%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM730^1 : 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 : n008.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 02:09:45 PM UTC 2025
% Result : Theorem 0.18s 0.42s
% Output : Proof 0.18s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_x,type,
x: frac ).
thf(ty_c1x,type,
c1x: frac > nat ).
thf(ty_c2x,type,
c2x: frac > nat ).
thf(ty_ts,type,
ts: nat > nat > nat ).
thf(ty_c1y,type,
c1y: frac > nat ).
thf(ty_more,type,
more: nat > nat > $o ).
thf(ty_y,type,
y: frac ).
thf(ty_c2y,type,
c2y: frac > nat ).
thf(ty_less,type,
less: nat > nat > $o ).
thf(ty_orec3,type,
orec3: $o > $o > $o > $o ).
thf(sP1,plain,
( sP1
<=> ( orec3
@ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
= ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: nat] :
( orec3
@ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
= X1 )
@ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ X1 )
@ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: nat,X2: nat] : ( orec3 @ ( X1 = X2 ) @ ( more @ X1 @ X2 ) @ ( less @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(satz41,conjecture,
sP1 ).
thf(h0,negated_conjecture,
~ sP1,
inference(assume_negation,[status(cth)],[satz41]) ).
thf(1,plain,
( ~ sP2
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(satz10,axiom,
sP3 ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,h0,satz10]) ).
thf(0,theorem,
sP1,
inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM730^1 : TPTP v9.2.0. Released v3.7.0.
% 0.11/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n008.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 : Wed Oct 8 22:13:08 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 % Mode: cade22grackle2xfee4
% 0.18/0.42 % Steps: 411
% 0.18/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------