TSTP Solution File: SWV085^7 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SWV085^7 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n006.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 : Wed Jul 20 21:23:38 EDT 2022
% Result : Theorem 9.31s 8.78s
% Output : Proof 9.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 29
% Syntax : Number of formulae : 35 ( 13 unt; 10 typ; 9 def)
% Number of atoms : 121 ( 9 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 375 ( 54 ~; 5 |; 0 &; 240 @)
% ( 5 <=>; 70 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 22 con; 0-3 aty)
% ( 1 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 60 ( 14 ^ 46 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mu,type,
mu: $tType ).
thf(ty_n0,type,
n0: mu ).
thf(ty_pv68,type,
pv68: mu ).
thf(ty_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_minus,type,
minus: mu > mu > mu ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_n1,type,
n1: mu ).
thf(ty_n5,type,
n5: mu ).
thf(ty_leq,type,
leq: mu > mu > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( ( rel_s4 @ eigen__2 @ X1 )
=> ( ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( leq @ n0 @ pv68 @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( leq @ n0 @ pv68 @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ n0 @ pv68 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ n0 @ pv68 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( leq @ n0 @ pv68 @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( leq @ n0 @ pv68 @ X2 ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( rel_s4 @ eigen__2 @ eigen__3 )
=> ( ~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( leq @ n0 @ pv68 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( leq @ n0 @ pv68 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( leq @ n0 @ pv68 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( leq @ n0 @ pv68 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ n0 @ pv68 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ n0 @ pv68 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( leq @ n0 @ pv68 @ X1 ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
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_mforall_ind,definition,
( mforall_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] :
( ( exists_in_world @ X3 @ X2 )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mvalid,definition,
mvalid = !! ).
thf(def_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ).
thf(cl5_nebula_array_0026,conjecture,
! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ~ ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ n0 @ pv68 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ n0 @ pv68 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X3 ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ sP4,
inference(assume_negation,[status(cth)],[cl5_nebula_array_0026]) ).
thf(1,plain,
( sP3
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP3
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP2
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP1
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(5,plain,
( sP4
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,h1]) ).
thf(7,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[6,h0]) ).
thf(0,theorem,
! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ~ ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ n0 @ pv68 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ n0 @ pv68 @ X3 ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ pv68 @ ( minus @ n5 @ n1 ) @ X3 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[6,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV085^7 : TPTP v8.1.0. Released v5.5.0.
% 0.10/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 03:02:11 EDT 2022
% 0.13/0.33 % CPUTime :
% 9.31/8.78 % SZS status Theorem
% 9.31/8.78 % Mode: mode84:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 9.31/8.78 % Inferences: 133
% 9.31/8.78 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------