TSTP Solution File: SYO462^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO462^5 : 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 : n011.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 19:32:31 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_p,type,
p: $i > $o ).
thf(ty_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_q,type,
q: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(sP1,plain,
( sP1
<=> ( ( rel_s4 @ eigen__0 @ eigen__2 )
=> ( q @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( rel_s4 @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( p @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP2
=> ~ ( ( sP3
=> ( q @ eigen__1 ) )
=> ~ ( ( q @ eigen__1 )
=> sP3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ( p @ eigen__2 )
=> ( q @ eigen__2 ) )
=> ~ ( ( q @ eigen__2 )
=> ( p @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( q @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( p @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( sP3
=> ( q @ eigen__1 ) )
=> ~ ( ( q @ eigen__1 )
=> sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP3
=> ( q @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__0 @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP6
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( q @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP2
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__0 @ X1 )
=> ( q @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( rel_s4 @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__0 @ X1 )
=> ~ ( ( ( p @ X1 )
=> ( q @ X1 ) )
=> ~ ( ( q @ X1 )
=> ( p @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP15
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
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_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ).
thf(def_mdia_s4,definition,
( mdia_s4
= ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X1 ) ) ) ) ) ).
thf(prove,conjecture,
! [X1: $i] :
( ~ ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ~ ( ~ ~ ( ~ ~ ( p @ X2 )
=> ( q @ X2 ) )
=> ~ ( ~ ~ ( q @ X2 )
=> ( p @ X2 ) ) ) )
=> ~ ( ~ ~ ( ~ ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( q @ X2 ) ) )
=> ~ ( ~ ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( q @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] :
( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ~ ( ( ( p @ X2 )
=> ( q @ X2 ) )
=> ~ ( ( q @ X2 )
=> ( p @ X2 ) ) ) )
=> ~ ( ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( q @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( q @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove]) ).
thf(h1,assumption,
~ ( sP16
=> ~ ( ( sP10
=> sP14 )
=> ~ ( sP14
=> sP10 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP16,
introduced(assumption,[]) ).
thf(h3,assumption,
( ( sP10
=> sP14 )
=> ~ ( sP14
=> sP10 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP10
=> sP14 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP14
=> sP10 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP10,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP2
=> sP12 ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP2,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP9
| ~ sP3
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP8
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP16
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| ~ sP2
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP10
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP13
| ~ sP2
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,h2,h6,h9,h10]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,7,h9,h10]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h7,8,h8]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,9,h6,h7]) ).
thf(h11,assumption,
sP14,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( sP15
=> sP7 ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP15,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(11,plain,
( ~ sP11
| ~ sP6
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP5
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP14
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP1
| ~ sP15
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP16
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP17
| ~ sP15
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h15,h13,h11,h12,h5,h2,h3,h1,h0])],[11,12,13,14,15,16,h2,h11,h14,h15]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,17,h14,h15]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h5,h2,h3,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__2)],[h12,18,h13]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h5,19,h11,h12]) ).
thf(21,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h3,h1,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[h3,10,20,h4,h5]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,21,h2,h3]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,22,h1]) ).
thf(0,theorem,
! [X1: $i] :
( ~ ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ~ ( ~ ~ ( ~ ~ ( p @ X2 )
=> ( q @ X2 ) )
=> ~ ( ~ ~ ( q @ X2 )
=> ( p @ X2 ) ) ) )
=> ~ ( ~ ~ ( ~ ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( q @ X2 ) ) )
=> ~ ( ~ ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( q @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( p @ X2 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[23,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYO462^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n011.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 : 600
% 0.12/0.33 % DateTime : Sat Jul 9 05:42:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % Mode: mode213
% 0.12/0.36 % Inferences: 25
% 0.12/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------