TSTP Solution File: SEU473^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU473^1 : TPTP v8.1.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n029.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 : 600s
% DateTime : Tue Jul 19 13:52:21 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 168
% Syntax : Number of formulae : 224 ( 105 unt; 16 typ; 33 def)
% Number of atoms : 515 ( 67 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 1803 ( 391 ~; 34 |; 0 &; 931 @)
% ( 35 <=>; 411 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 192 ( 192 >; 0 *; 0 +; 0 <<)
% Number of symbols : 84 ( 81 usr; 73 con; 0-2 aty)
% ( 1 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 471 ( 47 ^ 424 !; 0 ?; 471 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__16,type,
eigen__16: $i > $i > $o ).
thf(ty_eigen__7,type,
eigen__7: $i > $i > $o ).
thf(ty_eigen__24,type,
eigen__24: $i ).
thf(ty_eigen__15,type,
eigen__15: $i > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i > $i > $o ).
thf(ty_eigen__5,type,
eigen__5: $i > $i > $o ).
thf(ty_eigen__19,type,
eigen__19: $i ).
thf(ty_eigen__11,type,
eigen__11: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__17,type,
eigen__17: $i > $i > $o ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(ty_eigen__18,type,
eigen__18: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__0 @ eigen__8 @ X1 )
=> ( eigen__6 @ eigen__8 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__6 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__24,definition,
( eigen__24
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__0 @ eigen__19 @ X1 )
=> ( eigen__18 @ eigen__19 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__24])]) ).
thf(eigendef_eigen__19,definition,
( eigen__19
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__18 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__19])]) ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__18 @ X1 @ X2 )
=> ~ ( eigen__18 @ X2 @ X3 ) )
=> ( eigen__18 @ X1 @ X3 ) )
=> ~ ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__18 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__0 @ eigen__19 @ eigen__24 )
=> ( eigen__1 @ eigen__19 @ eigen__24 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__6 @ X1 @ X2 )
=> ~ ( eigen__6 @ X2 @ X3 ) )
=> ( eigen__6 @ X1 @ X3 ) )
=> ~ ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__6 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( eigen__1 @ eigen__8 @ X1 )
=> ( eigen__6 @ eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__0 @ eigen__19 @ eigen__24 )
=> ( eigen__18 @ eigen__19 @ eigen__24 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( eigen__1 @ eigen__19 @ X1 )
=> ( eigen__18 @ eigen__19 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__19 @ X1 )
=> ( eigen__1 @ eigen__19 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__8 @ X1 )
=> ( eigen__1 @ eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0 @ eigen__19 @ eigen__24 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__18 @ eigen__19 @ eigen__24 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__18 @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( eigen__1 @ eigen__8 @ eigen__11 )
=> ( eigen__6 @ eigen__8 @ eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__1 @ eigen__19 @ eigen__24 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__18 @ X1 @ X2 )
=> ~ ( eigen__18 @ X2 @ X3 ) )
=> ( eigen__18 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__18 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__6 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__6 @ eigen__8 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP13
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( eigen__0 @ eigen__8 @ eigen__11 )
=> ( eigen__1 @ eigen__8 @ eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__6 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__19 @ X1 )
=> ( eigen__18 @ eigen__19 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ sP1
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__18 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__0 @ eigen__8 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ sP3
=> ( eigen__6 @ eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP24
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__3 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eigen__6 @ eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__6 @ X1 @ X2 )
=> ~ ( eigen__6 @ X2 @ X3 ) )
=> ( eigen__6 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( eigen__1 @ eigen__8 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( eigen__2 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__8 @ X1 )
=> ( eigen__6 @ eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
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(transitive_reflexive_symmetric_closure_op_is_monotonic,conjecture,
! [X1: $i > $i > $o,X2: $i > $i > $o] :
( ! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ! [X3: $i,X4: $i] :
( ( ~ ( ( X4 != X3 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X4 @ X3 ) ) )
=> ( ( X3 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) ) )
=> ( ~ ( ( X4 != X3 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X4 @ X3 ) ) )
=> ( ( X3 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i > $i > $o,X2: $i > $i > $o] :
( ! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ! [X3: $i,X4: $i] :
( ( ~ ( ( X4 != X3 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X4 @ X3 ) ) )
=> ( ( X3 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) ) )
=> ( ~ ( ( X4 != X3 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X4 @ X3 ) ) )
=> ( ( X3 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[transitive_reflexive_symmetric_closure_op_is_monotonic]) ).
