%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV236^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n011.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 Oct 9 02:56:30 PM UTC 2025
% Result : Theorem 13.11s 13.51s
% Output : Proof 13.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 28
% Syntax : Number of formulae : 34 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 86 ( 2 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 145 ( 29 ~; 15 |; 0 &; 55 @)
% ( 13 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 17 con; 0-2 aty)
% Number of variables : 32 ( 4 ^; 28 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cS,type,
cS: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__45,type,
eigen__45: a ).
thf(ty_cK,type,
cK: ( a > $o ) > a > $o ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a] :
~ ( ( cS @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cS @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__45,definition,
( eigen__45
= ( eps__0
@ ^ [X1: a] :
~ ( ( cS @ X1 )
=> ( cS @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__45])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: a] :
( ( cK @ X1 @ X3 )
=> ( cK @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
( ( cS @ X1 )
=> ( cS @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ! [X1: a] :
( ( cS @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cS @ X3 ) )
=> ~ ( X2 @ X1 ) ) )
=> ! [X1: a] :
( ( cK @ cS @ X1 )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cS @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cS @ eigen__45 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( cS @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cK @ cS @ X2 )
=> ( cK @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cS @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP2
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ( cK @ cS @ X1 )
=> ( cK
@ ^ [X2: a] :
~ ! [X3: a > $o] :
( ! [X4: a] :
( ( X3 @ X4 )
=> ( cS @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP1
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP6
=> ~ ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cS @ X2 ) )
=> ~ ( X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP4
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cS @ X2 ) )
=> ~ ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a] :
( ( cS @ X1 )
=> ~ ! [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cS @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(cTHM91_pme,conjecture,
sP9 ).
thf(h1,negated_conjecture,
~ sP9,
inference(assume_negation,[status(cth)],[cTHM91_pme]) ).
thf(1,plain,
( sP11
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP11
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( sP2
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__45]) ).
thf(4,plain,
( ~ sP7
| ~ sP2
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP12
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( sP10
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP10
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP13
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(9,plain,
( ~ sP1
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP3
| ~ sP13
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP9
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( sP9
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h1]) ).
thf(15,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[14,h0]) ).
thf(0,theorem,
sP9,
inference(contra,[status(thm),contra(discharge,[h1])],[14,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV236^5 : TPTP v9.2.0. Released v4.0.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 19:34:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 13.11/13.51 % SZS status Theorem
% 13.11/13.51 % Mode: mode454
% 13.11/13.51 % Inferences: 744
% 13.11/13.51 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------