%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n002.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 : Tue May 5 07:06:12 PM UTC 2026
% Result : Theorem 28.03s 28.41s
% Output : Proof 28.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 140
% Syntax : Number of formulae : 146 ( 10 unt; 0 typ; 2 def)
% Number of atoms : 869 ( 226 equ; 0 cnn)
% Maximal formula atoms : 40 ( 5 avg)
% Number of connectives : 1970 ( 640 ~; 77 |; 0 &; 744 @)
% ( 69 <=>; 434 =>; 0 <=; 0 <~>)
% Maximal formula depth : 77 ( 5 avg)
% Number of types : 5 ( 3 usr)
% Number of type conns : 374 ( 374 >; 0 *; 0 +; 0 <<)
% Number of symbols : 110 ( 107 usr; 74 con; 0-3 aty)
% ( 6 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 544 ( 313 ^; 231 !; 0 ?; 544 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_d_unsorted,type,
d_unsorted: $tType ).
thf(ty_d_mu,type,
d_mu: $tType ).
thf(ty_mu,type,
mu: $tType ).
thf(ty_mand,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ty_mforall_ind,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(ty_mcountersatisfiable,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(ty_d2mu,type,
d2mu: d_mu > mu ).
thf(ty_mimplies,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ty_minvalid,type,
minvalid: ( $i > $o ) > $o ).
thf(ty_mxor,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ty_mimplied,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_mexists_prop,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(ty_mor,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ty_msatisfiable,type,
msatisfiable: ( $i > $o ) > $o ).
thf(ty_mtransitive,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(ty_mweakly_directed,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(ty_mbox,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ty_mtrue,type,
mtrue: $i > $o ).
thf(ty_mserial,type,
mserial: ( $i > $i > $o ) > $o ).
thf(ty_mforall_prop,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(ty_mvalid,type,
mvalid: ( $i > $o ) > $o ).
thf(ty_mweakly_connected,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(ty_mdia,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ty_mfalse,type,
mfalse: $i > $o ).
thf(ty_msymmetric,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(ty_meq_ind,type,
meq_ind: mu > mu > $i > $o ).
thf(ty_mreflexive,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(ty_mexists_ind,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(ty_d_unsorted_0,type,
d_unsorted_0: d_unsorted ).
thf(ty_mweakly_dense,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(ty_meuclidean,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(ty_mpartially_functional,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(ty_d_mu_0,type,
d_mu_0: d_mu ).
thf(ty_mequiv,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ty_meq_prop,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ty_mnot,type,
mnot: ( $i > $o ) > $i > $o ).
thf(ty_d2unsorted,type,
d2unsorted: d_unsorted > $i ).
thf(ty_mfunctional,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i > $o] :
( ( mequiv @ eigen__0 @ X1 )
!= ( mand @ ( mimplies @ eigen__0 @ X1 ) @ ( mimplies @ X1 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i > $o] :
( ( mequiv @ X1 )
!= ( ^ [X2: $i > $o] : ( mand @ ( mimplies @ X1 @ X2 ) @ ( mimplies @ X2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: mu] :
~ ! [X2: d_mu] :
( X1
!= ( d2mu @ X2 ) ) )
=> ~ ! [X1: d_mu] : ( X1 = d_mu_0 ) )
=> ~ ! [X1: d_mu,X2: d_mu] :
( ( ( d2mu @ X1 )
= ( d2mu @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( meq_prop
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ( mor
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ( mimplied
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) )
=> ( mequiv
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ) )
=> ( mxor
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ) )
=> ( mforall_ind
!= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] : ( X1 @ X3 @ X2 ) ) ) )
=> ( mforall_prop
!= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
! [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) )
=> ( mexists_ind
!= ( ^ [X1: mu > $i > $o,X2: $i] :
~ ! [X3: mu] :
~ ( X1 @ X3 @ X2 ) ) ) )
=> ( mexists_prop
!= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
~ ! [X3: $i > $o] :
~ ( X1 @ X3 @ X2 ) ) ) )
=> ( mbox
!= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) )
=> ( mdia
!= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
~ ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( mreflexive
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( msymmetric
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( mserial
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) )
=> ( mtransitive
