TSTP Solution File: SYO868^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO868^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n031.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 : Fri Sep 1 04:48:16 EDT 2023
% Result : Theorem 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 58
% Syntax : Number of formulae : 71 ( 19 unt; 22 typ; 2 def)
% Number of atoms : 299 ( 16 equ; 0 cnn)
% Maximal formula atoms : 22 ( 6 avg)
% Number of connectives : 633 ( 36 ~; 12 |; 0 &; 439 @)
% ( 12 <=>; 134 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 36 usr; 20 con; 0-2 aty)
% Number of variables : 48 ( 3 ^; 45 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_c_exactly2,type,
c_exactly2: $i > $o ).
thf(ty_c_exactly1of2,type,
c_exactly1of2: $o > $o > $o ).
thf(ty_c_Empty,type,
c_Empty: $i ).
thf(ty_c_SNoLt,type,
c_SNoLt: $i > $i > $o ).
thf(ty_c_binrep,type,
c_binrep: $i > $i > $i ).
thf(ty_c_and,type,
c_and: $o > $o > $o ).
thf(ty_c_ordsucc,type,
c_ordsucc: $i > $i ).
thf(ty_eigen__11,type,
eigen__11: $i ).
thf(ty_c_nat_p,type,
c_nat_p: $i > $o ).
thf(ty_eigen__5,type,
eigen__5: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_c_ordinal,type,
c_ordinal: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_c_atleast3,type,
c_atleast3: $i > $o ).
thf(ty_c_exactly5,type,
c_exactly5: $i > $o ).
thf(ty_c_In,type,
c_In: $i > $i > $o ).
thf(ty_c_Power,type,
c_Power: $i > $i ).
thf(ty_c_atleast2,type,
c_atleast2: $i > $o ).
thf(ty_c_TransSet,type,
c_TransSet: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_c_not,type,
c_not: $o > $o ).
thf(ty_c_atleast5,type,
c_atleast5: $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: $i] :
~ ( ( ( c_ordinal @ c_Empty )
=> ( c_and @ ( c_exactly2 @ c_Empty ) @ ( c_not @ ( c_exactly5 @ X1 ) ) ) )
=> ( ( ( ( c_ordinal @ c_Empty )
=> ( c_exactly2 @ c_Empty ) )
=> ( ( c_atleast2 @ c_Empty )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( c_Empty = X1 ) )
=> ( c_atleast3 @ c_Empty ) )
=> ( c_and @ ( c_atleast5 @ eigen__2 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ eigen__2 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X1 ) ) ) ) ) ) )
=> ( c_nat_p @ c_Empty ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(h1,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__1
@ ^ [X1: $i > $o] :
~ ( ( X1 @ c_Empty )
=> ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( c_ordsucc @ X2 ) ) )
=> ( X1 @ c_Empty ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( c_nat_p @ X1 )
= ( ! [X2: $i > $o] :
( ( X2 @ c_Empty )
=> ( ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( c_ordsucc @ X3 ) ) )
=> ( X2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ( ( c_ordinal @ c_Empty )
=> ( c_exactly2 @ c_Empty ) )
=> ( ( c_atleast2 @ c_Empty )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( c_Empty = eigen__11 ) )
=> ( c_atleast3 @ c_Empty ) )
=> ( c_and @ ( c_atleast5 @ eigen__2 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ eigen__2 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ eigen__11 ) ) ) ) ) ) )
=> ( c_nat_p @ c_Empty ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ( ( c_ordinal @ X1 )
=> ( c_and @ ( c_exactly2 @ X1 ) @ ( c_not @ ( c_exactly5 @ X2 ) ) ) )
=> ( ( ( ( c_ordinal @ X1 )
=> ( c_exactly2 @ X1 ) )
=> ( ( c_atleast2 @ X1 )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( X1 = X2 ) )
=> ( c_atleast3 @ X1 ) )
=> ( c_and @ ( c_atleast5 @ eigen__2 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ eigen__2 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X2 ) ) ) ) ) ) )
=> ( c_nat_p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__5 @ c_Empty ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ! [X1: $i] :
( ( eigen__5 @ X1 )
=> ( eigen__5 @ ( c_ordsucc @ X1 ) ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP4
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i > $o] :
