :
( ( rel_domain @ X1 @ X2 )
| ( rel_codomain @ X1 @ X2 ) ) ) ) ).
thf(def_well_founded,definition,
( well_founded
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X2 @ X3 )
@ ? [X4: $i] :
( ( X2 @ X4 )
& ! [X5: $i] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( X1 @ X4 @ X5 )
@ ( (~) @ ( X2 @ X5 ) ) ) ) ) ) ) ).
thf(def_upwards_well_founded,definition,
( upwards_well_founded
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X2 @ X3 )
@ ? [X4: $i] :
( ( X2 @ X4 )
& ! [X5: $i] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( X1 @ X4 @ X4 )
@ ( (~) @ ( X2 @ X5 ) ) ) ) ) ) ) ).
thf(thm,conjecture,
! [X1: $i > $i > $o] :
( ( ! [X2: $i > $o] :
~ ( ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X2 @ X5 ) ) ) )
=> ~ ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) )
= ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i > $o] :
( ( ! [X2: $i > $o] :
~ ( ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X2 @ X5 ) ) ) )
=> ~ ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) )
= ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
sP30,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP25
=> ~ sP24 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP30,
introduced(assumption,[]) ).
thf(h4,assumption,
( sP25
=> ~ sP24 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP25,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP24,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP23,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP10
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( sP34
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP30
| ~ sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h5,h1,h2,h0,h0])],[1,2,3,h1,h7]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h1,h2,h0,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__10)],[h5,4,h7]) ).
thf(h8,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ eigen__0
@ X1 )
=> ~ ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 ) )
=> ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ eigen__0
@ X2 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i] :
( ~ ( sP17
=> ~ ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__1
@ X1 ) )
=> ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__0
@ X1 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ~ ( sP17
=> ~ sP1 )
=> sP19 ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP17
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(h13,assumption,
sP17,
introduced(assumption,[]) ).
thf(h14,assumption,
sP1,
introduced(assumption,[]) ).
thf(6,plain,
( ~ sP29
| ~ sP1
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP33
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP8
| ~ sP17
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP28
| ~ sP5
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP2
| ~ sP31
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP6
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP16
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP32
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP32
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( sP21
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP21
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP30
| ~ sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h11,h12,h10,h9,h8,h6,h1,h2,h0,h0])],[6,7,8,9,10,11,12,13,14,15,16,17,h1,h13,h14,h12]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h10,h9,h8,h6,h1,h2,h0,h0]),tab_negimp(discharge,[h13,h14])],[h11,18,h13,h14]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h9,h8,h6,h1,h2,h0,h0]),tab_negimp(discharge,[h11,h12])],[h10,19,h11,h12]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h8,h6,h1,h2,h0,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__2)],[h9,20,h10]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h6,h1,h2,h0,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__1)],[h8,21,h9]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h1,h2,h0,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__0)],[h6,22,h8]) ).
thf(24,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h2,h0,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h2,5,23,h5,h6]) ).
thf(h15,assumption,
( ! [X1: $i] :
( ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 )
=> ( eigen__12 @ X2 ) )
=> ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 )
=> ! [X3: $i] :
( ( @+[X4: $i > $i > $o] :
( ( ! [X5: $i > $o] :
~ ( ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ( X5 @ X8 ) ) ) )
=> ~ ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) ) )
!= ( ~ ( ! [X5: $i] : ( X4 @ X5 @ X5 )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) ) ) )
@ X2
@ X3 )
=> ( eigen__12 @ X3 ) ) ) )
=> ~ ! [X1: $i] :
( ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 )
=> ( eigen__12 @ X2 ) )
=> ( eigen__12 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ! [X1: $i] :
( ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 )
=> ( eigen__12 @ X2 ) )
=> ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 )
=> ! [X3: $i] :
( ( @+[X4: $i > $i > $o] :
( ( ! [X5: $i > $o] :
~ ( ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ( X5 @ X8 ) ) ) )
=> ~ ! [X6: $i] :
( ! [X7: $i] :
( ( X4 @ X6 @ X7 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) ) )
!= ( ~ ( ! [X5: $i] : ( X4 @ X5 @ X5 )
=> ~ ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) ) ) )
@ X2
@ X3 )
=> ( eigen__12 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ! [X1: $i] :
( ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 )
=> ( eigen__12 @ X2 ) )
=> ( eigen__12 @ X1 ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( sP7
=> ! [X1: $i] :
( ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__15
@ X1 )
=> ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 )
=> ( eigen__12 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
sP7,
introduced(assumption,[]) ).
