TSTP Solution File: ALG259^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG259^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n024.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 : 600s
% DateTime : Thu Jul 14 17:57:48 EDT 2022
% Result : Theorem 0.59s 0.82s
% Output : Proof 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 33
% Syntax : Number of formulae : 40 ( 15 unt; 11 typ; 7 def)
% Number of atoms : 63 ( 19 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 142 ( 17 ~; 7 |; 0 &; 103 @)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 19 con; 0-2 aty)
% Number of variables : 40 ( 7 ^ 33 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subst,type,
subst: $tType ).
thf(ty_term,type,
term: $tType ).
thf(ty_eigen__2,type,
eigen__2: term ).
thf(ty_eigen__0,type,
eigen__0: subst > term > term ).
thf(ty_ap,type,
ap: term > term > term ).
thf(ty_id,type,
id: subst ).
thf(ty_one,type,
one: term ).
thf(ty_sub,type,
sub: term > subst > term ).
thf(ty_lam,type,
lam: term > term ).
thf(ty_sh,type,
sh: subst ).
thf(ty_comp,type,
comp: subst > subst > subst ).
thf(h0,assumption,
! [X1: ( subst > term > term ) > $o,X2: subst > term > term] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: subst > term > term] :
~ ( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ! [X2: term,X3: term] :
( ( lam @ ( X1 @ sh @ one ) )
!= ( ap @ ( sub @ X2 @ id ) @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h1,assumption,
! [X1: term > $o,X2: term] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: term] :
~ ! [X2: term] :
( ( lam @ ( eigen__0 @ sh @ one ) )
!= ( ap @ ( sub @ X1 @ id ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: term,X2: term,X3: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: term,X2: term] :
( ( lam @ ( eigen__0 @ sh @ one ) )
!= ( ap @ ( sub @ X1 @ id ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: term] :
( ( lam @ ( eigen__0 @ sh @ one ) )
!= ( ap @ ( sub @ eigen__2 @ id ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: subst > term > term] :
( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ! [X2: term,X3: term] :
( ( lam @ ( X1 @ sh @ one ) )
!= ( ap @ ( sub @ X2 @ id ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP1
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: term,X2: term] :
( ( lam @ ( eigen__0 @ sh @ one ) )
!= ( ap @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: subst,X2: term,X3: subst] :
( ( sub @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(def_lamnotap,definition,
lamnotap = sP1 ).
thf(def_hoasap,definition,
( hoasap
= ( ^ [X1: subst,X2: term,X3: subst] : ( ap @ ( sub @ X2 @ X3 ) ) ) ) ).
thf(def_hoaslam,definition,
( hoaslam
= ( ^ [X1: subst,X2: subst > term > term] : ( lam @ ( X2 @ sh @ one ) ) ) ) ).
thf(def_hoaslamnotap,definition,
( hoaslamnotap
= ( ! [X1: subst > term > term] :
( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ! [X2: term,X3: term] :
( ( hoaslam @ id @ X1 )
!= ( hoasap @ id @ X2 @ id @ X3 ) ) ) ) ) ).
thf(def_hoaslamnotap_lthm,definition,
( hoaslamnotap_lthm
= ( lamnotap
=> hoaslamnotap ) ) ).
thf(thm,conjecture,
sP5 ).
thf(h2,negated_conjecture,
~ sP5,
inference(assume_negation,[status(cth)],[thm]) ).
thf(1,plain,
( ~ sP1
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP2
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(4,plain,
( sP7
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP4
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(6,plain,
( sP5
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP5
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,h2]) ).
thf(9,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[8,h1]) ).
thf(10,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[9,h0]) ).
thf(0,theorem,
sP5,
inference(contra,[status(thm),contra(discharge,[h2])],[8,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG259^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n024.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 : 600
% 0.13/0.34 % DateTime : Wed Jun 8 07:50:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.59/0.82 % SZS status Theorem
% 0.59/0.82 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 0.59/0.82 % Inferences: 11
% 0.59/0.82 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------