TSTP Solution File: SEU474^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU474^1 : 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 : 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 : 600s
% DateTime : Tue Jul 19 13:52:21 EDT 2022
% Result : Theorem 0.12s 0.36s
% 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
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__2 = eigen__1 )
=> ( eigen__1 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__1 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__0 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( eigen__2 = X1 )
=> ( X1 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__2 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
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(composing_symmetric_closure_and_reflexive_closure,conjecture,
! [X1: $i > $i > $o] :
( ( ^ [X2: $i,X3: $i] :
( ~ ( ( X3 != X2 )
=> ( X1 @ X3 @ X2 ) )
=> ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) ) ) )
= ( ^ [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ( ~ ( X1 @ X3 @ X2 )
=> ( X1 @ X2 @ X3 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i > $o] :
( ( ^ [X2: $i,X3: $i] :
( ~ ( ( X3 != X2 )
=> ( X1 @ X3 @ X2 ) )
=> ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) ) ) )
= ( ^ [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ( ~ ( X1 @ X3 @ X2 )
=> ( X1 @ X2 @ X3 ) ) ) ) ),
inference(assume_negation,[status(cth)],[composing_symmetric_closure_and_reflexive_closure]) ).
thf(h1,assumption,
( ^ [X1: $i,X2: $i] :
( ~ ( ( X2 != X1 )
=> ( eigen__0 @ X2 @ X1 ) )
=> ( ( X1 != X2 )
=> ( eigen__0 @ X1 @ X2 ) ) ) )
!= ( ^ [X1: $i,X2: $i] :
( ( X1 != X2 )
=> ( ~ ( eigen__0 @ X2 @ X1 )
=> ( eigen__0 @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ( ^ [X2: $i] :
( ~ ( ( X2 != X1 )
=> ( eigen__0 @ X2 @ X1 ) )
=> ( ( X1 != X2 )
=> ( eigen__0 @ X1 @ X2 ) ) ) )
= ( ^ [X2: $i] :
( ( X1 != X2 )
=> ( ~ ( eigen__0 @ X2 @ X1 )
=> ( eigen__0 @ X1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
( ^ [X1: $i] :
( ~ ( ( X1 != eigen__1 )
=> ( eigen__0 @ X1 @ eigen__1 ) )
=> ( ( eigen__1 != X1 )
=> ( eigen__0 @ eigen__1 @ X1 ) ) ) )
!= ( ^ [X1: $i] :
( ( eigen__1 != X1 )
=> ( ~ ( eigen__0 @ X1 @ eigen__1 )
=> ( eigen__0 @ eigen__1 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ( ~ ( ( X1 != eigen__1 )
=> ( eigen__0 @ X1 @ eigen__1 ) )
=> ( ( eigen__1 != X1 )
=> ( eigen__0 @ eigen__1 @ X1 ) ) )
= ( ( eigen__1 != X1 )
=> ( ~ ( eigen__0 @ X1 @ eigen__1 )
=> ( eigen__0 @ eigen__1 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
( ~ ( ~ sP7
=> sP1 )
=> ( ~ sP4
=> sP5 ) )
!= ( ~ sP4
=> ( ~ sP1
=> sP5 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
( ~ ( ~ sP7
=> sP1 )
=> ( ~ sP4
=> sP5 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
( ~ sP4
=> ( ~ sP1
=> sP5 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( ~ sP7
=> sP1 )
=> ( ~ sP4
=> sP5 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ sP4
=> ( ~ sP1
=> sP5 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
( ~ sP7
=> sP1 ),
introduced(assumption,[]) ).
thf(h11,assumption,
( ~ sP4
=> sP5 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP7,
introduced(assumption,[]) ).
thf(h13,assumption,
sP1,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ~ sP1
=> sP5 ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| ~ sP7
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP2
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
sP2,
inference(eq_sym,[status(thm)],]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h17,h14,h15,h12,h10,h6,h7,h5,h4,h3,h2,h1,h0])],[1,2,3,4,h12,h14]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h12,h10,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,5,h16,h17]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h7,6,h14,h15]) ).
thf(8,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h17,h14,h15,h13,h10,h6,h7,h5,h4,h3,h2,h1,h0])],[h13,h16]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h13,h10,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,8,h16,h17]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h10,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h7,9,h14,h15]) ).
thf(11,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h10,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h12]),tab_imp(discharge,[h13])],[h10,7,10,h12,h13]) ).
thf(h18,assumption,
sP4,
introduced(assumption,[]) ).
thf(h19,assumption,
sP5,
introduced(assumption,[]) ).
thf(12,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h17,h14,h15,h18,h11,h6,h7,h5,h4,h3,h2,h1,h0])],[h18,h14]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h18,h11,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,12,h16,h17]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h11,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h7,13,h14,h15]) ).
thf(15,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h17,h14,h15,h19,h11,h6,h7,h5,h4,h3,h2,h1,h0])],[h19,h17]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h19,h11,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,15,h16,h17]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h11,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h7,16,h14,h15]) ).
thf(18,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h11,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h18]),tab_imp(discharge,[h19])],[h11,14,17,h18,h19]) ).
thf(19,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[h6,11,18,h10,h11]) ).
thf(h20,assumption,
~ ( ~ sP7
=> sP1 ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( ~ sP4
=> sP5 ),
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h23,assumption,
( ~ sP1
=> sP5 ),
introduced(assumption,[]) ).
thf(20,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h18,h14,h17,h22,h16,h20,h21,h8,h9,h5,h4,h3,h2,h1,h0])],[h18,h14]) ).
thf(21,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h13,h23,h14,h17,h22,h16,h20,h21,h8,h9,h5,h4,h3,h2,h1,h0])],[h13,h16]) ).
thf(22,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h19,h23,h14,h17,h22,h16,h20,h21,h8,h9,h5,h4,h3,h2,h1,h0])],[h19,h17]) ).
thf(23,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h23,h14,h17,h22,h16,h20,h21,h8,h9,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h13]),tab_imp(discharge,[h19])],[h23,21,22,h13,h19]) ).
thf(24,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h14,h17,h22,h16,h20,h21,h8,h9,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h18]),tab_imp(discharge,[h23])],[h9,20,23,h18,h23]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h16,h20,h21,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h17])],[h21,24,h14,h17]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h21,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h22,h16])],[h20,25,h22,h16]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h20,h21])],[h8,26,h20,h21]) ).
thf(28,plain,
$false,
inference(tab_be,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_be(discharge,[h6,h7]),tab_be(discharge,[h8,h9])],[h5,19,27,h6,h7,h8,h9]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,28,h5]) ).
thf(30,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h3,h2,h1,h0]),tab_fe(discharge,[h4])],[h3,29,h4]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,30,h3]) ).
thf(32,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h1,h0]),tab_fe(discharge,[h2])],[h1,31,h2]) ).
thf(33,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,32,h1]) ).
thf(0,theorem,
! [X1: $i > $i > $o] :
( ( ^ [X2: $i,X3: $i] :
( ~ ( ( X3 != X2 )
=> ( X1 @ X3 @ X2 ) )
=> ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) ) ) )
= ( ^ [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ( ~ ( X1 @ X3 @ X2 )
=> ( X1 @ X2 @ X3 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[33,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU474^1 : 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
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 18:35:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % Mode: mode213
% 0.12/0.36 % Inferences: 3
% 0.12/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------