TSTP Solution File: PHI003^2 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : PHI003^2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n017.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 : Thu Aug 31 12:56:22 EDT 2023
% Result : Theorem 0.18s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mu,type,
mu: $tType ).
thf(ty_rel,type,
rel: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_positive,type,
positive: ( mu > $i > $o ) > $i > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: mu > $i > $o] :
( ( positive @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( rel @ X1 @ X3 )
=> ! [X4: mu] :
~ ( X2 @ X4 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: mu > $i > $o] :
( ( positive @ X1 @ eigen__0 )
=> ~ ! [X2: $i] :
( ( rel @ eigen__0 @ X2 )
=> ! [X3: mu] :
~ ( X1 @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( positive
@ ^ [X1: mu,X2: $i] :
! [X3: mu > $i > $o] :
( ( positive @ X3 @ X2 )
=> ( X3 @ X1 @ X2 ) )
@ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP3
=> ~ ! [X1: $i] :
( ( rel @ eigen__0 @ X1 )
=> ! [X2: mu] :
~ ! [X3: mu > $i > $o] :
( ( positive @ X3 @ X1 )
=> ( X3 @ X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( rel @ eigen__0 @ X1 )
=> ! [X2: mu] :
~ ! [X3: mu > $i > $o] :
( ( positive @ X3 @ X1 )
=> ( X3 @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( positive
@ ^ [X2: mu,X3: $i] :
! [X4: mu > $i > $o] :
( ( positive @ X4 @ X3 )
=> ( X4 @ X2 @ X3 ) )
@ X1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(def_meq_ind,definition,
( meq_ind
= ( ^ [X1: mu,X2: mu,X3: $i] : ( X1 = X2 ) ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : $true ) ) ).
thf(def_mfalse,definition,
( mfalse
= ( ^ [X1: $i] : $false ) ) ).
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,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X3 )
@ ( X2 @ X3 ) ) ) ) ).
thf(def_mimplied,definition,
( mimplied
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X2 @ X3 )
@ ( X1 @ X3 ) ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
<=> ( X2 @ X3 ) ) ) ) ).
thf(def_mxor,definition,
( mxor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( ( X1 @ X3 )
& ( (~) @ ( X2 @ X3 ) ) )
| ( ( (~) @ ( X1 @ X3 ) )
& ( X2 @ X3 ) ) ) ) ) ).
thf(def_mforall_ind,definition,
( mforall_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mforall_indset,definition,
( mforall_indset
= ( ^ [X1: ( mu > $i > $o ) > $i > $o,X2: $i] :
! [X3: mu > $i > $o] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mforall_prop,definition,
( mforall_prop
= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
! [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists_ind,definition,
( mexists_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
? [X3: mu] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists_indset,definition,
( mexists_indset
= ( ^ [X1: ( mu > $i > $o ) > $i > $o,X2: $i] :
? [X3: mu > $i > $o] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists_prop,definition,
( mexists_prop
= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
? [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mbox_generic,definition,
( mbox_generic
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ( (~) @ ( X1 @ X3 @ X4 ) )
| ( X2 @ X4 ) ) ) ) ).
thf(def_mdia_generic,definition,
( mdia_generic
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
? [X4: $i] :
( ( X1 @ X3 @ X4 )
& ( X2 @ X4 ) ) ) ) ).
thf(def_mbox,definition,
( mbox
= ( mbox_generic @ rel ) ) ).
thf(def_mdia,definition,
( mdia
= ( mdia_generic @ rel ) ) ).
thf(def_mvalid,definition,
( mvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_minvalid,definition,
( minvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_god,definition,
( god
= ( ^ [X1: mu] :
( mforall_indset
@ ^ [X2: mu > $i > $o] : ( mimplies @ ( positive @ X2 ) @ ( X2 @ X1 ) ) ) ) ) ).
thf(corC,conjecture,
! [X1: $i] :
~ ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ! [X3: mu] :
~ ! [X4: mu > $i > $o] :
( ( positive @ X4 @ X2 )
=> ( X4 @ X3 @ X2 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] :
~ ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ! [X3: mu] :
~ ! [X4: mu > $i > $o] :
( ( positive @ X4 @ X2 )
=> ( X4 @ X3 @ X2 ) ) ),
inference(assume_negation,[status(cth)],[corC]) ).
thf(h1,assumption,
sP5,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| ~ sP3
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(thmT1,axiom,
sP1 ).
thf(axA3,axiom,
sP6 ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,h1,thmT1,axA3]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,5,h1]) ).
thf(0,theorem,
! [X1: $i] :
~ ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ! [X3: mu] :
~ ! [X4: mu > $i > $o] :
( ( positive @ X4 @ X2 )
=> ( X4 @ X3 @ X2 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : PHI003^2 : TPTP v8.1.2. Released v6.1.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n017.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 : Sun Aug 27 08:25:26 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 % Mode: cade22grackle2xfee4
% 0.18/0.40 % Steps: 27
% 0.18/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------