TSTP Solution File: SYO506^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO506^1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n013.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 : Thu Jul 21 19:33:06 EDT 2022
% Result : Theorem 64.01s 64.61s
% Output : Proof 64.01s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_c,type,
c: $o > $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ( ( c @ $false @ eigen__1 @ eigen__1 )
= ( c @ ( eigen__0 = eigen__1 ) @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i] :
( ( c @ ~ $false @ X1 @ X2 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> $false ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__1 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( c @ sP3 @ eigen__0 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( c @ ~ sP3 @ eigen__0 @ eigen__0 )
= ( c @ ( eigen__0 = eigen__1 ) @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( ( c @ ~ sP3 @ eigen__0 @ eigen__0 )
= X1 )
=> ( X1
= ( c @ ~ sP3 @ eigen__0 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( c @ ~ sP3 @ eigen__0 @ eigen__0 )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP10
=> ( eigen__0
= ( c @ ~ sP3 @ eigen__0 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP3
= ( eigen__0 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( c @ ( eigen__0 = eigen__1 ) @ eigen__0 @ eigen__1 )
= ( c @ sP3 @ eigen__1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( c @ sP3 @ eigen__0 @ eigen__1 )
= ( c @ ( eigen__0 = eigen__1 ) @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( ( c @ ( eigen__0 = eigen__1 ) @ eigen__0 @ eigen__1 )
= X1 )
=> ( X1
= ( c @ ( eigen__0 = eigen__1 ) @ eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__0
= ( c @ sP3 @ eigen__1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ( c @ sP3 @ eigen__1 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__0
= ( c @ ~ sP3 @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( c @ ~ sP3 @ eigen__0 @ X1 )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__1 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( ~ sP3 )
= ( eigen__0 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP13
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( c @ ( eigen__0 = eigen__1 ) @ eigen__0 @ eigen__1 )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( c @ sP3 @ eigen__0 @ eigen__1 )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i,X2: $i] :
( ( c @ sP3 @ X1 @ X2 )
= X2 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( c @ sP3 @ eigen__1 @ eigen__1 )
= ( c @ sP3 @ eigen__1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( c @ ~ sP3 @ eigen__0 @ eigen__0 )
= ( c @ sP3 @ eigen__1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ( c @ sP3 @ eigen__1 @ eigen__1 )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( c @ sP3 @ eigen__0 @ ( c @ ~ sP3 @ eigen__0 @ eigen__0 ) )
= ( c @ ~ sP3 @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( c @ ~ sP3 @ eigen__0 @ eigen__1 )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(claim,conjecture,
( ~ ( ~ ! [X1: $i,X2: $i] :
( ( c @ ( X1 = X2 ) @ X1 @ X2 )
= X2 )
=> ~ sP2 )
=> ~ sP25 ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ! [X1: $i,X2: $i] :
( ( c @ ( X1 = X2 ) @ X1 @ X2 )
= X2 )
=> ~ sP2 )
=> ~ sP25 ),
inference(assume_negation,[status(cth)],[claim]) ).
thf(h1,assumption,
~ ( ~ ! [X1: $i,X2: $i] :
( ( c @ ( X1 = X2 ) @ X1 @ X2 )
= X2 )
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP25,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i,X2: $i] :
( ( c @ ( X1 = X2 ) @ X1 @ X2 )
= X2 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP2,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ( c @ ( eigen__0 = X1 ) @ eigen__0 @ X1 )
= X1 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP23,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP28
| sP16
| ~ sP4
| ~ sP26 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP31
| sP27
| ~ sP18
| ~ sP16 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP30
| sP13
| ~ sP6
| ~ sP27 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(4,plain,
( sP6
| ~ sP21
| ~ sP9
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP21
| sP3
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP5
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP14
| ~ sP12
| ~ sP9
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP24
| sP23
| ~ sP14
| ~ sP20 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP5
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP11
| ~ sP10
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP7
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP8
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP19
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP19
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
sP26,
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
~ sP3,
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
sP9,
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP29
| sP4
| ~ sP20
| ~ sP9 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(19,plain,
( sP12
| sP3
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP2
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP25
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP22
| ~ sP13
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP15
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
sP20,
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP28
| sP23
| ~ sP1
| ~ sP28 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP17
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP25
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP8
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
sP8,
inference(eq_sym,[status(thm)],]) ).
thf(30,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h5,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,h6,h4,h2]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,30,h6]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h3,31,h5]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,32,h3,h4]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,33,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ! [X1: $i,X2: $i] :
( ( c @ ( X1 = X2 ) @ X1 @ X2 )
= X2 )
=> ~ sP2 )
=> ~ sP25 ),
inference(contra,[status(thm),contra(discharge,[h0])],[34,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO506^1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 21:34:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 64.01/64.61 % SZS status Theorem
% 64.01/64.61 % Mode: mode453
% 64.01/64.61 % Inferences: 4284
% 64.01/64.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------