%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM749^1 : 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 : n016.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 02:09:48 PM UTC 2025
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_frac,type,
frac: $tType ).
thf(ty_x,type,
x: frac ).
thf(ty_pf,type,
pf: frac > frac > frac ).
thf(ty_more,type,
more: frac > frac > $o ).
thf(ty_y,type,
y: frac ).
thf(ty_less,type,
less: frac > frac > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: frac,X2: frac] : ( more @ ( pf @ X1 @ X2 ) @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: frac] :
( ( more @ ( pf @ x @ y ) @ X1 )
=> ( less @ X1 @ ( pf @ x @ y ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( more @ ( pf @ x @ y ) @ x ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( less @ x @ ( pf @ x @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: frac,X2: frac] :
( ( more @ X1 @ X2 )
=> ( less @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: frac] : ( more @ ( pf @ x @ X1 ) @ x ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP3
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(satz60a,conjecture,
sP4 ).
thf(h0,negated_conjecture,
~ sP4,
inference(assume_negation,[status(cth)],[satz60a]) ).
thf(1,plain,
( ~ sP7
| ~ sP3
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP2
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP5
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP1
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(satz60,axiom,
sP1 ).
thf(satz42,axiom,
sP5 ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,h0,satz60,satz42]) ).
thf(0,theorem,
sP4,
inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM749^1 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 22:37:08 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % Mode: cade22grackle2xfee4
% 0.21/0.41 % Steps: 75
% 0.21/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------