TSTP Solution File: SYN978^4 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYN978^4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n018.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 : Thu Jul 21 11:47:26 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_b,type,
b: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_irel,type,
irel: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ( irel @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( a @ eigen__2 )
=> ~ ( b @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( irel @ eigen__0 @ eigen__3 )
=> ~ ( ( a @ eigen__3 )
=> ~ ( b @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( a @ eigen__3 )
=> ~ ( b @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( a @ X1 )
=> ~ ( b @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ( irel @ eigen__0 @ eigen__1 )
=> ~ ( irel @ eigen__1 @ eigen__3 ) )
=> ( irel @ eigen__0 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( a @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( irel @ eigen__0 @ eigen__1 )
=> ~ ( irel @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( irel @ X1 @ X2 )
=> ~ ( irel @ X2 @ X3 ) )
=> ( irel @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( ( irel @ eigen__0 @ eigen__1 )
=> ~ sP1 )
=> ( irel @ eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__0 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__0 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( irel @ eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( irel @ eigen__0 @ eigen__2 )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( irel @ eigen__0 @ eigen__1 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( irel @ eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( b @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( irel @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( irel @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ~ ( sP18
=> ~ ( irel @ eigen__1 @ X1 ) )
=> ( irel @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o] : ( mor @ ( mnot @ X1 ) ) ) ) ).
thf(def_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ).
thf(def_iatom,definition,
( iatom
= ( ^ [X1: $i > $o] : X1 ) ) ).
thf(def_inot,definition,
( inot
= ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ X1 ) ) ) ) ).
thf(def_itrue,definition,
( itrue
= ( ^ [X1: $i] : ~ $false ) ) ).
thf(def_ifalse,definition,
( ifalse
= ( inot @ itrue ) ) ).
thf(def_iand,definition,
iand = mand ).
thf(def_ior,definition,
( ior
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplies,definition,
( iimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mimplies @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplied,definition,
( iimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iimplies @ X2 @ X1 ) ) ) ).
thf(def_iequiv,definition,
( iequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iand @ ( iimplies @ X1 @ X2 ) @ ( iimplies @ X2 @ X1 ) ) ) ) ).
thf(def_ixor,definition,
( ixor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( inot @ ( iequiv @ X1 @ X2 ) ) ) ) ).
thf(def_ivalid,definition,
ivalid = !! ).
thf(def_isatisfiable,definition,
( isatisfiable
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_icountersatisfiable,definition,
( icountersatisfiable
= ( ^ [X1: $i > $o] :
~ ( !! @ X1 ) ) ) ).
thf(def_iinvalid,definition,
( iinvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(prove_this,conjecture,
! [X1: $i] :
( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( a @ X2 )
=> ~ ( b @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a @ X3 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( a @ X2 )
=> ~ ( b @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a @ X3 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
thf(h1,assumption,
~ ( sP5
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP5,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP18
=> ~ ( ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( b @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( b @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP18,
introduced(assumption,[]) ).
thf(h6,assumption,
( ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( b @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( b @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( b @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( b @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a @ X1 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( b @ X1 ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP1
=> sP16 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP1,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(1,plain,
( sP2
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP13
| ~ sP17
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP9
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP11
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP19
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP10
| sP14
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP14
| ~ sP18
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(trans_axiom,axiom,
sP9 ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h13,h11,h9,h10,h7,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,trans_axiom,h2,h5,h12,h13]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,9,h12,h13]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h10,10,h11]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,11,h9,h10]) ).
thf(h14,assumption,
! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( b @ X1 ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a @ X1 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( sP15
=> sP7 ),
introduced(assumption,[]) ).
thf(h17,assumption,
sP15,
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(13,plain,
( sP4
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP3
| ~ sP12
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP9
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP11
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP19
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP6
| sP8
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP8
| ~ sP18
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h18,h16,h14,h15,h8,h5,h6,h4,h2,h3,h1,h0])],[13,14,15,16,17,18,19,20,trans_axiom,h2,h5,h17,h18]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h14,h15,h8,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,21,h17,h18]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h15,h8,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__3)],[h15,22,h16]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h8,23,h14,h15]) ).
thf(25,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,12,24,h7,h8]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,25,h5,h6]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,26,h4]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,27,h2,h3]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,28,h1]) ).
thf(0,theorem,
! [X1: $i] :
( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( a @ X2 )
=> ~ ( b @ X2 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a @ X3 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[29,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SYN978^4 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 11 14:07:14 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.36 % SZS status Theorem
% 0.13/0.36 % Mode: mode213
% 0.13/0.36 % Inferences: 44
% 0.13/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------