TSTP Solution File: GRP001^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : GRP001^5 : 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 : n003.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 01:04:58 EDT 2023
% Result : Theorem 37.75s 37.72s
% Output : Proof 37.75s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_e,type,
e: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cP,type,
cP: $i > $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( cP @ ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ eigen__0 ) @ X1 )
= ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ ( cP @ eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cP @ eigen__1 @ ( cP @ eigen__0 @ eigen__0 ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( cP @ ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ ( cP @ eigen__0 @ eigen__1 ) ) @ X1 )
= ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ ( cP @ ( cP @ eigen__0 @ eigen__1 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( cP @ e @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( e
= ( cP @ ( cP @ eigen__0 @ eigen__1 ) @ ( cP @ eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> $false ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ ( cP @ ( cP @ eigen__0 @ eigen__1 ) @ ( cP @ eigen__0 @ eigen__1 ) ) )
= ( cP @ eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( cP @ ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ eigen__0 ) @ eigen__1 )
= ( cP @ ( cP @ eigen__0 @ eigen__1 ) @ ( cP @ eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ e )
= ( cP @ eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( cP @ ( cP @ eigen__0 @ eigen__1 ) @ ( cP @ eigen__0 @ eigen__1 ) )
= ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ ( cP @ eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( cP @ ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ eigen__0 ) @ eigen__1 )
= ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ ( cP @ eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( cP @ ( cP @ ( cP @ eigen__0 @ eigen__1 ) @ ( cP @ eigen__0 @ eigen__1 ) ) @ e )
= ( cP @ ( cP @ eigen__0 @ eigen__1 ) @ ( cP @ eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ ( cP @ eigen__0 @ eigen__1 ) )
= ( cP @ ( cP @ eigen__0 @ eigen__1 ) @ ( cP @ eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ X1 )
= ( cP @ eigen__1 @ ( cP @ eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( cP @ e @ e )
= e ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ eigen__0 )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ e )
= ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ ( cP @ ( cP @ eigen__0 @ eigen__1 ) @ ( cP @ eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( cP @ ( cP @ eigen__0 @ eigen__1 ) @ ( cP @ eigen__0 @ eigen__1 ) )
= e ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( cP @ eigen__1 @ eigen__1 )
= ( cP @ ( cP @ eigen__0 @ eigen__1 ) @ ( cP @ eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i,X2: $i] :
( ( cP @ ( cP @ eigen__1 @ X1 ) @ X2 )
= ( cP @ eigen__1 @ ( cP @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( cP @ e @ ( cP @ eigen__0 @ eigen__1 ) )
= ( cP @ eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( cP @ eigen__1 @ eigen__1 )
= ( cP @ ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ eigen__0 ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ ( cP @ ( cP @ eigen__0 @ eigen__1 ) @ ( cP @ eigen__0 @ eigen__1 ) ) )
= ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ e ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( cP @ eigen__1 @ e )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
( ( cP @ X1 @ X1 )
= e ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( cP @ e @ ( cP @ eigen__0 @ eigen__1 ) )
= ( cP @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ( cP @ eigen__0 @ eigen__1 )
= ( cP @ eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( cP @ ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ ( cP @ eigen__0 @ eigen__1 ) ) @ ( cP @ eigen__0 @ eigen__1 ) )
= ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ ( cP @ ( cP @ eigen__0 @ eigen__1 ) @ ( cP @ eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( cP @ eigen__1 @ ( cP @ eigen__0 @ eigen__0 ) )
= ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ e )
= ( cP @ eigen__1 @ ( cP @ eigen__0 @ e ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( cP @ ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ eigen__0 ) @ eigen__1 )
= ( cP @ eigen__1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i,X2: $i] :
( ( cP @ ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ X1 ) @ X2 )
= ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ ( cP @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ eigen__0 )
= ( cP @ eigen__1 @ ( cP @ eigen__0 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ( cP @ eigen__1 @ e )
= ( cP @ eigen__1 @ ( cP @ eigen__0 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( cP @ eigen__1 @ eigen__1 )
= e ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ( cP @ eigen__0 @ eigen__0 )
= e ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( cP @ ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ ( cP @ eigen__0 @ eigen__1 ) ) @ ( cP @ eigen__0 @ eigen__1 ) )
