%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG268^4 : TPTP v9.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n023.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 01:12:16 PM UTC 2025
% Result : Theorem 0.43s 0.61s
% Output : Proof 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 15
% Syntax : Number of formulae : 23 ( 14 unt; 0 typ; 5 def)
% Number of atoms : 42 ( 13 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 91 ( 13 ~; 4 |; 0 &; 67 @)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 13 con; 0-2 aty)
% Number of variables : 21 ( 3 ^; 18 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subst,type,
subst: $tType ).
thf(ty_term,type,
term: $tType ).
thf(ty_push,type,
push: term > subst > subst ).
thf(ty_eigen__2,type,
eigen__2: subst ).
thf(ty_eigen__1,type,
eigen__1: term ).
thf(ty_eigen__0,type,
eigen__0: term ).
thf(ty_sub,type,
sub: term > subst > term ).
thf(h0,assumption,
! [X1: term > $o,X2: term] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: term] :
~ ! [X2: subst] :
( ( sub @ eigen__0 @ ( push @ X1 @ X2 ) )
= ( sub @ eigen__0 @ ( push @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: term] :
~ ~ ! [X2: subst > term > term] :
~ ! [X3: term,X4: subst] :
( ( X2 @ X4 @ X3 )
= ( sub @ X1 @ ( push @ X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h1,assumption,
! [X1: subst > $o,X2: subst] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: subst] :
( ( sub @ eigen__0 @ ( push @ eigen__1 @ X1 ) )
!= ( sub @ eigen__0 @ ( push @ eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: subst > term > term] :
~ ! [X2: term,X3: subst] :
( ( X1 @ X3 @ X2 )
= ( sub @ eigen__0 @ ( push @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( sub @ eigen__0 @ ( push @ eigen__1 @ eigen__2 ) )
= ( sub @ eigen__0 @ ( push @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: term,X2: subst] :
( ( sub @ eigen__0 @ ( push @ X1 @ X2 ) )
= ( sub @ eigen__0 @ ( push @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: term] :
~ ! [X2: subst > term > term] :
~ ! [X3: term,X4: subst] :
( ( X2 @ X4 @ X3 )
= ( sub @ X1 @ ( push @ X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: subst] :
( ( sub @ eigen__0 @ ( push @ eigen__1 @ X1 ) )
= ( sub @ eigen__0 @ ( push @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(def_hoasinduction_lem3v2_f,definition,
hoasinduction_lem3v2_f = sP4 ).
thf(def_hoasinduction_lem3v2_f_lthm,definition,
hoasinduction_lem3v2_f_lthm = hoasinduction_lem3v2_f ).
thf(thm,conjecture,
sP4 ).
thf(h2,negated_conjecture,
~ sP4,
inference(assume_negation,[status(cth)],[thm]) ).
thf(1,plain,
sP2,
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP5
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(3,plain,
( sP3
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(4,plain,
( ~ sP1
| ~ sP3 ),
inference(all_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([h2,h1,h0])],[1,2,3,4,5,h2]) ).
thf(7,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[6,h1]) ).
thf(8,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[7,h0]) ).
thf(0,theorem,
sP4,
inference(contra,[status(thm),contra(discharge,[h2])],[6,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG268^4 : TPTP v9.2.0. Bugfixed v5.2.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n023.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 : Wed Oct 8 23:40:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.43/0.61 % SZS status Theorem
% 0.43/0.61 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 0.43/0.61 % Inferences: 6
% 0.43/0.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------