%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV076^5 : 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 02:56:14 PM UTC 2025
% Result : Theorem 1.08s 1.30s
% Output : Proof 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 22
% Syntax : Number of formulae : 31 ( 14 unt; 0 typ; 3 def)
% Number of atoms : 85 ( 3 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 279 ( 61 ~; 9 |; 0 &; 139 @)
% ( 9 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 77 ( 3 ^; 74 !; 0 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a > $o ).
thf(ty_eigen__1,type,
eigen__1: ( a > $o ) > a ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(h0,assumption,
! [X1: ( ( a > $o ) > a ) > $o,X2: ( a > $o ) > a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: ( a > $o ) > a] :
~ ( ~ ( ! [X2: a,X3: a,X4: a] :
( ~ ( ( eigen__0 @ X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( eigen__0 @ X2 @ X4 ) )
=> ~ ! [X2: a > $o] :
~ ( ! [X3: a] :
( ( X2 @ X3 )
=> ( eigen__0 @ X3 @ ( X1 @ X2 ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( X2 @ X4 )
=> ( eigen__0 @ X4 @ X3 ) )
=> ( eigen__0 @ ( X1 @ X2 ) @ X3 ) ) ) )
=> ! [X2: a > $o] :
~ ! [X3: a] :
~ ! [X4: a] :
( ( X2 @ X4 )
=> ( eigen__0 @ X4 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: ( a > a > $o ) > $o,X2: a > a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: a > a > $o] :
~ ! [X2: ( a > $o ) > a] :
( ~ ( ! [X3: a,X4: a,X5: a] :
( ~ ( ( X1 @ X3 @ X4 )
=> ~ ( X1 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X5 ) )
=> ~ ! [X3: a > $o] :
~ ( ! [X4: a] :
( ( X3 @ X4 )
=> ( X1 @ X4 @ ( X2 @ X3 ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( X3 @ X5 )
=> ( X1 @ X5 @ X4 ) )
=> ( X1 @ ( X2 @ X3 ) @ X4 ) ) ) )
=> ! [X3: a > $o] :
~ ! [X4: a] :
~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X1 @ X5 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h2,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__2
@ ^ [X1: a > $o] :
~ ~ ! [X2: a] :
~ ! [X3: a] :
( ( X1 @ X3 )
=> ( eigen__0 @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: ( a > $o ) > a] :
( ~ ( ! [X2: a,X3: a,X4: a] :
( ~ ( ( eigen__0 @ X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( eigen__0 @ X2 @ X4 ) )
=> ~ ! [X2: a > $o] :
~ ( ! [X3: a] :
( ( X2 @ X3 )
=> ( eigen__0 @ X3 @ ( X1 @ X2 ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( X2 @ X4 )
=> ( eigen__0 @ X4 @ X3 ) )
=> ( eigen__0 @ ( X1 @ X2 ) @ X3 ) ) ) )
=> ! [X2: a > $o] :
~ ! [X3: a] :
~ ! [X4: a] :
( ( X2 @ X4 )
=> ( eigen__0 @ X4 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a > $o] :
~ ! [X2: a] :
~ ! [X3: a] :
( ( X1 @ X3 )
=> ( eigen__0 @ X3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
~ ! [X2: a] :
( ( eigen__2 @ X2 )
=> ( eigen__0 @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( eigen__2 @ X1 )
=> ( eigen__0 @ X1 @ ( eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP4
=> ~ ! [X1: a] :
( ! [X2: a] :
( ( eigen__2 @ X2 )
=> ( eigen__0 @ X2 @ X1 ) )
=> ( eigen__0 @ ( eigen__1 @ eigen__2 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) )
=> ~ ! [X1: a > $o] :
~ ( ! [X2: a] :
( ( X1 @ X2 )
=> ( eigen__0 @ X2 @ ( eigen__1 @ X1 ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( eigen__0 @ X3 @ X2 ) )
=> ( eigen__0 @ ( eigen__1 @ X1 ) @ X2 ) ) ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a > a > $o,X2: ( a > $o ) > a] :
( ~ ( ! [X3: a,X4: a,X5: a] :
( ~ ( ( X1 @ X3 @ X4 )
=> ~ ( X1 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X5 ) )
=> ~ ! [X3: a > $o] :
~ ( ! [X4: a] :
( ( X3 @ X4 )
=> ( X1 @ X4 @ ( X2 @ X3 ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( X3 @ X5 )
=> ( X1 @ X5 @ X4 ) )
=> ( X1 @ ( X2 @ X3 ) @ X4 ) ) ) )
=> ! [X3: a > $o] :
~ ! [X4: a] :
~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X1 @ X5 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a > $o] :
~ ( ! [X2: a] :
( ( X1 @ X2 )
=> ( eigen__0 @ X2 @ ( eigen__1 @ X1 ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( eigen__0 @ X3 @ X2 ) )
=> ( eigen__0 @ ( eigen__1 @ X1 ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) )
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(cTHM401B_pme,conjecture,
sP7 ).
thf(h3,negated_conjecture,
~ sP7,
inference(assume_negation,[status(cth)],[cTHM401B_pme]) ).
thf(1,plain,
( ~ sP3
| ~ sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( sP5
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP8
| ~ sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( sP9
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP2
| sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__2]) ).
thf(6,plain,
( sP6
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP6
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP1
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(9,plain,
( sP7
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,h3]) ).
thf(11,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[10,h2]) ).
thf(12,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[11,h1]) ).
thf(13,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[12,h0]) ).
thf(0,theorem,
sP7,
inference(contra,[status(thm),contra(discharge,[h3])],[10,h3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV076^5 : TPTP v9.2.0. Released v4.0.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n008.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 19:17:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.08/1.30 % SZS status Theorem
% 1.08/1.30 % Mode: mode506
% 1.08/1.30 % Inferences: 19450
% 1.08/1.30 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------