%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU498^1 : TPTP v9.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n020.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 02:43:17 PM UTC 2025
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ~ ( ( eigen__0 @ eigen__4 @ eigen__5 )
=> ~ ( eigen__0 @ eigen__5 @ X1 ) )
=> ( eigen__0 @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP3
=> ~ ( eigen__0 @ eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__3 = eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP5
=> ( eigen__5 = eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( eigen__3 = X1 )
=> ( X1 = eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ~ ( sP3
=> ~ ( eigen__0 @ eigen__4 @ X1 ) )
=> ( eigen__0 @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__3 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP3
=> ~ ( eigen__0 @ eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__4 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__0 @ eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__0 @ eigen__4 @ eigen__5 )
=> ~ ( eigen__0 @ eigen__5 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__3 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__0 @ eigen__3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__0 @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X1 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ~ ( ( eigen__0 @ eigen__3 @ X1 )
=> ~ ( eigen__0 @ X1 @ eigen__3 ) )
=> ( eigen__3 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__5 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ sP13
=> ( eigen__0 @ eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ sP4
=> ( eigen__0 @ eigen__3 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ~ ( ( eigen__0 @ eigen__2 @ X1 )
=> ~ ( eigen__0 @ X1 @ eigen__2 ) )
=> ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__0 @ eigen__5 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ ( sP1
=> ~ ( eigen__0 @ eigen__1 @ eigen__2 ) )
=> ( eigen__2 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__2 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ sP11
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP1
=> ~ ( eigen__0 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__0 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eigen__0 @ eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( eigen__0 @ eigen__3 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(def_subrel,definition,
( subrel
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) ).
thf(def_inv,definition,
( inv
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_idem,definition,
( idem
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ ( X1 @ X2 ) )
= ( X1 @ X2 ) ) ) ) ).
thf(def_infl,definition,
( infl
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] : ( subrel @ X2 @ ( X1 @ X2 ) ) ) ) ).
thf(def_mono,definition,
( mono
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o] :
( ( subrel @ X2 @ X3 )
=> ( subrel @ ( X1 @ X2 ) @ ( X1 @ X3 ) ) ) ) ) ).
thf(def_refl,definition,
( refl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_irrefl,definition,
( irrefl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) ).
thf(def_rc,definition,
( rc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) ) ) ) ).
thf(def_symm,definition,
( symm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_antisymm,definition,
( antisymm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) ).
thf(def_asymm,definition,
( asymm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_sc,definition,
( sc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ~ ( X1 @ X3 @ X2 )
=> ( X1 @ X2 @ X3 ) ) ) ) ).
thf(def_trans,definition,
( trans
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_tc,definition,
( tc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ~ ( ( trans @ X4 )
=> ~ ( subrel @ X1 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ).
thf(def_trc,definition,
( trc
= ( ^ [X1: $i > $i > $o] : ( rc @ ( tc @ X1 ) ) ) ) ).
thf(def_trsc,definition,
( trsc
= ( ^ [X1: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X1 ) ) ) ) ) ).
thf(def_po,definition,
( po
= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ( refl @ X1 )
=> ~ ( antisymm @ X1 ) )
=> ~ ( trans @ X1 ) ) ) ) ).
thf(def_so,definition,
( so
= ( ^ [X1: $i > $i > $o] :
~ ( ( asymm @ X1 )
=> ~ ( trans @ X1 ) ) ) ) ).
thf(def_total,definition,
( total
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_term,definition,
( term
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o] :
( ~ ! [X3: $i] :
~ ( X2 @ X3 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) ) ) ).
thf(def_ind,definition,
( ind
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( tc @ X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) )
=> ( !! @ X2 ) ) ) ) ).
thf(def_innf,definition,
( innf
= ( ^ [X1: $i > $i > $o,X2: $i] :
! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) ).
thf(def_nfof,definition,
( nfof
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
~ ( ( trc @ X1 @ X3 @ X2 )
=> ~ ( innf @ X1 @ X2 ) ) ) ) ).
thf(def_norm,definition,
( norm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
~ ( nfof @ X1 @ X3 @ X2 ) ) ) ).
thf(def_join,definition,
( join
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
~ ! [X4: $i] :
( ( trc @ X1 @ X2 @ X4 )
=> ~ ( trc @ X1 @ X3 @ X4 ) ) ) ) ).
