TSTP Solution File: SEU458^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU458^1 : 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 : n022.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 13:52:16 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : Proof 0.12s
% 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(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
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(symmetric_closure_op_is_idempotent,conjecture,
! [X1: $i > $i > $o] :
( ( ^ [X2: $i,X3: $i] :
( ~ ( ~ ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) )
=> ( ~ ( X1 @ X3 @ X2 )
=> ( X1 @ X2 @ X3 ) ) ) )
= ( ^ [X2: $i,X3: $i] :
( ~ ( X1 @ X3 @ X2 )
=> ( X1 @ X2 @ X3 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i > $o] :
( ( ^ [X2: $i,X3: $i] :
( ~ ( ~ ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) )
=> ( ~ ( X1 @ X3 @ X2 )
=> ( X1 @ X2 @ X3 ) ) ) )
= ( ^ [X2: $i,X3: $i] :
( ~ ( X1 @ X3 @ X2 )
=> ( X1 @ X2 @ X3 ) ) ) ),
inference(assume_negation,[status(cth)],[symmetric_closure_op_is_idempotent]) ).
thf(h1,assumption,
( ^ [X1: $i,X2: $i] :
( ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__0 @ X2 @ X1 ) )
=> ( ~ ( eigen__0 @ X2 @ X1 )
=> ( eigen__0 @ X1 @ X2 ) ) ) )
!= ( ^ [X1: $i,X2: $i] :
( ~ ( eigen__0 @ X2 @ X1 )
=> ( eigen__0 @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ( ^ [X2: $i] :
( ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__0 @ X2 @ X1 ) )
=> ( ~ ( eigen__0 @ X2 @ X1 )
=> ( eigen__0 @ X1 @ X2 ) ) ) )
= ( ^ [X2: $i] :
( ~ ( eigen__0 @ X2 @ X1 )
=> ( eigen__0 @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
( ^ [X1: $i] :
( ~ ( ~ ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__0 @ X1 @ eigen__1 ) )
=> ( ~ ( eigen__0 @ X1 @ eigen__1 )
=> ( eigen__0 @ eigen__1 @ X1 ) ) ) )
!= ( ^ [X1: $i] :
( ~ ( eigen__0 @ X1 @ eigen__1 )
=> ( eigen__0 @ eigen__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ( ~ ( ~ ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__0 @ X1 @ eigen__1 ) )
=> ( ~ ( eigen__0 @ X1 @ eigen__1 )
=> ( eigen__0 @ eigen__1 @ X1 ) ) )
= ( ~ ( eigen__0 @ X1 @ eigen__1 )
=> ( eigen__0 @ eigen__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
( ~ ( ~ sP2
=> sP1 )
=> ( ~ sP1
=> sP2 ) )
!= ( ~ sP1
=> sP2 ),
introduced(assumption,[]) ).
thf(h6,assumption,
( ~ ( ~ sP2
=> sP1 )
=> ( ~ sP1
=> sP2 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
( ~ sP1
=> sP2 ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( ~ sP2
=> sP1 )
=> ( ~ sP1
=> sP2 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ sP1
=> sP2 ),
introduced(assumption,[]) ).
thf(h10,assumption,
( ~ sP2
=> sP1 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP2,
introduced(assumption,[]) ).
thf(h12,assumption,
sP1,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h13,h14,h11,h10,h6,h7,h5,h4,h3,h2,h1,h0])],[h11,h14]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h10,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h7,1,h13,h14]) ).
thf(3,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h13,h14,h12,h10,h6,h7,h5,h4,h3,h2,h1,h0])],[h12,h13]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h7,3,h13,h14]) ).
thf(5,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h10,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h12])],[h10,2,4,h11,h12]) ).
thf(6,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h13,h14,h12,h7,h6,h7,h5,h4,h3,h2,h1,h0])],[h12,h13]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h7,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h7,6,h13,h14]) ).
thf(8,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h13,h14,h11,h7,h6,h7,h5,h4,h3,h2,h1,h0])],[h11,h14]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h7,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h7,8,h13,h14]) ).
thf(10,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h7,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h12]),tab_imp(discharge,[h11])],[h7,7,9,h12,h11]) ).
thf(11,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h7])],[h6,5,10,h10,h7]) ).
thf(h15,assumption,
~ ( ~ sP2
=> sP1 ),
introduced(assumption,[]) ).
thf(12,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h13,h14,h14,h13,h15,h9,h8,h9,h5,h4,h3,h2,h1,h0])],[h12,h13]) ).
thf(13,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h11,h13,h14,h14,h13,h15,h9,h8,h9,h5,h4,h3,h2,h1,h0])],[h11,h14]) ).
thf(14,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h13,h14,h14,h13,h15,h9,h8,h9,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h12]),tab_imp(discharge,[h11])],[h9,12,13,h12,h11]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h13,h15,h9,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h9,14,h13,h14]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h9,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h13])],[h15,15,h14,h13]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h15,h9])],[h8,16,h15,h9]) ).
thf(18,plain,
$false,
inference(tab_be,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_be(discharge,[h6,h7]),tab_be(discharge,[h8,h9])],[h5,11,17,h6,h7,h8,h9]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,18,h5]) ).
thf(20,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h3,h2,h1,h0]),tab_fe(discharge,[h4])],[h3,19,h4]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,20,h3]) ).
thf(22,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h1,h0]),tab_fe(discharge,[h2])],[h1,21,h2]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,22,h1]) ).
thf(0,theorem,
! [X1: $i > $i > $o] :
( ( ^ [X2: $i,X3: $i] :
( ~ ( ~ ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) )
=> ( ~ ( X1 @ X3 @ X2 )
=> ( X1 @ X2 @ X3 ) ) ) )
= ( ^ [X2: $i,X3: $i] :
( ~ ( X1 @ X3 @ X2 )
=> ( X1 @ X2 @ X3 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[23,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU458^1 : TPTP v8.1.0. Released v3.6.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n022.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 19:46:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.35 % SZS status Theorem
% 0.12/0.35 % Mode: mode213
% 0.12/0.35 % Inferences: 0
% 0.12/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------