TSTP Solution File: SEV044^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV044^5 : 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 : n028.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 18:04:35 EDT 2022
% Result : Theorem 0.17s 0.35s
% Output : Proof 0.17s
% 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: b > a ).
thf(ty_eigen__2,type,
eigen__2: b > a ).
thf(ty_eigen__7,type,
eigen__7: b > a ).
thf(ty_eigen__1,type,
eigen__1: b > a > a > $o ).
thf(ty_eigen__0,type,
eigen__0: b > $o ).
thf(ty_eigen__4,type,
eigen__4: b ).
thf(ty_eigen__5,type,
eigen__5: b > a ).
thf(ty_eigen__3,type,
eigen__3: b > a ).
thf(ty_eigen__8,type,
eigen__8: b ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: a,X2: a] :
( ( eigen__1 @ eigen__8 @ X1 @ X2 )
=> ( eigen__1 @ eigen__8 @ X2 @ X1 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__1 @ eigen__8 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__8 @ X2 @ X3 ) )
=> ( eigen__1 @ eigen__8 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__0 @ eigen__8 )
=> ( eigen__1 @ eigen__8 @ ( eigen__5 @ eigen__8 ) @ ( eigen__6 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: a,X2: a] :
( ( eigen__1 @ eigen__4 @ X1 @ X2 )
=> ( eigen__1 @ eigen__4 @ X2 @ X1 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__1 @ eigen__4 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__4 @ X2 @ X3 ) )
=> ( eigen__1 @ eigen__4 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__1 @ eigen__8 @ ( eigen__5 @ eigen__8 ) @ ( eigen__6 @ eigen__8 ) )
=> ~ ( eigen__1 @ eigen__8 @ ( eigen__6 @ eigen__8 ) @ ( eigen__7 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__1 @ eigen__8 @ X1 @ X2 )
=> ~ ( eigen__1 @ eigen__8 @ X2 @ X3 ) )
=> ( eigen__1 @ eigen__8 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__4 ) @ ( eigen__3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP5
=> ( eigen__1 @ eigen__8 @ ( eigen__5 @ eigen__8 ) @ ( eigen__7 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__1 @ eigen__8 @ ( eigen__5 @ eigen__8 ) @ ( eigen__6 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a] :
( ~ ( sP9
=> ~ ( eigen__1 @ eigen__8 @ ( eigen__6 @ eigen__8 ) @ X1 ) )
=> ( eigen__1 @ eigen__8 @ ( eigen__5 @ eigen__8 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP2
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__0 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: b] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ ( eigen__5 @ X1 ) @ ( eigen__6 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a,X2: a] :
( ( eigen__1 @ eigen__4 @ X1 @ X2 )
=> ( eigen__1 @ eigen__4 @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP12
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__1 @ eigen__8 @ ( eigen__6 @ eigen__8 ) @ ( eigen__7 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__1 @ eigen__8 @ ( eigen__5 @ eigen__8 ) @ ( eigen__7 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: b] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ ( eigen__2 @ X1 ) @ ( eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__1 @ eigen__4 @ ( eigen__3 @ eigen__4 ) @ ( eigen__2 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP2
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a] :
( ( eigen__1 @ eigen__4 @ ( eigen__2 @ eigen__4 ) @ X1 )
=> ( eigen__1 @ eigen__4 @ X1 @ ( eigen__2 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP7
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: b] :
( ( eigen__0 @ X1 )
=> ~ ( ! [X2: a,X3: a] :
( ( eigen__1 @ X1 @ X2 @ X3 )
=> ( eigen__1 @ X1 @ X3 @ X2 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( eigen__1 @ X1 @ X2 @ X3 )
=> ~ ( eigen__1 @ X1 @ X3 @ X4 ) )
=> ( eigen__1 @ X1 @ X2 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__1 @ eigen__8 @ ( eigen__5 @ eigen__8 ) @ X1 )
=> ~ ( eigen__1 @ eigen__8 @ X1 @ X2 ) )
=> ( eigen__1 @ eigen__8 @ ( eigen__5 @ eigen__8 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP12
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: b] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ ( eigen__6 @ X1 ) @ ( eigen__7 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(cTHM506_pme,conjecture,
! [X1: b > $o,X2: b > a > a > $o] :
( ! [X3: b] :
( ( X1 @ X3 )
=> ~ ( ! [X4: a,X5: a] :
( ( X2 @ X3 @ X4 @ X5 )
=> ( X2 @ X3 @ X5 @ X4 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X2 @ X3 @ X4 @ X5 )
=> ~ ( X2 @ X3 @ X5 @ X6 ) )
=> ( X2 @ X3 @ X4 @ X6 ) ) ) )
=> ~ ( ! [X3: b > a,X4: b > a] :
( ! [X5: b] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X5 ) ) )
=> ! [X5: b] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ ( X4 @ X5 ) @ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: b > a,X4: b > a,X5: b > a] :
( ~ ( ! [X6: b] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X4 @ X6 ) ) )
=> ~ ! [X6: b] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ ( X4 @ X6 ) @ ( X5 @ X6 ) ) ) )
=> ! [X6: b] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X5 @ X6 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: b > $o,X2: b > a > a > $o] :
( ! [X3: b] :