thf(h20,assumption,
~ ! [X1: $i] :
( ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__15
@ X1 )
=> ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
( ( ! [X4: $i > $o] :
~ ( ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ( X4 @ X7 ) ) ) )
=> ~ ! [X5: $i] :
( ! [X6: $i] :
( ( X3 @ X5 @ X6 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) ) )
!= ( ~ ( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ~ ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) ) ) )
@ X1
@ X2 )
=> ( eigen__12 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( sP9
=> ! [X1: $i] :
( ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__16
@ X1 )
=> ( eigen__12 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
sP9,
introduced(assumption,[]) ).
thf(h23,assumption,
~ ! [X1: $i] :
( ( @+[X2: $i > $i > $o] :
( ( ! [X3: $i > $o] :
~ ( ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ( X3 @ X6 ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( X2 @ X4 @ X5 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) ) )
!= ( ~ ( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ~ ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) ) ) )
@ eigen__16
@ X1 )
=> ( eigen__12 @ X1 ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
~ ( sP12
=> sP3 ),
introduced(assumption,[]) ).
thf(h25,assumption,
sP12,
introduced(assumption,[]) ).
thf(h26,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h27,assumption,
sP25,
introduced(assumption,[]) ).
thf(h28,assumption,
sP24,
introduced(assumption,[]) ).
thf(25,plain,
( ~ sP18
| ~ sP9
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP22
| sP18
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP11
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP15
| ~ sP14
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP13
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP7
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP24
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h27,h28,h25,h26,h24,h22,h23,h21,h19,h20,h18,h16,h15,h3,h4,h0,h0])],[25,26,27,28,29,30,31,h19,h22,h25,h26,h28]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h25,h26,h24,h22,h23,h21,h19,h20,h18,h16,h15,h3,h4,h0,h0]),tab_negimp(discharge,[h27,h28])],[h4,32,h27,h28]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h22,h23,h21,h19,h20,h18,h16,h15,h3,h4,h0,h0]),tab_negimp(discharge,[h25,h26])],[h24,33,h25,h26]) ).
thf(35,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h22,h23,h21,h19,h20,h18,h16,h15,h3,h4,h0,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__17)],[h23,34,h24]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h19,h20,h18,h16,h15,h3,h4,h0,h0]),tab_negimp(discharge,[h22,h23])],[h21,35,h22,h23]) ).
thf(37,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h19,h20,h18,h16,h15,h3,h4,h0,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__16)],[h20,36,h21]) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h16,h15,h3,h4,h0,h0]),tab_negimp(discharge,[h19,h20])],[h18,37,h19,h20]) ).
thf(39,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h15,h3,h4,h0,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__15)],[h16,38,h18]) ).
thf(h29,assumption,
~ ( sP20
=> sP4 ),
introduced(assumption,[]) ).
thf(h30,assumption,
sP20,
introduced(assumption,[]) ).
thf(h31,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(40,plain,
( ~ sP27
| ~ sP26
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP20
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP25
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(43,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h27,h28,h30,h31,h29,h17,h15,h3,h4,h0,h0])],[40,41,42,h30,h31,h27]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h30,h31,h29,h17,h15,h3,h4,h0,h0]),tab_negimp(discharge,[h27,h28])],[h4,43,h27,h28]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h29,h17,h15,h3,h4,h0,h0]),tab_negimp(discharge,[h30,h31])],[h29,44,h30,h31]) ).
thf(46,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h17,h15,h3,h4,h0,h0]),tab_negall(discharge,[h29]),tab_negall(eigenvar,eigen__13)],[h17,45,h29]) ).
thf(47,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h15,h3,h4,h0,h0]),tab_imp(discharge,[h16]),tab_imp(discharge,[h17])],[h15,39,46,h16,h17]) ).
thf(48,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h0,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__12)],[h3,47,h15]) ).
thf(49,plain,
$false,
inference(tab_be,[status(thm),assumptions([h0,h0]),tab_be(discharge,[h1,h2]),tab_be(discharge,[h3,h4])],[h0,24,48,h1,h2,h3,h4]) ).
thf(0,theorem,
! [X1: $i > $i > $o] :
( ( ! [X2: $i > $o] :
~ ( ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X2 @ X5 ) ) ) )
=> ~ ! [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) )
= ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[49,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL602^1 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 06:53:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 86.61/86.94 % SZS status Theorem
% 86.61/86.94 % Mode: cade22grackle2x4fb9
% 86.61/86.94 % Steps: 2796
% 86.61/86.94 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------