%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU901^5 : 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 : n008.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 02:42:07 PM UTC 2025
% Result : Theorem 1.06s 1.23s
% Output : Proof 1.06s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_a,type,
a: $tType ).
thf(ty_g,type,
g: $tType ).
thf(ty_eigen__3,type,
eigen__3: g > g ).
thf(ty_eigen__6,type,
eigen__6: a > $o ).
thf(ty_eigen__1,type,
eigen__1: b > a ).
thf(ty_eigen__2,type,
eigen__2: g > $o ).
thf(ty_eigen__5,type,
eigen__5: b > b ).
thf(ty_eigen__7,type,
eigen__7: a > a ).
thf(ty_eigen__4,type,
eigen__4: b > $o ).
thf(ty_eigen__8,type,
eigen__8: g ).
thf(ty_eigen__0,type,
eigen__0: g > b ).
thf(sP1,plain,
( sP1
<=> ( eigen__2 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( ( eigen__0 @ ( eigen__3 @ X1 ) )
= ( eigen__5 @ ( eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> $false ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__4 @ ( eigen__0 @ eigen__8 ) )
=> ( ( eigen__1 @ ( eigen__5 @ ( eigen__0 @ eigen__8 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__5 @ ( eigen__0 @ eigen__8 ) )
= ( eigen__0 @ ( eigen__3 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP1
=> ( eigen__4 @ ( eigen__0 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__1 @ ( eigen__5 @ ( eigen__0 @ eigen__8 ) ) )
= ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ eigen__8 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( ( eigen__1 @ ( eigen__5 @ X1 ) )
= ( eigen__7 @ ( eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ eigen__8 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__4 @ ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP1
=> ( ( eigen__0 @ ( eigen__3 @ eigen__8 ) )
= ( eigen__5 @ ( eigen__0 @ eigen__8 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( eigen__1 @ ( eigen__5 @ ( eigen__0 @ eigen__8 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__0 @ ( eigen__3 @ eigen__8 ) )
= ( eigen__5 @ ( eigen__0 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__4 @ ( eigen__0 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(cTHM131D_pme,conjecture,
! [X1: g > b,X2: b > a,X3: g > $o,X4: g > g,X5: b > $o,X6: b > b,X7: a > $o,X8: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X9: g] :
( ( X3 @ X9 )
=> ( X3 @ ( X4 @ X9 ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X5 @ ( X6 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( ( X1 @ ( X4 @ X9 ) )
= ( X6 @ ( X1 @ X9 ) ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X5 @ ( X6 @ X9 ) ) ) )
=> ~ ! [X9: a] :
( ( X7 @ X9 )
=> ( X7 @ ( X8 @ X9 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X7 @ ( X2 @ X9 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( ( X2 @ ( X6 @ X9 ) )
= ( X8 @ ( X2 @ X9 ) ) ) ) )
=> ! [X9: g] :
( ( X3 @ X9 )
=> ( ( X2 @ ( X1 @ ( X4 @ X9 ) ) )
= ( X8 @ ( X2 @ ( X1 @ X9 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: g > b,X2: b > a,X3: g > $o,X4: g > g,X5: b > $o,X6: b > b,X7: a > $o,X8: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X9: g] :
( ( X3 @ X9 )
=> ( X3 @ ( X4 @ X9 ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X5 @ ( X6 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( ( X1 @ ( X4 @ X9 ) )
= ( X6 @ ( X1 @ X9 ) ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X5 @ ( X6 @ X9 ) ) ) )
=> ~ ! [X9: a] :
( ( X7 @ X9 )
=> ( X7 @ ( X8 @ X9 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X7 @ ( X2 @ X9 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( ( X2 @ ( X6 @ X9 ) )
= ( X8 @ ( X2 @ X9 ) ) ) ) )
=> ! [X9: g] :
( ( X3 @ X9 )
=> ( ( X2 @ ( X1 @ ( X4 @ X9 ) ) )
= ( X8 @ ( X2 @ ( X1 @ X9 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM131D_pme]) ).