thf(def_lconfl,definition,
( lconfl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X2 @ X3 ) )
=> ( join @ X1 @ X4 @ X3 ) ) ) ) ).
thf(def_sconfl,definition,
( sconfl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( trc @ X1 @ X2 @ X3 ) )
=> ( join @ X1 @ X4 @ X3 ) ) ) ) ).
thf(def_confl,definition,
( confl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( trc @ X1 @ X2 @ X4 )
=> ~ ( trc @ X1 @ X2 @ X3 ) )
=> ( join @ X1 @ X4 @ X3 ) ) ) ) ).
thf(def_cr,definition,
( cr
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( trsc @ X1 @ X2 @ X3 )
=> ( join @ X1 @ X2 @ X3 ) ) ) ) ).
thf(partial_order_induces_strict_order,conjecture,
! [X1: $i > $i > $o] :
( ~ ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ~ ( ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ( X2 = X3 ) )
=> ~ ~ ( ( X1 @ X3 @ X2 )
=> ( X3 = X2 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ( X1 @ X2 @ X3 )
=> ( X2 = X3 ) )
=> ~ ~ ( ( X1 @ X3 @ X4 )
=> ( X3 = X4 ) ) )
=> ~ ( ( X1 @ X2 @ X4 )
=> ( X2 = X4 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i > $o] :
( ~ ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ~ ( ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ( X2 = X3 ) )
=> ( ( X1 @ X3 @ X2 )
=> ( X3 = X2 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ( X1 @ X2 @ X3 )
=> ( X2 = X3 ) )
=> ( ( X1 @ X3 @ X4 )
=> ( X3 = X4 ) ) )
=> ~ ( ( X1 @ X2 @ X4 )
=> ( X2 = X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[partial_order_induces_strict_order]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( ! [X1: $i] : ( eigen__0 @ X1 @ X1 )
=> ~ sP16 )
=> ~ sP9 )
=> ~ ( ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ( X1 = X2 ) )
=> ( ( eigen__0 @ X2 @ X1 )
=> ( X2 = X1 ) ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( eigen__0 @ X1 @ X2 )
=> ( X1 = X2 ) )
=> ( ( eigen__0 @ X2 @ X3 )
=> ( X2 = X3 ) ) )
=> ~ ( ( eigen__0 @ X1 @ X3 )
=> ( X1 = X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ~ ( ! [X1: $i] : ( eigen__0 @ X1 @ X1 )
=> ~ sP16 )
=> ~ sP9 ),
introduced(assumption,[]) ).
thf(h3,assumption,
( ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ( X1 = X2 ) )
=> ( ( eigen__0 @ X2 @ X1 )
=> ( X2 = X1 ) ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( eigen__0 @ X1 @ X2 )
=> ( X1 = X2 ) )
=> ( ( eigen__0 @ X2 @ X3 )
=> ( X2 = X3 ) ) )
=> ~ ( ( eigen__0 @ X1 @ X3 )
=> ( X1 = X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ! [X1: $i] : ( eigen__0 @ X1 @ X1 )
=> ~ sP16 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP9,
introduced(assumption,[]) ).
thf(h6,assumption,
! [X1: $i] : ( eigen__0 @ X1 @ X1 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP16,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ( X1 = X2 ) )
=> ( ( eigen__0 @ X2 @ X1 )
=> ( X2 = X1 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( eigen__0 @ X1 @ X2 )
=> ( X1 = X2 ) )
=> ( ( eigen__0 @ X2 @ X3 )
=> ( X2 = X3 ) ) )
=> ~ ( ( eigen__0 @ X1 @ X3 )
=> ( X1 = X3 ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i] :
( ~ ( ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__1 = X1 ) )
=> ( ( eigen__0 @ X1 @ eigen__1 )
=> ( X1 = eigen__1 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ ( sP28
=> ( eigen__1 = eigen__2 ) )
=> ( sP1
=> sP24 ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP28
=> ( eigen__1 = eigen__2 ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( sP1
=> sP24 ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP28,
introduced(assumption,[]) ).
thf(h15,assumption,
eigen__1 != eigen__2,
introduced(assumption,[]) ).
thf(h16,assumption,
sP1,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP24,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP16
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP21
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP23
| sP27
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP27
| ~ sP1
| ~ sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h17,h14,h15,h12,h13,h11,h10,h8,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,h7,h14,h16,h17]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h12,h13,h11,h10,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h13,5,h16,h17]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h11,h10,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,6,h14,h15]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h10,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,7,h12,h13]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h10,8,h11]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[h8,9,h10]) ).
