TSTP Solution File: SEV085^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV085^5 : 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 : n024.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 19:32:34 EDT 2023
% Result : Theorem 282.46s 283.05s
% Output : Proof 282.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 42
% Syntax : Number of formulae : 49 ( 16 unt; 4 typ; 3 def)
% Number of atoms : 100 ( 3 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 217 ( 54 ~; 21 |; 0 &; 69 @)
% ( 18 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 21 con; 0-2 aty)
% Number of variables : 37 ( 3 ^; 34 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__242,type,
eigen__242: $i > $o ).
thf(ty_eigen__243,type,
eigen__243: $i > $o ).
thf(ty_eigen__213,type,
eigen__213: $i ).
thf(ty_eigen__244,type,
eigen__244: $i > $o ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__244,definition,
( eigen__244
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ~ ( ( ( eigen__243 @ eigen__213 )
=> ( eigen__242 @ eigen__213 ) )
=> ~ ( ( X1 @ eigen__213 )
=> ( eigen__243 @ eigen__213 ) ) )
=> ( ( X1 @ eigen__213 )
=> ( eigen__242 @ eigen__213 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__244])]) ).
thf(eigendef_eigen__243,definition,
( eigen__243
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o] :
( ~ ( ( ( X1 @ eigen__213 )
=> ( eigen__242 @ eigen__213 ) )
=> ~ ( ( X2 @ eigen__213 )
=> ( X1 @ eigen__213 ) ) )
=> ( ( X2 @ eigen__213 )
=> ( eigen__242 @ eigen__213 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__243])]) ).
thf(eigendef_eigen__242,definition,
( eigen__242
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o,X3: $i > $o] :
( ~ ( ( ( X2 @ eigen__213 )
=> ( X1 @ eigen__213 ) )
=> ~ ( ( X3 @ eigen__213 )
=> ( X2 @ eigen__213 ) ) )
=> ( ( X3 @ eigen__213 )
=> ( X1 @ eigen__213 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__242])]) ).
thf(sP1,plain,
( sP1
<=> $false ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ~ ! [X1: $i > $o,X2: $i > $o] :
~ ( ( X2 @ eigen__213 )
=> ( X1 @ eigen__213 ) )
=> ! [X1: $i > $o,X2: $i > $o] :
( ( X2 @ eigen__213 )
=> ( X1 @ eigen__213 ) ) )
=> ~ ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ( ( X2 @ eigen__213 )
=> ( X1 @ eigen__213 ) )
=> ~ ( ( X3 @ eigen__213 )
=> ( X2 @ eigen__213 ) ) )
=> ( ( X3 @ eigen__213 )
=> ( X1 @ eigen__213 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__244 @ eigen__213 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP3
=> ( eigen__242 @ eigen__213 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i > $o,X2: $i > $o] :
~ ( ( X2 @ eigen__213 )
=> ( X1 @ eigen__213 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__243 @ eigen__213 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP3
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i > $o] :
~ ( X1 @ eigen__213 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ( ( X2 @ eigen__213 )
=> ( X1 @ eigen__213 ) )
=> ~ ( ( X3 @ eigen__213 )
=> ( X2 @ eigen__213 ) ) )
=> ( ( X3 @ eigen__213 )
=> ( X1 @ eigen__213 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__242 @ eigen__213 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( ~ ( ~ ! [X2: $i > $o,X3: $i > $o] :
~ ( X1 @ X2 @ X3 )
=> ! [X2: $i > $o,X3: $i > $o] : ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: $i > $o] : ( X1 @ X2 @ X2 ) )
=> ~ ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( sP6
=> sP10 )
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i > $o,X2: $i > $o] :
( ~ ( ( ( X1 @ eigen__213 )
=> sP10 )
=> ~ ( ( X2 @ eigen__213 )
=> ( X1 @ eigen__213 ) ) )
=> ( ( X2 @ eigen__213 )
=> sP10 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ sP12
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i > $o] :
( ~ ( ( sP6
=> sP10 )
=> ~ ( ( X1 @ eigen__213 )
=> sP6 ) )
=> ( ( X1 @ eigen__213 )
=> sP10 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP5
=> ! [X1: $i > $o,X2: $i > $o] :
( ( X2 @ eigen__213 )
=> ( X1 @ eigen__213 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP6
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i > $o,X2: $i > $o] :
( ( X2 @ eigen__213 )
=> ( X1 @ eigen__213 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(cTHM120_2_pme,conjecture,
~ sP11 ).
thf(h1,negated_conjecture,
sP11,
inference(assume_negation,[status(cth)],[cTHM120_2_pme]) ).
thf(1,plain,
( ~ sP18
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP4
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP4
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP7
| ~ sP3
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP17
| ~ sP6
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP12
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP12
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP14
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP14
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP15
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__244]) ).
thf(13,plain,
( sP13
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__243]) ).
thf(14,plain,
( ~ sP16
| sP5
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP9
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__242]) ).
thf(16,plain,
( ~ sP2
| sP16
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP11
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
~ sP1,
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,h1]) ).
thf(20,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[19,h0]) ).
thf(0,theorem,
~ sP11,
inference(contra,[status(thm),contra(discharge,[h1])],[19,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV085^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 03:12:24 EDT 2023
% 0.13/0.34 % CPUTime :
% 282.46/283.05 % SZS status Theorem
% 282.46/283.05 % Mode: cade22grackle2x1158
% 282.46/283.05 % Steps: 1471374
% 282.46/283.05 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------