TSTP Solution File: SEV006^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV006^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n003.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 19:32:18 EDT 2023
% Result : Theorem 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: a > a > a ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__8,type,
eigen__8: a ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(ty_eigen__7,type,
eigen__7: a ).
thf(ty_eigen__9,type,
eigen__9: a ).
thf(ty_eigen__1,type,
eigen__1: a > a > a ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( eigen__1 @ eigen__7 @ eigen__7 )
= eigen__7 )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( eigen__1 @ eigen__7 @ eigen__7 )
= eigen__7 )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ X1 )
!= X1 ) )
=> ( ( eigen__0 @ eigen__7 @ X1 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ X1 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ X1 )
!= X1 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ X1 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ X1 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ X1 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ X1 @ eigen__7 )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( eigen__1 @ eigen__7 @ eigen__7 )
= eigen__7 )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ sP2
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ sP5
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( eigen__1 @ eigen__7 @ eigen__7 )
= eigen__7 )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ X1 )
!= X1 ) )
=> ( ( eigen__0 @ eigen__7 @ X1 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ X2 )
!= X2 ) )
=> ( ( eigen__0 @ eigen__7 @ X2 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ X3 )
!= X3 ) )
=> ( ( eigen__0 @ eigen__7 @ X3 )
!= eigen__7 ) )
=> ( ( eigen__1 @ X1 @ X2 )
!= eigen__7 ) )
=> ( ( eigen__0 @ X1 @ X2 )
!= eigen__7 ) )
=> ( ( eigen__1 @ X1 @ X3 )
!= X1 ) )
=> ( ( eigen__0 @ X1 @ X3 )
!= X3 ) )
=> ( ( eigen__1 @ X1 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ X1 @ eigen__7 )
!= X1 ) )
=> ( ( eigen__1 @ X2 @ X3 )
!= eigen__7 ) )
=> ( ( eigen__0 @ X2 @ X3 )
!= eigen__7 ) )
=> ( ( eigen__1 @ X2 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ X2 @ eigen__7 )
!= X2 ) )
=> ( ( eigen__1 @ X3 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ X3 @ eigen__7 )
!= X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( ~ sP4
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( eigen__1 @ eigen__7 @ eigen__7 )
= eigen__7 )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( eigen__1 @ eigen__7 @ eigen__7 )
= eigen__7 )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( ~ ( ~ ( ~ ( ~ sP10
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ( eigen__1 @ eigen__7 @ eigen__7 )
= eigen__7 )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a,X2: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ sP12
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ X1 )
!= X1 ) )
=> ( ( eigen__0 @ eigen__7 @ X1 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ X2 )
!= X2 ) )
=> ( ( eigen__0 @ eigen__7 @ X2 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ X1 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ X1 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ X2 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ X2 )
