TSTP Solution File: PUZ107^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : PUZ107^5 : 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 : 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 : 300s
% DateTime : Thu Aug 31 13:21:53 EDT 2023
% Result : Theorem 20.25s 20.55s
% Output : Proof 20.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 57
% Syntax : Number of formulae : 69 ( 19 unt; 6 typ; 6 def)
% Number of atoms : 218 ( 103 equ; 2 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 446 ( 150 ~; 23 |; 7 &; 139 @)
% ( 19 <=>; 108 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 30 usr; 31 con; 0-4 aty)
% Number of variables : 113 ( 13 ^; 95 !; 5 ?; 113 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $i > $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_c1,type,
c1: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ~ ( ( eigen__0 @ c1 @ c1 @ X1 @ X2 )
=> ( ( X1 = c1 )
=> ( X2 != c1 ) ) )
=> ~ ( ( X1 = eigen__1 )
=> ( X2 != eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ( eigen__0 @ c1 @ c1 @ eigen__3 @ X1 )
=> ( ( eigen__3 = c1 )
=> ( X1 != c1 ) ) )
=> ~ ( ( eigen__3 = eigen__1 )
=> ( X1 != eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__2 = c1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__0 @ c1 @ c1 @ eigen__3 @ eigen__4 )
=> ( ( eigen__3 = c1 )
=> ( eigen__4 != c1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( X1 = c1 )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ c1 @ X1 @ X2 @ X3 )
=> ( ( X2 = c1 )
=> ( X3 != c1 ) ) )
=> ~ ( ( X2 = eigen__1 )
=> ( X3 != eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__4 = c1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__3 = c1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ sP2
=> ~ ( ( eigen__3 = eigen__1 )
=> ( eigen__4 != eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__1 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__4 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eigen__3 = eigen__1 )
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__3 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( c1 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( c1 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ c1 @ c1 @ X1 @ X2 )
=> ( ( X1 = c1 )
=> ( X2 != c1 ) ) )
=> ~ ( ( X1 = eigen__1 )
=> ( X2 != eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( c1 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP5
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__1 = c1 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i,X2: $i] :
( ~ ( ( X1 = c1 )
=> ( X2 != c1 ) )
=> ~ ! [X3: $i,X4: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 @ X3 @ X4 )
=> ( ( X3 = c1 )
=> ( X4 != c1 ) ) )
=> ~ ( ( X3 = eigen__1 )
=> ( X4 != eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ~ ( ( eigen__0 @ c1 @ c1 @ eigen__3 @ X1 )
=> ( sP5
=> ( X1 != c1 ) ) )
=> ~ ( sP10
=> ( X1 != eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> $false ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(def_cCKB_INJ,definition,
( cCKB_INJ
= ( ^ [X1: $i > $i > $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ^ [X8: $o,X9: $o] :
( X8
=> X9 )
@ ( ( X1 @ X2 @ X3 @ X6 @ X7 )
& ( X1 @ X4 @ X5 @ X6 @ X7 ) )
@ ( ( X2 = X4 )
& ( X3 = X5 ) ) ) ) ) ).
thf(def_cCKB_XPL,definition,
( cCKB_XPL
= ( ^ [X1: $i > $i > $i > $i > $o,X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
& ! [X5: $i,X6: $i] :
( ^ [X7: $o,X8: $o] :
( X7
=> X8 )
@ ( X2 @ X5 @ X6 )
@ ? [X7: $i,X8: $i] :
( ( X1 @ X5 @ X6 @ X7 @ X8 )
& ( X2 @ X7 @ X8 )
& ( (~)
@ ( ( X7 = X3 )
& ( X8 = X4 ) ) ) ) ) ) ) ) ).
thf(def_cCKB_INF,definition,
( cCKB_INF
= ( ^ [X1: $i > $i > $o] :
? [X2: $i > $i > $i > $i > $o,X3: $i,X4: $i] :
( ( cCKB_INJ @ X2 )
& ( cCKB_XPL @ X2 @ X1 @ X3 @ X4 ) ) ) ) ).
thf(def_cCKB_FIN,definition,
( cCKB_FIN
= ( ^ [X1: $i > $i > $o] : ( (~) @ ( cCKB_INF @ X1 ) ) ) ) ).
