TSTP Solution File: SWV061^7 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SWV061^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -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 : 300s
% DateTime : Thu Aug 31 22:47:51 EDT 2023
% Result : Theorem 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mu,type,
mu: $tType ).
thf(ty_n1,type,
n1: mu ).
thf(ty_true,type,
true: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(ty_gt,type,
gt: mu > mu > $i > $o ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_loopcounter,type,
loopcounter: mu ).
thf(sP1,plain,
( sP1
<=> ( true @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( true @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( rel_s4 @ eigen__5 @ eigen__5 )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( true @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( rel_s4 @ eigen__5 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__5 @ X1 )
=> ( true @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( true @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( rel_s4 @ eigen__3 @ eigen__3 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] : ( rel_s4 @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( rel_s4 @ eigen__3 @ eigen__3 ) ),
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] : ( mnot @ ( mor @ ( mnot @ X1 ) @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_mforall_ind,definition,
( mforall_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( exists_in_world @ X3 @ X2 )
@ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mreflexive,definition,
( mreflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_mtransitive,definition,
( mtransitive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X3 @ X4 ) )
@ ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_mvalid,definition,
( mvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( (~) @ ( rel_s4 @ X2 @ X3 ) )
| ( X1 @ X3 ) ) ) ) ).
thf(cl5_nebula_array_0002,conjecture,
! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( true @ X3 ) )
=> ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ~ ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( gt @ loopcounter @ n1 @ X5 ) ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( true @ X4 ) ) ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( gt @ loopcounter @ n1 @ X4 ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( true @ X4 ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( true @ X3 ) )
=> ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ~ ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( gt @ loopcounter @ n1 @ X5 ) ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( true @ X4 ) ) ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( gt @ loopcounter @ n1 @ X4 ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( true @ X4 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_array_0002]) ).
thf(h1,assumption,
~ ! [X1: $i] :
( ( rel_s4 @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( true @ X2 ) )
=> ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( gt @ loopcounter @ n1 @ X4 ) ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( true @ X3 ) ) ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( gt @ loopcounter @ n1 @ X3 ) )
=> ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( true @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ( rel_s4 @ eigen__0 @ eigen__1 )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( true @ X1 ) )
=> ~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( gt @ loopcounter @ n1 @ X3 ) ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( true @ X2 ) ) ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( gt @ loopcounter @ n1 @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( true @ X2 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
rel_s4 @ eigen__0 @ eigen__1,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( true @ X1 ) )
=> ~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( gt @ loopcounter @ n1 @ X3 ) ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( true @ X2 ) ) ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( gt @ loopcounter @ n1 @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( true @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( true @ X1 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
( ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( gt @ loopcounter @ n1 @ X3 ) ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( true @ X2 ) ) ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( gt @ loopcounter @ n1 @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( true @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( gt @ loopcounter @ n1 @ X3 ) ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( true @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] :
( ( rel_s4 @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( gt @ loopcounter @ n1 @ X2 ) )
=> ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( true @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ( rel_s4 @ eigen__1 @ eigen__4 )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__4 @ X1 )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( gt @ loopcounter @ n1 @ X2 ) ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__4 @ X1 )
=> ( true @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
rel_s4 @ eigen__1 @ eigen__4,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__4 @ X1 )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( gt @ loopcounter @ n1 @ X2 ) ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__4 @ X1 )
=> ( true @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
! [X1: $i] :
( ( rel_s4 @ eigen__4 @ X1 )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( gt @ loopcounter @ n1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: $i] :
( ( rel_s4 @ eigen__4 @ X1 )
=> ( true @ X1 ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ( rel_s4 @ eigen__4 @ eigen__5 )
=> sP1 ),
introduced(assumption,[]) ).
thf(h15,assumption,
rel_s4 @ eigen__4 @ eigen__5,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| ~ sP5
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP9
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP7
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(ttrue,axiom,
sP7 ).
thf(a1,axiom,
sP9 ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h16,h14,h12,h13,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0])],[1,2,3,4,h16,ttrue,a1]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,5,h15,h16]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h13,h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__5)],[h13,6,h14]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,7,h12,h13]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,8,h10,h11]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__4)],[h7,9,h9]) ).
thf(h17,assumption,
~ ( ( rel_s4 @ eigen__1 @ eigen__2 )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( gt @ loopcounter @ n1 @ X1 ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( true @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
rel_s4 @ eigen__1 @ eigen__2,
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( gt @ loopcounter @ n1 @ X1 ) )
=> ! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( true @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( gt @ loopcounter @ n1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( true @ X1 ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
~ ( ( rel_s4 @ eigen__2 @ eigen__3 )
=> sP2 ),
introduced(assumption,[]) ).
thf(h23,assumption,
rel_s4 @ eigen__2 @ eigen__3,
introduced(assumption,[]) ).
thf(h24,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(11,plain,
( ~ sP8
| ~ sP10
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP4
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP9
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP7
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h23,h24,h22,h20,h21,h18,h19,h17,h8,h5,h6,h3,h4,h2,h1,h0])],[11,12,13,14,h24,ttrue,a1]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h20,h21,h18,h19,h17,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h23,h24])],[h22,15,h23,h24]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h20,h21,h18,h19,h17,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h22]),tab_negall(eigenvar,eigen__3)],[h21,16,h22]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h19,h17,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h20,h21])],[h19,17,h20,h21]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,18,h18,h19]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__2)],[h8,19,h17]) ).
thf(21,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,10,20,h7,h8]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,21,h5,h6]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,22,h3,h4]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,23,h2]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,24,h1]) ).
thf(0,theorem,
! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( true @ X3 ) )
=> ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ~ ! [X5: $i] :
( ( rel_s4 @ X4 @ X5 )
=> ( gt @ loopcounter @ n1 @ X5 ) ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( true @ X4 ) ) ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( gt @ loopcounter @ n1 @ X4 ) )
=> ! [X4: $i] :
( ( rel_s4 @ X3 @ X4 )
=> ( true @ X4 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[25,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SWV061^7 : TPTP v8.1.2. Released v5.5.0.
% 0.09/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n011.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 : Tue Aug 29 06:35:56 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 % Mode: cade22sinegrackle2x6978
% 0.20/0.45 % Steps: 198
% 0.20/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------