!= X2 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ X1 @ X2 )
!= eigen__7 ) )
=> ( ( eigen__0 @ X1 @ X2 )
!= eigen__7 ) )
=> ( ( eigen__1 @ X1 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ X1 @ eigen__7 )
!= X1 ) )
=> ( ( eigen__1 @ X2 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ X2 @ eigen__7 )
!= X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ ( ~ ( ~ sP12
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ sP6
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ ( ~ sP10
=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ sP12
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: a,X2: a,X3: a,X4: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( eigen__1 @ eigen__7 @ X1 )
= X1 )
=> ( ( eigen__0 @ eigen__7 @ X1 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ X2 )
!= X2 ) )
=> ( ( eigen__0 @ eigen__7 @ X2 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ X3 )
!= X3 ) )
=> ( ( eigen__0 @ eigen__7 @ X3 )
!= eigen__7 ) )
=> ( ( eigen__1 @ eigen__7 @ X4 )
!= X4 ) )
=> ( ( eigen__0 @ eigen__7 @ X4 )
!= eigen__7 ) )
=> ( ( eigen__1 @ X2 @ X3 )
!= X1 ) )
=> ( ( eigen__0 @ X2 @ X3 )
!= eigen__7 ) )
=> ( ( eigen__1 @ X2 @ X4 )
!= X2 ) )
=> ( ( eigen__0 @ X2 @ X4 )
!= X4 ) )
=> ( ( eigen__1 @ X2 @ X1 )
!= X1 ) )
=> ( ( eigen__0 @ X2 @ X1 )
!= X2 ) )
=> ( ( eigen__1 @ X3 @ X4 )
!= X1 ) )
=> ( ( eigen__0 @ X3 @ X4 )
!= eigen__7 ) )
=> ( ( eigen__1 @ X3 @ X1 )
!= X1 ) )
=> ( ( eigen__0 @ X3 @ X1 )
!= X3 ) )
=> ( ( eigen__1 @ X4 @ X1 )
!= X1 ) )
=> ( ( eigen__0 @ X4 @ X1 )
!= X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( eigen__0 @ eigen__7 @ eigen__7 )
= eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a,X2: a,X3: a,X4: a,X5: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( eigen__1 @ X1 @ X2 )
= X2 )
=> ( ( eigen__0 @ X1 @ X2 )
!= X1 ) )
=> ( ( eigen__1 @ X1 @ X3 )
!= X3 ) )
=> ( ( eigen__0 @ X1 @ X3 )
!= X1 ) )
=> ( ( eigen__1 @ X1 @ X4 )
!= X4 ) )
=> ( ( eigen__0 @ X1 @ X4 )
!= X1 ) )
=> ( ( eigen__1 @ X1 @ X5 )
!= X5 ) )
=> ( ( eigen__0 @ X1 @ X5 )
!= X1 ) )
=> ( ( eigen__1 @ X3 @ X4 )
!= X2 ) )
=> ( ( eigen__0 @ X3 @ X4 )
!= X1 ) )
=> ( ( eigen__1 @ X3 @ X5 )
!= X3 ) )
=> ( ( eigen__0 @ X3 @ X5 )
!= X5 ) )
=> ( ( eigen__1 @ X3 @ X2 )
!= X2 ) )
=> ( ( eigen__0 @ X3 @ X2 )
!= X3 ) )
=> ( ( eigen__1 @ X4 @ X5 )
!= X2 ) )
=> ( ( eigen__0 @ X4 @ X5 )
!= X1 ) )
=> ( ( eigen__1 @ X4 @ X2 )
!= X2 ) )
=> ( ( eigen__0 @ X4 @ X2 )
!= X4 ) )
=> ( ( eigen__1 @ X5 @ X2 )
!= X2 ) )
=> ( ( eigen__0 @ X5 @ X2 )
!= X5 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ sP4
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ sP14
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ sP18
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ ( ~ sP17
=> ~ sP20 )
=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
!= eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ~ sP10
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( eigen__1 @ eigen__7 @ eigen__7 )
= eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ sP17
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(cPENTAGON_THM2D_pme,conjecture,
! [X1: a > a > a,X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: a] :