= ( cP @ e @ ( cP @ eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $i] :
( ( cP @ X1 @ e )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( e
= ( cP @ eigen__1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ( cP @ ( cP @ eigen__1 @ eigen__0 ) @ ( cP @ eigen__0 @ eigen__1 ) )
= e ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ( cP @ eigen__1 @ ( cP @ eigen__0 @ eigen__0 ) )
= ( cP @ eigen__1 @ e ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(cGRP_COMM2,conjecture,
( ~ ( ~ ( ~ ( sP5
=> ~ sP39 )
=> ~ sP26 )
=> ~ sP1 )
=> ! [X1: $i,X2: $i] :
( ( cP @ X1 @ X2 )
= ( cP @ X2 @ X1 ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( sP5
=> ~ sP39 )
=> ~ sP26 )
=> ~ sP1 )
=> ! [X1: $i,X2: $i] :
( ( cP @ X1 @ X2 )
= ( cP @ X2 @ X1 ) ) ),
inference(assume_negation,[status(cth)],[cGRP_COMM2]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( sP5
=> ~ sP39 )
=> ~ sP26 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i] :
( ( cP @ X1 @ X2 )
= ( cP @ X2 @ X1 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( sP5
=> ~ sP39 )
=> ~ sP26 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP5
=> ~ sP39 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP26,
introduced(assumption,[]) ).
thf(h7,assumption,
sP5,
introduced(assumption,[]) ).
thf(h8,assumption,
sP39,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i] :
( ( cP @ eigen__0 @ X1 )
= ( cP @ X1 @ eigen__0 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP28,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP13
| sP41
| ~ sP11
| ~ sP19 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP16
| sP20
| ~ sP40
| ~ sP6 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP12
| sP14
| sP7
| ~ sP9 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP36
| sP9
| ~ sP23
| ~ sP20 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP31
| sP8
| ~ sP18
| ~ sP10 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP25
| sP3
| ~ sP35
| sP7 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP34
| sP17
| ~ sP30
| ~ sP3 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(8,plain,
( sP38
| sP7
| ~ sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP24
| ~ sP19
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP24
| sP18 ),
inference(symeq,[status(thm)],]) ).
thf(11,plain,
( sP42
| ~ sP37
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP42
| sP35 ),
inference(symeq,[status(thm)],]) ).
thf(13,plain,
( sP32
| sP7
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP32
| sP23 ),
inference(symeq,[status(thm)],]) ).
thf(15,plain,
( ~ sP14
| sP11 ),
inference(symeq,[status(thm)],]) ).
thf(16,plain,
( ~ sP29
| sP22
| ~ sP38
| ~ sP8 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP39
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
~ sP7,
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP34
| sP30 ),
inference(symeq,[status(thm)],]) ).
thf(20,plain,
( ~ sP27
| sP28
| ~ sP27
| ~ sP22 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP2
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP4
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP15
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP15
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP36
| sP40 ),
inference(symeq,[status(thm)],]) ).
thf(26,plain,
( ~ sP19
| sP6 ),
inference(symeq,[status(thm)],]) ).
thf(27,plain,
( ~ sP33
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP33
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP21
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP5
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP5
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP39
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP39
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP26
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP26
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP26
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP1
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP1
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h9,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,h7,h8,h6,h4,h10]) ).
thf(40,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[h9,39,h10]) ).
thf(41,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__0)],[h2,40,h9]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,41,h7,h8]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,42,h5,h6]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,43,h3,h4]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,44,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( sP5
=> ~ sP39 )
=> ~ sP26 )
=> ~ sP1 )
=> ! [X1: $i,X2: $i] :
( ( cP @ X1 @ X2 )
= ( cP @ X2 @ X1 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[45,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP001^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n003.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 : 300
% 0.12/0.33 % DateTime : Tue Aug 29 01:14:55 EDT 2023
% 0.12/0.34 % CPUTime :
% 37.75/37.72 % SZS status Theorem
% 37.75/37.72 % Mode: cade22grackle2x798d
% 37.75/37.72 % Steps: 37149
% 37.75/37.72 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------