%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU996^5 : TPTP v9.2.0. 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 Oct 9 02:42:15 PM UTC 2025
% Result : Theorem 22.79s 22.95s
% Output : Proof 22.79s
% 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__3,type,
eigen__3: a ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(ty_eigen__1,type,
eigen__1: a > a > a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(sP1,plain,
( sP1
<=> ( ( eigen__0 @ eigen__2 @ eigen__4 )
= eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
( ( eigen__0 @ eigen__2 @ ( eigen__1 @ eigen__3 @ X1 ) )
= ( eigen__1 @ ( eigen__0 @ eigen__2 @ eigen__3 ) @ ( eigen__0 @ eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
= ( eigen__1 @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__1 @ ( eigen__0 @ eigen__2 @ eigen__3 ) @ ( eigen__0 @ eigen__2 @ eigen__4 ) )
= ( eigen__0 @ eigen__2 @ ( eigen__1 @ eigen__3 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
( ( eigen__1 @ ( eigen__0 @ eigen__2 @ eigen__3 ) @ X1 )
= ( eigen__1 @ X1 @ ( eigen__0 @ eigen__2 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> $false ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__0 @ eigen__2 @ ( eigen__1 @ eigen__3 @ eigen__4 ) )
= ( eigen__1 @ ( eigen__0 @ eigen__2 @ eigen__3 ) @ ( eigen__0 @ eigen__2 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__1 @ ( eigen__0 @ eigen__2 @ eigen__3 ) @ ( eigen__0 @ eigen__2 @ eigen__4 ) )
= ( eigen__1 @ ( eigen__0 @ eigen__2 @ eigen__4 ) @ ( eigen__0 @ eigen__2 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ eigen__2 @ ( eigen__1 @ X1 @ X2 ) )
= ( eigen__1 @ ( eigen__0 @ eigen__2 @ X1 ) @ ( eigen__0 @ eigen__2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__0 @ eigen__2 @ ( eigen__1 @ eigen__3 @ eigen__4 ) )
= ( eigen__1 @ ( eigen__0 @ eigen__2 @ eigen__3 ) @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eigen__1 @ ( eigen__0 @ eigen__2 @ eigen__3 ) @ ( eigen__0 @ eigen__2 @ eigen__4 ) )
= ( eigen__1 @ ( eigen__0 @ eigen__2 @ eigen__3 ) @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ X1 @ ( eigen__1 @ X2 @ X3 ) )
= ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ ( eigen__0 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(cMODULAR_THM_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] :
( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ X3 @ ( X1 @ X4 @ X5 ) )
= ( X1 @ ( X2 @ X3 @ X4 ) @ ( X2 @ X3 @ X5 ) ) ) )
=> ! [X3: a,X4: a,X5: a] :
( ( ( X1 @ X3 @ X5 )
= X5 )
=> ( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ X5 ) ) ) ) ).
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] :
( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ X3 @ ( X1 @ X4 @ X5 ) )
= ( X1 @ ( X2 @ X3 @ X4 ) @ ( X2 @ X3 @ X5 ) ) ) )
=> ! [X3: a,X4: a,X5: a] :
( ( ( X1 @ X3 @ X5 )
= X5 )
=> ( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ X5 ) ) ) ),
inference(assume_negation,[status(cth)],[cMODULAR_THM_pme]) ).
thf(h1,assumption,
~ ! [X1: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X2: a] :
( ( eigen__0 @ X2 @ X2 )
= X2 )
=> ~ ! [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] :
( ( eigen__0 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( eigen__0 @ X2 @ X3 ) @ ( eigen__0 @ X2 @ X4 ) ) ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ( X1 @ X2 @ ( eigen__0 @ X3 @ X4 ) )
= ( eigen__0 @ ( X1 @ X2 @ X3 ) @ ( X1 @ X2 @ X4 ) ) ) )
=> ! [X2: a,X3: a,X4: a] :
( ( ( eigen__0 @ X2 @ X4 )
= X4 )
=> ( ( eigen__0 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( eigen__0 @ X2 @ X3 ) @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ) )
=> ~ ! [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 ) ) )
=> ~ sP3 )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ~ sP12 )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ X1 @ ( eigen__0 @ X2 @ X3 ) )
= ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ ( eigen__1 @ X1 @ X3 ) ) ) )
=> ! [X1: a,X2: a,X3: a] :
( ( ( eigen__0 @ X1 @ X3 )
= X3 )
=> ( ( eigen__0 @ X1 @ ( eigen__1 @ X2 @ X3 ) )
= ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ) )
=> ~ ! [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 ) ) )
=> ~ sP3 )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ~ sP12 )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ X1 @ ( eigen__0 @ X2 @ X3 ) )
= ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ ( eigen__1 @ X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: a,X2: a,X3: a] :
( ( ( eigen__0 @ X1 @ X3 )
= X3 )
=> ( ( eigen__0 @ X1 @ ( eigen__1 @ X2 @ X3 ) )
= ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ) )
=> ~ ! [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 ) ) )
=> ~ sP3 )
=> ~ ! [X1: a,X2: a] :
( ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__1 @ ( eigen__0 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h6,assumption,
! [X1: a,X2: a,X3: a] :
( ( eigen__1 @ X1 @ ( eigen__0 @ X2 @ X3 ) )
= ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ ( eigen__1 @ X1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ) )
=> ~ ! [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 ) ) )
=> ~ sP3 )
=> ~ ! [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,
sP12,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ) )
=> ~ ! [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 ) ) )
=> ~ sP3 )
=> ~ ! [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,
~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ) )
=> ~ ! [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 ) ) )
=> ~ sP3 ),
introduced(assumption,[]) ).