thf(h2,assumption,
~ ! [X1: $i > $i > $o] :
( ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ! [X2: $i,X3: $i] :
( ( ~ ( ( X3 != X2 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X3 @ X2 ) ) )
=> ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) )
=> ( ~ ( ( X3 != X2 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X3 @ X2 ) ) )
=> ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP26
=> ! [X1: $i,X2: $i] :
( ( ~ ( ( X2 != X1 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X2 @ X1 ) ) )
=> ( ( X1 != X2 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) )
=> ( ~ ( ( X2 != X1 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__1 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X2 @ X1 ) ) )
=> ( ( X1 != X2 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__1 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP26,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i,X2: $i] :
( ( ~ ( ( X2 != X1 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X2 @ X1 ) ) )
=> ( ( X1 != X2 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) )
=> ( ~ ( ( X2 != X1 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__1 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X2 @ X1 ) ) )
=> ( ( X1 != X2 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__1 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ( ~ ( ( X1 != eigen__2 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ X1 @ eigen__2 ) ) )
=> ( ( eigen__2 != X1 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__2 @ X1 ) ) ) )
=> ( ~ ( ( X1 != eigen__2 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ X1 @ eigen__2 ) ) )
=> ( ( eigen__2 != X1 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__2 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ( ~ ( ~ sP28
=> sP31 )
=> ( ~ sP34
=> sP30 ) )
=> ( ~ ( ~ sP28
=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__3 @ eigen__2 ) ) )
=> ( ~ sP34
=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__2 @ eigen__3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
( ~ ( ~ sP28
=> sP31 )
=> ( ~ sP34
=> sP30 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( ~ sP28
=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__3 @ eigen__2 ) ) )
=> ( ~ sP34
=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__2 @ eigen__3 ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
( ~ sP28
=> sP31 ),
introduced(assumption,[]) ).
thf(h11,assumption,
( ~ sP34
=> sP30 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP28,
introduced(assumption,[]) ).
thf(h13,assumption,
sP31,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ~ sP28
=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__3 @ eigen__2 ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ~ sP34
=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__2 @ eigen__3 ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP28,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__3 @ eigen__2 ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__4 @ X1 @ X2 )
=> ~ ( eigen__4 @ X2 @ X3 ) )
=> ( eigen__4 @ X1 @ X3 ) )
=> ~ ! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__4 @ X1 @ X2 ) ) )
=> ( eigen__4 @ eigen__3 @ eigen__2 ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__4 @ X1 @ X2 )
=> ~ ( eigen__4 @ X2 @ X3 ) )
=> ( eigen__4 @ X1 @ X3 ) )
=> ~ ! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__4 @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( eigen__4 @ eigen__3 @ eigen__2 ),
introduced(assumption,[]) ).
thf(h21,assumption,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__4 @ X1 @ X2 )
=> ~ ( eigen__4 @ X2 @ X3 ) )
=> ( eigen__4 @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__4 @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h23,assumption,
~ sP34,
introduced(assumption,[]) ).
thf(h24,assumption,
~ ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__2 @ eigen__3 ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
~ ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__5 @ X1 @ X2 )
=> ~ ( eigen__5 @ X2 @ X3 ) )
=> ( eigen__5 @ X1 @ X3 ) )
=> ~ ! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__5 @ X1 @ X2 ) ) )
=> ( eigen__5 @ eigen__2 @ eigen__3 ) ),
introduced(assumption,[]) ).
thf(h26,assumption,
~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__5 @ X1 @ X2 )
=> ~ ( eigen__5 @ X2 @ X3 ) )
=> ( eigen__5 @ X1 @ X3 ) )
=> ~ ! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__5 @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
~ ( eigen__5 @ eigen__2 @ eigen__3 ),
introduced(assumption,[]) ).
