TSTP Solution File: SEV031^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV031^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n017.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 18:04:32 EDT 2022
% Result : Theorem 0.11s 0.38s
% Output : Proof 0.11s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__2,type,
eigen__2: a > b ).
thf(ty_eigen__7,type,
eigen__7: a > b ).
thf(ty_eigen__1,type,
eigen__1: a > ( a > b ) > ( a > b ) > $o ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(ty_eigen__4,type,
eigen__4: a > b ).
thf(ty_eigen__5,type,
eigen__5: a > b ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__10,type,
eigen__10: a ).
thf(ty_eigen__8,type,
eigen__8: a > b ).
thf(ty_eigen__9,type,
eigen__9: a > b ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__1 @ eigen__10 @ eigen__7 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__1 @ eigen__10 @ eigen__7 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a > b,X2: a > b] :
( ~ ( ( eigen__1 @ eigen__10 @ eigen__7 @ X1 )
=> ~ ( eigen__1 @ eigen__10 @ X1 @ X2 ) )
=> ( eigen__1 @ eigen__10 @ eigen__7 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__1 @ eigen__6 @ eigen__5 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ! [X1: a > b] : ( eigen__1 @ eigen__10 @ X1 @ X1 )
=> ~ ! [X1: a > b,X2: a > b] :
( ( eigen__1 @ eigen__10 @ X1 @ X2 )
=> ( eigen__1 @ eigen__10 @ X2 @ X1 ) ) )
=> ~ ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ( eigen__1 @ eigen__10 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__10 @ X2 @ X3 ) )
=> ( eigen__1 @ eigen__10 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__1 @ eigen__10 @ eigen__8 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( sP2
=> ~ sP7 )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP1
=> ~ ( ~ ( ! [X1: a > b] : ( eigen__1 @ eigen__3 @ X1 @ X1 )
=> ~ ! [X1: a > b,X2: a > b] :
( ( eigen__1 @ eigen__3 @ X1 @ X2 )
=> ( eigen__1 @ eigen__3 @ X2 @ X1 ) ) )
=> ~ ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ( eigen__1 @ eigen__3 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__3 @ X2 @ X3 ) )
=> ( eigen__1 @ eigen__3 @ X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__0 @ eigen__10 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a > b] :
( ~ ( sP2
=> ~ ( eigen__1 @ eigen__10 @ eigen__8 @ X1 ) )
=> ( eigen__1 @ eigen__10 @ eigen__7 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a > b] :
( ( eigen__1 @ eigen__6 @ eigen__4 @ X1 )
=> ( eigen__1 @ eigen__6 @ X1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a > b,X2: a > b] :
( ( eigen__1 @ eigen__6 @ X1 @ X2 )
=> ( eigen__1 @ eigen__6 @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eigen__0 @ eigen__10 )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( eigen__0 @ eigen__10 )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( eigen__1 @ eigen__6 @ eigen__4 @ eigen__5 )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ! [X1: a > b] : ( eigen__1 @ eigen__3 @ X1 @ X1 )
=> ~ ! [X1: a > b,X2: a > b] :
( ( eigen__1 @ eigen__3 @ X1 @ X2 )
=> ( eigen__1 @ eigen__3 @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ eigen__7 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ! [X1: a > b] : ( eigen__1 @ eigen__6 @ X1 @ X1 )
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP2
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ sP19
=> ~ ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ( eigen__1 @ eigen__6 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__6 @ X2 @ X3 ) )
=> ( eigen__1 @ eigen__6 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__0 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP22
=> ( eigen__1 @ eigen__6 @ eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ~ ( ~ ( ! [X2: a > b] : ( eigen__1 @ X1 @ X2 @ X2 )
=> ~ ! [X2: a > b,X3: a > b] :
( ( eigen__1 @ X1 @ X2 @ X3 )
=> ( eigen__1 @ X1 @ X3 @ X2 ) ) )
=> ~ ! [X2: a > b,X3: a > b,X4: a > b] :
( ~ ( ( eigen__1 @ X1 @ X2 @ X3 )
=> ~ ( eigen__1 @ X1 @ X3 @ X4 ) )
=> ( eigen__1 @ X1 @ X2 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__1 @ eigen__3 @ eigen__2 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: a > b] : ( eigen__1 @ eigen__3 @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ eigen__8 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eigen__1 @ eigen__6 @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP22
=> ~ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( eigen__0 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ sP17
=> ~ ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ( eigen__1 @ eigen__3 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__3 @ X2 @ X3 ) )
=> ( eigen__1 @ eigen__3 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ( eigen__1 @ eigen__10 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__10 @ X2 @ X3 ) )
=> ( eigen__1 @ eigen__10 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(cTHM512_pme,conjecture,
! [X1: a > $o,X2: a > ( a > b ) > ( a > b ) > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( ~ ( ! [X4: a > b] : ( X2 @ X3 @ X4 @ X4 )
=> ~ ! [X4: a > b,X5: a > b] :
( ( X2 @ X3 @ X4 @ X5 )
=> ( X2 @ X3 @ X5 @ X4 ) ) )
=> ~ ! [X4: a > b,X5: a > b,X6: a > b] :
( ~ ( ( X2 @ X3 @ X4 @ X5 )
=> ~ ( X2 @ X3 @ X5 @ X6 ) )