( ( X1 @ c_Empty )
=> ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( c_ordsucc @ X2 ) ) )
=> ( X1 @ c_Empty ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( ( c_ordinal @ c_Empty )
=> ( c_and @ ( c_exactly2 @ c_Empty ) @ ( c_not @ ( c_exactly5 @ X1 ) ) ) )
=> ( ( ( ( c_ordinal @ c_Empty )
=> ( c_exactly2 @ c_Empty ) )
=> ( ( c_atleast2 @ c_Empty )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( c_Empty = X1 ) )
=> ( c_atleast3 @ c_Empty ) )
=> ( c_and @ ( c_atleast5 @ eigen__2 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ eigen__2 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X1 ) ) ) ) ) ) )
=> ( c_nat_p @ c_Empty ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( c_nat_p @ c_Empty ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP9 = sP7 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( c_nat_p
= ( ^ [X1: $i] :
! [X2: $i > $o] :
( ( X2 @ c_Empty )
=> ( ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( c_ordsucc @ X3 ) ) )
=> ( X2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ( c_ordinal @ c_Empty )
=> ( c_and @ ( c_exactly2 @ c_Empty ) @ ( c_not @ ( c_exactly5 @ eigen__11 ) ) ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(conj,conjecture,
! [X1: $i] :
( ( c_In @ X1 @ c_Empty )
=> ! [X2: $i] :
( ( c_In @ X2 @ X1 )
=> ! [X3: $i] :
( ( c_In @ X3 @ X2 )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( ( ( c_ordinal @ X4 )
=> ( c_and @ ( c_exactly2 @ X4 ) @ ( c_not @ ( c_exactly5 @ X5 ) ) ) )
=> ( ( ( ( c_ordinal @ X4 )
=> ( c_exactly2 @ X4 ) )
=> ( ( c_atleast2 @ X4 )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( X4 = X5 ) )
=> ( c_atleast3 @ X4 ) )
=> ( c_and @ ( c_atleast5 @ X3 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X3 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X5 ) ) ) ) ) ) )
=> ( c_nat_p @ X4 ) ) ) ) ) ) ).
thf(h2,negated_conjecture,
~ ! [X1: $i] :
( ( c_In @ X1 @ c_Empty )
=> ! [X2: $i] :
( ( c_In @ X2 @ X1 )
=> ! [X3: $i] :
( ( c_In @ X3 @ X2 )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( ( ( c_ordinal @ X4 )
=> ( c_and @ ( c_exactly2 @ X4 ) @ ( c_not @ ( c_exactly5 @ X5 ) ) ) )
=> ( ( ( ( c_ordinal @ X4 )
=> ( c_exactly2 @ X4 ) )
=> ( ( c_atleast2 @ X4 )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( X4 = X5 ) )
=> ( c_atleast3 @ X4 ) )
=> ( c_and @ ( c_atleast5 @ X3 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X3 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X5 ) ) ) ) ) ) )
=> ( c_nat_p @ X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h3,assumption,
~ ( ( c_In @ eigen__0 @ c_Empty )
=> ! [X1: $i] :
( ( c_In @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( c_In @ X2 @ X1 )
=> ~ ! [X3: $i] :
~ ! [X4: $i] :
( ( ( c_ordinal @ X3 )
=> ( c_and @ ( c_exactly2 @ X3 ) @ ( c_not @ ( c_exactly5 @ X4 ) ) ) )
=> ( ( ( ( c_ordinal @ X3 )
=> ( c_exactly2 @ X3 ) )
=> ( ( c_atleast2 @ X3 )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( X3 = X4 ) )
=> ( c_atleast3 @ X3 ) )
=> ( c_and @ ( c_atleast5 @ X2 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X2 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X4 ) ) ) ) ) ) )
=> ( c_nat_p @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
c_In @ eigen__0 @ c_Empty,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ( c_In @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( c_In @ X2 @ X1 )
=> ~ ! [X3: $i] :
~ ! [X4: $i] :
( ( ( c_ordinal @ X3 )
=> ( c_and @ ( c_exactly2 @ X3 ) @ ( c_not @ ( c_exactly5 @ X4 ) ) ) )
=> ( ( ( ( c_ordinal @ X3 )
=> ( c_exactly2 @ X3 ) )
=> ( ( c_atleast2 @ X3 )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( X3 = X4 ) )
=> ( c_atleast3 @ X3 ) )
=> ( c_and @ ( c_atleast5 @ X2 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X2 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X4 ) ) ) ) ) ) )
