TSTP Solution File: SEU484^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU484^1 : TPTP v8.1.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n014.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 : Tue Jul 19 13:52:24 EDT 2022
% Result : Theorem 2.12s 2.30s
% Output : Proof 2.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 59
% Syntax : Number of formulae : 66 ( 40 unt; 3 typ; 31 def)
% Number of atoms : 166 ( 35 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 353 ( 87 ~; 14 |; 0 &; 180 @)
% ( 12 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 97 ( 97 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 46 usr; 47 con; 0-2 aty)
% ( 1 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 119 ( 45 ^ 74 !; 0 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(h0,assumption,
! [X1: ( $i > $i > $o ) > $o,X2: $i > $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i > $o] :
( ~ ! [X3: $i] :
~ ( X2 @ X3 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: $i] :
~ ( ( eigen__0 @ eigen__1 @ eigen__1 )
=> ~ ! [X2: $i] :
( ( eigen__0 @ eigen__1 @ eigen__1 )
=> ~ ( eigen__0 @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: $i] : ( eigen__0 @ X1 @ X1 )
=> ~ ! [X1: $i > $o] :
( ~ ! [X2: $i] :
~ ( X1 @ X2 )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ( eigen__0 @ X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__0 @ eigen__1 @ eigen__1 )
=> ~ ( eigen__0 @ eigen__2 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
~ ( eigen__0 @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0 @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( sP4
=> ~ ( eigen__0 @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ sP3
=> ~ ! [X1: $i] :
( sP4
=> ~ ! [X2: $i] :
( sP4
=> ~ ( eigen__0 @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( sP4
=> ~ ! [X2: $i] :
( sP4
=> ~ ( eigen__0 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__0 @ eigen__2 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] : ( eigen__0 @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i > $i > $o] :
( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i > $o] :
( ~ ! [X3: $i] :
~ ( X2 @ X3 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i > $o] :
( ~ ! [X2: $i] :
~ ( X1 @ X2 )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ( eigen__0 @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP4
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(def_subrel,definition,
( subrel
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) ).
thf(def_inv,definition,
( inv
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_idem,definition,
( idem
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ ( X1 @ X2 ) )
= ( X1 @ X2 ) ) ) ) ).
thf(def_infl,definition,
( infl
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] : ( subrel @ X2 @ ( X1 @ X2 ) ) ) ) ).
thf(def_mono,definition,
( mono
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o] :
( ( subrel @ X2 @ X3 )
=> ( subrel @ ( X1 @ X2 ) @ ( X1 @ X3 ) ) ) ) ) ).
thf(def_refl,definition,
( refl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_irrefl,definition,
( irrefl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) ).
thf(def_rc,definition,
( rc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) ) ) ) ).
thf(def_symm,definition,
( symm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_antisymm,definition,
( antisymm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) ).
thf(def_asymm,definition,
( asymm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_sc,definition,
( sc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ~ ( X1 @ X3 @ X2 )
=> ( X1 @ X2 @ X3 ) ) ) ) ).
thf(def_trans,definition,
( trans
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_tc,definition,
( tc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ~ ( ( trans @ X4 )
=> ~ ( subrel @ X1 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ).
thf(def_trc,definition,
( trc
= ( ^ [X1: $i > $i > $o] : ( rc @ ( tc @ X1 ) ) ) ) ).
thf(def_trsc,definition,
( trsc
= ( ^ [X1: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X1 ) ) ) ) ) ).
thf(def_po,definition,
( po
= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ( refl @ X1 )
=> ~ ( antisymm @ X1 ) )
=> ~ ( trans @ X1 ) ) ) ) ).
thf(def_so,definition,
( so
= ( ^ [X1: $i > $i > $o] :
~ ( ( asymm @ X1 )
=> ~ ( trans @ X1 ) ) ) ) ).
thf(def_total,definition,
( total
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_term,definition,
( term
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o] :
( ~ ! [X3: $i] :
~ ( X2 @ X3 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) ) ) ).
thf(def_ind,definition,
( ind
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( tc @ X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) )
=> ( !! @ X2 ) ) ) ) ).
thf(def_innf,definition,
( innf
= ( ^ [X1: $i > $i > $o,X2: $i] :
! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) ).
thf(def_nfof,definition,
( nfof
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
~ ( ( trc @ X1 @ X3 @ X2 )
=> ~ ( innf @ X1 @ X2 ) ) ) ) ).
thf(def_norm,definition,
( norm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
~ ( nfof @ X1 @ X3 @ X2 ) ) ) ).
thf(def_join,definition,
( join
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
~ ! [X4: $i] :
( ( trc @ X1 @ X2 @ X4 )
=> ~ ( trc @ X1 @ X3 @ X4 ) ) ) ) ).
thf(def_lconfl,definition,
( lconfl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X2 @ X3 ) )
=> ( join @ X1 @ X4 @ X3 ) ) ) ) ).
thf(def_sconfl,definition,
( sconfl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( trc @ X1 @ X2 @ X3 ) )
=> ( join @ X1 @ X4 @ X3 ) ) ) ) ).
thf(def_confl,definition,
( confl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( trc @ X1 @ X2 @ X4 )
=> ~ ( trc @ X1 @ X2 @ X3 ) )
=> ( join @ X1 @ X4 @ X3 ) ) ) ) ).
thf(def_cr,definition,
( cr
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( trsc @ X1 @ X2 @ X3 )
=> ( join @ X1 @ X2 @ X3 ) ) ) ) ).
thf(reflexive_implies_non_terminating,conjecture,
sP10 ).
thf(h2,negated_conjecture,
~ sP10,
inference(assume_negation,[status(cth)],[reflexive_implies_non_terminating]) ).
thf(1,plain,
( ~ sP2
| ~ sP4
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP9
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP12
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP7
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(6,plain,
( ~ sP3
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP6
| sP3
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP11
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP9
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( sP1
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP1
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP10
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h2]) ).
thf(14,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[13,h1]) ).
thf(15,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[14,h0]) ).
thf(0,theorem,
sP10,
inference(contra,[status(thm),contra(discharge,[h2])],[13,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU484^1 : TPTP v8.1.0. Released v3.6.0.
% 0.10/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 10:21:03 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.12/2.30 % SZS status Theorem
% 2.12/2.30 % Mode: mode506
% 2.12/2.30 % Inferences: 40707
% 2.12/2.30 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------