TSTP Solution File: SEU466^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU466^1 : 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 : n032.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 13:52:19 EDT 2022
% Result : Theorem 0.14s 0.32s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 88
% Syntax : Number of formulae : 107 ( 65 unt; 7 typ; 31 def)
% Number of atoms : 248 ( 43 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 1078 ( 225 ~; 18 |; 0 &; 583 @)
% ( 18 <=>; 233 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 160 ( 160 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 55 usr; 54 con; 0-2 aty)
% ( 1 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 346 ( 65 ^ 281 !; 0 ?; 346 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i > $i > $o ).
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(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__3,type,
eigen__3: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ( eigen__3 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ( ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__4 @ X1 ) )
=> ( eigen__3 @ eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__3 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__3 @ X1 @ X2 )
=> ~ ( eigen__3 @ X2 @ X3 ) )
=> ( eigen__3 @ X1 @ X3 ) )
=> ~ ! [X1: $i,X2: $i] :
( ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ( eigen__3 @ X1 @ X2 ) ) )
=> ( eigen__3 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ( eigen__6 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__3 @ X1 @ X2 )
=> ~ ( eigen__3 @ X2 @ X3 ) )
=> ( eigen__3 @ X1 @ X3 ) )
=> ~ ! [X1: $i,X2: $i] :
( ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ( eigen__3 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__4 @ X1 ) )
=> ( eigen__3 @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP3
=> ( eigen__6 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__3 @ X1 @ X2 )
=> ~ ( eigen__3 @ X2 @ X3 ) )
=> ( eigen__3 @ X1 @ X3 ) )
=> ~ sP1 )
=> ( eigen__3 @ eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__3 @ X1 @ X2 )
=> ~ ( eigen__3 @ X2 @ X3 ) )
=> ( eigen__3 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__3 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ( eigen__3 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP5
=> ( eigen__3 @ eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP10
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__3 @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__1 @ X1 ) )
=> ( eigen__6 @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__6 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
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(transitive_closure_op_is_idempotent,conjecture,
! [X1: $i > $i > $o] :
( ( ^ [X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ! [X7: $i > $i > $o] :
( ~ ( ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) )
=> ~ ! [X8: $i,X9: $i] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i > $i > $o] :
( ( ^ [X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ! [X7: $i > $i > $o] :
( ~ ( ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) )
=> ~ ! [X8: $i,X9: $i] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
inference(assume_negation,[status(cth)],[transitive_closure_op_is_idempotent]) ).
thf(h2,assumption,
( ^ [X1: $i,X2: $i] :
! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( eigen__0 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
!= ( ^ [X1: $i,X2: $i] :
! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( ^ [X2: $i] :
! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( eigen__0 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
= ( ^ [X2: $i] :
! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ^ [X1: $i] :
! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__1 @ X1 ) ) )
!= ( ^ [X1: $i] :
! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ( ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__1 @ X1 ) ) )
= ( ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__1 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP16 != sP3,
introduced(assumption,[]) ).
thf(h7,assumption,
sP16,
introduced(assumption,[]) ).
thf(h8,assumption,
sP3,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ sP14
=> sP11 ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h14,assumption,
sP10,
introduced(assumption,[]) ).
thf(h15,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP9
| sP14
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP14
| ~ sP10
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP13
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP13
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP7
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(7,plain,
( sP12
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(8,plain,
( ~ sP16
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP2
| sP6
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP6
| ~ sP10
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h15,h12,h13,h11,h7,h8,h6,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h7,h14,h15,h13]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h11,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,11,h14,h15]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,12,h12,h13]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__3)],[h8,13,h11]) ).
thf(h16,assumption,
~ ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__6 @ X1 @ X2 )
=> ~ ( eigen__6 @ X2 @ X3 ) )
=> ( eigen__6 @ X1 @ X3 ) )
=> ~ sP4 )
=> sP18 ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__6 @ X1 @ X2 )
=> ~ ( eigen__6 @ X2 @ X3 ) )
=> ( eigen__6 @ X1 @ X3 ) )
=> ~ sP4 ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP18,
introduced(assumption,[]) ).
thf(h19,assumption,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__6 @ X1 @ X2 )
=> ~ ( eigen__6 @ X2 @ X3 ) )
=> ( eigen__6 @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
sP4,
introduced(assumption,[]) ).
thf(15,plain,
( ~ sP4
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP17
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP8
| ~ sP3
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h19,h20,h17,h18,h16,h9,h10,h6,h5,h4,h3,h2,h1,h0])],[15,16,17,h20,h18,h10]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h16,h9,h10,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h17,18,h19,h20]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h9,h10,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,19,h17,h18]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__6)],[h9,20,h16]) ).
thf(22,plain,
$false,
inference(tab_be,[status(thm),assumptions([h6,h5,h4,h3,h2,h1,h0]),tab_be(discharge,[h7,h8]),tab_be(discharge,[h9,h10])],[h6,14,21,h7,h8,h9,h10]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,22,h6]) ).
thf(24,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_fe(discharge,[h5])],[h4,23,h5]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,24,h4]) ).
thf(26,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h2,h1,h0]),tab_fe(discharge,[h3])],[h2,25,h3]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,26,h2]) ).
thf(28,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[27,h0]) ).
thf(0,theorem,
! [X1: $i > $i > $o] :
( ( ^ [X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ! [X7: $i > $i > $o] :
( ~ ( ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) )
=> ~ ! [X8: $i,X9: $i] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[27,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SEU466^1 : TPTP v8.1.0. Released v3.6.0.
% 0.06/0.10 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Sun Jun 19 15:09:48 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.14/0.32 % SZS status Theorem
% 0.14/0.32 % Mode: mode213
% 0.14/0.32 % Inferences: 17
% 0.14/0.32 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------