TSTP Solution File: SEU492^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU492^1 : 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 : n032.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 13:52:27 EDT 2022
% Result : Theorem 0.13s 0.31s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__7,type,
eigen__7: $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(ty_eigen__8,type,
eigen__8: $i ).
thf(ty_eigen__9,type,
eigen__9: $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__6 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__0 @ eigen__6 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__0 @ eigen__7 @ eigen__8 )
=> ~ ( eigen__0 @ eigen__8 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0 @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( ( eigen__0 @ eigen__2 @ eigen__3 )
=> ~ sP4 )
=> ( eigen__0 @ eigen__2 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ~ ( eigen__0 @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0 @ eigen__7 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__0 @ eigen__8 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0 @ eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__0 @ eigen__6 @ eigen__5 )
=> ~ ( eigen__0 @ eigen__5 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__7 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__0 @ eigen__7 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ~ ( ( eigen__0 @ eigen__6 @ eigen__5 )
=> ~ ( eigen__0 @ eigen__5 @ X1 ) )
=> ( eigen__0 @ eigen__6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
~ ( eigen__0 @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eigen__0 @ eigen__2 @ eigen__3 )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ~ ( ( eigen__0 @ eigen__2 @ eigen__3 )
=> ~ ( eigen__0 @ eigen__3 @ X1 ) )
=> ( eigen__0 @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__0 @ eigen__7 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__0 @ eigen__6 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__0 @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__0 @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__2 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__0 @ eigen__2 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ~ ( sP7
=> ~ ( eigen__0 @ eigen__8 @ X1 ) )
=> ( eigen__0 @ eigen__7 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__0 @ eigen__5 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__0 @ eigen__6 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ sP3
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP19
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ sP10
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
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(alternative_definition_of_strict_order,conjecture,
( ( ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) )
= ( ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i] :
~ ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) ).
thf(h0,negated_conjecture,
( ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) )
!= ( ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i] :
~ ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[alternative_definition_of_strict_order]) ).
thf(h1,assumption,
~ ! [X1: $i > $i > $o] :
( ( ~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) )
= ( ~ ( ! [X2: $i] :
~ ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ~ ( sP18
=> ~ sP2 ) )
!= ( ~ ( sP13
=> ~ sP2 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP18
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP13
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h5,assumption,
( sP18
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h6,assumption,
( sP13
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP18,
introduced(assumption,[]) ).
thf(h8,assumption,
sP2,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h11,assumption,
sP19,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP18
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP26
| ~ sP19
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h9,h7,h8,h3,h4,h2,h1,h0])],[1,2,3,h7,h11]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__1)],[h9,4,h11]) ).
thf(h12,assumption,
~ sP21,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h17,assumption,
sP20,
introduced(assumption,[]) ).
thf(h18,assumption,
sP4,
introduced(assumption,[]) ).
thf(6,plain,
( ~ sP2
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP21
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP15
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP5
| sP14
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP14
| ~ sP20
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h18,h15,h16,h14,h13,h12,h10,h7,h8,h3,h4,h2,h1,h0])],[6,7,8,9,10,h8,h17,h18,h16]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h14,h13,h12,h10,h7,h8,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,11,h17,h18]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h13,h12,h10,h7,h8,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,12,h15,h16]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h12,h10,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__4)],[h13,13,h14]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h10,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__3)],[h12,14,h13]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__2)],[h10,15,h12]) ).
thf(17,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h7,h8,h3,h4,h2,h1,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h4,5,16,h9,h10]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h3,17,h7,h8]) ).
thf(h19,assumption,
~ sP18,
introduced(assumption,[]) ).
thf(h20,assumption,
~ ! [X1: $i] :
( ( eigen__0 @ eigen__5 @ X1 )
=> ~ ( eigen__0 @ X1 @ eigen__5 ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( sP23
=> ~ sP24 ),
introduced(assumption,[]) ).
thf(h22,assumption,
sP23,
introduced(assumption,[]) ).
thf(h23,assumption,
sP24,
introduced(assumption,[]) ).
thf(h24,assumption,
sP13,
introduced(assumption,[]) ).
thf(19,plain,
( ~ sP13
| ~ sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP2
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP1
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP12
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP27
| sP10
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP10
| ~ sP24
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h24,h8,h22,h23,h21,h20,h19,h5,h6,h2,h1,h0])],[19,20,21,22,23,24,h22,h23,h24,h8]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h23,h21,h20,h19,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h24,h8])],[h6,25,h24,h8]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h20,h19,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,26,h22,h23]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h20,h19,h5,h6,h2,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__6)],[h20,27,h21]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h19,h5,h6,h2,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__5)],[h19,28,h20]) ).
thf(h25,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h26,assumption,
~ sP22,
introduced(assumption,[]) ).
thf(h27,assumption,
~ sP25,
introduced(assumption,[]) ).
thf(h28,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h29,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(h30,assumption,
sP7,
introduced(assumption,[]) ).
thf(h31,assumption,
sP8,
introduced(assumption,[]) ).
thf(30,plain,
( ~ sP2
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP11
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP22
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP25
| sP3
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP3
| ~ sP7
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h24,h8,h30,h31,h28,h29,h27,h26,h25,h10,h5,h6,h2,h1,h0])],[30,31,32,33,34,h30,h31,h29,h8]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h30,h31,h28,h29,h27,h26,h25,h10,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h24,h8])],[h6,35,h24,h8]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h28,h29,h27,h26,h25,h10,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h30,h31])],[h28,36,h30,h31]) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h26,h25,h10,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h28,h29])],[h27,37,h28,h29]) ).
thf(39,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h26,h25,h10,h5,h6,h2,h1,h0]),tab_negall(discharge,[h27]),tab_negall(eigenvar,eigen__9)],[h26,38,h27]) ).
thf(40,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h25,h10,h5,h6,h2,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__8)],[h25,39,h26]) ).
thf(41,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h5,h6,h2,h1,h0]),tab_negall(discharge,[h25]),tab_negall(eigenvar,eigen__7)],[h10,40,h25]) ).
thf(42,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_imp(discharge,[h19]),tab_imp(discharge,[h10])],[h5,29,41,h19,h10]) ).
thf(43,plain,
$false,
inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,18,42,h3,h4,h5,h6]) ).
thf(44,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,43,h2]) ).
thf(45,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h0]),tab_fe(discharge,[h1])],[h0,44,h1]) ).
thf(0,theorem,
( ( ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) )
= ( ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i] :
~ ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[45,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.09 % Problem : SEU492^1 : TPTP v8.1.0. Released v3.6.0.
% 0.06/0.09 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Sun Jun 19 22:31:33 EDT 2022
% 0.09/0.28 % CPUTime :
% 0.13/0.31 % SZS status Theorem
% 0.13/0.31 % Mode: mode213
% 0.13/0.31 % Inferences: 18
% 0.13/0.31 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------