( ( X1 @ X3 @ X3 )
= X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 @ X3 )
= X3 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ X3 @ ( X2 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
= ( X1 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ X3 @ X4 )
= ( X2 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ ( X2 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( X1 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ! [X3: a,X4: a,X5: a,X6: a,X7: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X5 != X6 )
=> ( X5 = X7 ) )
=> ( X5 = X3 ) )
=> ( X5 = X4 ) )
=> ( X6 = X7 ) )
=> ( X6 = X3 ) )
=> ( X6 = X4 ) )
=> ( X7 = X3 ) )
=> ( X7 = X4 ) )
=> ( X3 = X4 ) ) )
=> ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ ( X1 @ X3 @ X5 ) ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a,X6: a,X7: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( X2 @ X3 @ X4 )
= X4 )
=> ( ( X1 @ X3 @ X4 )
!= X3 ) )
=> ( ( X2 @ X3 @ X5 )
!= X5 ) )
=> ( ( X1 @ X3 @ X5 )
!= X3 ) )
=> ( ( X2 @ X3 @ X6 )
!= X6 ) )
=> ( ( X1 @ X3 @ X6 )
!= X3 ) )
=> ( ( X2 @ X3 @ X7 )
!= X7 ) )
=> ( ( X1 @ X3 @ X7 )
!= X3 ) )
=> ( ( X2 @ X5 @ X6 )
!= X4 ) )
=> ( ( X1 @ X5 @ X6 )
!= X3 ) )
=> ( ( X2 @ X5 @ X7 )
!= X5 ) )
=> ( ( X1 @ X5 @ X7 )
!= X7 ) )
=> ( ( X2 @ X5 @ X4 )
!= X4 ) )
=> ( ( X1 @ X5 @ X4 )
!= X5 ) )
=> ( ( X2 @ X6 @ X7 )
!= X4 ) )
=> ( ( X1 @ X6 @ X7 )
!= X3 ) )
=> ( ( X2 @ X6 @ X4 )
!= X4 ) )
=> ( ( X1 @ X6 @ X4 )
!= X6 ) )
=> ( ( X2 @ X7 @ X4 )
!= X4 ) )
=> ( ( X1 @ X7 @ X4 )
!= X7 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > a > a,X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: a] :
( ( X1 @ X3 @ X3 )
= X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 @ X3 )
= X3 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ X3 @ ( X2 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
= ( X1 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ X3 @ X4 )
= ( X2 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ ( X2 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( X1 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ! [X3: a,X4: a,X5: a,X6: a,X7: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X5 != X6 )
=> ( X5 = X7 ) )
=> ( X5 = X3 ) )
=> ( X5 = X4 ) )
=> ( X6 = X7 ) )
=> ( X6 = X3 ) )
=> ( X6 = X4 ) )
=> ( X7 = X3 ) )
=> ( X7 = X4 ) )
=> ( X3 = X4 ) ) )
=> ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ ( X1 @ X3 @ X5 ) ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a,X6: a,X7: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( X2 @ X3 @ X4 )
= X4 )
=> ( ( X1 @ X3 @ X4 )
!= X3 ) )
=> ( ( X2 @ X3 @ X5 )
!= X5 ) )
=> ( ( X1 @ X3 @ X5 )
!= X3 ) )
=> ( ( X2 @ X3 @ X6 )
!= X6 ) )
=> ( ( X1 @ X3 @ X6 )
!= X3 ) )
=> ( ( X2 @ X3 @ X7 )
!= X7 ) )
=> ( ( X1 @ X3 @ X7 )
!= X3 ) )
=> ( ( X2 @ X5 @ X6 )
!= X4 ) )
=> ( ( X1 @ X5 @ X6 )
!= X3 ) )
=> ( ( X2 @ X5 @ X7 )
!= X5 ) )
=> ( ( X1 @ X5 @ X7 )
!= X7 ) )
=> ( ( X2 @ X5 @ X4 )
!= X4 ) )
=> ( ( X1 @ X5 @ X4 )
!= X5 ) )
=> ( ( X2 @ X6 @ X7 )
!= X4 ) )
=> ( ( X1 @ X6 @ X7 )
!= X3 ) )
=> ( ( X2 @ X6 @ X4 )
!= X4 ) )
=> ( ( X1 @ X6 @ X4 )
!= X6 ) )
=> ( ( X2 @ X7 @ X4 )
!= X4 ) )
=> ( ( X1 @ X7 @ X4 )
!= X7 ) ) ),
inference(assume_negation,[status(cth)],[cPENTAGON_THM2D_pme]) ).
