TSTP Solution File: NUM707^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM707^1 : 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 : n009.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 11:40:38 EDT 2023
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_x,type,
x: nat ).
thf(ty_ts,type,
ts: nat > nat > nat ).
thf(ty_suc,type,
suc: nat > nat ).
thf(ty_y,type,
y: nat ).
thf(ty_pl,type,
pl: nat > nat > nat ).
thf(sP1,plain,
( sP1
<=> ( ( pl @ ( ts @ x @ y ) @ x )
= ( ts @ x @ ( suc @ y ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ts @ x @ ( suc @ y ) )
= ( pl @ ( ts @ x @ y ) @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: nat] :
( ( ts @ x @ ( suc @ X1 ) )
= ( pl @ ( ts @ x @ X1 ) @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: nat,X2: nat] :
( ( ts @ X1 @ ( suc @ X2 ) )
= ( pl @ ( ts @ X1 @ X2 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> $false ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(satz28f,conjecture,
sP1 ).
thf(h0,negated_conjecture,
~ sP1,
inference(assume_negation,[status(cth)],[satz28f]) ).
thf(1,plain,
( ~ sP2
| sP1
| ~ sP2
| sP5 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(2,plain,
~ sP5,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(satz28b,axiom,
sP4 ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,h0,satz28b]) ).
thf(0,theorem,
sP1,
inference(contra,[status(thm),contra(discharge,[h0])],[5,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM707^1 : TPTP v8.1.2. Released v3.7.0.
% 0.13/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n009.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 : 300
% 0.13/0.33 % DateTime : Fri Aug 25 09:28:35 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % Mode: cade22grackle2xfee4
% 0.19/0.39 % Steps: 139
% 0.19/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------