%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV163^5 : 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 : n025.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 02:56:23 PM UTC 2025
% Result : Theorem 1.08s 1.29s
% Output : Proof 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 10
% Syntax : Number of formulae : 15 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 29 ( 11 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 5 ~; 3 |; 0 &; 28 @)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 37 ( 31 ^; 6 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: ( a > a > a ) > a ).
thf(h0,assumption,
! [X1: ( ( a > a > a ) > a ) > $o,X2: ( a > a > a ) > a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: ( a > a > a ) > a] :
~ ( ( X1
= ( ^ [X2: a > a > a] :
( X2
@ ( X1
@ ^ [X3: a,X4: a] : X3 )
@ ( X1
@ ^ [X3: a,X4: a] : X4 ) ) ) )
=> ( ( ^ [X2: a > a > a] :
( X2
@ ( X1
@ ^ [X3: a,X4: a] : X3 )
@ ( X1
@ ^ [X3: a,X4: a] : X4 ) ) )
= X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ( ( eigen__0
= ( ^ [X1: a > a > a] :
( X1
@ ( eigen__0
@ ^ [X2: a,X3: a] : X2 )
@ ( eigen__0
@ ^ [X2: a,X3: a] : X3 ) ) ) )
=> ( ( ^ [X1: a > a > a] :
( X1
@ ( eigen__0
@ ^ [X2: a,X3: a] : X2 )
@ ( eigen__0
@ ^ [X2: a,X3: a] : X3 ) ) )
= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: ( a > a > a ) > a,X2: ( a > a > a ) > a] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: ( a > a > a ) > a] :
( ( X1
= ( ^ [X2: a > a > a] :
( X2
@ ( X1
@ ^ [X3: a,X4: a] : X3 )
@ ( X1
@ ^ [X3: a,X4: a] : X4 ) ) ) )
=> ( ( ^ [X2: a > a > a] :
( X2
@ ( X1
@ ^ [X3: a,X4: a] : X3 )
@ ( X1
@ ^ [X3: a,X4: a] : X4 ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: ( a > a > a ) > a] :
( ( eigen__0 = X1 )
=> ( X1 = eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(cTHM187_pme,conjecture,
sP3 ).
thf(h1,negated_conjecture,
~ sP3,
inference(assume_negation,[status(cth)],[cTHM187_pme]) ).
thf(1,plain,
( ~ sP4
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
sP2,
inference(eq_sym,[status(thm)],[]) ).
thf(4,plain,
( sP3
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,h1]) ).
thf(6,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[5,h0]) ).
thf(0,theorem,
sP3,
inference(contra,[status(thm),contra(discharge,[h1])],[5,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEV163^5 : TPTP v9.2.0. Released v4.0.0.
% 0.07/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % 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 : Wed Oct 8 19:23:53 EDT 2025
% 0.14/0.35 % CPUTime :
% 1.08/1.29 % SZS status Theorem
% 1.08/1.29 % Mode: mode506
% 1.08/1.29 % Inferences: 3
% 1.08/1.29 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------