( ( X1 @ X3 )
=> ~ ( ! [X4: a,X5: a] :
( ( X2 @ X3 @ X4 @ X5 )
=> ( X2 @ X3 @ X5 @ X4 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X2 @ X3 @ X4 @ X5 )
=> ~ ( X2 @ X3 @ X5 @ X6 ) )
=> ( X2 @ X3 @ X4 @ X6 ) ) ) )
=> ~ ( ! [X3: b > a,X4: b > a] :
( ! [X5: b] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X5 ) ) )
=> ! [X5: b] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ ( X4 @ X5 ) @ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: b > a,X4: b > a,X5: b > a] :
( ~ ( ! [X6: b] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X4 @ X6 ) ) )
=> ~ ! [X6: b] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ ( X4 @ X6 ) @ ( X5 @ X6 ) ) ) )
=> ! [X6: b] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X5 @ X6 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM506_pme]) ).
thf(h1,assumption,
~ ! [X1: b > a > a > $o] :
( ! [X2: b] :
( ( eigen__0 @ X2 )
=> ~ ( ! [X3: a,X4: a] :
( ( X1 @ X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X4 @ X3 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X1 @ X2 @ X3 @ X4 )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X2 @ X3 @ X5 ) ) ) )
=> ~ ( ! [X2: b > a,X3: b > a] :
( ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X4 ) ) )
=> ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( X1 @ X4 @ ( X3 @ X4 ) @ ( X2 @ X4 ) ) ) )
=> ~ ! [X2: b > a,X3: b > a,X4: b > a] :
( ~ ( ! [X5: b] :
( ( eigen__0 @ X5 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X3 @ X5 ) ) )
=> ~ ! [X5: b] :
( ( eigen__0 @ X5 )
=> ( X1 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X5 ) ) ) )
=> ! [X5: b] :
( ( eigen__0 @ X5 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X4 @ X5 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP23
=> ~ ( ! [X1: b > a,X2: b > a] :
( ! [X3: b] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) )
=> ! [X3: b] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ ( X2 @ X3 ) @ ( X1 @ X3 ) ) ) )
=> ~ ! [X1: b > a,X2: b > a,X3: b > a] :
( ~ ( ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) )
=> ~ ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X4 ) ) ) )
=> ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ ( X1 @ X4 ) @ ( X3 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP23,
introduced(assumption,[]) ).
thf(h4,assumption,
( ! [X1: b > a,X2: b > a] :
( ! [X3: b] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) )
=> ! [X3: b] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ ( X2 @ X3 ) @ ( X1 @ X3 ) ) ) )
=> ~ ! [X1: b > a,X2: b > a,X3: b > a] :
( ~ ( ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) )
=> ~ ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X4 ) ) ) )
=> ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ ( X1 @ X4 ) @ ( X3 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: b > a,X2: b > a] :
( ! [X3: b] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) )
=> ! [X3: b] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ ( X2 @ X3 ) @ ( X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: b > a,X2: b > a,X3: b > a] :
( ~ ( ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) )
=> ~ ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X4 ) ) ) )
=> ! [X4: b] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ X4 @ ( X1 @ X4 ) @ ( X3 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: b > a] :
( ! [X2: b] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ ( eigen__2 @ X2 ) @ ( X1 @ X2 ) ) )
=> ! [X2: b] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ ( X1 @ X2 ) @ ( eigen__2 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP18
=> ! [X1: b] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ ( eigen__3 @ X1 ) @ ( eigen__2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP18,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: b] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ ( eigen__3 @ X1 ) @ ( eigen__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP2
=> sP19 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP2,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP14
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP21
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP22
| ~ sP7
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP4
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP23
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP20
| ~ sP2
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP18
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP11
| ~ sP2
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h13,h11,h9,h10,h8,h7,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,h3,h9,h12,h13]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h8,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,9,h12,h13]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h8,h7,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__4)],[h10,10,h11]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,11,h9,h10]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h7,12,h8]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h5,13,h7]) ).