thf(h1,assumption,
~ ! [X1: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP1
=> ~ ! [X2: a] :
( ( X1 @ X2 @ X2 )
= X2 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ( eigen__0 @ ( eigen__0 @ X2 @ X3 ) @ X4 )
= ( eigen__0 @ X2 @ ( eigen__0 @ X3 @ X4 ) ) ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ( X1 @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ X2 @ ( X1 @ X3 @ X4 ) ) ) )
=> ~ ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
= ( eigen__0 @ X3 @ X2 ) ) )
=> ~ ! [X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
= ( X1 @ X3 @ X2 ) ) )
=> ~ ! [X2: a,X3: a] :
( ( eigen__0 @ ( X1 @ X2 @ X3 ) @ X3 )
= X3 ) )
=> ~ ! [X2: a,X3: a] :
( ( X1 @ ( eigen__0 @ X2 @ X3 ) @ X3 )
= X3 ) )
=> ! [X2: a,X3: a,X4: a,X5: a,X6: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X4 != X5 )
=> ( X4 = X6 ) )
=> ( X4 = X2 ) )
=> ( X4 = X3 ) )
=> ( X5 = X6 ) )
=> ( X5 = X2 ) )
=> ( X5 = X3 ) )
=> ( X6 = X2 ) )
=> ( X6 = X3 ) )
=> ( X2 = X3 ) ) )
=> ! [X2: a,X3: a,X4: a] :
( ( eigen__0 @ X2 @ ( X1 @ X3 @ ( eigen__0 @ X2 @ X4 ) ) )
= ( X1 @ ( eigen__0 @ X2 @ X3 ) @ ( eigen__0 @ X2 @ X4 ) ) ) )
=> ~ ! [X2: a,X3: a,X4: a,X5: a,X6: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( X1 @ X2 @ X3 )
= X3 )
=> ( ( eigen__0 @ X2 @ X3 )
!= X2 ) )
=> ( ( X1 @ X2 @ X4 )
!= X4 ) )
=> ( ( eigen__0 @ X2 @ X4 )
!= X2 ) )
=> ( ( X1 @ X2 @ X5 )
!= X5 ) )
=> ( ( eigen__0 @ X2 @ X5 )
!= X2 ) )
=> ( ( X1 @ X2 @ X6 )
!= X6 ) )
=> ( ( eigen__0 @ X2 @ X6 )
!= X2 ) )
=> ( ( X1 @ X4 @ X5 )
!= X3 ) )
=> ( ( eigen__0 @ X4 @ X5 )
!= X2 ) )
=> ( ( X1 @ X4 @ X6 )
!= X4 ) )
=> ( ( eigen__0 @ X4 @ X6 )
!= X6 ) )
=> ( ( X1 @ X4 @ X3 )
!= X3 ) )
=> ( ( eigen__0 @ X4 @ X3 )
!= X4 ) )
=> ( ( X1 @ X5 @ X6 )
!= X3 ) )
=> ( ( eigen__0 @ X5 @ X6 )
!= X2 ) )
=> ( ( X1 @ X5 @ X3 )
!= X3 ) )
=> ( ( eigen__0 @ X5 @ X3 )
!= X5 ) )
=> ( ( X1 @ X6 @ X3 )
!= X3 ) )
=> ( ( eigen__0 @ X6 @ X3 )
!= X6 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP1
=> ~ sP16 )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ X1 @ ( eigen__0 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ ( eigen__1 @ X1 @ X2 ) @ X3 )
= ( eigen__1 @ X1 @ ( eigen__1 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
= ( eigen__0 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
= ( eigen__1 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ! [X1: a,X2: a,X3: a,X4: a,X5: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X3 != X4 )
=> ( X3 = X5 ) )
=> ( X3 = X1 ) )
=> ( X3 = X2 ) )
=> ( X4 = X5 ) )
=> ( X4 = X1 ) )
=> ( X4 = X2 ) )
=> ( X5 = X1 ) )
=> ( X5 = X2 ) )
=> ( X1 = X2 ) ) )
=> ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ X1 @ ( eigen__1 @ X2 @ ( eigen__0 @ X1 @ X3 ) ) )
= ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ ( eigen__0 @ X1 @ X3 ) ) ) )
=> ~ sP21 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP1
=> ~ sP16 )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ X1 @ ( eigen__0 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ ( eigen__1 @ X1 @ X2 ) @ X3 )
= ( eigen__1 @ X1 @ ( eigen__1 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
= ( eigen__0 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
= ( eigen__1 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ! [X1: a,X2: a,X3: a,X4: a,X5: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X3 != X4 )
=> ( X3 = X5 ) )
=> ( X3 = X1 ) )
=> ( X3 = X2 ) )
=> ( X4 = X5 ) )
=> ( X4 = X1 ) )
=> ( X4 = X2 ) )
=> ( X5 = X1 ) )
=> ( X5 = X2 ) )
=> ( X1 = X2 ) ) )
=> ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ X1 @ ( eigen__1 @ X2 @ ( eigen__0 @ X1 @ X3 ) ) )
= ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ ( eigen__0 @ X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP21,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP1
=> ~ sP16 )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ X1 @ ( eigen__0 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ ( eigen__1 @ X1 @ X2 ) @ X3 )
