%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM658^1 : 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 : n026.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 02:09:29 PM UTC 2025
% 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_less,type,
less: nat > nat > $o ).
thf(ty_y,type,
y: nat ).
thf(ty_more,type,
more: nat > nat > $o ).
thf(sP1,plain,
( sP1
<=> ( more @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( x != y )
=> ( ~ sP1
=> ( less @ x @ y ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: nat] :
( ( x != X1 )
=> ( ~ ( more @ x @ X1 )
=> ( less @ x @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ sP1
=> ( less @ x @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: nat,X2: nat] :
( ( X1 != X2 )
=> ( ~ ( more @ X1 @ X2 )
=> ( less @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( less @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(satz10j,conjecture,
sP7 ).
thf(h0,negated_conjecture,
~ sP7,
inference(assume_negation,[status(cth)],[satz10j]) ).
thf(h1,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| sP1
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP2
| sP6
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(satz10a,axiom,
sP5 ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h2,h0])],[1,2,3,4,h0,satz10a,h1,h2]) ).
thf(n,axiom,
~ ( ~ sP1
=> sP6 ) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[n,5,h1,h2]) ).
thf(0,theorem,
sP7,
inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM658^1 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n026.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 22:27:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % Mode: cade22grackle2xfee4
% 0.19/0.39 % Steps: 13
% 0.19/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------