TSTP Solution File: SEU494^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU494^1 : 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 : 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 : Tue Jul 19 13:52:28 EDT 2022
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ( eigen__0 @ eigen__5 @ eigen__4 )
=> ~ ( eigen__0 @ eigen__4 @ eigen__3 ) )
=> ( eigen__0 @ eigen__5 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0 @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__5 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__0 @ eigen__5 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__0 @ eigen__1 @ eigen__2 )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__0 @ eigen__5 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP5
=> ~ ( eigen__0 @ eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ~ ( sP5
=> ~ ( eigen__0 @ eigen__4 @ X1 ) )
=> ( eigen__0 @ eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__0 @ eigen__5 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__0 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ~ ( eigen__0 @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__0 @ eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
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(inverse_of_strict_order_is_strict_order,conjecture,
! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X3 @ X2 )
=> ~ ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X3 @ X2 )
=> ~ ( X1 @ X4 @ X3 ) )
=> ( X1 @ X4 @ X2 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X3 @ X2 )
=> ~ ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X3 @ X2 )
=> ~ ( X1 @ X4 @ X3 ) )
=> ( X1 @ X4 @ X2 ) ) ) ),
inference(assume_negation,[status(cth)],[inverse_of_strict_order_is_strict_order]) ).
thf(h1,assumption,
~ ( ~ ( sP12
=> ~ sP9 )
=> ~ ( ! [X1: $i,X2: $i] :
( ( eigen__0 @ X2 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X2 @ X1 )
=> ~ ( eigen__0 @ X3 @ X2 ) )
=> ( eigen__0 @ X3 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP12
=> ~ sP9 ),
introduced(assumption,[]) ).
thf(h3,assumption,
( ! [X1: $i,X2: $i] :
( ( eigen__0 @ X2 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X2 @ X1 )
=> ~ ( eigen__0 @ X3 @ X2 ) )
=> ( eigen__0 @ X3 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP12,
introduced(assumption,[]) ).
thf(h5,assumption,
sP9,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i,X2: $i] :
( ( eigen__0 @ X2 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X2 @ X1 )
=> ~ ( eigen__0 @ X3 @ X2 ) )
=> ( eigen__0 @ X3 @ X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] :
( ( eigen__0 @ X1 @ eigen__1 )
=> ~ ( eigen__0 @ eigen__1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP2
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP2,
introduced(assumption,[]) ).
thf(h11,assumption,
sP10,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP12
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP11
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP4
| ~ sP10
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h8,h6,h4,h5,h2,h3,h1,h0])],[1,2,3,h4,h10,h11]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,4,h10,h11]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h8,5,h9]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h6,6,h8]) ).
thf(h12,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ X1 @ eigen__3 )
=> ~ ( eigen__0 @ X2 @ X1 ) )
=> ( eigen__0 @ X2 @ eigen__3 ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: $i] :
( ~ ( sP13
=> ~ ( eigen__0 @ X1 @ eigen__4 ) )
=> ( eigen__0 @ X1 @ eigen__3 ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ~ ( sP13
=> ~ sP5 )
=> sP8 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP13
=> ~ sP5 ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h17,assumption,
sP13,
introduced(assumption,[]) ).
thf(h18,assumption,
sP5,
introduced(assumption,[]) ).
thf(8,plain,
( ~ sP9
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP3
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP7
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP1
| sP6
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP6
| ~ sP5
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h18,h15,h16,h14,h13,h12,h7,h4,h5,h2,h3,h1,h0])],[8,9,10,11,12,h5,h17,h18,h16]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h14,h13,h12,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,13,h17,h18]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h13,h12,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,14,h15,h16]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h12,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__5)],[h13,15,h14]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h12,16,h13]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__3)],[h7,17,h12]) ).
thf(19,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[h3,7,18,h6,h7]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,19,h4,h5]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,20,h2,h3]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,21,h1]) ).
thf(0,theorem,
! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X3 @ X2 )
=> ~ ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X3 @ X2 )
=> ~ ( X1 @ X4 @ X3 ) )
=> ( X1 @ X4 @ X2 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[22,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU494^1 : TPTP v8.1.0. Released v3.6.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 21:51:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % Mode: mode213
% 0.19/0.37 % Inferences: 6
% 0.19/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------