= ( eigen__1 @ X1 @ ( eigen__1 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
= ( eigen__0 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
= ( eigen__1 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ! [X1: a,X2: a,X3: a,X4: a,X5: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X3 != X4 )
=> ( X3 = X5 ) )
=> ( X3 = X1 ) )
=> ( X3 = X2 ) )
=> ( X4 = X5 ) )
=> ( X4 = X1 ) )
=> ( X4 = X2 ) )
=> ( X5 = X1 ) )
=> ( X5 = X2 ) )
=> ( X1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ X1 @ ( eigen__1 @ X2 @ ( eigen__0 @ X1 @ X3 ) ) )
= ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ ( eigen__0 @ X1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP1
=> ~ sP16 )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ X1 @ ( eigen__0 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ ( eigen__1 @ X1 @ X2 ) @ X3 )
= ( eigen__1 @ X1 @ ( eigen__1 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
= ( eigen__0 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
= ( eigen__1 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ X2 )
= X2 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: a,X2: a,X3: a,X4: a,X5: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X3 != X4 )
=> ( X3 = X5 ) )
=> ( X3 = X1 ) )
=> ( X3 = X2 ) )
=> ( X4 = X5 ) )
=> ( X4 = X1 ) )
=> ( X4 = X2 ) )
=> ( X5 = X1 ) )
=> ( X5 = X2 ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP1
=> ~ sP16 )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ X1 @ ( eigen__0 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ ( eigen__1 @ X1 @ X2 ) @ X3 )
= ( eigen__1 @ X1 @ ( eigen__1 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
= ( eigen__0 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
= ( eigen__1 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ X2 )
= X2 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
! [X1: a,X2: a] :
( ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ X2 )
= X2 ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( sP1
=> ~ sP16 )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ X1 @ ( eigen__0 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ ( eigen__1 @ X1 @ X2 ) @ X3 )
= ( eigen__1 @ X1 @ ( eigen__1 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
= ( eigen__0 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
= ( eigen__1 @ X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
! [X1: a,X2: a] :
( ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ X2 )
= X2 ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( ~ ( ~ ( sP1
=> ~ sP16 )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ X1 @ ( eigen__0 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ ( eigen__1 @ X1 @ X2 ) @ X3 )
= ( eigen__1 @ X1 @ ( eigen__1 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
= ( eigen__0 @ X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
= ( eigen__1 @ X2 @ X1 ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ~ ( ~ ( sP1
=> ~ sP16 )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ X1 @ ( eigen__0 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ ( eigen__1 @ X1 @ X2 ) @ X3 )
= ( eigen__1 @ X1 @ ( eigen__1 @ X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
= ( eigen__0 @ X2 @ X1 ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( ~ ( sP1
=> ~ sP16 )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ X1 @ ( eigen__0 @ X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ ( eigen__1 @ X1 @ X2 ) @ X3 )
= ( eigen__1 @ X1 @ ( eigen__1 @ X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( sP1
=> ~ sP16 ),
introduced(assumption,[]) ).
thf(h20,assumption,
! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ X1 @ ( eigen__0 @ X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP1,
introduced(assumption,[]) ).
thf(h22,assumption,
sP16,
introduced(assumption,[]) ).