thf(h1,assumption,
~ ! [X1: b > a,X2: g > $o,X3: g > g,X4: b > $o,X5: b > b,X6: a > $o,X7: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X8: g] :
( ( X2 @ X8 )
=> ( X2 @ ( X3 @ X8 ) ) )
=> ~ ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( eigen__0 @ X8 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( ( eigen__0 @ ( X3 @ X8 ) )
= ( X5 @ ( eigen__0 @ X8 ) ) ) ) )
=> ~ ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) ) )
=> ~ ! [X8: a] :
( ( X6 @ X8 )
=> ( X6 @ ( X7 @ X8 ) ) ) )
=> ~ ! [X8: b] :
( ( X4 @ X8 )
=> ( X6 @ ( X1 @ X8 ) ) ) )
=> ~ ! [X8: b] :
( ( X4 @ X8 )
=> ( ( X1 @ ( X5 @ X8 ) )
= ( X7 @ ( X1 @ X8 ) ) ) ) )
=> ! [X8: g] :
( ( X2 @ X8 )
=> ( ( X1 @ ( eigen__0 @ ( X3 @ X8 ) ) )
= ( X7 @ ( X1 @ ( eigen__0 @ X8 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: g > $o,X2: g > g,X3: b > $o,X4: b > b,X5: a > $o,X6: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X7: g] :
( ( X1 @ X7 )
=> ( X1 @ ( X2 @ X7 ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( X3 @ ( X4 @ X7 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( X3 @ ( eigen__0 @ X7 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( ( eigen__0 @ ( X2 @ X7 ) )
= ( X4 @ ( eigen__0 @ X7 ) ) ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( X3 @ ( X4 @ X7 ) ) ) )
=> ~ ! [X7: a] :
( ( X5 @ X7 )
=> ( X5 @ ( X6 @ X7 ) ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( X5 @ ( eigen__1 @ X7 ) ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( ( eigen__1 @ ( X4 @ X7 ) )
= ( X6 @ ( eigen__1 @ X7 ) ) ) ) )
=> ! [X7: g] :
( ( X1 @ X7 )
=> ( ( eigen__1 @ ( eigen__0 @ ( X2 @ X7 ) ) )
= ( X6 @ ( eigen__1 @ ( eigen__0 @ X7 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: g > g,X2: b > $o,X3: b > b,X4: a > $o,X5: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( eigen__2 @ ( X1 @ X6 ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( X2 @ ( X3 @ X6 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( X2 @ ( eigen__0 @ X6 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( ( eigen__0 @ ( X1 @ X6 ) )
= ( X3 @ ( eigen__0 @ X6 ) ) ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( X2 @ ( X3 @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X4 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( X4 @ ( eigen__1 @ X6 ) ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( ( eigen__1 @ ( X3 @ X6 ) )
= ( X5 @ ( eigen__1 @ X6 ) ) ) ) )
=> ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( ( eigen__1 @ ( eigen__0 @ ( X1 @ X6 ) ) )
= ( X5 @ ( eigen__1 @ ( eigen__0 @ X6 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: b > $o,X2: b > b,X3: a > $o,X4: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( eigen__2 @ ( eigen__3 @ X5 ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( X1 @ ( X2 @ X5 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( X1 @ ( eigen__0 @ X5 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( ( eigen__0 @ ( eigen__3 @ X5 ) )
= ( X2 @ ( eigen__0 @ X5 ) ) ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( X1 @ ( X2 @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X3 @ ( X4 @ X5 ) ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( X3 @ ( eigen__1 @ X5 ) ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( ( eigen__1 @ ( X2 @ X5 ) )
= ( X4 @ ( eigen__1 @ X5 ) ) ) ) )
=> ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X5 ) ) )
= ( X4 @ ( eigen__1 @ ( eigen__0 @ X5 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: b > b,X2: a > $o,X3: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( eigen__2 @ ( eigen__3 @ X4 ) ) )
=> ~ ! [X4: b] :
( ( eigen__4 @ X4 )
=> ( eigen__4 @ ( X1 @ X4 ) ) ) )
=> ~ sP10 )
=> ~ ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( ( eigen__0 @ ( eigen__3 @ X4 ) )
= ( X1 @ ( eigen__0 @ X4 ) ) ) ) )
=> ~ ! [X4: b] :
( ( eigen__4 @ X4 )
=> ( eigen__4 @ ( X1 @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X2 @ ( X3 @ X4 ) ) ) )
=> ~ ! [X4: b] :
( ( eigen__4 @ X4 )
=> ( X2 @ ( eigen__1 @ X4 ) ) ) )
=> ~ ! [X4: b] :
( ( eigen__4 @ X4 )
=> ( ( eigen__1 @ ( X1 @ X4 ) )
= ( X3 @ ( eigen__1 @ X4 ) ) ) ) )
=> ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X4 ) ) )
= ( X3 @ ( eigen__1 @ ( eigen__0 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: a > $o,X2: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( eigen__2 @ ( eigen__3 @ X3 ) ) )
=> ~ ! [X3: b] :
( ( eigen__4 @ X3 )
=> ( eigen__4 @ ( eigen__5 @ X3 ) ) ) )
=> ~ sP10 )
=> ~ sP2 )
=> ~ ! [X3: b] :
( ( eigen__4 @ X3 )
=> ( eigen__4 @ ( eigen__5 @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) ) )
=> ~ ! [X3: b] :
( ( eigen__4 @ X3 )
=> ( X1 @ ( eigen__1 @ X3 ) ) ) )
=> ~ ! [X3: b] :
( ( eigen__4 @ X3 )
=> ( ( eigen__1 @ ( eigen__5 @ X3 ) )
= ( X2 @ ( eigen__1 @ X3 ) ) ) ) )
=> ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X3 ) ) )
= ( X2 @ ( eigen__1 @ ( eigen__0 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X2: g] :
( ( eigen__2 @ X2 )
=> ( eigen__2 @ ( eigen__3 @ X2 ) ) )
=> ~ ! [X2: b] :
( ( eigen__4 @ X2 )
=> ( eigen__4 @ ( eigen__5 @ X2 ) ) ) )
=> ~ sP10 )
=> ~ sP2 )
=> ~ ! [X2: b] :
( ( eigen__4 @ X2 )
=> ( eigen__4 @ ( eigen__5 @ X2 ) ) ) )
=> ~ ! [X2: a] :
( ( eigen__6 @ X2 )
=> ( eigen__6 @ ( X1 @ X2 ) ) ) )
=> ~ ! [X2: b] :
( ( eigen__4 @ X2 )
=> ( eigen__6 @ ( eigen__1 @ X2 ) ) ) )
=> ~ ! [X2: b] :
( ( eigen__4 @ X2 )
=> ( ( eigen__1 @ ( eigen__5 @ X2 ) )
= ( X1 @ ( eigen__1 @ X2 ) ) ) ) )
=> ! [X2: g] :
( ( eigen__2 @ X2 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X2 ) ) )
= ( X1 @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__2 @ ( eigen__3 @ X1 ) ) )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ sP10 )
=> ~ sP2 )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ ! [X1: a] :
( ( eigen__6 @ X1 )
