TSTP Solution File: SYO060^4 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO060^4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n023.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 : Fri Sep 1 04:44:58 EDT 2023
% Result : Theorem 0.12s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $i > $o ).
thf(ty_a,type,
a: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_irel,type,
irel: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(sP1,plain,
( sP1
<=> ( irel @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a @ X2 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( irel @ eigen__0 @ eigen__2 )
=> ~ ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( a @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( irel @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( b @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a @ X3 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP1
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( a @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
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,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( 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] : $true ) ) ).
thf(def_ifalse,definition,
( ifalse
= ( inot @ itrue ) ) ).
thf(def_iand,definition,
( iand
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ X1 @ X2 ) ) ) ).
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
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_isatisfiable,definition,
( isatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_icountersatisfiable,definition,
( icountersatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_iinvalid,definition,
( iinvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(con,conjecture,
! [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b @ X3 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a @ X3 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b @ X3 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a @ X3 ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h1,assumption,
~ ( ~ sP9
=> sP5 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
sP6,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h8,assumption,
sP4,
introduced(assumption,[]) ).
thf(h9,assumption,
sP10,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP8
| ~ sP1
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP9
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| ~ sP4
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| sP5
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(axiom1,axiom,
sP7 ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,h5,h6,h8,h9,axiom1]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,7,h8,h9]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h3,8,h7]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,9,h5,h6]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,10,h4]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,11,h2,h3]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,12,h1]) ).
thf(0,theorem,
! [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b @ X3 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a @ X3 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[13,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO060^4 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n023.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 : 300
% 0.12/0.33 % DateTime : Sat Aug 26 06:04:56 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % Mode: cade22grackle2xfee4
% 0.12/0.40 % Steps: 122
% 0.12/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------