thf(h23,assumption,
~ ! [X1: a,X2: a,X3: a,X4: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X2 != X3 )
=> ( X2 = X4 ) )
=> ( X2 = eigen__2 ) )
=> ( X2 = X1 ) )
=> ( X3 = X4 ) )
=> ( X3 = eigen__2 ) )
=> ( X3 = X1 ) )
=> ( X4 = eigen__2 ) )
=> ( X4 = X1 ) )
=> ( eigen__2 = X1 ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
~ ! [X1: a,X2: a,X3: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 != X2 )
=> ( X1 = X3 ) )
=> ( X1 = eigen__2 ) )
=> ( X1 = eigen__3 ) )
=> ( X2 = X3 ) )
=> ( X2 = eigen__2 ) )
=> ( X2 = eigen__3 ) )
=> ( X3 = eigen__2 ) )
=> ( X3 = eigen__3 ) )
=> ( eigen__2 = eigen__3 ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
~ ! [X1: a,X2: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__4 != X1 )
=> ( eigen__4 = X2 ) )
=> ( eigen__4 = eigen__2 ) )
=> ( eigen__4 = eigen__3 ) )
=> ( X1 = X2 ) )
=> ( X1 = eigen__2 ) )
=> ( X1 = eigen__3 ) )
=> ( X2 = eigen__2 ) )
=> ( X2 = eigen__3 ) )
=> ( eigen__2 = eigen__3 ) ),
introduced(assumption,[]) ).
thf(h26,assumption,
~ ! [X1: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__4 != eigen__5 )
=> ( eigen__4 = X1 ) )
=> ( eigen__4 = eigen__2 ) )
=> ( eigen__4 = eigen__3 ) )
=> ( eigen__5 = X1 ) )
=> ( eigen__5 = eigen__2 ) )
=> ( eigen__5 = eigen__3 ) )
=> ( X1 = eigen__2 ) )
=> ( X1 = eigen__3 ) )
=> ( eigen__2 = eigen__3 ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__4 != eigen__5 )
=> ( eigen__4 = eigen__6 ) )
=> ( eigen__4 = eigen__2 ) )
=> ( eigen__4 = eigen__3 ) )
=> ( eigen__5 = eigen__6 ) )
=> ( eigen__5 = eigen__2 ) )
=> ( eigen__5 = eigen__3 ) )
=> ( eigen__6 = eigen__2 ) )
=> ( eigen__6 = eigen__3 ) )
=> ( eigen__2 = eigen__3 ) ),
introduced(assumption,[]) ).
thf(h28,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__4 != eigen__5 )
=> ( eigen__4 = eigen__6 ) )
=> ( eigen__4 = eigen__2 ) )
=> ( eigen__4 = eigen__3 ) )
=> ( eigen__5 = eigen__6 ) )
=> ( eigen__5 = eigen__2 ) )
=> ( eigen__5 = eigen__3 ) )
=> ( eigen__6 = eigen__2 ) )
=> ( eigen__6 = eigen__3 ) ),
introduced(assumption,[]) ).
thf(h29,assumption,
eigen__2 != eigen__3,
introduced(assumption,[]) ).
thf(h30,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__4 != eigen__5 )
=> ( eigen__4 = eigen__6 ) )
=> ( eigen__4 = eigen__2 ) )
=> ( eigen__4 = eigen__3 ) )
=> ( eigen__5 = eigen__6 ) )
=> ( eigen__5 = eigen__2 ) )
=> ( eigen__5 = eigen__3 ) )
=> ( eigen__6 = eigen__2 ) ),
introduced(assumption,[]) ).
thf(h31,assumption,
eigen__6 != eigen__3,
introduced(assumption,[]) ).
thf(h32,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__4 != eigen__5 )
=> ( eigen__4 = eigen__6 ) )
=> ( eigen__4 = eigen__2 ) )
=> ( eigen__4 = eigen__3 ) )
=> ( eigen__5 = eigen__6 ) )
=> ( eigen__5 = eigen__2 ) )
=> ( eigen__5 = eigen__3 ) ),
introduced(assumption,[]) ).
thf(h33,assumption,
eigen__6 != eigen__2,
introduced(assumption,[]) ).
thf(h34,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__4 != eigen__5 )
=> ( eigen__4 = eigen__6 ) )
=> ( eigen__4 = eigen__2 ) )
=> ( eigen__4 = eigen__3 ) )
=> ( eigen__5 = eigen__6 ) )
=> ( eigen__5 = eigen__2 ) ),
introduced(assumption,[]) ).
thf(h35,assumption,
eigen__5 != eigen__3,
introduced(assumption,[]) ).
