%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM695^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n027.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 Oct 9 02:09:38 PM UTC 2025
% Result : Theorem 20.26s 20.47s
% Output : Proof 20.26s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_x,type,
x: nat ).
thf(ty_n_1,type,
n_1: nat ).
thf(ty_pl,type,
pl: nat > nat > nat ).
thf(ty_more,type,
more: nat > nat > $o ).
thf(ty_suc,type,
suc: nat > nat ).
thf(sP1,plain,
( sP1
<=> ! [X1: nat] :
( ( suc @ X1 )
= ( pl @ n_1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( suc @ x )
= ( pl @ n_1 @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: nat] :
( ( X1 != n_1 )
=> ~ ! [X2: nat] :
( X1
!= ( suc @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( more @ ( pl @ n_1 @ x ) @ n_1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> $false ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( pl @ n_1 @ x )
= ( suc @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: nat] : ( more @ ( pl @ n_1 @ X1 ) @ n_1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: nat,X2: nat] : ( more @ ( pl @ X1 @ X2 ) @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( more @ ( suc @ x ) @ n_1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(satz24b,conjecture,
sP9 ).
thf(h0,negated_conjecture,
~ sP9,
inference(assume_negation,[status(cth)],[satz24b]) ).
thf(1,plain,
( ~ sP4
| sP9
| sP5
| ~ sP6 ),
inference(mating_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP7
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP2
| sP6 ),
inference(symeq,[status(thm)],[]) ).
thf(4,plain,
( ~ sP3
| ~ sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP8
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(satz3,axiom,
sP3 ).
thf(satz18,axiom,
sP8 ).
thf(satz4g,axiom,
sP1 ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,satz3,satz18,satz4g,h0]) ).
thf(0,theorem,
sP9,
inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM695^1 : TPTP v9.2.0. Released v3.7.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 22:06:23 EDT 2025
% 0.13/0.35 % CPUTime :
% 20.26/20.47 % SZS status Theorem
% 20.26/20.47 % Mode: cade22grackle2x798d
% 20.26/20.47 % Steps: 65
% 20.26/20.47 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------