TSTP Solution File: NUM736^4 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM736^4 : TPTP v8.1.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n026.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 : Mon Jul 18 13:55:52 EDT 2022
% Result : Theorem 45.59s 45.66s
% Output : Proof 45.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 46
% Syntax : Number of formulae : 52 ( 25 unt; 15 typ; 19 def)
% Number of atoms : 179 ( 64 equ; 0 cnn)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 439 ( 53 ~; 6 |; 0 &; 358 @)
% ( 6 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 45 usr; 36 con; 0-3 aty)
% Number of variables : 88 ( 81 ^ 7 !; 0 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_times,type,
times: $i > $i ).
thf(ty_d_1to,type,
d_1to: $i > $i ).
thf(ty_d_Pi,type,
d_Pi: $i > ( $i > $i ) > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_d_Sep,type,
d_Sep: $i > ( $i > $o ) > $i ).
thf(ty_second1,type,
second1: $i > $i > $i ).
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_first1,type,
first1: $i > $i > $i ).
thf(ty_ap,type,
ap: $i > $i > $i ).
thf(ty_n_some,type,
n_some: ( $i > $o ) > $o ).
thf(ty_diffprop,type,
diffprop: $i > $i > $i > $o ).
thf(ty_omega,type,
omega: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_n_2,type,
n_2: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [X2: $i] :
( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [X3: $i] :
( d_Sep @ omega
@ ^ [X4: $i] : ( X4 != emptyset ) ) ) )
=> ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) )
@ X2 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) )
@ X2 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) )
@ X1 ) ) ) )
=> ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) )
@ X2 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) )
@ X2 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) )
@ X1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [X2: $i] :
( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) ) ) )
=> ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [X2: $i] : ( X2 != emptyset ) )
@ eigen__1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [X2: $i] : ( X2 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [X2: $i] : ( X2 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [X2: $i] : ( X2 != emptyset ) )
@ eigen__1 ) ) ) )
=> ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [X2: $i] : ( X2 != emptyset ) )
@ eigen__1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [X2: $i] : ( X2 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [X2: $i] : ( X2 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [X2: $i] : ( X2 != emptyset ) )
@ eigen__1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [X1: $i] : ( X1 != emptyset ) )
@ eigen__1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [X1: $i] : ( X1 != emptyset ) )
@ eigen__2 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [X1: $i] : ( X1 != emptyset ) )
@ eigen__2 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [X1: $i] : ( X1 != emptyset ) )
@ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( in @ eigen__2
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [X1: $i] :
( d_Sep @ omega
@ ^ [X2: $i] : ( X2 != emptyset ) ) ) )
=> ( sP1
=> sP1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [X2: $i] :
( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) ) ) )
=> ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [X2: $i] : ( X2 != emptyset ) )
@ eigen__1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [X2: $i] : ( X2 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [X2: $i] : ( X2 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [X2: $i] : ( X2 != emptyset ) )
@ eigen__1 ) ) ) )
=> ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [X2: $i] : ( X2 != emptyset ) )
@ eigen__1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [X2: $i] : ( X2 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [X2: $i] : ( X2 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [X2: $i] : ( X2 != emptyset ) )
@ eigen__1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( in @ eigen__1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [X1: $i] :
( d_Sep @ omega
@ ^ [X2: $i] : ( X2 != emptyset ) ) ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [X2: $i] :
( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) ) ) )
=> ! [X2: $i] :
( ( in @ X2
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [X3: $i] :
( d_Sep @ omega
@ ^ [X4: $i] : ( X4 != emptyset ) ) ) )
=> ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) )
@ X2 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) )
@ X2 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) )
@ X1 ) ) ) )
=> ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) )
@ X2 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) )
@ X2 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [X3: $i] : ( X3 != emptyset ) )
@ X1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP1
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(def_is_of,definition,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).
thf(def_all_of,definition,
( all_of
= ( ^ [X1: $i > $o,X2: $i > $o] :
! [X3: $i] :
( ( is_of @ X3 @ X1 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_or3,definition,
( or3
= ( ^ [X1: $o,X2: $o,X3: $o] : ( l_or @ X1 @ ( l_or @ X2 @ X3 ) ) ) ) ).
thf(def_ec3,definition,
( ec3
= ( ^ [X1: $o,X2: $o,X3: $o] : ( and3 @ ( l_ec @ X1 @ X2 ) @ ( l_ec @ X2 @ X3 ) @ ( l_ec @ X3 @ X1 ) ) ) ) ).
thf(def_orec3,definition,
( orec3
= ( ^ [X1: $o,X2: $o,X3: $o] : ( d_and @ ( or3 @ X1 @ X2 @ X3 ) @ ( ec3 @ X1 @ X2 @ X3 ) ) ) ) ).
thf(def_nat,definition,
( nat
= ( d_Sep @ omega
@ ^ [X1: $i] : ( X1 != emptyset ) ) ) ).
thf(def_d_29_ii,definition,
( d_29_ii
= ( ^ [X1: $i,X2: $i] : ( n_some @ ( diffprop @ X1 @ X2 ) ) ) ) ).
thf(def_iii,definition,
( iii
= ( ^ [X1: $i,X2: $i] : ( n_some @ ( diffprop @ X2 @ X1 ) ) ) ) ).
thf(def_n_ts,definition,
( n_ts
= ( ^ [X1: $i] : ( ap @ ( times @ X1 ) ) ) ) ).
thf(def_pair1type,definition,
( pair1type
= ( ^ [X1: $i] :
( d_Pi @ ( d_1to @ n_2 )
@ ^ [X2: $i] : X1 ) ) ) ).
thf(def_frac,definition,
( frac
= ( pair1type @ nat ) ) ).
thf(def_n_fr,definition,
( n_fr
= ( pair1 @ nat ) ) ).
thf(def_num,definition,
( num
= ( first1 @ nat ) ) ).
thf(def_den,definition,
( den
= ( second1 @ nat ) ) ).
thf(def_n_eq,definition,
( n_eq
= ( ^ [X1: $i,X2: $i] : ( n_is @ ( n_ts @ ( num @ X1 ) @ ( den @ X2 ) ) @ ( n_ts @ ( num @ X2 ) @ ( den @ X1 ) ) ) ) ) ).
thf(def_moref,definition,
( moref
= ( ^ [X1: $i,X2: $i] : ( d_29_ii @ ( n_ts @ ( num @ X1 ) @ ( den @ X2 ) ) @ ( n_ts @ ( num @ X2 ) @ ( den @ X1 ) ) ) ) ) ).
thf(def_lessf,definition,
( lessf
= ( ^ [X1: $i,X2: $i] : ( iii @ ( n_ts @ ( num @ X1 ) @ ( den @ X2 ) ) @ ( n_ts @ ( num @ X2 ) @ ( den @ X1 ) ) ) ) ) ).
thf(satz42,conjecture,
sP5 ).
thf(h1,negated_conjecture,
~ sP5,
inference(assume_negation,[status(cth)],[satz42]) ).
thf(1,plain,
( sP6
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP6
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP2
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP3
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(5,plain,
( sP4
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP5
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,h1]) ).
thf(8,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[7,h0]) ).
thf(0,theorem,
sP5,
inference(contra,[status(thm),contra(discharge,[h1])],[7,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM736^4 : TPTP v8.1.0. Released v7.1.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n026.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 Jul 7 16:04:24 EDT 2022
% 0.13/0.33 % CPUTime :
% 45.59/45.66 % SZS status Theorem
% 45.59/45.66 % Mode: mode84:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 45.59/45.66 % Inferences: 106
% 45.59/45.66 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------