TSTP Solution File: SEV300^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV300^5 : TPTP v8.1.2. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n027.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 19:33:16 EDT 2023
% Result : Theorem 20.23s 20.59s
% Output : Proof 20.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 66
% Syntax : Number of formulae : 77 ( 17 unt; 5 typ; 7 def)
% Number of atoms : 210 ( 70 equ; 3 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 248 ( 99 ~; 35 |; 2 &; 55 @)
% ( 25 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 34 usr; 36 con; 0-2 aty)
% Number of variables : 69 ( 25 ^; 42 !; 2 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( X2 != X1 )
=> ~ ( eigen__0 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: $i] :
( ( eigen__0 @ X1 )
!= ( eigen__1 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
( eigen__0
!= ( ^ [X2: $i] : ( X1 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: $i] :
~ ( ( X1 != eigen__2 )
=> ~ ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(sP1,plain,
( sP1
<=> ( ( eigen__0 @ eigen__2 )
= ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0
= ( ^ [X1: $i] : ( eigen__2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__8 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( X1 != eigen__2 )
=> ~ ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( eigen__0
!= ( ^ [X2: $i] : ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__7 != eigen__2 )
=> ~ ( eigen__0 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__7 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__0 @ eigen__8 )
= ( eigen__1 = eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eigen__0 @ eigen__1 )
=> ~ ! [X1: $i] :
( ( X1 != eigen__1 )
=> ~ ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__2 = eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( X1 != eigen__1 )
=> ~ ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
= ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
= ( eigen__1 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> $false ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( ~ ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( X2 != X1 )
=> ~ ( eigen__0 @ X2 ) ) ) )
= ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__0
= ( ^ [X1: $i] : ( eigen__1 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ sP4
=> ~ ( eigen__0 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP3
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP9 = sP12 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__0 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__1 = eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( X2 != X1 )
=> ~ ( eigen__0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(def_cZERO,definition,
( cZERO
= ( ^ [X1: $i > $o] :
( (~)
@ ? [X2: $i] : ( X1 @ X2 ) ) ) ) ).
thf(def_cSUCC,definition,
( cSUCC
= ( ^ [X1: ( $i > $o ) > $o,X2: $i > $o] :
? [X3: $i] :
( ( X2 @ X3 )
& ( X1
@ ^ [X4: $i] :
( ( (~) @ ( X4 = X3 ) )
& ( X2 @ X4 ) ) ) ) ) ) ).
thf(def_cONE,definition,
( cONE
= ( cSUCC @ cZERO ) ) ).
thf(cX6101_EXT_pme,conjecture,
( ! [X1: $i > $i,X2: $i > $i] :
( ! [X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) )
=> ( X1 = X2 ) )
=> ( ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) )
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
( X1
!= ( ^ [X3: $i] : ( X2 = X3 ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( ! [X1: $i > $i,X2: $i > $i] :
( ! [X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) )
=> ( X1 = X2 ) )
=> ( ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) )
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
( X1
!= ( ^ [X3: $i] : ( X2 = X3 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cX6101_EXT_pme]) ).
thf(h2,assumption,
! [X1: $i > $i,X2: $i > $i] :
( ! [X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
( ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) )
!= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
( X1
!= ( ^ [X3: $i] : ( X2 = X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i > $o] :
( ( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) )
= ( ~ ! [X2: $i] :
( X1
!= ( ^ [X3: $i] : ( X2 = X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
( ~ sP25
!= ( ~ ! [X1: $i] :
( eigen__0
!= ( (=) @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP19
| sP4
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| sP24 ),
inference(symeq,[status(thm)],]) ).
thf(3,plain,
( ~ sP13
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP20
| sP23
| ~ sP24 ),
inference(mating_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP22
| ~ sP9
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP14
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP10
| ~ sP23
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP10
| sP23
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP12
| sP8 ),
inference(symeq,[status(thm)],]) ).
thf(10,plain,
( sP15
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(11,plain,
( sP7
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP7
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP18
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP5
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(15,plain,
( ~ sP6
| ~ sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP21
| ~ sP3
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP1
| sP3
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
~ sP16,
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP25
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP14
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP2
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP11
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP11
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP6
| sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(25,plain,
( sP25
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(26,plain,
( sP17
| sP25
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP17
| ~ sP25
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h4,h2,h3,h1,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,h5]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,28,h5]) ).
thf(30,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h2,h3,h1,h0]),tab_fe(discharge,[h4])],[h3,29,h4]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,30,h2,h3]) ).
thf(32,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[31,h0]) ).
thf(0,theorem,
( ! [X1: $i > $i,X2: $i > $i] :
( ! [X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) )
=> ( X1 = X2 ) )
=> ( ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) )
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
( X1
!= ( ^ [X3: $i] : ( X2 = X3 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[31,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV300^5 : TPTP v8.1.2. Bugfixed v6.2.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n027.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 03:32:32 EDT 2023
% 0.12/0.34 % CPUTime :
% 20.23/20.59 % SZS status Theorem
% 20.23/20.59 % Mode: cade22grackle2x798d
% 20.23/20.59 % Steps: 558
% 20.23/20.59 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------