TSTP Solution File: NUM699^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM699^1 : 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 : n003.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 11:40:34 EDT 2023
% Result : Theorem 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_x,type,
x: nat ).
thf(ty_pl,type,
pl: nat > nat > nat ).
thf(ty_lessis,type,
lessis: nat > nat > $o ).
thf(ty_suc,type,
suc: nat > nat ).
thf(ty_y,type,
y: nat ).
thf(ty_n_1,type,
n_1: nat ).
thf(ty_less,type,
less: nat > nat > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: nat,X2: nat] :
( ( less @ X2 @ X1 )
=> ( lessis @ ( pl @ X2 @ n_1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> $false ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( pl @ y @ n_1 )
= ( suc @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( lessis @ ( pl @ y @ n_1 ) @ x ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: nat] :
( ( pl @ X1 @ n_1 )
= ( suc @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( less @ y @ x ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: nat] :
( ( less @ X1 @ x )
=> ( lessis @ ( pl @ X1 @ n_1 ) @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( lessis @ ( suc @ y ) @ x ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP6
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(satz25c,conjecture,
sP8 ).
thf(h0,negated_conjecture,
~ sP8,
inference(assume_negation,[status(cth)],[satz25c]) ).
thf(1,plain,
( ~ sP4
| sP8
| sP2
| ~ sP3 ),
inference(mating_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP9
| ~ sP6
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP1
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
~ sP2,
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(satz4a,axiom,
sP5 ).
thf(satz25b,axiom,
sP1 ).
thf(l,axiom,
sP6 ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,h0,satz4a,satz25b,l]) ).
thf(0,theorem,
sP8,
inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM699^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.32 % Computer : n003.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Fri Aug 25 11:46:08 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.18/0.38 % SZS status Theorem
% 0.18/0.38 % Mode: cade22grackle2xfee4
% 0.18/0.38 % Steps: 62
% 0.18/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------