TSTP Solution File: SEU460^1 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU460^1 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n011.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 Aug 31 17:17:41 EDT 2023
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ( eigen__1 @ eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 @ eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0 @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP4
=> ( eigen__1 @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP3
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ sP3
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__1 @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__3 @ X1 )
=> ( eigen__1 @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(def_subrel,definition,
( subrel
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( 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] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( 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] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X2 @ X3 )
@ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_antisymm,definition,
( antisymm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X3 @ X2 ) )
@ ( X2 = X3 ) ) ) ) ).
thf(def_asymm,definition,
( asymm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( 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] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( 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] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( 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: $o,X4: $o] :
( X3
=> X4 )
@ ? [X3: $i] : ( X2 @ X3 )
@ ? [X3: $i] :
( ( X2 @ X3 )
& ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X2 @ X4 )
@ ( (~) @ ( X1 @ X3 @ X4 ) ) ) ) ) ) ) ).
thf(def_ind,definition,
( ind
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( tc @ X1 @ X3 @ X4 )
@ ( X2 @ X4 ) )
@ ( X2 @ X3 ) )
@ ! [X3: $i] : ( X2 @ X3 ) ) ) ) ).
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] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( 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] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( 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] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( 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] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( trsc @ X1 @ X2 @ X3 )
@ ( join @ X1 @ X2 @ X3 ) ) ) ) ).
thf(symmetric_closure_op_is_monotonic,conjecture,
! [X1: $i > $i > $o,X2: $i > $i > $o] :
( ! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ! [X3: $i,X4: $i] :
( ( ~ ( X1 @ X4 @ X3 )
=> ( X1 @ X3 @ X4 ) )
=> ( ~ ( X2 @ X4 @ X3 )
=> ( X2 @ X3 @ X4 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i > $o,X2: $i > $i > $o] :
( ! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ! [X3: $i,X4: $i] :
( ( ~ ( X1 @ X4 @ X3 )
=> ( X1 @ X3 @ X4 ) )
=> ( ~ ( X2 @ X4 @ X3 )
=> ( X2 @ X3 @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[symmetric_closure_op_is_monotonic]) ).
thf(h1,assumption,
~ ! [X1: $i > $i > $o] :
( ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ! [X2: $i,X3: $i] :
( ( ~ ( eigen__0 @ X3 @ X2 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ( ~ ( X1 @ X3 @ X2 )
=> ( X1 @ X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP10
=> ! [X1: $i,X2: $i] :
( ( ~ ( eigen__0 @ X2 @ X1 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ( ~ ( eigen__1 @ X2 @ X1 )
=> ( eigen__1 @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP10,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i,X2: $i] :
( ( ~ ( eigen__0 @ X2 @ X1 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ( ~ ( eigen__1 @ X2 @ X1 )
=> ( eigen__1 @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ( ~ ( eigen__0 @ X1 @ eigen__2 )
=> ( eigen__0 @ eigen__2 @ X1 ) )
=> ( ~ ( eigen__1 @ X1 @ eigen__2 )
=> ( eigen__1 @ eigen__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP7
=> ( ~ sP1
=> sP8 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP7,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ sP1
=> sP8 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP6
| ~ sP3
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP9
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| ~ sP4
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP10
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP10
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP7
| sP3
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h7,h8,h6,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,h3,h7,h9,h10]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h6,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,8,h9,h10]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,9,h7,h8]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__3)],[h5,10,h6]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,11,h5]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,12,h3,h4]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,13,h2]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,14,h1]) ).
thf(0,theorem,
! [X1: $i > $i > $o,X2: $i > $i > $o] :
( ! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ! [X3: $i,X4: $i] :
( ( ~ ( X1 @ X4 @ X3 )
=> ( X1 @ X3 @ X4 ) )
=> ( ~ ( X2 @ X4 @ X3 )
=> ( X2 @ X3 @ X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU460^1 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.16/0.35 % Computer : n011.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Wed Aug 23 13:26:37 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % Mode: cade22grackle2xfee4
% 0.21/0.42 % Steps: 26
% 0.21/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------