%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU823^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n005.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 02:52:32 PM UTC 2025
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% 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_nonempty,type,
nonempty: $i > $o ).
thf(ty_transitiveset,type,
transitiveset: $i > $o ).
thf(ty_powerset,type,
powerset: $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) )
=> ( in @ X2 @ X1 ) ) ) ) )
=> ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ~ ( in @ X1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( transitiveset @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1
=> ( in @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( in @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( ( X1 != X2 )
=> ( in @ X1 @ X2 ) )
=> ( in @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( in @ eigen__1 @ eigen__0 )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( in @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ eigen__0 @ X1 )
=> sP10 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP10
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ( ( in @ eigen__1 @ eigen__0 )
=> ~ ( in @ eigen__0 @ X1 ) )
=> ( in @ eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ~ ( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X3 ) )
=> ( in @ X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( in @ eigen__1 @ eigen__0 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( ( in @ eigen__1 @ X1 )
=> ~ ( in @ X1 @ X2 ) )
=> ( in @ eigen__1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ! [X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X2 @ X3 )
=> ( in @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( in @ eigen__1 @ eigen__0 )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ( ( in @ eigen__1 @ eigen__0 )
=> ~ ( in @ eigen__0 @ X1 ) )
=> ( in @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ ( ( in @ eigen__1 @ eigen__0 )
=> ~ sP1 )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ( ( nonempty @ X1 )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( in @ eigen__1 @ eigen__0 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( in @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ ( sP3
=> ( ~ sP2
=> ~ sP19 ) )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP3
=> ( ~ sP2
=> ~ sP19 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ sP2
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ~ ( in @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP21
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( ( in @ eigen__1 @ X1 )
=> ~ ( in @ X1 @ X2 ) )
=> ( in @ eigen__1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(def_stricttotalorderedByIn,definition,
( stricttotalorderedByIn
= ( ^ [X1: $i] :
~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) ) ) ) ).
thf(def_wellorderedByIn,definition,
( wellorderedByIn
= ( ^ [X1: $i] :
~ ( ( stricttotalorderedByIn @ X1 )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) ) ) ).
thf(def_ordinal,definition,
( ordinal
= ( ^ [X1: $i] :
~ ( ( transitiveset @ X1 )
=> ~ ( wellorderedByIn @ X1 ) ) ) ) ).
thf(def_ordinalTransSet,definition,
( ordinalTransSet
= ( ! [X1: $i] :
( ( ordinal @ X1 )
=> ! [X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X2 @ X3 )
=> ( in @ X2 @ X1 ) ) ) ) ) ) ).
thf(def_ordinalIrrefl,definition,
( ordinalIrrefl
= ( ! [X1: $i] :
( ( ordinal @ X1 )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) ) ) ) ).
thf(ordinalNoCycle,conjecture,
( ! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ~ ~ ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ! [X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X2 @ X3 )
=> ( in @ X2 @ X1 ) ) ) )
=> ( ! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ~ ~ ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ~ ~ ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X1 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP15
=> ( ! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X1 ) ) ) ) ),
inference(assume_negation,[status(cth)],[ordinalNoCycle]) ).
thf(h1,assumption,
sP15,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ sP23
=> ! [X1: $i] :
( ( in @ eigen__0 @ X1 )
=> ~ ( in @ X1 @ eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP23,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ( in @ eigen__0 @ X1 )
=> ~ ( in @ X1 @ eigen__0 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP3,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP24,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h11,assumption,
sP19,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h13,assumption,
sP25,
introduced(assumption,[]) ).
thf(h14,assumption,
sP13,
introduced(assumption,[]) ).
thf(h15,assumption,
sP6,
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( sP1
=> ~ sP21 ),
introduced(assumption,[]) ).
thf(h17,assumption,
sP1,
introduced(assumption,[]) ).
thf(h18,assumption,
sP21,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP7
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP11
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP8
| ~ sP21
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP4
| ~ sP1
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP15
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP22
| sP23
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP23
| ~ sP3
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP24
| sP2
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP2
| sP9
| ~ sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP9
| ~ sP13
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP27
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP12
| ~ sP10
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP17
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP26
| ~ sP21
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP18
| sP20
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP20
| ~ sP21
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP13
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP14
| ~ sP21
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP25
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP16
| ~ sP21
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h18,h16,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,h1,h8,h14,h15,h13,h11,h17,h18]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h16,21,h17,h18]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__1)],[h7,22,h16]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h14,h15])],[h12,23,h14,h15]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h10,24,h12,h13]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,25,h10,h11]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h6,26,h8,h9]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[h5,27,h6,h7]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,28,h5]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,29,h3,h4]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,30,h1,h2]) ).
thf(0,theorem,
( ! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ~ ~ ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ! [X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X2 @ X3 )
=> ( in @ X2 @ X1 ) ) ) )
=> ( ! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ~ ~ ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ! [X1: $i] :
( ~ ( ( transitiveset @ X1 )
=> ~ ~ ( ~ ( ~ ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( ( X2 != X3 )
=> ( in @ X2 @ X3 ) )
=> ( in @ X3 @ X2 ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X2 ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X2 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( X3 != X4 )
=> ( in @ X3 @ X4 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X1 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[31,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU823^2 : TPTP v9.2.0. Released v3.7.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n005.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 : Wed Oct 8 21:37:23 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % Mode: mode213
% 0.13/0.39 % Inferences: 9
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------