=> ( X2 @ X3 @ X4 @ X6 ) ) ) )
=> ~ ( ~ ( ! [X3: a > b,X4: a] :
( ( X1 @ X4 )
=> ( X2 @ X4 @ X3 @ X3 ) )
=> ~ ! [X3: a > b,X4: a > b] :
( ! [X5: a] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ X3 @ X4 ) )
=> ! [X5: a] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ X4 @ X3 ) ) ) )
=> ~ ! [X3: a > b,X4: a > b,X5: a > b] :
( ~ ( ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ X3 @ X4 ) )
=> ~ ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ X4 @ X5 ) ) )
=> ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ X3 @ X5 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > $o,X2: a > ( a > b ) > ( a > b ) > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( ~ ( ! [X4: a > b] : ( X2 @ X3 @ X4 @ X4 )
=> ~ ! [X4: a > b,X5: a > b] :
( ( X2 @ X3 @ X4 @ X5 )
=> ( X2 @ X3 @ X5 @ X4 ) ) )
=> ~ ! [X4: a > b,X5: a > b,X6: a > b] :
( ~ ( ( X2 @ X3 @ X4 @ X5 )
=> ~ ( X2 @ X3 @ X5 @ X6 ) )
=> ( X2 @ X3 @ X4 @ X6 ) ) ) )
=> ~ ( ~ ( ! [X3: a > b,X4: a] :
( ( X1 @ X4 )
=> ( X2 @ X4 @ X3 @ X3 ) )
=> ~ ! [X3: a > b,X4: a > b] :
( ! [X5: a] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ X3 @ X4 ) )
=> ! [X5: a] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ X4 @ X3 ) ) ) )
=> ~ ! [X3: a > b,X4: a > b,X5: a > b] :
( ~ ( ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ X3 @ X4 ) )
=> ~ ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ X4 @ X5 ) ) )
=> ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ X3 @ X5 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM512_pme]) ).
thf(h1,assumption,
~ ! [X1: a > ( a > b ) > ( a > b ) > $o] :
( ! [X2: a] :
( ( eigen__0 @ X2 )
=> ~ ( ~ ( ! [X3: a > b] : ( X1 @ X2 @ X3 @ X3 )
=> ~ ! [X3: a > b,X4: a > b] :
( ( X1 @ X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X4 @ X3 ) ) )
=> ~ ! [X3: a > b,X4: a > b,X5: a > b] :
( ~ ( ( X1 @ X2 @ X3 @ X4 )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X2 @ X3 @ X5 ) ) ) )
=> ~ ( ~ ( ! [X2: a > b,X3: a] :
( ( eigen__0 @ X3 )
=> ( X1 @ X3 @ X2 @ X2 ) )
=> ~ ! [X2: a > b,X3: a > b] :
( ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( X1 @ X4 @ X2 @ X3 ) )
=> ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( X1 @ X4 @ X3 @ X2 ) ) ) )
=> ~ ! [X2: a > b,X3: a > b,X4: a > b] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ X5 )
=> ( X1 @ X5 @ X2 @ X3 ) )
=> ~ ! [X5: a] :
( ( eigen__0 @ X5 )
=> ( X1 @ X5 @ X3 @ X4 ) ) )
=> ! [X5: a] :
( ( eigen__0 @ X5 )
=> ( X1 @ X5 @ X2 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP24
=> ~ ( ~ ( ! [X1: a > b,X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ X1 @ X1 ) )
=> ~ ! [X1: a > b,X2: a > b] :
( ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ X1 @ X2 ) )
=> ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ X2 @ X1 ) ) ) )
=> ~ ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ X1 @ X2 ) )
=> ~ ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ X2 @ X3 ) ) )
=> ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ X1 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP24,
introduced(assumption,[]) ).
thf(h4,assumption,
( ~ ( ! [X1: a > b,X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ X1 @ X1 ) )
=> ~ ! [X1: a > b,X2: a > b] :
( ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ X1 @ X2 ) )
=> ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ X2 @ X1 ) ) ) )
=> ~ ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ X1 @ X2 ) )
=> ~ ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ X2 @ X3 ) ) )
=> ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
( ! [X1: a > b,X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ X1 @ X1 ) )
=> ~ ! [X1: a > b,X2: a > b] :
( ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ X1 @ X2 ) )
=> ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ X2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ X1 @ X2 ) )
=> ~ ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ X2 @ X3 ) ) )
=> ! [X4: a] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ X1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: a > b,X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ X1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: a > b,X2: a > b] :
( ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ X1 @ X2 ) )
=> ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ eigen__2 @ eigen__2 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP1
=> sP25 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP1,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP25,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP26
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( sP17
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP32
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP24
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP9
| ~ sP1
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h10,h9,h7,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,h3,h11,h12]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h9,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,6,h11,h12]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h7,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h9,7,h10]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h7,8,h9]) ).