thf(h36,assumption,
~ ( ~ ( ~ ( ~ ( ( eigen__4 != eigen__5 )
=> ( eigen__4 = eigen__6 ) )
=> ( eigen__4 = eigen__2 ) )
=> ( eigen__4 = eigen__3 ) )
=> ( eigen__5 = eigen__6 ) ),
introduced(assumption,[]) ).
thf(h37,assumption,
eigen__5 != eigen__2,
introduced(assumption,[]) ).
thf(h38,assumption,
~ ( ~ ( ~ ( ( eigen__4 != eigen__5 )
=> ( eigen__4 = eigen__6 ) )
=> ( eigen__4 = eigen__2 ) )
=> ( eigen__4 = eigen__3 ) ),
introduced(assumption,[]) ).
thf(h39,assumption,
eigen__5 != eigen__6,
introduced(assumption,[]) ).
thf(h40,assumption,
~ ( ~ ( ( eigen__4 != eigen__5 )
=> ( eigen__4 = eigen__6 ) )
=> ( eigen__4 = eigen__2 ) ),
introduced(assumption,[]) ).
thf(h41,assumption,
eigen__4 != eigen__3,
introduced(assumption,[]) ).
thf(h42,assumption,
~ ( ( eigen__4 != eigen__5 )
=> ( eigen__4 = eigen__6 ) ),
introduced(assumption,[]) ).
thf(h43,assumption,
eigen__4 != eigen__2,
introduced(assumption,[]) ).
thf(h44,assumption,
eigen__4 != eigen__5,
introduced(assumption,[]) ).
thf(h45,assumption,
eigen__4 != eigen__6,
introduced(assumption,[]) ).
thf(h46,assumption,
~ ! [X1: a,X2: a] :
( ( eigen__0 @ eigen__7 @ ( eigen__1 @ X1 @ ( eigen__0 @ eigen__7 @ X2 ) ) )
= ( eigen__1 @ ( eigen__0 @ eigen__7 @ X1 ) @ ( eigen__0 @ eigen__7 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h47,assumption,
~ ! [X1: a] :
( ( eigen__0 @ eigen__7 @ ( eigen__1 @ eigen__8 @ ( eigen__0 @ eigen__7 @ X1 ) ) )
= ( eigen__1 @ ( eigen__0 @ eigen__7 @ eigen__8 ) @ ( eigen__0 @ eigen__7 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h48,assumption,
( ( eigen__0 @ eigen__7 @ ( eigen__1 @ eigen__8 @ ( eigen__0 @ eigen__7 @ eigen__9 ) ) )
!= ( eigen__1 @ ( eigen__0 @ eigen__7 @ eigen__8 ) @ ( eigen__0 @ eigen__7 @ eigen__9 ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP12
| ~ sP27
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP18
| sP12
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP24
| sP18
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP14
| sP24
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP23
| sP14
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP10
| sP23
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP26
| sP10
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP17
| sP26
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP28
| sP17
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP25
| sP28
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP11
| sP25
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP9
| sP11
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP4
| sP9
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP22
| sP4
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP8
| sP22
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP2
| sP8
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP5
| sP2
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP6
| sP5
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP15
| sP6
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP3
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP13
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP7
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP19
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP16
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP1
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP21
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h48,h47,h46,h44,h45,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h27,h26,h25,h24,h23,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,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,h21,h22,h4]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h47,h46,h44,h45,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h27,h26,h25,h24,h23,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h48]),tab_negall(eigenvar,eigen__9)],[h47,27,h48]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h46,h44,h45,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h27,h26,h25,h24,h23,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h47]),tab_negall(eigenvar,eigen__8)],[h46,28,h47]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h44,h45,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h27,h26,h25,h24,h23,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h46]),tab_negall(eigenvar,eigen__7)],[h6,29,h46]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h27,h26,h25,h24,h23,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h44,h45])],[h42,30,h44,h45]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h27,h26,h25,h24,h23,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h42,h43])],[h40,31,h42,h43]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h27,h26,h25,h24,h23,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h40,h41])],[h38,32,h40,h41]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h27,h26,h25,h24,h23,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h38,h39])],[h36,33,h38,h39]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h34,h35,h32,h33,h30,h31,h28,h29,h27,h26,h25,h24,h23,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h36,h37])],[h34,34,h36,h37]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h32,h33,h30,h31,h28,h29,h27,h26,h25,h24,h23,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h34,h35])],[h32,35,h34,h35]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h30,h31,h28,h29,h27,h26,h25,h24,h23,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h32,h33])],[h30,36,h32,h33]) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h28,h29,h27,h26,h25,h24,h23,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h30,h31])],[h28,37,h30,h31]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h26,h25,h24,h23,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h28,h29])],[h27,38,h28,h29]) ).
