TSTP Solution File: NUM693^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM693^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n014.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 11:40:31 EDT 2023
% Result : Theorem 30.23s 30.52s
% Output : Proof 30.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 48
% Syntax : Number of formulae : 55 ( 12 unt; 7 typ; 2 def)
% Number of atoms : 101 ( 19 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 126 ( 37 ~; 22 |; 0 &; 41 @)
% ( 19 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 25 con; 0-2 aty)
% Number of variables : 13 ( 2 ^; 11 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_x,type,
x: nat ).
thf(ty_eigen__0,type,
eigen__0: nat ).
thf(ty_suc,type,
suc: nat > nat ).
thf(ty_pl,type,
pl: nat > nat > nat ).
thf(ty_more,type,
more: nat > nat > $o ).
thf(ty_n_1,type,
n_1: nat ).
thf(h0,assumption,
! [X1: nat > $o,X2: nat] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: nat] :
( x
!= ( suc @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: nat] :
( ( suc @ eigen__0 )
!= ( suc @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(sP1,plain,
( sP1
<=> ( more @ x @ n_1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( more @ ( pl @ n_1 @ eigen__0 ) @ n_1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( suc @ eigen__0 )
= x ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: nat] : ( more @ ( pl @ n_1 @ X1 ) @ n_1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: nat] :
( ( X1 != n_1 )
=> ~ ! [X2: nat] :
( X1
!= ( suc @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( x
= ( suc @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( suc @ eigen__0 )
= n_1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( pl @ n_1 @ eigen__0 )
= x ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( suc @ eigen__0 )
= ( pl @ n_1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( n_1 = x ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ sP7
=> ~ ! [X1: nat] :
( ( suc @ eigen__0 )
!= ( suc @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: nat] :
( x
!= ( suc @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( x != n_1 )
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( suc @ eigen__0 )
= ( suc @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: nat] :
( ( suc @ X1 )
= ( pl @ n_1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( x = n_1 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> $false ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: nat] :
( ( suc @ eigen__0 )
!= ( suc @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: nat,X2: nat] : ( more @ ( pl @ X1 @ X2 ) @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(satz24,conjecture,
( ~ sP1
=> sP16 ) ).
thf(h1,negated_conjecture,
~ ( ~ sP1
=> sP16 ),
inference(assume_negation,[status(cth)],[satz24]) ).
thf(h2,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP14
| sP8
| ~ sP9
| ~ sP3 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP1
| sP17
| ~ sP8 ),
inference(mating_rule,[status(thm)],]) ).
thf(3,plain,
( sP18
| sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(4,plain,
( ~ sP15
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP4
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP11
| sP7
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP5
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP6
| sP10
| ~ sP7
| sP17 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(9,plain,
~ sP17,
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP6
| sP3 ),
inference(symeq,[status(thm)],]) ).
thf(11,plain,
( sP12
| sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(12,plain,
( ~ sP13
| sP16
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP5
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP19
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP10
| sP16 ),
inference(symeq,[status(thm)],]) ).
thf(satz3,axiom,
sP5 ).
thf(satz18,axiom,
sP19 ).
thf(satz4g,axiom,
sP15 ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,satz3,satz18,satz4g,h2,h3]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,16,h2,h3]) ).
thf(18,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[17,h0]) ).
thf(0,theorem,
( ~ sP1
=> sP16 ),
inference(contra,[status(thm),contra(discharge,[h1])],[17,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM693^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 17:53:32 EDT 2023
% 0.13/0.35 % CPUTime :
% 30.23/30.52 % SZS status Theorem
% 30.23/30.52 % Mode: cade22grackle2x798d
% 30.23/30.52 % Steps: 64508
% 30.23/30.52 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------