TSTP Solution File: SEV045^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV045^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 19:32:25 EDT 2023
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_cQ,type,
cQ: a > b > b > $o ).
thf(ty_cP,type,
cP: a > a > $o ).
thf(ty_g,type,
g: a > b ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_f,type,
f: a > b ).
thf(sP1,plain,
( sP1
<=> ( cP @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
=> ( cQ @ X1 @ ( f @ X1 ) @ ( f @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cP @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP3
=> ( ( cQ @ eigen__1 )
= ( cQ @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cQ @ eigen__0 @ ( f @ eigen__0 ) @ ( g @ eigen__0 ) )
=> ~ ( cQ @ eigen__0 @ ( g @ eigen__0 ) @ ( g @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a,X2: a] :
( ~ ( ( cP @ eigen__0 @ X1 )
=> ~ ( cP @ X1 @ X2 ) )
=> ( cP @ eigen__0 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( cQ @ eigen__1 @ ( f @ eigen__1 ) @ ( g @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( cQ @ eigen__0 @ ( g @ eigen__0 ) @ ( f @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cP @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: b,X2: b] :
( ~ ( ( cQ @ eigen__0 @ ( g @ eigen__0 ) @ X1 )
=> ~ ( cQ @ eigen__0 @ X1 @ X2 ) )
=> ( cQ @ eigen__0 @ ( g @ eigen__0 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a] :
( ( cP @ eigen__1 @ X1 )
=> ( ( cQ @ eigen__1 )
= ( cQ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a,X2: a] :
( ~ ( ( cP @ eigen__1 @ X1 )
=> ~ ( cP @ X1 @ X2 ) )
=> ( cP @ eigen__1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( cQ @ eigen__0 @ ( g @ eigen__0 ) @ ( f @ eigen__1 ) )
=> ~ ( cQ @ eigen__0 @ ( f @ eigen__1 ) @ ( g @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( cP @ X1 @ X2 )
=> ~ ( cP @ X2 @ X3 ) )
=> ( cP @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP3
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a] :
( ~ ( sP1
=> ~ ( cP @ eigen__1 @ X1 ) )
=> ( cP @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: b] :
( ( cQ @ eigen__1 @ ( f @ eigen__1 ) @ X1 )
= ( cQ @ eigen__0 @ ( f @ eigen__1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ sP13
=> ( cQ @ eigen__0 @ ( g @ eigen__0 ) @ ( g @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP9
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP1
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ sP15
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP8
=> ~ ( cQ @ eigen__0 @ ( f @ eigen__0 ) @ ( f @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( cQ @ eigen__0 @ ( f @ eigen__1 ) @ ( g @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
=> ( cP @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( cQ @ eigen__0 @ ( f @ eigen__0 ) @ ( f @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( cQ @ eigen__1 @ ( f @ eigen__1 ) )
= ( cQ @ eigen__0 @ ( f @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( cQ @ eigen__0 @ ( g @ eigen__0 ) @ ( f @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: b] :
( ( cQ @ eigen__1 @ X1 )
= ( cQ @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: a] :
( ( cP @ eigen__0 @ X1 )
=> ( cP @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( cP @ eigen__0 @ eigen__0 )
=> ~ ( ! [X1: b,X2: b] :
( ( cQ @ eigen__0 @ X1 @ X2 )
=> ( cQ @ eigen__0 @ X2 @ X1 ) )
=> ~ ! [X1: b,X2: b,X3: b] :
( ~ ( ( cQ @ eigen__0 @ X1 @ X2 )
=> ~ ( cQ @ eigen__0 @ X2 @ X3 ) )
=> ( cQ @ eigen__0 @ X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( cP @ eigen__0 @ eigen__0 )
=> ( cQ @ eigen__0 @ ( f @ eigen__0 ) @ ( g @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: b] :
( ~ ( sP8
=> ~ ( cQ @ eigen__0 @ ( f @ eigen__0 ) @ X1 ) )
=> ( cQ @ eigen__0 @ ( g @ eigen__0 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( cQ @ eigen__0 @ ( f @ eigen__0 ) @ ( g @ eigen__0 ) )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: b,X2: b] :
( ( cQ @ eigen__0 @ X1 @ X2 )
=> ( cQ @ eigen__0 @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( cQ @ eigen__0 @ ( f @ eigen__0 ) @ ( g @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
=> ( ( cQ @ X1 )
= ( cQ @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sP34
=> ~ ! [X1: b,X2: b,X3: b] :
( ~ ( ( cQ @ eigen__0 @ X1 @ X2 )
=> ~ ( cQ @ eigen__0 @ X2 @ X3 ) )
=> ( cQ @ eigen__0 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( cQ @ eigen__0 @ ( f @ eigen__0 ) @ ( g @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ~ sP20
=> ( cP @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: a] :
( ( cP @ X1 @ X1 )
=> ( cQ @ X1 @ ( f @ X1 ) @ ( g @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: b] :
( ~ ( sP35
=> ~ ( cQ @ eigen__0 @ ( g @ eigen__0 ) @ X1 ) )
=> ( cQ @ eigen__0 @ ( f @ eigen__0 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: a] :
( ( cP @ eigen__0 @ X1 )
=> ( cQ @ eigen__0 @ ( f @ eigen__0 ) @ ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( sP1
=> sP25 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: a] :
( ~ ( sP3
=> ~ ( cP @ eigen__0 @ X1 ) )
=> ( cP @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: b,X2: b] :
( ~ ( ( cQ @ eigen__0 @ ( f @ eigen__0 ) @ X1 )
=> ~ ( cQ @ eigen__0 @ X1 @ X2 ) )
=> ( cQ @ eigen__0 @ ( f @ eigen__0 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ~ sP22
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( cP @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( sP1
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ! [X1: b] :
( ~ ( sP27
=> ~ ( cQ @ eigen__0 @ ( f @ eigen__1 ) @ X1 ) )
=> ( cQ @ eigen__0 @ ( g @ eigen__0 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( cQ @ eigen__0 @ ( g @ eigen__0 ) @ ( g @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ! [X1: a] :
( ( cP @ X1 @ X1 )
=> ~ ( ! [X2: b,X3: b] :
( ( cQ @ X1 @ X2 @ X3 )
=> ( cQ @ X1 @ X3 @ X2 ) )
=> ~ ! [X2: b,X3: b,X4: b] :
( ~ ( ( cQ @ X1 @ X2 @ X3 )
=> ~ ( cQ @ X1 @ X3 @ X4 ) )
=> ( cQ @ X1 @ X2 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( ~ sP5
=> sP38 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ! [X1: b,X2: b,X3: b] :
( ~ ( ( cQ @ eigen__0 @ X1 @ X2 )
=> ~ ( cQ @ eigen__0 @ X2 @ X3 ) )
=> ( cQ @ eigen__0 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ( cQ @ eigen__1 )
= ( cQ @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ! [X1: b] :
( ( cQ @ eigen__0 @ ( f @ eigen__0 ) @ X1 )
=> ( cQ @ eigen__0 @ X1 @ ( f @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP7 = sP23 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(cTHM509_pme,conjecture,