thf(cL3000,conjecture,
! [X1: $i > $i > $i > $i > $o,X2: $i,X3: $i] :
( ! [X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
( ~ ( ( X1 @ X4 @ X5 @ X8 @ X9 )
=> ~ ( X1 @ X6 @ X7 @ X8 @ X9 ) )
=> ~ ( ( X4 = X6 )
=> ( X5 != X7 ) ) )
=> ( ~ ( ( X2 = c1 )
=> ( X3 != c1 ) )
=> ~ ! [X4: $i,X5: $i] :
( ~ ( ( X4 = c1 )
=> ( X5 != c1 ) )
=> ~ ! [X6: $i,X7: $i] :
( ~ ( ( X1 @ X4 @ X5 @ X6 @ X7 )
=> ( ( X6 = c1 )
=> ( X7 != c1 ) ) )
=> ~ ( ( X6 = X2 )
=> ( X7 != X3 ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i > $i > $i > $i > $o,X2: $i,X3: $i] :
( ! [X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
( ~ ( ( X1 @ X4 @ X5 @ X8 @ X9 )
=> ~ ( X1 @ X6 @ X7 @ X8 @ X9 ) )
=> ~ ( ( X4 = X6 )
=> ( X5 != X7 ) ) )
=> ( ~ ( ( X2 = c1 )
=> ( X3 != c1 ) )
=> ~ ! [X4: $i,X5: $i] :
( ~ ( ( X4 = c1 )
=> ( X5 != c1 ) )
=> ~ ! [X6: $i,X7: $i] :
( ~ ( ( X1 @ X4 @ X5 @ X6 @ X7 )
=> ( ( X6 = c1 )
=> ( X7 != c1 ) ) )
=> ~ ( ( X6 = X2 )
=> ( X7 != X3 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cL3000]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i] :
( ! [X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ~ ( ( eigen__0 @ X3 @ X4 @ X7 @ X8 )
=> ~ ( eigen__0 @ X5 @ X6 @ X7 @ X8 ) )
=> ~ ( ( X3 = X5 )
=> ( X4 != X6 ) ) )
=> ( ~ ( ( X1 = c1 )
=> ( X2 != c1 ) )
=> ~ ! [X3: $i,X4: $i] :
( ~ ( ( X3 = c1 )
=> ( X4 != c1 ) )
=> ~ ! [X5: $i,X6: $i] :
( ~ ( ( eigen__0 @ X3 @ X4 @ X5 @ X6 )
=> ( ( X5 = c1 )
=> ( X6 != c1 ) ) )
=> ~ ( ( X5 = X1 )
=> ( X6 != X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ! [X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ~ ( ( eigen__0 @ X2 @ X3 @ X6 @ X7 )
=> ~ ( eigen__0 @ X4 @ X5 @ X6 @ X7 ) )
=> ~ ( ( X2 = X4 )
=> ( X3 != X5 ) ) )
=> ( ~ ( sP16
=> ( X1 != c1 ) )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( X2 = c1 )
=> ( X3 != c1 ) )
=> ~ ! [X4: $i,X5: $i] :
( ~ ( ( eigen__0 @ X2 @ X3 @ X4 @ X5 )
=> ( ( X4 = c1 )
=> ( X5 != c1 ) ) )
=> ~ ( ( X4 = eigen__1 )
=> ( X5 != X1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 @ X5 @ X6 )
=> ~ ( eigen__0 @ X3 @ X4 @ X5 @ X6 ) )
=> ~ ( ( X1 = X3 )
=> ( X2 != X4 ) ) )
=> ( ~ ( sP16
=> ~ sP1 )
=> ~ sP17 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 @ X5 @ X6 )
=> ~ ( eigen__0 @ X3 @ X4 @ X5 @ X6 ) )
=> ~ ( ( X1 = X3 )
=> ( X2 != X4 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ( sP16
=> ~ sP1 )
=> ~ sP17 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP16
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP17,
introduced(assumption,[]) ).
thf(h9,assumption,
sP16,
introduced(assumption,[]) ).
thf(h10,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP16
| sP8
| ~ sP11
| ~ sP7 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP16
| sP10
| ~ sP12
| sP19 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP4
| sP11 ),
inference(symeq,[status(thm)],]) ).
thf(4,plain,
( ~ sP5
| sP12 ),
inference(symeq,[status(thm)],]) ).
thf(5,plain,
( ~ sP1
| sP7
| ~ sP14
| sP19 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(6,plain,
( sP15
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP15
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
~ sP19,
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP9
| ~ sP10
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP2
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP6
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP6
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP18
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(14,plain,
( sP13
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(15,plain,
( ~ sP3
| ~ sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP16
| sP14 ),
inference(symeq,[status(thm)],]) ).
thf(17,plain,
( ~ sP17
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,h9,h10,h8]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,18,h9,h10]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,19,h7,h8]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,20,h5,h6]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,21,h4]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,22,h3]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,23,h2]) ).
thf(25,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[24,h0]) ).
thf(0,theorem,
! [X1: $i > $i > $i > $i > $o,X2: $i,X3: $i] :
( ! [X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
( ~ ( ( X1 @ X4 @ X5 @ X8 @ X9 )
=> ~ ( X1 @ X6 @ X7 @ X8 @ X9 ) )
=> ~ ( ( X4 = X6 )
=> ( X5 != X7 ) ) )
=> ( ~ ( ( X2 = c1 )
=> ( X3 != c1 ) )
=> ~ ! [X4: $i,X5: $i] :
( ~ ( ( X4 = c1 )
=> ( X5 != c1 ) )
=> ~ ! [X6: $i,X7: $i] :
( ~ ( ( X1 @ X4 @ X5 @ X6 @ X7 )
=> ( ( X6 = c1 )
=> ( X7 != c1 ) ) )
=> ~ ( ( X6 = X2 )
=> ( X7 != X3 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[24,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : PUZ107^5 : TPTP v8.1.2. Bugfixed v6.2.0.
% 0.11/0.13 % Command : lash -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 : 300
% 0.12/0.33 % DateTime : Sat Aug 26 22:36:32 EDT 2023
% 0.12/0.33 % CPUTime :
% 20.25/20.55 % SZS status Theorem
% 20.25/20.55 % Mode: cade22grackle2x798d
% 20.25/20.55 % Steps: 1099
% 20.25/20.55 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------