thf(h13,assumption,
~ ! [X1: a > b] :
( ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ eigen__4 @ X1 ) )
=> ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ X1 @ eigen__4 ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP27
=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ eigen__5 @ eigen__4 ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP27,
introduced(assumption,[]) ).
thf(h16,assumption,
~ ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ eigen__5 @ eigen__4 ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP22
=> sP5 ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP22,
introduced(assumption,[]) ).
thf(h19,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(10,plain,
( ~ sP13
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP12
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP16
| ~ sP29
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP19
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP21
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP27
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP23
| ~ sP22
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP24
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP30
| ~ sP22
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h18,h19,h17,h15,h16,h14,h13,h8,h5,h3,h4,h2,h1,h0])],[10,11,12,13,14,15,16,17,18,h3,h15,h18,h19]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h15,h16,h14,h13,h8,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,19,h18,h19]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h16,h14,h13,h8,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__6)],[h16,20,h17]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h13,h8,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,21,h15,h16]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h8,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__5)],[h13,22,h14]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h8,23,h13]) ).
thf(25,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h5,9,24,h7,h8]) ).
thf(h20,assumption,
~ ! [X1: a > b,X2: a > b] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ eigen__7 @ X1 ) )
=> ~ ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ X1 @ X2 ) ) )
=> ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ eigen__7 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ! [X1: a > b] :
( ~ ( sP18
=> ~ ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ eigen__8 @ X1 ) ) )
=> ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ eigen__7 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
~ ( ~ ( sP18
=> ~ sP28 )
=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ eigen__7 @ eigen__9 ) ) ),
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( sP18
=> ~ sP28 ),
introduced(assumption,[]) ).
thf(h24,assumption,
~ ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ eigen__7 @ eigen__9 ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
sP18,
introduced(assumption,[]) ).
thf(h26,assumption,
sP28,
introduced(assumption,[]) ).
thf(h27,assumption,
~ ( sP31
=> sP3 ),
introduced(assumption,[]) ).
thf(h28,assumption,
sP31,
introduced(assumption,[]) ).
thf(h29,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(26,plain,
( ~ sP33
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP4
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP11
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP8
| sP20
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP20
| ~ sP2
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP6
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP18
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP10
| ~ sP31
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP28
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP15
| ~ sP31
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP24
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP14
| ~ sP31
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h28,h29,h27,h25,h26,h23,h24,h22,h21,h20,h6,h3,h4,h2,h1,h0])],[26,27,28,29,30,31,32,33,34,35,36,37,h3,h25,h26,h28,h29]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h25,h26,h23,h24,h22,h21,h20,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h28,h29])],[h27,38,h28,h29]) ).
thf(40,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h25,h26,h23,h24,h22,h21,h20,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h27]),tab_negall(eigenvar,eigen__10)],[h24,39,h27]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h24,h22,h21,h20,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h25,h26])],[h23,40,h25,h26]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h21,h20,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h23,h24])],[h22,41,h23,h24]) ).
thf(43,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h20,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h22]),tab_negall(eigenvar,eigen__9)],[h21,42,h22]) ).
thf(44,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h20,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__8)],[h20,43,h21]) ).
thf(45,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__7)],[h6,44,h20]) ).
thf(46,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h4,25,45,h5,h6]) ).
thf(47,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,46,h3,h4]) ).
thf(48,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,47,h2]) ).
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: a > $o,X2: a > ( a > b ) > ( a > b ) > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( ~ ( ! [X4: a > b] : ( X2 @ X3 @ X4 @ X4 )
=> ~ ! [X4: a > b,X5: a > b] :
( ( X2 @ X3 @ X4 @ X5 )
=> ( X2 @ X3 @ X5 @ X4 ) ) )
=> ~ ! [X4: a > b,X5: a > b,X6: a > b] :
( ~ ( ( X2 @ X3 @ X4 @ X5 )
=> ~ ( X2 @ X3 @ X5 @ X6 ) )
=> ( X2 @ X3 @ X4 @ X6 ) ) ) )
=> ~ ( ~ ( ! [X3: a > b,X4: a] :
( ( X1 @ X4 )
=> ( X2 @ X4 @ X3 @ X3 ) )
=> ~ ! [X3: a > b,X4: a > b] :
( ! [X5: a] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ X3 @ X4 ) )
=> ! [X5: a] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ X4 @ X3 ) ) ) )
=> ~ ! [X3: a > b,X4: a > b,X5: a > b] :
( ~ ( ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ X3 @ X4 ) )
=> ~ ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ X4 @ X5 ) ) )
=> ! [X6: a] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ X3 @ X5 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[49,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEV031^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33 % Computer : n017.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Tue Jun 28 14:45:07 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % Mode: mode213
% 0.11/0.38 % Inferences: 49
% 0.11/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------