## TSTP Solution File: SEV070^5 by Satallax---3.5

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV070^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n014.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
% DateTime : Tue Mar 30 22:04:54 EDT 2021

% Result   : Theorem 0.12s
% Output   : Proof 0.12s
% Verified :
% SZS Type : None (MakeTreeStats fails)
% Syntax   : Number of formulae    : 45

%------------------------------------------------------------------------------
thf(ty_cS,type,
cS: \$i > \$i ).

thf(ty_eigen__2,type,
eigen__2: \$i ).

thf(ty_eigen__1,type,
eigen__1: \$i ).

thf(ty_eigen__0,type,
eigen__0: \$i ).

thf(ty_eigen__3,type,
eigen__3: \$i > \$o ).

thf(sP1,plain,
( sP1
<=> ! [X1: \$i] :
( ( eigen__3 @ X1 )
=> ( eigen__3 @ ( cS @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
( sP2
<=> ( ~ ( ( eigen__3 @ eigen__1 )
=> ~ sP1 )
=> ( eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
( sP3
<=> ! [X1: \$i > \$o] :
( ~ ( ( X1 @ eigen__0 )
=> ~ ! [X2: \$i] :
( ( X1 @ X2 )
=> ( X1 @ ( cS @ X2 ) ) ) )
=> ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
( sP4
<=> ( ( eigen__3 @ eigen__1 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
( sP5
<=> ( ( eigen__3 @ eigen__0 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
( sP6
<=> ( eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
( sP7
<=> ( eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
( sP8
<=> ( eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
( sP9
<=> ( ~ sP5
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
( sP10
<=> ! [X1: \$i > \$o] :
( ~ ( ( X1 @ eigen__1 )
=> ~ ! [X2: \$i] :
( ( X1 @ X2 )
=> ( X1 @ ( cS @ X2 ) ) ) )
=> ( X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(cTHM577_pme,conjecture,
! [X1: \$i,X2: \$i,X3: \$i] :
( ~ ( ! [X4: \$i > \$o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: \$i] :
( ( X4 @ X5 )
=> ( X4 @ ( cS @ X5 ) ) ) )
=> ( X4 @ X2 ) )
=> ~ ! [X4: \$i > \$o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: \$i] :
( ( X4 @ X5 )
=> ( X4 @ ( cS @ X5 ) ) ) )
=> ( X4 @ X3 ) ) )
=> ! [X4: \$i > \$o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: \$i] :
( ( X4 @ X5 )
=> ( X4 @ ( cS @ X5 ) ) ) )
=> ( X4 @ X3 ) ) ) ).

thf(h0,negated_conjecture,
~ ! [X1: \$i,X2: \$i,X3: \$i] :
( ~ ( ! [X4: \$i > \$o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: \$i] :
( ( X4 @ X5 )
=> ( X4 @ ( cS @ X5 ) ) ) )
=> ( X4 @ X2 ) )
=> ~ ! [X4: \$i > \$o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: \$i] :
( ( X4 @ X5 )
=> ( X4 @ ( cS @ X5 ) ) ) )
=> ( X4 @ X3 ) ) )
=> ! [X4: \$i > \$o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: \$i] :
( ( X4 @ X5 )
=> ( X4 @ ( cS @ X5 ) ) ) )
=> ( X4 @ X3 ) ) ),
inference(assume_negation,[status(cth)],[cTHM577_pme]) ).

thf(h1,assumption,
~ ! [X1: \$i,X2: \$i] :
( ~ ( ! [X3: \$i > \$o] :
( ~ ( ( X3 @ eigen__0 )
=> ~ ! [X4: \$i] :
( ( X3 @ X4 )
=> ( X3 @ ( cS @ X4 ) ) ) )
=> ( X3 @ X1 ) )
=> ~ ! [X3: \$i > \$o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: \$i] :
( ( X3 @ X4 )
=> ( X3 @ ( cS @ X4 ) ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: \$i > \$o] :
( ~ ( ( X3 @ eigen__0 )
=> ~ ! [X4: \$i] :
( ( X3 @ X4 )
=> ( X3 @ ( cS @ X4 ) ) ) )
=> ( X3 @ X2 ) ) ),
introduced(assumption,[]) ).

