TSTP Solution File: SYO276^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO276^5 : 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 : Fri Sep 1 04:46:07 EDT 2023
% Result : Theorem 0.12s 0.34s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 31
% Syntax : Number of formulae : 39 ( 11 unt; 7 typ; 2 def)
% Number of atoms : 68 ( 15 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 89 ( 23 ~; 10 |; 0 &; 29 @)
% ( 10 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 17 con; 0-2 aty)
% Number of variables : 11 ( 2 ^; 9 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_cO,type,
cO: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_n,type,
n: $i ).
thf(ty_m,type,
m: $i ).
thf(ty_s,type,
s: $i > $i ).
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 )
=> ( ( s @ eigen__0 )
= ( s @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ( X1 = X2 )
=> ( ( s @ X1 )
= ( s @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ( cP @ n ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( s @ X1 )
= ( s @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP2
=> ( n = m ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP3
=> ( ( s @ eigen__0 )
= ( s @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( s @ eigen__0 )
= ( s @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i > $i > $o] :
( ~ ( ( X1 @ cO @ cO )
=> ~ ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ ( s @ X2 ) @ ( s @ X3 ) ) ) )
=> ( X1 @ n @ m ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( cP @ m ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( eigen__0 = X1 )
=> ( ( s @ eigen__0 )
= ( s @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( n = m ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(cBLEDSOE_FENG_SV_I2,conjecture,
( ~ ( sP7
=> ~ sP1 )
=> sP8 ) ).
thf(h1,negated_conjecture,
~ ( ~ ( sP7
=> ~ sP1 )
=> sP8 ),
inference(assume_negation,[status(cth)],[cBLEDSOE_FENG_SV_I2]) ).
thf(h2,assumption,
~ ( sP7
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h4,assumption,
sP7,
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( sP6
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP5
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP5
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP9
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(5,plain,
( sP2
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(6,plain,
( ~ sP4
| ~ sP2
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP7
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP1
| sP8
| ~ sP10 ),
inference(mating_rule,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,h4,h5,h3]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,9,h4,h5]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,10,h2,h3]) ).
thf(12,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[11,h0]) ).
thf(0,theorem,
( ~ ( sP7
=> ~ sP1 )
=> sP8 ),
inference(contra,[status(thm),contra(discharge,[h1])],[11,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO276^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.09 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.10/0.28 % Computer : n032.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8042.1875MB
% 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 300
% 0.10/0.28 % DateTime : Sat Aug 26 02:57:58 EDT 2023
% 0.10/0.28 % CPUTime :
% 0.12/0.34 % SZS status Theorem
% 0.12/0.34 % Mode: cade22grackle2xfee4
% 0.12/0.34 % Steps: 405
% 0.12/0.34 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------