thf(h28,assumption,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__5 @ X1 @ X2 )
=> ~ ( eigen__5 @ X2 @ X3 ) )
=> ( eigen__5 @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(h29,assumption,
! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__5 @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h28,h29,h26,h27,h25,h23,h24,h21,h22,h19,h20,h18,h16,h17,h14,h15,h12,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0])],[h12,h16]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h26,h27,h25,h23,h24,h21,h22,h19,h20,h18,h16,h17,h14,h15,h12,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h28,h29])],[h26,1,h28,h29]) ).
thf(3,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h25,h23,h24,h21,h22,h19,h20,h18,h16,h17,h14,h15,h12,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h26,h27])],[h25,2,h26,h27]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h23,h24,h21,h22,h19,h20,h18,h16,h17,h14,h15,h12,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h25]),tab_negall(eigenvar,eigen__5)],[h24,3,h25]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h22,h19,h20,h18,h16,h17,h14,h15,h12,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h23,h24])],[h15,4,h23,h24]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h18,h16,h17,h14,h15,h12,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h19,5,h21,h22]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h16,h17,h14,h15,h12,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,6,h19,h20]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h17,h14,h15,h12,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__4)],[h17,7,h18]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h12,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h14,8,h16,h17]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h9,9,h14,h15]) ).
thf(h30,assumption,
~ ( ~ ( sP32
=> ~ sP20 )
=> sP29 ),
introduced(assumption,[]) ).
thf(h31,assumption,
~ ( sP32
=> ~ sP20 ),
introduced(assumption,[]) ).
thf(h32,assumption,
~ sP29,
introduced(assumption,[]) ).
thf(h33,assumption,
sP32,
introduced(assumption,[]) ).
thf(h34,assumption,
sP20,
introduced(assumption,[]) ).
thf(h35,assumption,
~ ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__7 @ X1 @ X2 )
=> ~ ( eigen__7 @ X2 @ X3 ) )
=> ( eigen__7 @ X1 @ X3 ) )
=> ~ ! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__7 @ X1 @ X2 ) ) )
=> ( eigen__7 @ eigen__2 @ eigen__3 ) ),
introduced(assumption,[]) ).
thf(h36,assumption,
~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__7 @ X1 @ X2 )
=> ~ ( eigen__7 @ X2 @ X3 ) )
=> ( eigen__7 @ X1 @ X3 ) )
=> ~ ! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__7 @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h37,assumption,
~ ( eigen__7 @ eigen__2 @ eigen__3 ),
introduced(assumption,[]) ).
thf(h38,assumption,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__7 @ X1 @ X2 )
=> ~ ( eigen__7 @ X2 @ X3 ) )
=> ( eigen__7 @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(h39,assumption,
! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__7 @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(11,plain,
( ~ sP20
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP4
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP12
| ~ sP33
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP26
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP8
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP19
| ~ sP24
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP27
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP27
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP35
| ~ sP27 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(20,plain,
( sP16
| ~ sP35 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(21,plain,
( ~ sP31
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP25
| sP3
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP3
| ~ sP32
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h38,h39,h36,h37,h35,h23,h24,h33,h34,h31,h32,h30,h16,h17,h14,h15,h13,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0])],[11,12,13,14,15,16,17,18,19,20,21,22,23,h4,h13,h33,h34,h32]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h36,h37,h35,h23,h24,h33,h34,h31,h32,h30,h16,h17,h14,h15,h13,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h38,h39])],[h36,24,h38,h39]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h35,h23,h24,h33,h34,h31,h32,h30,h16,h17,h14,h15,h13,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h36,h37])],[h35,25,h36,h37]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h23,h24,h33,h34,h31,h32,h30,h16,h17,h14,h15,h13,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h35]),tab_negall(eigenvar,eigen__7)],[h24,26,h35]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h33,h34,h31,h32,h30,h16,h17,h14,h15,h13,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h23,h24])],[h15,27,h23,h24]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h31,h32,h30,h16,h17,h14,h15,h13,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h33,h34])],[h31,28,h33,h34]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h30,h16,h17,h14,h15,h13,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h31,h32])],[h30,29,h31,h32]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h17,h14,h15,h13,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h30]),tab_negall(eigenvar,eigen__6)],[h17,30,h30]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h13,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h14,31,h16,h17]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h9,32,h14,h15]) ).