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ( meuclidean
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ) )
=> ( mpartially_functional
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( mfunctional
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( mweakly_dense
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X4 @ X3 ) ) ) ) ) )
=> ( mweakly_connected
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) )
=> ( X3 = X4 ) )
=> ( X1 @ X4 @ X3 ) ) ) ) )
=> ( mweakly_directed
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ~ ! [X5: $i] :
( ( X1 @ X3 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) )
=> ( mvalid != !! ) )
=> ( minvalid
!= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ( msatisfiable
!= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ( mcountersatisfiable
!= ( ^ [X1: $i > $o] :
~ ( !! @ X1 ) ) ) )
=> ~ ( meq_ind @ ( d2mu @ d_mu_0 ) @ ( d2mu @ d_mu_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) )
=> ~ ( mtrue @ ( d2unsorted @ d_unsorted_0 ) ) )
=> ( mfalse @ ( d2unsorted @ d_unsorted_0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: mu] :
~ ! [X2: d_mu] :
( X1
!= ( d2mu @ X2 ) ) )
=> ~ ! [X1: d_mu] : ( X1 = d_mu_0 ) )
=> ~ ! [X1: d_mu,X2: d_mu] :
( ( ( d2mu @ X1 )
= ( d2mu @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( meq_prop
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ( mor
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ( mimplied
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) )
=> ( mequiv
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ) )
=> ( mxor
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ) )
=> ( mforall_ind
!= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] : ( X1 @ X3 @ X2 ) ) ) )
=> ( mforall_prop
!= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
! [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) )
=> ( mexists_ind
!= ( ^ [X1: mu > $i > $o,X2: $i] :
~ ! [X3: mu] :
~ ( X1 @ X3 @ X2 ) ) ) )
=> ( mexists_prop
!= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
~ ! [X3: $i > $o] :
~ ( X1 @ X3 @ X2 ) ) ) )
=> ( mbox
!= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) )
=> ( mdia
!= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
~ ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( mreflexive
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( msymmetric
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( mserial
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) )
=> ( mtransitive
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ( meuclidean
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ) )
=> ( mpartially_functional
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( mfunctional
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( mweakly_dense
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X4 @ X3 ) ) ) ) ) )
=> ( mweakly_connected
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) )
=> ( X3 = X4 ) )
=> ( X1 @ X4 @ X3 ) ) ) ) )
=> ( mweakly_directed
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ~ ! [X5: $i] :
( ( X1 @ X3 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) )
=> ( mvalid != !! ) )
=> ( minvalid
!= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: mu] :
~ ! [X2: d_mu] :
( X1
!= ( d2mu @ X2 ) ) )
=> ~ ! [X1: d_mu] : ( X1 = d_mu_0 ) )
=> ~ ! [X1: d_mu,X2: d_mu] :
( ( ( d2mu @ X1 )
= ( d2mu @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( meq_prop
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) )
=> ( mnot
!= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ( mor
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ( mand
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: ( ( $i > $o ) > $i > $o ) > $o] :
( ( X1
@ ( mand
@ ^ [X2: $i] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 ) ) ) )
=> ! [X2: ( $i > $o ) > $i > $o] :
( ( ( mand
@ ^ [X3: $i] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ X3 ) ) )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ( mimplies @ eigen__1 )
= ( ^ [X1: $i > $o,X2: $i] :
( ( eigen__1 @ X2 )
=> ( X1 @ X2 ) ) ) )
=> ( ( ^ [X1: $i] :
~ ( ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
=> ~ ( ( eigen__1 @ X1 )
=> ( eigen__0 @ X1 ) ) ) )
!= ( ^ [X1: $i] :
~ ( ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
=> ~ ( ( eigen__1 @ X1 )
=> ( eigen__0 @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: ( $i > $o ) > $i > $o] :
( ( ( mimplies @ eigen__1 )
= X1 )
=> ( ( ^ [X2: $i] :
~ ( ( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 ) )
=> ~ ( ( eigen__1 @ X2 )
=> ( eigen__0 @ X2 ) ) ) )
!= ( ^ [X2: $i] :
~ ( ( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 ) )
=> ~ ( X1 @ eigen__0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( ~ ( ~ ( ~ sP2
