TSTP Solution File: SEV242^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV242^5 : 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 : n032.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 19:33:05 EDT 2023
% Result : Theorem 0.14s 0.52s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 53
% Syntax : Number of formulae : 65 ( 14 unt; 5 typ; 2 def)
% Number of atoms : 185 ( 48 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 257 ( 82 ~; 27 |; 0 &; 74 @)
% ( 18 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 22 con; 0-2 aty)
% Number of variables : 64 ( 18 ^; 46 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__6,type,
eigen__6: $i > $o ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__2,type,
eigen__2: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: ( $i > $o ) > $o ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ( ( X1 != eigen__1 )
=> ( X1 = eigen__2 ) )
=> ~ ( X1 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__1
@ ^ [X1: $i] :
( ( ~ ! [X2: $i > $o] :
( ( ( X2 != eigen__1 )
=> ( X2 = eigen__2 ) )
=> ~ ( X2 @ X1 ) ) )
!= ( ~ ( eigen__1 @ X1 )
=> ( eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ( ( X2 != eigen__1 )
=> ( X2 = eigen__2 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ( ( X2 != eigen__1 )
=> ( X2 = eigen__2 ) )
=> ~ ( X2 @ X1 ) ) )
= ( ^ [X1: $i] :
( ~ ( eigen__1 @ X1 )
=> ( eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__6 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( eigen__6 @ X1 )
= ( eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP3
= ( eigen__2 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__6 != eigen__1 )
=> ( eigen__6 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ~ ! [X1: $i > $o] :
( ( ( X1 != eigen__1 )
=> ( X1 = eigen__2 ) )
=> ~ ( X1 @ eigen__5 ) ) )
= ( ~ ( eigen__1 @ eigen__5 )
=> ( eigen__2 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP3
= ( eigen__1 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__2 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( eigen__6 @ X1 )
= ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__1 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( ~ ! [X2: $i > $o] :
( ( ( X2 != eigen__1 )
=> ( X2 = eigen__2 ) )
=> ~ ( X2 @ X1 ) ) )
= ( ~ ( eigen__1 @ X1 )
=> ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ sP11
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i > $o] :
( ( ( X1 != eigen__1 )
=> ( X1 = eigen__2 ) )
=> ~ ( X1 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__0
@ ^ [X1: $i] :
( ~ ( eigen__1 @ X1 )
=> ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__6 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__6 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP6
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(cTHM4A_pme,conjecture,
( ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) )
=> ( X1 = X2 ) )
=> ! [X1: ( $i > $o ) > $o,X2: $i > $o,X3: $i > $o] :
( ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ( ( X5 != X2 )
=> ( X5 = X3 ) )
=> ~ ( X5 @ X4 ) ) )
=> ( X1
@ ^ [X4: $i] :
( ~ ( X2 @ X4 )
=> ( X3 @ X4 ) ) ) ) ) ).
thf(h2,negated_conjecture,
~ ( ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) )
=> ( X1 = X2 ) )
=> ! [X1: ( $i > $o ) > $o,X2: $i > $o,X3: $i > $o] :
( ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ( ( X5 != X2 )
=> ( X5 = X3 ) )
=> ~ ( X5 @ X4 ) ) )
=> ( X1
@ ^ [X4: $i] :
( ~ ( X2 @ X4 )
=> ( X3 @ X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM4A_pme]) ).
thf(h3,assumption,
! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: ( $i > $o ) > $o,X2: $i > $o,X3: $i > $o] :
( ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ( ( X5 != X2 )
=> ( X5 = X3 ) )
=> ~ ( X5 @ X4 ) ) )
=> ( X1
@ ^ [X4: $i] :
( ~ ( X2 @ X4 )
=> ( X3 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i > $o,X2: $i > $o] :
( ( eigen__0
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ( ( X4 != X1 )
=> ( X4 = X2 ) )
=> ~ ( X4 @ X3 ) ) )
=> ( eigen__0
@ ^ [X3: $i] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i > $o] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ( ( X3 != eigen__1 )
=> ( X3 = X1 ) )
=> ~ ( X3 @ X2 ) ) )
=> ( eigen__0
@ ^ [X2: $i] :
( ~ ( eigen__1 @ X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP1
=> sP15 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP1,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP8
| ~ sP3
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| ~ sP3
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP10
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP16
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP17
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP6
| sP17
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP18
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP18
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP13
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP13
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP14
| ~ sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP14
| ~ sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP13
| sP11
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP14
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(16,plain,
( sP7
| sP14
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP7
| ~ sP14
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP12
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__5]) ).
thf(19,plain,
( sP2
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP1
| sP15
| ~ sP2 ),
inference(mating_rule,[status(thm)],]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h6,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,h8,h9]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h6,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,21,h8,h9]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,22,h7]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,23,h6]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,24,h5]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,25,h3,h4]) ).
thf(27,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[26,h1]) ).
thf(28,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[27,h0]) ).
thf(0,theorem,
( ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) )
=> ( X1 = X2 ) )
=> ! [X1: ( $i > $o ) > $o,X2: $i > $o,X3: $i > $o] :
( ( X1
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ( ( X5 != X2 )
=> ( X5 = X3 ) )
=> ~ ( X5 @ X4 ) ) )
=> ( X1
@ ^ [X4: $i] :
( ~ ( X2 @ X4 )
=> ( X3 @ X4 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[26,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV242^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.09 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Thu Aug 24 03:05:56 EDT 2023
% 0.09/0.28 % CPUTime :
% 0.14/0.52 % SZS status Theorem
% 0.14/0.52 % Mode: cade22grackle2xfee4
% 0.14/0.52 % Steps: 3763
% 0.14/0.52 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------