%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO218^5 : 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 : n015.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 03:25:09 PM UTC 2025
% Result : Theorem 1.07s 1.30s
% Output : Proof 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 24
% Syntax : Number of formulae : 30 ( 10 unt; 0 typ; 2 def)
% Number of atoms : 83 ( 37 equ; 12 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 80 ( 13 ~; 11 |; 0 &; 29 @)
% ( 11 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 16 con; 0-2 aty)
% Number of variables : 17 ( 2 ^; 15 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ! [X2: ( $i > $o ) > $i] :
( ( eigen__0
= ( X2 @ ( (=) @ eigen__0 ) ) )
=> ( X1
= ( X2 @ ( (=) @ X1 ) ) ) )
=> ( eigen__0 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ! [X3: ( $i > $o ) > $i] :
( ( X1
= ( X3 @ ( (=) @ X1 ) ) )
=> ( X2
= ( X3 @ ( (=) @ X2 ) ) ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ! [X2: ( $i > $o ) > $i] :
( ( eigen__0
= ( X2 @ ( (=) @ eigen__0 ) ) )
=> ( X1
= ( X2 @ ( (=) @ X1 ) ) ) )
=> ( eigen__0 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( eigen__1 = X1 )
=> ( X1 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__1 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__0 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP5
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ! [X1: ( $i > $o ) > $i] :
( ( eigen__0
= ( X1 @ ( (=) @ eigen__0 ) ) )
=> ( eigen__1
= ( X1 @ ( (=) @ eigen__1 ) ) ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i] :
( ! [X3: ( $i > $o ) > $i] :
( ( X1
= ( X3 @ ( (=) @ X1 ) ) )
=> ( X2
= ( X3 @ ( (=) @ X2 ) ) ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP6
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: ( $i > $o ) > $i] :
( ( eigen__0
= ( X1 @ ( (=) @ eigen__0 ) ) )
=> ( eigen__1
= ( X1 @ ( (=) @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(cTHM7B_pme,conjecture,
sP9 ).
thf(h1,negated_conjecture,
~ sP9,
inference(assume_negation,[status(cth)],[cTHM7B_pme]) ).
thf(1,plain,
sP6,
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP10
| ~ sP6
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP11
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP7
| ~ sP5
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP3
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
sP2,
inference(eq_sym,[status(thm)],[]) ).
thf(8,plain,
( sP8
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP8
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP1
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(11,plain,
( sP9
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h1]) ).
thf(13,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[12,h0]) ).
thf(0,theorem,
sP9,
inference(contra,[status(thm),contra(discharge,[h1])],[12,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYO218^5 : 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
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Oct 9 00:35:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 1.07/1.30 % SZS status Theorem
% 1.07/1.30 % Mode: mode506
% 1.07/1.30 % Inferences: 19452
% 1.07/1.30 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------