thf(40,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h26,h25,h24,h23,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h27]),tab_negall(eigenvar,eigen__6)],[h26,39,h27]) ).
thf(41,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h25,h24,h23,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__5)],[h25,40,h26]) ).
thf(42,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h24,h23,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h25]),tab_negall(eigenvar,eigen__4)],[h24,41,h25]) ).
thf(43,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h23,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__3)],[h23,42,h24]) ).
thf(44,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__2)],[h8,43,h23]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h19,44,h21,h22]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h17,45,h19,h20]) ).
thf(47,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,46,h17,h18]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h13,47,h15,h16]) ).
thf(49,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,48,h13,h14]) ).
thf(50,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,49,h11,h12]) ).
thf(51,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,50,h9,h10]) ).
thf(52,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,51,h7,h8]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,52,h5,h6]) ).
thf(54,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,53,h3,h4]) ).
thf(55,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,54,h2]) ).
thf(56,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,55,h1]) ).
thf(0,theorem,
! [X1: a > a > a,X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: a] :
( ( X1 @ X3 @ X3 )
= X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 @ X3 )
= X3 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ X3 @ ( X2 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
= ( X1 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ X3 @ X4 )
= ( X2 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ ( X2 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( X1 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ! [X3: a,X4: a,X5: a,X6: a,X7: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X5 != X6 )
=> ( X5 = X7 ) )
=> ( X5 = X3 ) )
=> ( X5 = X4 ) )
=> ( X6 = X7 ) )
=> ( X6 = X3 ) )
=> ( X6 = X4 ) )
=> ( X7 = X3 ) )
=> ( X7 = X4 ) )
=> ( X3 = X4 ) ) )
=> ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ ( X1 @ X3 @ X5 ) ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a,X6: a,X7: a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( X2 @ X3 @ X4 )
= X4 )
=> ( ( X1 @ X3 @ X4 )
!= X3 ) )
=> ( ( X2 @ X3 @ X5 )
!= X5 ) )
=> ( ( X1 @ X3 @ X5 )
!= X3 ) )
=> ( ( X2 @ X3 @ X6 )
!= X6 ) )
=> ( ( X1 @ X3 @ X6 )
!= X3 ) )
=> ( ( X2 @ X3 @ X7 )
!= X7 ) )
=> ( ( X1 @ X3 @ X7 )
!= X3 ) )
=> ( ( X2 @ X5 @ X6 )
!= X4 ) )
=> ( ( X1 @ X5 @ X6 )
!= X3 ) )
=> ( ( X2 @ X5 @ X7 )
!= X5 ) )
=> ( ( X1 @ X5 @ X7 )
!= X7 ) )
=> ( ( X2 @ X5 @ X4 )
!= X4 ) )
=> ( ( X1 @ X5 @ X4 )
!= X5 ) )
=> ( ( X2 @ X6 @ X7 )
!= X4 ) )
=> ( ( X1 @ X6 @ X7 )
!= X3 ) )
=> ( ( X2 @ X6 @ X4 )
!= X4 ) )
=> ( ( X1 @ X6 @ X4 )
!= X6 ) )
=> ( ( X2 @ X7 @ X4 )
!= X4 ) )
=> ( ( X1 @ X7 @ X4 )
!= X7 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[56,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV006^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 03:18:52 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 % Mode: cade22grackle2xfee4
% 0.21/0.45 % Steps: 61
% 0.21/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------