TSTP Solution File: SEV116^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV116^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n007.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 19:32:39 EDT 2023
% Result : Theorem 20.09s 20.45s
% Output : Proof 20.09s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_x,type,
x: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(ty_y,type,
y: $i ).
thf(ty_cS,type,
cS: ( $i > $i > $o ) > $o ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ y @ x ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ( cS
@ ^ [X1: $i,X2: $i] :
! [X3: $i > $i > $o] :
( ~ ( ( cS @ X3 )
=> ~ ( X3 @ X1 @ X2 ) )
=> ( X3 @ X2 @ X1 ) ) )
=> ~ ! [X1: $i > $i > $o] :
( ~ ( ( cS @ X1 )
=> ~ ( X1 @ x @ y ) )
=> ( X1 @ y @ x ) ) )
=> ! [X1: $i > $i > $o] :
( ~ ( ( cS @ X1 )
=> ~ ( X1 @ y @ x ) )
=> ( X1 @ x @ y ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cS
@ ^ [X1: $i,X2: $i] :
! [X3: $i > $i > $o] :
( ~ ( ( cS @ X3 )
=> ~ ( X3 @ X1 @ X2 ) )
=> ( X3 @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( cS @ eigen__0 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP3
=> ~ ! [X1: $i > $i > $o] :
( ~ ( ( cS @ X1 )
=> ~ ( X1 @ x @ y ) )
=> ( X1 @ y @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cS @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0 @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i > $i > $o] :
( ~ ( ( cS @ X1 )
=> ~ ( X1 @ y @ x ) )
=> ( X1 @ x @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ sP4
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i > $i > $o] :
( ~ ( ( cS @ X1 )
=> ~ ( X1 @ x @ y ) )
=> ( X1 @ y @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(def_cSTRANGE_HO_ABBR,definition,
( cSTRANGE_HO_ABBR
= ( ^ [X1: ( $i > $i > $o ) > $o,X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X4 )
& ( X4 @ X2 @ X3 ) )
@ ( X4 @ X3 @ X2 ) ) ) ) ).
thf(cSTRANGE_HO_EXAMPLE,conjecture,
sP2 ).
thf(h0,negated_conjecture,
~ sP2,
inference(assume_negation,[status(cth)],[cSTRANGE_HO_EXAMPLE]) ).
thf(h1,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h3,assumption,
sP3,
introduced(assumption,[]) ).
thf(h4,assumption,
sP10,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h8,assumption,
sP6,
introduced(assumption,[]) ).
thf(h9,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| ~ sP6
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP9
| sP4
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP8
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP5
| ~ sP3
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| sP5
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP10
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h6,h7,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,h3,h4,h8,h9,h7]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h6,7,h8,h9]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[h5,8,h6,h7]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h2,9,h5]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,10,h3,h4]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,11,h1,h2]) ).
thf(0,theorem,
sP2,
inference(contra,[status(thm),contra(discharge,[h0])],[12,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEV116^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.07/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.10/0.32 % Computer : n007.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Thu Aug 24 03:05:54 EDT 2023
% 0.10/0.32 % CPUTime :
% 20.09/20.45 % SZS status Theorem
% 20.09/20.45 % Mode: cade22grackle2x798d
% 20.09/20.45 % Steps: 52
% 20.09/20.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------