thf(h14,assumption,
~ ! [X1: b > a,X2: b > a] :
( ~ ( ! [X3: b] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ ( eigen__5 @ X3 ) @ ( X1 @ X3 ) ) )
=> ~ ! [X3: b] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) ) )
=> ! [X3: b] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 @ ( eigen__5 @ X3 ) @ ( X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: b > a] :
( ~ ( sP13
=> ~ ! [X2: b] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ ( eigen__6 @ X2 ) @ ( X1 @ X2 ) ) ) )
=> ! [X2: b] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 @ ( eigen__5 @ X2 ) @ ( X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( ~ ( sP13
=> ~ sP26 )
=> ! [X1: b] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ ( eigen__5 @ X1 ) @ ( eigen__7 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP13
=> ~ sP26 ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ ! [X1: b] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 @ ( eigen__5 @ X1 ) @ ( eigen__7 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
sP13,
introduced(assumption,[]) ).
thf(h20,assumption,
sP26,
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( sP12
=> sP17 ),
introduced(assumption,[]) ).
thf(h22,assumption,
sP12,
introduced(assumption,[]) ).
thf(h23,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(15,plain,
( ~ sP6
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP24
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP10
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP8
| sP5
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP5
| ~ sP9
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP1
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP13
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP3
| ~ sP12
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP26
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP25
| ~ sP12
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP23
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP15
| ~ sP12
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h22,h23,h21,h19,h20,h17,h18,h16,h15,h14,h6,h3,h4,h2,h1,h0])],[15,16,17,18,19,20,21,22,23,24,25,26,h3,h19,h20,h22,h23]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h19,h20,h17,h18,h16,h15,h14,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,27,h22,h23]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h19,h20,h17,h18,h16,h15,h14,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__8)],[h18,28,h21]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h16,h15,h14,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h17,29,h19,h20]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h15,h14,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,30,h17,h18]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h14,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__7)],[h15,31,h16]) ).
thf(33,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__6)],[h14,32,h15]) ).
thf(34,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__5)],[h6,33,h14]) ).
thf(35,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h4,14,34,h5,h6]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,35,h3,h4]) ).
thf(37,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,36,h2]) ).
thf(38,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,37,h1]) ).
thf(0,theorem,
! [X1: b > $o,X2: b > a > a > $o] :
( ! [X3: b] :
( ( X1 @ X3 )
=> ~ ( ! [X4: a,X5: a] :
( ( X2 @ X3 @ X4 @ X5 )
=> ( X2 @ X3 @ X5 @ X4 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X2 @ X3 @ X4 @ X5 )
=> ~ ( X2 @ X3 @ X5 @ X6 ) )
=> ( X2 @ X3 @ X4 @ X6 ) ) ) )
=> ~ ( ! [X3: b > a,X4: b > a] :
( ! [X5: b] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X5 ) ) )
=> ! [X5: b] :
( ( X1 @ X5 )
=> ( X2 @ X5 @ ( X4 @ X5 ) @ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: b > a,X4: b > a,X5: b > a] :
( ~ ( ! [X6: b] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X4 @ X6 ) ) )
=> ~ ! [X6: b] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ ( X4 @ X6 ) @ ( X5 @ X6 ) ) ) )
=> ! [X6: b] :
( ( X1 @ X6 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X5 @ X6 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[38,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SEV044^5 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.11 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.10/0.32 % Computer : n028.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 600
% 0.10/0.32 % DateTime : Mon Jun 27 17:13:56 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.17/0.35 % SZS status Theorem
% 0.17/0.35 % Mode: mode213
% 0.17/0.35 % Inferences: 28
% 0.17/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------