thf(34,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h10,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h12]),tab_imp(discharge,[h13])],[h10,10,33,h12,h13]) ).
thf(h40,assumption,
sP34,
introduced(assumption,[]) ).
thf(h41,assumption,
sP30,
introduced(assumption,[]) ).
thf(h42,assumption,
~ ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__15 @ X1 @ X2 )
=> ~ ( eigen__15 @ X2 @ X3 ) )
=> ( eigen__15 @ X1 @ X3 ) )
=> ~ ! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__15 @ X1 @ X2 ) ) )
=> ( eigen__15 @ eigen__3 @ eigen__2 ) ),
introduced(assumption,[]) ).
thf(h43,assumption,
~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__15 @ X1 @ X2 )
=> ~ ( eigen__15 @ X2 @ X3 ) )
=> ( eigen__15 @ X1 @ X3 ) )
=> ~ ! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__15 @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h44,assumption,
~ ( eigen__15 @ eigen__3 @ eigen__2 ),
introduced(assumption,[]) ).
thf(h45,assumption,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__15 @ X1 @ X2 )
=> ~ ( eigen__15 @ X2 @ X3 ) )
=> ( eigen__15 @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(h46,assumption,
! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__15 @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h47,assumption,
~ ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__16 @ X1 @ X2 )
=> ~ ( eigen__16 @ X2 @ X3 ) )
=> ( eigen__16 @ X1 @ X3 ) )
=> ~ ! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__16 @ X1 @ X2 ) ) )
=> ( eigen__16 @ eigen__2 @ eigen__3 ) ),
introduced(assumption,[]) ).
thf(h48,assumption,
~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__16 @ X1 @ X2 )
=> ~ ( eigen__16 @ X2 @ X3 ) )
=> ( eigen__16 @ X1 @ X3 ) )
=> ~ ! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__16 @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h49,assumption,
~ ( eigen__16 @ eigen__2 @ eigen__3 ),
introduced(assumption,[]) ).
thf(h50,assumption,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__16 @ X1 @ X2 )
=> ~ ( eigen__16 @ X2 @ X3 ) )
=> ( eigen__16 @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(h51,assumption,
! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__16 @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(35,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h50,h51,h48,h49,h47,h23,h24,h45,h46,h43,h44,h42,h16,h17,h14,h15,h40,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0])],[h40,h23]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h48,h49,h47,h23,h24,h45,h46,h43,h44,h42,h16,h17,h14,h15,h40,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h50,h51])],[h48,35,h50,h51]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h47,h23,h24,h45,h46,h43,h44,h42,h16,h17,h14,h15,h40,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h48,h49])],[h47,36,h48,h49]) ).
thf(38,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h23,h24,h45,h46,h43,h44,h42,h16,h17,h14,h15,h40,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h47]),tab_negall(eigenvar,eigen__16)],[h24,37,h47]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h45,h46,h43,h44,h42,h16,h17,h14,h15,h40,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h23,h24])],[h15,38,h23,h24]) ).
thf(40,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h43,h44,h42,h16,h17,h14,h15,h40,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h45,h46])],[h43,39,h45,h46]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h42,h16,h17,h14,h15,h40,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h43,h44])],[h42,40,h43,h44]) ).
thf(42,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h17,h14,h15,h40,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h42]),tab_negall(eigenvar,eigen__15)],[h17,41,h42]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h40,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h14,42,h16,h17]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h40,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h9,43,h14,h15]) ).
thf(h52,assumption,
~ ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__17 @ X1 @ X2 )
=> ~ ( eigen__17 @ X2 @ X3 ) )
=> ( eigen__17 @ X1 @ X3 ) )
=> ~ ! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__17 @ X1 @ X2 ) ) )
=> ( eigen__17 @ eigen__3 @ eigen__2 ) ),
introduced(assumption,[]) ).