=> ( msatisfiable
!= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ( mcountersatisfiable
!= ( ^ [X1: $i > $o] :
~ ( !! @ X1 ) ) ) )
=> ~ ( meq_ind @ ( d2mu @ d_mu_0 ) @ ( d2mu @ d_mu_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) )
=> ~ ( mtrue @ ( d2unsorted @ d_unsorted_0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( ~ sP2
=> ( msatisfiable
!= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ( mcountersatisfiable
!= ( ^ [X1: $i > $o] :
~ ( !! @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i > $o] :
( ( mimplies @ X1 )
= ( ^ [X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( mand
@ ^ [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) ) )
= ( ^ [X1: $i > $o,X2: $i] :
~ ( ( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 ) )
=> ~ ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( mimplies @ eigen__1 )
= ( ^ [X1: $i > $o,X2: $i] :
( ( eigen__1 @ X2 )
=> ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i > $o] :
( ( ^ [X2: $i] :
~ ( ( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ( ( X1 @ X2 )
=> ( eigen__0 @ X2 ) ) ) )
= ( ^ [X2: $i] :
~ ( ( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ( ( X1 @ X2 )
=> ( eigen__0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( mequiv @ eigen__0 )
= ( ^ [X1: $i > $o] : ( mand @ ( mimplies @ eigen__0 @ X1 ) @ ( mimplies @ X1 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ sP3
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ( mimplied
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) )
=> ( mequiv
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ) )
=> ( mxor
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ) )
=> ( mforall_ind
!= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] : ( X1 @ X3 @ X2 ) ) ) )
=> ( mforall_prop
!= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
! [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) )
=> ( mexists_ind
!= ( ^ [X1: mu > $i > $o,X2: $i] :
~ ! [X3: mu] :
~ ( X1 @ X3 @ X2 ) ) ) )
=> ( mexists_prop
!= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
~ ! [X3: $i > $o] :
~ ( X1 @ X3 @ X2 ) ) ) )
=> ( mbox
!= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) )
=> ( mdia
!= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
~ ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( mreflexive
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( msymmetric
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( ^ [X1: $i] :
~ ( ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
=> ~ ( ( eigen__1 @ X1 )
=> ( eigen__0 @ X1 ) ) ) )
= ( mand
@ ^ [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
@ ( mimplies @ eigen__1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP2
=> ( msatisfiable
!= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP8
=> ~ ( meq_ind @ ( d2mu @ d_mu_0 ) @ ( d2mu @ d_mu_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( ( mequiv @ eigen__0 )
= ( ^ [X1: $i > $o,X2: $i] :
~ ( ( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ( ( X1 @ X2 )
=> ( eigen__0 @ X2 ) ) ) ) )
=> ( ( ^ [X1: $i > $o,X2: $i] :
~ ( ( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ( ( X1 @ X2 )
=> ( eigen__0 @ X2 ) ) ) )
= ( ^ [X1: $i > $o,X2: $i] :
~ ( ( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ( ( X1 @ X2 )
=> ( eigen__0 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ sP14
=> ( mserial
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) )
=> ( mtransitive
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ( meuclidean
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ) )
=> ( mpartially_functional
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( mfunctional
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( mweakly_dense
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X4 @ X3 ) ) ) ) ) )
=> ( mweakly_connected
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) )
=> ( X3 = X4 ) )
=> ( X1 @ X4 @ X3 ) ) ) ) )
=> ( mweakly_directed
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ~ ! [X5: $i] :
( ( X1 @ X3 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ sP3
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ( mimplied
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) )
=> ( mequiv
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ) )
=> ( mxor
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ) )
=> ( mforall_ind
!= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] : ( X1 @ X3 @ X2 ) ) ) )
=> ( mforall_prop
!= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
! [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) )
=> ( mexists_ind
!= ( ^ [X1: mu > $i > $o,X2: $i] :
~ ! [X3: mu] :
~ ( X1 @ X3 @ X2 ) ) ) )
=> ( mexists_prop
!= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
~ ! [X3: $i > $o] :
~ ( X1 @ X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i > $o] :
( ( mequiv @ X1 )
= ( ^ [X2: $i > $o,X3: $i] :
~ ( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: ( ( $i > $o ) > $i > $o ) > $o] :
( ( X1 @ ( mimplies @ eigen__0 ) )
=> ! [X2: ( $i > $o ) > $i > $o] :
( ( ( mimplies @ eigen__0 )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ sP3
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ( mimplied
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) )
=> ( mequiv
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ) )
=> ( mxor
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ) )
=> ( mforall_ind
!= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] : ( X1 @ X3 @ X2 ) ) ) )
=> ( mforall_prop
!= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
! [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) )
=> ( mexists_ind
!= ( ^ [X1: mu > $i > $o,X2: $i] :
~ ! [X3: mu] :
~ ( X1 @ X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( ( ^ [X1: $i] :
~ ( ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
=> ~ ( ( eigen__1 @ X1 )
=> ( eigen__0 @ X1 ) ) ) )
!= ( mand @ ( mimplies @ eigen__0 @ eigen__1 ) @ ( mimplies @ eigen__1 @ eigen__0 ) ) )
=> ! [X1: ( $i > $o ) > $i > $o] :
( ( ( mimplies @ eigen__0 )
= X1 )
=> ( ( ^ [X2: $i] :
~ ( ( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 ) )
=> ~ ( ( eigen__1 @ X2 )
=> ( eigen__0 @ X2 ) ) ) )
!= ( mand @ ( X1 @ eigen__1 ) @ ( mimplies @ eigen__1 @ eigen__0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ sP14
=> ( mserial
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) )
=> ( mtransitive
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ( meuclidean
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ) )
=> ( mpartially_functional
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( mfunctional
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( mweakly_dense
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X4 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ~ ( ~ ( ~ ( ~ ( ~ sP14
=> ( mserial
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) )
=> ( mtransitive
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ( meuclidean
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ) )
=> ( mpartially_functional
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) )
=> ( mfunctional
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ ( ~ ( ~ ( ~ sP14
=> ( mserial
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) )
=> ( mtransitive
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ( meuclidean
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ) )
=> ( mpartially_functional
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ sP14
=> ( mserial
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( mequiv @ eigen__0 )
= ( ^ [X1: $i > $o,X2: $i] :
~ ( ( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ( ( X1 @ X2 )
=> ( eigen__0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ sP25
=> ( mweakly_connected
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) )
=> ( X3 = X4 ) )
=> ( X1 @ X4 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ~ ( ~ ( ~ sP20
=> ( mbox
!= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) )
=> ( mdia
!= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
~ ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( mreflexive
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ ( ~ ( ~ ( ~ ( ~ sP3
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ( mimplied
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) )
=> ( mequiv
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ) )
=> ( mxor
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ) )
=> ( mforall_ind
!= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] : ( X1 @ X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: ( $i > $o ) > $i > $o] :
( ( ( mand
@ ^ [X2: $i] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 ) ) )
= X1 )
=> ( ( ^ [X2: $i] :
~ ( ( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 ) )
=> ~ ( ( eigen__1 @ X2 )
=> ( eigen__0 @ X2 ) ) ) )
!= ( X1 @ ( mimplies @ eigen__1 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( ^ [X1: $i] :
~ ( ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
=> ~ ( ( eigen__1 @ X1 )
=> ( eigen__0 @ X1 ) ) ) )
= ( ^ [X1: $i] :
~ ( ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
=> ~ ( ( eigen__1 @ X1 )
=> ( eigen__0 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i > $o] :
( ( mequiv @ eigen__0 @ X1 )
= ( mand @ ( mimplies @ eigen__0 @ X1 ) @ ( mimplies @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ~ sP20
=> ( mbox
!= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ( ^ [X1: $i > $o,X2: $i] :
~ ( ( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ( ( X1 @ X2 )
=> ( eigen__0 @ X2 ) ) ) )
= ( ^ [X1: $i > $o,X2: $i] :
~ ( ( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ( ( X1 @ X2 )
=> ( eigen__0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ sP3
=> ( mimplies
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: ( $i > $o ) > $i > $o] :
( ( ( mimplies @ eigen__0 )
= X1 )
=> ( ( ^ [X2: $i] :
~ ( ( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 ) )
=> ~ ( ( eigen__1 @ X2 )
=> ( eigen__0 @ X2 ) ) ) )
!= ( mand @ ( X1 @ eigen__1 ) @ ( mimplies @ eigen__1 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $i > $o] :
( ( mequiv @ X1 )
= ( ^ [X2: $i > $o] : ( mand @ ( mimplies @ X1 @ X2 ) @ ( mimplies @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ( ^ [X1: $i] :
~ ( ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
=> ~ ( ( eigen__1 @ X1 )
=> ( eigen__0 @ X1 ) ) ) )
= ( ^ [X1: $i] :
~ ( ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
=> ~ ( mimplies @ eigen__1 @ eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( mequiv
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ( ^ [X1: $i] :
~ ( ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
=> ~ ( ( eigen__1 @ X1 )
=> ( eigen__0 @ X1 ) ) ) )
= ( mand @ ( mimplies @ eigen__0 @ eigen__1 ) @ ( mimplies @ eigen__1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: ( ( $i > $o ) > $i > $o ) > $o] :
( ( X1 @ ( mimplies @ eigen__1 ) )
=> ! [X2: ( $i > $o ) > $i > $o] :
( ( ( mimplies @ eigen__1 )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: ( ( $i > $o ) > $i > $o ) > $o] :
( ( X1 @ ( mequiv @ eigen__0 ) )
=> ! [X2: ( $i > $o ) > $i > $o] :
( ( ( mequiv @ eigen__0 )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( mand
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ~ sP38
=> ( mimplied
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: ( $i > $o ) > $i > $o,X2: ( ( $i > $o ) > $i > $o ) > $o] :
( ( X2 @ X1 )
=> ! [X3: ( $i > $o ) > $i > $o] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ~ sP32
=> ( mforall_prop
!= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
! [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: ( $i > $o ) > $i > $o] :
( ( ( mequiv @ eigen__0 )
= X1 )
=> ( X1
= ( ^ [X2: $i > $o,X3: $i] :
~ ( ( ( eigen__0 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( eigen__0 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( mimplies
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( mequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimplies @ X1 @ X2 ) @ ( mimplies @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ~ sP41
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ~ ( ~ sP28
=> ( mtransitive
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ( meuclidean
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( ~ sP47
=> ~ sP42 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( ~ sP55
=> ( mxor
!= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ( ( mequiv @ eigen__0 @ eigen__1 )
!= ( mand @ ( mimplies @ eigen__0 @ eigen__1 ) @ ( mimplies @ eigen__1 @ eigen__0 ) ) )
=> ! [X1: ( $i > $o ) > $i > $o] :
( ( ( mequiv @ eigen__0 )
= X1 )
=> ( ( X1 @ eigen__1 )
!= ( mand @ ( mimplies @ eigen__0 @ eigen__1 ) @ ( mimplies @ eigen__1 @ eigen__0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( ~ sP36
=> ( mdia
!= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
~ ! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( ~ sP15
=> sP33 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( ( ( mimplies @ eigen__0 )
= ( ^ [X1: $i > $o,X2: $i] :
( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) ) ) )
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( sP10
=> ~ sP41 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( ( mimplies @ eigen__0 )
= ( ^ [X1: $i > $o,X2: $i] :
( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( sP29
=> sP50 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( sP29
=> ~ sP43 ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ! [X1: ( $i > $o ) > $i > $o] :
( ( ( mequiv @ eigen__0 )
= X1 )
=> ( ( X1 @ eigen__1 )
!= ( mand @ ( mimplies @ eigen__0 @ eigen__1 ) @ ( mimplies @ eigen__1 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( ~ sP19
=> ( mvalid != !! ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( ~ sP28
=> ( mtransitive
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( ( mequiv @ eigen__0 @ eigen__1 )
= ( mand @ ( mimplies @ eigen__0 @ eigen__1 ) @ ( mimplies @ eigen__1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ! [X1: $i > $o] :
( ( mand @ X1 )
= ( ^ [X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(mequiv,conjecture,
sP52 ).