=> ( c_nat_p @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ( c_In @ eigen__1 @ eigen__0 )
=> ! [X1: $i] :
( ( c_In @ X1 @ eigen__1 )
=> ~ ! [X2: $i] :
~ ! [X3: $i] :
( ( ( c_ordinal @ X2 )
=> ( c_and @ ( c_exactly2 @ X2 ) @ ( c_not @ ( c_exactly5 @ X3 ) ) ) )
=> ( ( ( ( c_ordinal @ X2 )
=> ( c_exactly2 @ X2 ) )
=> ( ( c_atleast2 @ X2 )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( X2 = X3 ) )
=> ( c_atleast3 @ X2 ) )
=> ( c_and @ ( c_atleast5 @ X1 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X1 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X3 ) ) ) ) ) ) )
=> ( c_nat_p @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
c_In @ eigen__1 @ eigen__0,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] :
( ( c_In @ X1 @ eigen__1 )
=> ~ ! [X2: $i] :
~ ! [X3: $i] :
( ( ( c_ordinal @ X2 )
=> ( c_and @ ( c_exactly2 @ X2 ) @ ( c_not @ ( c_exactly5 @ X3 ) ) ) )
=> ( ( ( ( c_ordinal @ X2 )
=> ( c_exactly2 @ X2 ) )
=> ( ( c_atleast2 @ X2 )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( X2 = X3 ) )
=> ( c_atleast3 @ X2 ) )
=> ( c_and @ ( c_atleast5 @ X1 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X1 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X3 ) ) ) ) ) ) )
=> ( c_nat_p @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ( c_In @ eigen__2 @ eigen__1 )
=> ~ sP3 ),
introduced(assumption,[]) ).
thf(h10,assumption,
c_In @ eigen__2 @ eigen__1,
introduced(assumption,[]) ).
thf(h11,assumption,
sP3,
introduced(assumption,[]) ).
thf(1,plain,
( sP2
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP12
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP8
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(4,plain,
( sP5
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP6
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP6
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP7
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__5]) ).
thf(8,plain,
( ~ sP10
| sP9
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP1
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP3
| ~ sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP11
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(ax63,axiom,
sP11 ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h7,h8,h6,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h11,ax63]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,12,h10,h11]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h8,13,h9]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,14,h7,h8]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,15,h6]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,16,h4,h5]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,17,h3]) ).
thf(19,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[18,h1]) ).
thf(20,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[19,h0]) ).
thf(0,theorem,
! [X1: $i] :
( ( c_In @ X1 @ c_Empty )
=> ! [X2: $i] :
( ( c_In @ X2 @ X1 )
=> ! [X3: $i] :
( ( c_In @ X3 @ X2 )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( ( ( c_ordinal @ X4 )
=> ( c_and @ ( c_exactly2 @ X4 ) @ ( c_not @ ( c_exactly5 @ X5 ) ) ) )
=> ( ( ( ( c_ordinal @ X4 )
=> ( c_exactly2 @ X4 ) )
=> ( ( c_atleast2 @ X4 )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( X4 = X5 ) )
=> ( c_atleast3 @ X4 ) )
=> ( c_and @ ( c_atleast5 @ X3 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X3 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X5 ) ) ) ) ) ) )
=> ( c_nat_p @ X4 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[18,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYO868^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n031.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 06:51:52 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 % Mode: cade22sinegrackle2x6978
% 0.19/0.45 % Steps: 220
% 0.19/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------