TSTP Solution File: SYO066^4.001 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO066^4.001 : 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 : n029.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 04:45:01 EDT 2023
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_o21,type,
o21: $i > $o ).
thf(ty_o11,type,
o11: $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
<=> ( o21 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] : ( o21 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
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 )
=> ( o11 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( o21 @ X2 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( o11 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( o21 @ X2 ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h1,assumption,
~ ( ~ ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( o11 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( o21 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( o11 @ X1 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( o21 @ X1 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ( irel @ eigen__0 @ eigen__1 )
=> ( o11 @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
irel @ eigen__0 @ eigen__1,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( o11 @ eigen__1 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ( irel @ eigen__0 @ eigen__2 )
=> sP1 ),
introduced(assumption,[]) ).
thf(h8,assumption,
irel @ eigen__0 @ eigen__2,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(axiom2,axiom,
sP2 ).
thf(2,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0])],[1,h9,axiom2]) ).
thf(3,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,2,h8,h9]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h3,3,h7]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,4,h5,h6]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,5,h4]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,6,h2,h3]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,7,h1]) ).
thf(0,theorem,
! [X1: $i] :
( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( o11 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( o21 @ X2 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[8,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO066^4.001 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 05:13:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % Mode: cade22grackle2xfee4
% 0.19/0.40 % Steps: 13
% 0.19/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------