thf(h18,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( eigen__0 @ eigen__3 @ X1 )
=> ( eigen__3 = X1 ) )
=> ( ( eigen__0 @ X1 @ X2 )
=> ( X1 = X2 ) ) )
=> ~ ( ( eigen__0 @ eigen__3 @ X2 )
=> ( eigen__3 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ! [X1: $i] :
( ~ ( ~ ( sP3
=> sP10 )
=> ( ( eigen__0 @ eigen__4 @ X1 )
=> ( eigen__4 = X1 ) ) )
=> ~ ( ( eigen__0 @ eigen__3 @ X1 )
=> ( eigen__3 = X1 ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( ~ ( ~ ( sP3
=> sP10 )
=> ( sP15
=> ( eigen__4 = eigen__5 ) ) )
=> ~ ( sP30
=> sP5 ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( ~ ( sP3
=> sP10 )
=> ( sP15
=> ( eigen__4 = eigen__5 ) ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
( sP30
=> sP5 ),
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( sP3
=> sP10 ),
introduced(assumption,[]) ).
thf(h24,assumption,
~ ( sP15
=> ( eigen__4 = eigen__5 ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
sP3,
introduced(assumption,[]) ).
thf(h26,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h27,assumption,
sP15,
introduced(assumption,[]) ).
thf(h28,assumption,
eigen__4 != eigen__5,
introduced(assumption,[]) ).
thf(h29,assumption,
~ sP30,
introduced(assumption,[]) ).
thf(h30,assumption,
sP5,
introduced(assumption,[]) ).
thf(11,plain,
( ~ sP9
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP14
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP8
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP20
| sP4
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP4
| ~ sP3
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h29,h27,h28,h25,h26,h23,h24,h21,h22,h20,h19,h18,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[11,12,13,14,15,h5,h25,h27,h29]) ).
thf(17,plain,
( ~ sP30
| sP22
| ~ sP5
| ~ sP18 ),
inference(mating_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP12
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP2
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP19
| sP13
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP13
| ~ sP15
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP16
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP17
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP25
| sP11
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP11
| ~ sP3
| ~ sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP9
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP9
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP14
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP8
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP20
| sP4
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP4
| ~ sP3
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP6
| ~ sP5
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP7
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP26
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(35,plain,
sP26,
inference(eq_sym,[status(thm)],[]) ).
thf(36,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h30,h27,h28,h25,h26,h23,h24,h21,h22,h20,h19,h18,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,h7,h5,h25,h26,h27,h30]) ).
thf(37,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h27,h28,h25,h26,h23,h24,h21,h22,h20,h19,h18,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h29]),tab_imp(discharge,[h30])],[h22,16,36,h29,h30]) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h25,h26,h23,h24,h21,h22,h20,h19,h18,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h27,h28])],[h24,37,h27,h28]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h24,h21,h22,h20,h19,h18,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h25,h26])],[h23,38,h25,h26]) ).
thf(40,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h22,h20,h19,h18,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h23,h24])],[h21,39,h23,h24]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h19,h18,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,40,h21,h22]) ).
thf(42,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h19,h18,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__5)],[h19,41,h20]) ).
thf(43,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h18,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__4)],[h18,42,h19]) ).
thf(44,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__3)],[h9,43,h18]) ).
thf(45,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h9])],[h3,10,44,h8,h9]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,45,h6,h7]) ).
thf(47,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,46,h4,h5]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,47,h2,h3]) ).
thf(49,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,48,h1]) ).
thf(0,theorem,
! [X1: $i > $i > $o] :
( ~ ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ~ ( ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ( X2 = X3 ) )
=> ~ ~ ( ( X1 @ X3 @ X2 )
=> ( X3 = X2 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ( X1 @ X2 @ X3 )
=> ( X2 = X3 ) )
=> ~ ~ ( ( X1 @ X3 @ X4 )
=> ( X3 = X4 ) ) )
=> ~ ( ( X1 @ X2 @ X4 )
=> ( X2 = X4 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[49,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU498^1 : TPTP v9.2.0. Released v3.6.0.
% 0.08/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Oct 8 21:20:23 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % Mode: mode213
% 0.21/0.42 % Inferences: 129
% 0.21/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------