thf(h2,assumption,
~ ! [X1: \$i] :
( ~ ( sP3
=> ~ ! [X2: \$i > \$o] :
( ~ ( ( X2 @ eigen__1 )
=> ~ ! [X3: \$i] :
( ( X2 @ X3 )
=> ( X2 @ ( cS @ X3 ) ) ) )
=> ( X2 @ X1 ) ) )
=> ! [X2: \$i > \$o] :
( ~ ( ( X2 @ eigen__0 )
=> ~ ! [X3: \$i] :
( ( X2 @ X3 )
=> ( X2 @ ( cS @ X3 ) ) ) )
=> ( X2 @ X1 ) ) ),
introduced(assumption,[]) ).

thf(h3,assumption,
~ ( ~ ( sP3
=> ~ sP10 )
=> ! [X1: \$i > \$o] :
( ~ ( ( X1 @ eigen__0 )
=> ~ ! [X2: \$i] :
( ( X1 @ X2 )
=> ( X1 @ ( cS @ X2 ) ) ) )
=> ( X1 @ eigen__2 ) ) ),
introduced(assumption,[]) ).

thf(h4,assumption,
~ ( sP3
=> ~ sP10 ),
introduced(assumption,[]) ).

thf(h5,assumption,
~ ! [X1: \$i > \$o] :
( ~ ( ( X1 @ eigen__0 )
=> ~ ! [X2: \$i] :
( ( X1 @ X2 )
=> ( X1 @ ( cS @ X2 ) ) ) )
=> ( X1 @ eigen__2 ) ),
introduced(assumption,[]) ).

thf(h6,assumption,
sP3,
introduced(assumption,[]) ).

thf(h7,assumption,
sP10,
introduced(assumption,[]) ).

thf(h8,assumption,
~ ( ~ sP5
=> sP7 ),
introduced(assumption,[]) ).

thf(h9,assumption,
~ sP5,
introduced(assumption,[]) ).

thf(h10,assumption,
~ sP7,
introduced(assumption,[]) ).

thf(h11,assumption,
sP6,
introduced(assumption,[]) ).

thf(h12,assumption,
sP1,
introduced(assumption,[]) ).

thf(1,plain,
( ~ sP3
| sP9 ),
inference(all_rule,[status(thm)],]) ).

thf(2,plain,
( ~ sP9
| sP5
| sP8 ),
inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
( ~ sP5
| ~ sP6
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
( ~ sP10
| sP2 ),
inference(all_rule,[status(thm)],]) ).

thf(5,plain,
( ~ sP2
| sP4
| sP7 ),
inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
( ~ sP4
| ~ sP8
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
\$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,h6,h7,h11,h12,h10]) ).

thf(8,plain,
\$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,7,h11,h12]) ).

thf(9,plain,
\$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,8,h9,h10]) ).

thf(10,plain,
\$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h5,9,h8]) ).

thf(11,plain,
\$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,10,h6,h7]) ).

thf(12,plain,
\$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,11,h4,h5]) ).

thf(13,plain,
\$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,12,h3]) ).

thf(14,plain,
\$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,13,h2]) ).

thf(15,plain,
\$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,14,h1]) ).

thf(0,theorem,
! [X1: \$i,X2: \$i,X3: \$i] :
( ~ ( ! [X4: \$i > \$o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: \$i] :
( ( X4 @ X5 )
=> ( X4 @ ( cS @ X5 ) ) ) )
=> ( X4 @ X2 ) )
=> ~ ! [X4: \$i > \$o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: \$i] :
( ( X4 @ X5 )
=> ( X4 @ ( cS @ X5 ) ) ) )
=> ( X4 @ X3 ) ) )
=> ! [X4: \$i > \$o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: \$i] :
( ( X4 @ X5 )
=> ( X4 @ ( cS @ X5 ) ) ) )
=> ( X4 @ X3 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SEV070^5 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n014.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  : 600
% 0.12/0.33  % DateTime : Fri Mar 26 14:06:37 EDT 2021
% 0.12/0.33  % CPUTime  :
% 0.12/0.35  % SZS status Theorem
% 0.12/0.35  % Mode: mode213
% 0.12/0.35  % Inferences: 5
% 0.12/0.35  % SZS output start Proof
% See solution above
% 0.12/0.35  % SZS output end Proof
%------------------------------------------------------------------------------
```