%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO535^1 : TPTP v9.2.0. Released v5.2.0.
% 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 03:25:58 PM UTC 2025
% Result : Theorem 1.09s 1.28s
% Output : Proof 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 21 ( 10 unt; 0 typ; 3 def)
% Number of atoms : 41 ( 3 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 123 ( 38 ~; 5 |; 0 &; 69 @)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 39 ( 13 ^; 26 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eps,type,
eps: ( $i > $o ) > $i ).
thf(ty_eigen__0,type,
eigen__0: $i > ( $i > $i ) > $o ).
thf(ty_epsii,type,
epsii: ( ( $i > $i ) > $o ) > $i > $i ).
thf(h0,assumption,
! [X1: ( $i > ( $i > $i ) > $o ) > $o,X2: $i > ( $i > $i ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i > ( $i > $i ) > $o] :
~ ( ~ ! [X2: $i,X3: $i > $i] :
~ ( X1 @ X2 @ X3 )
=> ( X1
@ ( eps
@ ^ [X2: $i] :
~ ! [X3: $i > $i] :
~ ( X1 @ X2 @ X3 ) )
@ ( epsii
@ ( X1
@ ( eps
@ ^ [X2: $i] :
~ ! [X3: $i > $i] :
~ ( X1 @ X2 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ! [X1: $i,X2: $i > $i] :
~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__0
@ ( eps
@ ^ [X1: $i] :
~ ! [X2: $i > $i] :
~ ( eigen__0 @ X1 @ X2 ) )
@ ( epsii
@ ( eigen__0
@ ( eps
@ ^ [X1: $i] :
~ ! [X2: $i > $i] :
~ ( eigen__0 @ X1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i > $i] :
~ ( eigen__0
@ ( eps
@ ^ [X2: $i] :
~ ! [X3: $i > $i] :
~ ( eigen__0 @ X2 @ X3 ) )
@ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i > $i] :
~ ( eigen__0 @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i > ( $i > $i ) > $o] :
( ~ ! [X2: $i,X3: $i > $i] :
~ ( X1 @ X2 @ X3 )
=> ( X1
@ ( eps
@ ^ [X2: $i] :
~ ! [X3: $i > $i] :
~ ( X1 @ X2 @ X3 ) )
@ ( epsii
@ ( X1
@ ( eps
@ ^ [X2: $i] :
~ ! [X3: $i > $i] :
~ ( X1 @ X2 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__0
@ ( eps
@ ^ [X1: $i] :
~ ! [X2: $i > $i] :
~ ( eigen__0 @ X1 @ X2 ) )
@ ( epsii
@ ( eigen__0
@ ( eps
@ ^ [X1: $i] :
~ ! [X2: $i > $i] :
~ ( eigen__0 @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(def_epsa,definition,
( epsa
= ( ^ [X1: $i > ( $i > $i ) > $o] :
( eps
@ ^ [X2: $i] :
~ ! [X3: $i > $i] :
~ ( X1 @ X2 @ X3 ) ) ) ) ).
thf(def_epsb,definition,
( epsb
= ( ^ [X1: $i > ( $i > $i ) > $o] : ( epsii @ ( X1 @ ( epsa @ X1 ) ) ) ) ) ).
thf(conj,conjecture,
sP4 ).
thf(h1,negated_conjecture,
~ sP4,
inference(assume_negation,[status(cth)],[conj]) ).
thf(choiceaxii,axiom,
! [X1: ( $i > $i ) > $o] :
( ~ ! [X2: $i > $i] :
~ ( X1 @ X2 )
=> ( X1 @ ( epsii @ X1 ) ) ) ).
thf(1,plain,
( sP5
| sP2 ),
inference(choice_rule,[status(thm)],[choiceaxii]) ).
thf(choiceax,axiom,
! [X1: $i > $o] :
( ~ ! [X2: $i] :
~ ( X1 @ X2 )
=> ( X1 @ ( eps @ X1 ) ) ) ).
thf(2,plain,
( ~ sP2
| sP3 ),
inference(choice_rule,[status(thm)],[choiceax]) ).
thf(3,plain,
( sP1
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP1
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP4
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,h1]) ).
thf(7,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[6,h0]) ).
thf(0,theorem,
sP4,
inference(contra,[status(thm),contra(discharge,[h1])],[6,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO535^1 : TPTP v9.2.0. Released v5.2.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Oct 9 01:06:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 1.09/1.28 % SZS status Theorem
% 1.09/1.28 % Mode: mode506
% 1.09/1.28 % Inferences: 3068
% 1.09/1.28 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------