thf(h12,assumption,
! [X1: a,X2: a] :
( ( eigen__0 @ ( eigen__1 @ X1 @ X2 ) @ X2 )
= X2 ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( ~ ( ~ ( ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ) )
=> ~ ! [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,
sP3,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ~ ( ~ ( ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ) )
=> ~ ! [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,
~ ( ~ ( ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ) )
=> ~ ! [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,
~ ( ! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ) ),
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,
! [X1: a] :
( ( eigen__0 @ X1 @ X1 )
= X1 ),
introduced(assumption,[]) ).
thf(h22,assumption,
! [X1: a] :
( ( eigen__1 @ X1 @ X1 )
= X1 ),
introduced(assumption,[]) ).
thf(h23,assumption,
~ ! [X1: a,X2: a] :
( ( ( eigen__0 @ eigen__2 @ X2 )
= X2 )
=> ( ( eigen__0 @ eigen__2 @ ( eigen__1 @ X1 @ X2 ) )
= ( eigen__1 @ ( eigen__0 @ eigen__2 @ X1 ) @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
~ ! [X1: a] :
( ( ( eigen__0 @ eigen__2 @ X1 )
= X1 )
=> ( ( eigen__0 @ eigen__2 @ ( eigen__1 @ eigen__3 @ X1 ) )
= ( eigen__1 @ ( eigen__0 @ eigen__2 @ eigen__3 ) @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
~ ( sP1
=> sP10 ),
introduced(assumption,[]) ).
thf(h26,assumption,
sP1,
introduced(assumption,[]) ).
thf(h27,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(1,plain,
( sP11
| ~ sP1
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP8
| sP10
| ~ sP4
| ~ sP11 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP7
| sP4 ),
inference(symeq,[status(thm)],[]) ).
thf(4,plain,
~ sP6,
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP2
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP5
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP9
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP3
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP12
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h26,h27,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,h14,h8,h26,h27]) ).
thf(11,plain,
$false,
inference(tab_negimp,[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_negimp(discharge,[h26,h27])],[h25,10,h26,h27]) ).
thf(12,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)],[h24,11,h25]) ).
thf(13,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)],[h23,12,h24]) ).
thf(14,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)],[h4,13,h23]) ).
thf(15,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])],[h19,14,h21,h22]) ).
thf(16,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])],[h17,15,h19,h20]) ).
thf(17,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])],[h15,16,h17,h18]) ).
thf(18,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])],[h13,17,h15,h16]) ).
thf(19,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])],[h11,18,h13,h14]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,19,h11,h12]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,20,h9,h10]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,21,h7,h8]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,22,h5,h6]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,23,h3,h4]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,24,h2]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,25,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] :
( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ X3 @ ( X1 @ X4 @ X5 ) )
= ( X1 @ ( X2 @ X3 @ X4 ) @ ( X2 @ X3 @ X5 ) ) ) )
=> ! [X3: a,X4: a,X5: a] :
( ( ( X1 @ X3 @ X5 )
= X5 )
=> ( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ X5 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[26,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU996^5 : TPTP v9.2.0. Released v4.0.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 8 20:37:23 EDT 2025
% 0.14/0.35 % CPUTime :
% 22.79/22.95 % SZS status Theorem
% 22.79/22.95 % Mode: cade22grackle2x798d
% 22.79/22.95 % Steps: 7376
% 22.79/22.95 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------