thf(h53,assumption,
~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__17 @ X1 @ X2 )
=> ~ ( eigen__17 @ X2 @ X3 ) )
=> ( eigen__17 @ X1 @ X3 ) )
=> ~ ! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__17 @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h54,assumption,
~ ( eigen__17 @ eigen__3 @ eigen__2 ),
introduced(assumption,[]) ).
thf(h55,assumption,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__17 @ X1 @ X2 )
=> ~ ( eigen__17 @ X2 @ X3 ) )
=> ( eigen__17 @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(h56,assumption,
! [X1: $i,X2: $i] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__17 @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h57,assumption,
~ ( ~ ( sP14
=> ~ sP15 )
=> sP11 ),
introduced(assumption,[]) ).
thf(h58,assumption,
~ ( sP14
=> ~ sP15 ),
introduced(assumption,[]) ).
thf(h59,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h60,assumption,
sP14,
introduced(assumption,[]) ).
thf(h61,assumption,
sP15,
introduced(assumption,[]) ).
thf(45,plain,
( ~ sP15
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP6
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP18
| ~ sP13
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP26
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP2
| ~ sP9
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
( sP5
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
( sP5
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(53,plain,
( sP21
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__24]) ).
thf(54,plain,
( sP23
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__19]) ).
thf(55,plain,
( ~ sP30
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP22
| sP1
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(57,plain,
( ~ sP1
| ~ sP14
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(58,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h60,h61,h58,h59,h57,h23,h24,h55,h56,h53,h54,h52,h16,h17,h14,h15,h41,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0])],[45,46,47,48,49,50,51,52,53,54,55,56,57,h4,h41,h60,h61,h59]) ).
thf(59,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h58,h59,h57,h23,h24,h55,h56,h53,h54,h52,h16,h17,h14,h15,h41,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h60,h61])],[h58,58,h60,h61]) ).
thf(60,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h57,h23,h24,h55,h56,h53,h54,h52,h16,h17,h14,h15,h41,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h58,h59])],[h57,59,h58,h59]) ).
thf(61,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h23,h24,h55,h56,h53,h54,h52,h16,h17,h14,h15,h41,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h57]),tab_negall(eigenvar,eigen__18)],[h24,60,h57]) ).
thf(62,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h55,h56,h53,h54,h52,h16,h17,h14,h15,h41,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h23,h24])],[h15,61,h23,h24]) ).
thf(63,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h53,h54,h52,h16,h17,h14,h15,h41,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h55,h56])],[h53,62,h55,h56]) ).
thf(64,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h52,h16,h17,h14,h15,h41,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h53,h54])],[h52,63,h53,h54]) ).
thf(65,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h17,h14,h15,h41,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h52]),tab_negall(eigenvar,eigen__17)],[h17,64,h52]) ).
thf(66,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h41,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h14,65,h16,h17]) ).
thf(67,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h41,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h9,66,h14,h15]) ).
thf(68,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h40]),tab_imp(discharge,[h41])],[h11,44,67,h40,h41]) ).
thf(69,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h9,h7,h6,h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[h8,34,68,h10,h11]) ).
thf(70,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,69,h8,h9]) ).
thf(71,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__3)],[h6,70,h7]) ).
thf(72,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,71,h6]) ).
thf(73,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,72,h4,h5]) ).
thf(74,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,73,h3]) ).
thf(75,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,74,h2]) ).
thf(76,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[75,h0]) ).
thf(0,theorem,
! [X1: $i > $i > $o,X2: $i > $i > $o] :
( ! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ! [X3: $i,X4: $i] :
( ( ~ ( ( X4 != X3 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X4 @ X3 ) ) )
=> ( ( X3 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) ) )
=> ( ~ ( ( X4 != X3 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X4 @ X3 ) ) )
=> ( ( X3 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[75,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU473^1 : TPTP v8.1.0. Released v3.6.0.
% 0.06/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n029.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 : 600
% 0.12/0.34 % DateTime : Sat Jun 18 20:34:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % Mode: mode213
% 0.19/0.43 % Inferences: 155
% 0.19/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------