( sP40
=> ( sP2
=> ( ~ ( sP24
=> ~ sP14 )
=> ( ~ ( sP51
=> ~ sP36 )
=> ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
=> ( cQ @ X1 @ ( f @ X1 ) @ ( g @ X2 ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP40
=> ( sP2
=> ( ~ ( sP24
=> ~ sP14 )
=> ( ~ ( sP51
=> ~ sP36 )
=> ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
=> ( cQ @ X1 @ ( f @ X1 ) @ ( g @ X2 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM509_pme]) ).
thf(h1,assumption,
sP40,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP2
=> ( ~ ( sP24
=> ~ sP14 )
=> ( ~ ( sP51
=> ~ sP36 )
=> ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
=> ( cQ @ X1 @ ( f @ X1 ) @ ( g @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP2,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( sP24
=> ~ sP14 )
=> ( ~ ( sP51
=> ~ sP36 )
=> ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
=> ( cQ @ X1 @ ( f @ X1 ) @ ( g @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP24
=> ~ sP14 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ( sP51
=> ~ sP36 )
=> ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
=> ( cQ @ X1 @ ( f @ X1 ) @ ( g @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP24,
introduced(assumption,[]) ).
thf(h8,assumption,
sP14,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP51
=> ~ sP36 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
=> ( cQ @ X1 @ ( f @ X1 ) @ ( g @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP51,
introduced(assumption,[]) ).
thf(h12,assumption,
sP36,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: a] :
( ( cP @ eigen__0 @ X1 )
=> ( cQ @ eigen__0 @ ( f @ eigen__0 ) @ ( g @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP1
=> sP38 ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP1,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP38,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP13
| ~ sP27
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP56
| ~ sP7
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP18
| sP13
| sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP22
| ~ sP8
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP17
| sP56 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP49
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP46
| sP22
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP26
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP28
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP10
| sP49 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP32
| sP46 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP5
| ~ sP35
| ~ sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP52
| sP5
| sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP10
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP41
| sP52 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP33
| ~ sP35
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP53
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP45
| sP41 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP55
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP34
| sP55 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP53
| sP45 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP15
| ~ sP3
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP21
| sP15
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP44
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP20
| ~ sP1
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP39
| sP20
| sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP12
| sP44 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP16
| sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP54
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP4
| ~ sP3
| sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP11
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP19
| ~ sP9
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP43
| ~ sP1
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP48
| ~ sP1
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP36
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP40
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP14
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP42
| sP43 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP29
| sP48 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP6
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( sP37
| sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP37
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP30
| ~ sP47
| ~ sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP31
| ~ sP47
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP24
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP2
| sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP40
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP14
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP51
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(50,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h16,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,h1,h3,h7,h8,h11,h12,h15,h16]) ).
thf(51,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,50,h15,h16]) ).
thf(52,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__1)],[h13,51,h14]) ).
thf(53,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__0)],[h10,52,h13]) ).
thf(54,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h9,53,h11,h12]) ).
thf(55,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h6,54,h9,h10]) ).
thf(56,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,55,h7,h8]) ).
thf(57,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,56,h5,h6]) ).
thf(58,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,57,h3,h4]) ).
thf(59,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,58,h1,h2]) ).
thf(0,theorem,
( sP40
=> ( sP2
=> ( ~ ( sP24
=> ~ sP14 )
=> ( ~ ( sP51
=> ~ sP36 )
=> ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
=> ( cQ @ X1 @ ( f @ X1 ) @ ( g @ X2 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[59,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEV045^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n022.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 : 300
% 0.12/0.34 % DateTime : Thu Aug 24 02:53:26 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % Mode: cade22grackle2xfee4
% 0.20/0.46 % Steps: 505
% 0.20/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------