thf(h1,negated_conjecture,
~ sP52,
inference(assume_negation,[status(cth)],[mequiv]) ).
thf(1,plain,
( ~ sP5
| ~ sP11
| ~ sP34 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP6
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP53
| sP41
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP44
| sP53 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP12
| sP34 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP69
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP61
| ~ sP10
| ~ sP41 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP33
| sP61 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP59
| sP15
| sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP4
| sP59 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP48
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP37
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP9
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP48
| sP44 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP60
| ~ sP62
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP39
| sP60 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP24
| sP43
| sP39 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP22
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP9
| sP62 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP48
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP46
| sP69 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP18
| ~ sP29
| sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP50
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP63
| ~ sP29
| sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP45
| sP63 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP51
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( sP3
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP64
| ~ sP29
| ~ sP43 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP65
| sP64 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP57
| sP68
| sP65 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP45
| sP57 ),
inference(all_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP21
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP48
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
sP48,
inference(eq_ind,[status(thm)],[]) ).
thf(35,plain,
( sP38
| sP51 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( sP38
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP42
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( sP47
| ~ sP38 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( sP55
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( sP55
| ~ sP47 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( sP56
| ~ sP55 ),
inference(prop_rule,[status(thm)],[]) ).
thf(42,plain,
( sP32
| ~ sP56 ),
inference(prop_rule,[status(thm)],[]) ).
thf(43,plain,
( sP49
| ~ sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( sP23
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(45,plain,
( sP20
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( sP36
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(47,plain,
( sP58
| ~ sP36 ),
inference(prop_rule,[status(thm)],[]) ).
thf(48,plain,
( sP31
| ~ sP58 ),
inference(prop_rule,[status(thm)],[]) ).
thf(49,plain,
( sP14
| ~ sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(50,plain,
( sP28
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(51,plain,
( sP67
| ~ sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(52,plain,
( sP54
| ~ sP67 ),
inference(prop_rule,[status(thm)],[]) ).
thf(53,plain,
( sP27
| ~ sP54 ),
inference(prop_rule,[status(thm)],[]) ).
thf(54,plain,
( sP26
| ~ sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(55,plain,
( sP25
| ~ sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(56,plain,
( sP30
| ~ sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(57,plain,
( sP19
| ~ sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(58,plain,
( sP66
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(59,plain,
( sP2
| ~ sP66 ),
inference(prop_rule,[status(thm)],[]) ).
thf(60,plain,
( sP16
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(61,plain,
( sP8
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(62,plain,
( sP17
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(63,plain,
( sP7
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(64,plain,
( sP1
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(65,plain,
( sP35
| ~ sP68 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(66,plain,
( sP13
| ~ sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(67,plain,
( sP40
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(68,plain,
( sP52
| ~ sP40 ),
inference(prop_rule,[status(thm)],[]) ).
thf(lcl698_1,axiom,
~ sP1 ).
thf(69,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,lcl698_1,h1]) ).
thf(70,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[69,h0]) ).
thf(0,theorem,
sP52,
inference(contra,[status(thm),contra(discharge,[h1])],[69,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.16 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.06/0.18 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.41 % Computer : n002.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8042.1875MB
% 0.12/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Tue May 5 09:28:31 EDT 2026
% 0.12/0.41 % CPUTime :
% 28.03/28.41 % SZS status Theorem
% 28.03/28.41 % Mode: mode371
% 28.03/28.41 % Inferences: 7216
% 28.03/28.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------