TSTP Solution File: SYO478^6 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO478^6 : 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 : 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 : 600s
% DateTime : Thu Jul 21 19:32:52 EDT 2022
% Result : Theorem 0.15s 0.40s
% Output : Proof 0.15s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mu,type,
mu: $tType ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: mu ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_rel_s5,type,
rel_s5: $i > $i > $o ).
thf(ty_f,type,
f: mu > $i > $o ).
thf(sP1,plain,
( sP1
<=> ( rel_s5 @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( f @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( rel_s5 @ eigen__0 @ X1 )
=> ( f @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: mu] :
~ ( f @ X1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP1
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(def_meq_ind,definition,
( meq_ind
= ( ^ [X1: mu,X2: mu,X3: $i] : ( X1 = X2 ) ) ) ).
thf(def_meq_prop,definition,
( meq_prop
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ).
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] : ( mnot @ ( mor @ ( mnot @ X1 ) @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o] : ( mor @ ( mnot @ X1 ) ) ) ) ).
thf(def_mimplied,definition,
( mimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X2 ) @ X1 ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimplies @ X1 @ X2 ) @ ( mimplies @ X2 @ X1 ) ) ) ) ).
thf(def_mxor,definition,
( mxor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mequiv @ X1 @ X2 ) ) ) ) ).
thf(def_mforall_ind,definition,
( mforall_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] : ( 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] :
( mnot
@ ( mforall_ind
@ ^ [X2: mu] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mexists_prop,definition,
( mexists_prop
= ( ^ [X1: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : ~ $false ) ) ).
thf(def_mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: $i > $i > $o,X2: $i > $o] : ( mnot @ ( mbox @ X1 @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mreflexive,definition,
( mreflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_msymmetric,definition,
( msymmetric
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mserial,definition,
( mserial
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) ).
thf(def_mtransitive,definition,
( mtransitive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_meuclidean,definition,
( meuclidean
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ) ).
thf(def_mpartially_functional,definition,
( mpartially_functional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) ).
thf(def_mfunctional,definition,
( mfunctional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ).
thf(def_mweakly_dense,definition,
( mweakly_dense
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X5: $i] :
( ( X1 @ X2 @ X5 )
=> ~ ( X1 @ X5 @ X3 ) ) ) ) ) ).
thf(def_mweakly_connected,definition,
( mweakly_connected
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( ~ ( ~ ( X1 @ X3 @ X4 )
=> ( X3 = X4 ) )
=> ( X1 @ X4 @ X3 ) ) ) ) ) ).
thf(def_mweakly_directed,definition,
( mweakly_directed
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ~ ! [X5: $i] :
( ( X1 @ X3 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ).
thf(def_mvalid,definition,
mvalid = !! ).
thf(def_minvalid,definition,
( minvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_msatisfiable,definition,
( msatisfiable
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [X1: $i > $o] :
~ ( !! @ X1 ) ) ) ).
thf(def_mbox_s5,definition,
( mbox_s5
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( rel_s5 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ).
thf(def_mdia_s5,definition,
( mdia_s5
= ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X1 ) ) ) ) ) ).
thf(prove,conjecture,
! [X1: $i] :
( ~ ~ ~ ! [X2: mu] :
~ ! [X3: $i] :
( ( rel_s5 @ X1 @ X3 )
=> ( f @ X2 @ X3 ) )
=> ! [X2: $i] :
( ( rel_s5 @ X1 @ X2 )
=> ~ ! [X3: mu] :
~ ( f @ X3 @ X2 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] :
( ~ ! [X2: mu] :
~ ! [X3: $i] :
( ( rel_s5 @ X1 @ X3 )
=> ( f @ X2 @ X3 ) )
=> ! [X2: $i] :
( ( rel_s5 @ X1 @ X2 )
=> ~ ! [X3: mu] :
~ ( f @ X3 @ X2 ) ) ),
inference(assume_negation,[status(cth)],[prove]) ).
thf(h1,assumption,
~ ( ~ ! [X1: mu] :
~ ! [X2: $i] :
( ( rel_s5 @ eigen__0 @ X2 )
=> ( f @ X1 @ X2 ) )
=> ! [X1: $i] :
( ( rel_s5 @ eigen__0 @ X1 )
=> ~ ! [X2: mu] :
~ ( f @ X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: mu] :
~ ! [X2: $i] :
( ( rel_s5 @ eigen__0 @ X2 )
=> ( f @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( rel_s5 @ eigen__0 @ X1 )
=> ~ ! [X2: mu] :
~ ( f @ X2 @ X1 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP3,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP1
=> ~ sP4 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
sP4,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| ~ sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP3
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| ~ sP1
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h7,h5,h4,h2,h3,h1,h0])],[1,2,3,h4,h6,h7]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,4,h6,h7]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h3,5,h5]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,6,h4]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,7,h2,h3]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,8,h1]) ).
thf(0,theorem,
! [X1: $i] :
( ~ ~ ~ ! [X2: mu] :
~ ! [X3: $i] :
( ( rel_s5 @ X1 @ X3 )
=> ( f @ X2 @ X3 ) )
=> ! [X2: $i] :
( ( rel_s5 @ X1 @ X2 )
=> ~ ! [X3: mu] :
~ ( f @ X3 @ X2 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SYO478^6 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.15 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.15/0.37 % Computer : n023.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Sat Jul 9 04:41:26 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.40 % SZS status Theorem
% 0.15/0.40 % Mode: mode213
% 0.15/0.40 % Inferences: 6
% 0.15/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------