=> ( eigen__6 @ ( eigen__7 @ X1 ) ) ) )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ X1 ) ) ) )
=> ~ sP8 )
=> ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X1 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__2 @ ( eigen__3 @ X1 ) ) )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ sP10 )
=> ~ sP2 )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ ! [X1: a] :
( ( eigen__6 @ X1 )
=> ( eigen__6 @ ( eigen__7 @ X1 ) ) ) )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ X1 ) ) ) )
=> ~ sP8 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X1 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__2 @ ( eigen__3 @ X1 ) ) )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ sP10 )
=> ~ sP2 )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ ! [X1: a] :
( ( eigen__6 @ X1 )
=> ( eigen__6 @ ( eigen__7 @ X1 ) ) ) )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP8,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__2 @ ( eigen__3 @ X1 ) ) )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ sP10 )
=> ~ sP2 )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ ! [X1: a] :
( ( eigen__6 @ X1 )
=> ( eigen__6 @ ( eigen__7 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ~ ( ~ ( ~ ( ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__2 @ ( eigen__3 @ X1 ) ) )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ sP10 )
=> ~ sP2 )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
! [X1: a] :
( ( eigen__6 @ X1 )
=> ( eigen__6 @ ( eigen__7 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( ~ ( ~ ( ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__2 @ ( eigen__3 @ X1 ) ) )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ sP10 )
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h18,assumption,
! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( ~ ( ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__2 @ ( eigen__3 @ X1 ) ) )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h20,assumption,
sP2,
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__2 @ ( eigen__3 @ X1 ) ) )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
sP10,
introduced(assumption,[]) ).
thf(h23,assumption,
! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__2 @ ( eigen__3 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
~ ( sP1
=> sP9 ),
introduced(assumption,[]) ).
thf(h25,assumption,
sP1,
introduced(assumption,[]) ).
thf(h26,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP13
| sP5
| ~ sP13
| sP3 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(2,plain,
~ sP3,
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP12
| sP9
| ~ sP7
| ~ sP12 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(4,plain,
( sP7
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP4
| ~ sP14
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP8
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP11
| ~ sP1
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP6
| ~ sP1
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP2
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP10
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h25,h26,h24,h23,h18,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h22,h20,h12,h25,h26]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h23,h18,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h25,h26])],[h24,11,h25,h26]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h23,h18,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__8)],[h10,12,h24]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h23,h18])],[h21,13,h23,h18]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,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,h8,h7,h6,h5,h4,h3,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,h8,h7,h6,h5,h4,h3,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,h8,h7,h6,h5,h4,h3,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,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,18,h13,h14]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,19,h11,h12]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,20,h9,h10]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__7)],[h7,21,h8]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__6)],[h6,22,h7]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__5)],[h5,23,h6]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__4)],[h4,24,h5]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__3)],[h3,25,h4]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,26,h3]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,27,h2]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,28,h1]) ).
thf(0,theorem,
! [X1: g > b,X2: b > a,X3: g > $o,X4: g > g,X5: b > $o,X6: b > b,X7: a > $o,X8: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X9: g] :
( ( X3 @ X9 )
=> ( X3 @ ( X4 @ X9 ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X5 @ ( X6 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( ( X1 @ ( X4 @ X9 ) )
= ( X6 @ ( X1 @ X9 ) ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X5 @ ( X6 @ X9 ) ) ) )
=> ~ ! [X9: a] :
( ( X7 @ X9 )
=> ( X7 @ ( X8 @ X9 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X7 @ ( X2 @ X9 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( ( X2 @ ( X6 @ X9 ) )
= ( X8 @ ( X2 @ X9 ) ) ) ) )
=> ! [X9: g] :
( ( X3 @ X9 )
=> ( ( X2 @ ( X1 @ ( X4 @ X9 ) ) )
= ( X8 @ ( X2 @ ( X1 @ X9 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[29,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU901^5 : TPTP v9.2.0. Released v4.0.0.
% 0.11/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 21:11:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.06/1.23 % SZS status Theorem
% 1.06/1.23 % Mode: cade22grackle2xfee4
% 1.06/1.23 % Steps: 23597
% 1.06/1.23 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------