%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV049^5 : 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 : n008.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 02:56:10 PM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 16
% Syntax : Number of formulae : 23 ( 10 unt; 0 typ; 3 def)
% Number of atoms : 53 ( 3 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 62 ( 24 ~; 7 |; 0 &; 14 @)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 12 con; 0-2 aty)
% Number of variables : 21 ( 5 ^; 16 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o] :
( $false
=> ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o,X3: $i > $o] :
( $false
=> ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( $false
=> ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ $false
=> ~ ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( $false
=> ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( $false
=> ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i > $o,X2: $i > $o] : sP2 ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i > $o] : sP2 ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> $false ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( X1
@ ^ [X2: $i] : ~ sP5
@ ^ [X2: $i] : sP5 )
=> ~ ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i > $o] : sP3 ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(cTHM120A_pme,conjecture,
~ sP6 ).
thf(h1,negated_conjecture,
sP6,
inference(assume_negation,[status(cth)],[cTHM120A_pme]) ).
thf(1,plain,
( sP2
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP4
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(3,plain,
( sP3
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(4,plain,
( sP7
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(5,plain,
~ sP5,
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP1
| sP5
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP6
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,h1]) ).
thf(9,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[8,h0]) ).
thf(0,theorem,
~ sP6,
inference(contra,[status(thm),contra(discharge,[h1])],[8,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEV049^5 : TPTP v9.2.0. Released v4.0.0.
% 0.08/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n008.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 : 300
% 0.12/0.33 % DateTime : Wed Oct 8 19:17:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % Mode: mode213
% 0.12/0.36 % Inferences: 51
% 0.12/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------