%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM747^1 : 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 : n011.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 02:09:47 PM UTC 2025
% Result : Theorem 21.58s 21.78s
% Output : Proof 21.58s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_frac,type,
frac: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_x1,type,
x1: nat ).
thf(ty_fr,type,
fr: nat > nat > frac ).
thf(ty_eq,type,
eq: frac > frac > $o ).
thf(ty_pf,type,
pf: frac > frac > frac ).
thf(ty_x2,type,
x2: nat ).
thf(ty_pl,type,
pl: nat > nat > nat ).
thf(ty_n,type,
n: nat ).
thf(sP1,plain,
( sP1
<=> ! [X1: nat,X2: nat,X3: nat] : ( eq @ ( pf @ ( fr @ X1 @ X3 ) @ ( fr @ X2 @ X3 ) ) @ ( fr @ ( pl @ X1 @ X2 ) @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: nat,X2: nat] : ( eq @ ( pf @ ( fr @ x1 @ X2 ) @ ( fr @ X1 @ X2 ) ) @ ( fr @ ( pl @ x1 @ X1 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eq @ ( pf @ ( fr @ x1 @ n ) @ ( fr @ x2 @ n ) ) @ ( fr @ ( pl @ x1 @ x2 ) @ n ) )
=> ( eq @ ( fr @ ( pl @ x1 @ x2 ) @ n ) @ ( pf @ ( fr @ x1 @ n ) @ ( fr @ x2 @ n ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: frac] :
( ( eq @ ( pf @ ( fr @ x1 @ n ) @ ( fr @ x2 @ n ) ) @ X1 )
=> ( eq @ X1 @ ( pf @ ( fr @ x1 @ n ) @ ( fr @ x2 @ n ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eq @ ( pf @ ( fr @ x1 @ n ) @ ( fr @ x2 @ n ) ) @ ( fr @ ( pl @ x1 @ x2 ) @ n ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: frac,X2: frac] :
( ( eq @ X1 @ X2 )
=> ( eq @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eq @ ( fr @ ( pl @ x1 @ x2 ) @ n ) @ ( pf @ ( fr @ x1 @ n ) @ ( fr @ x2 @ n ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: nat] : ( eq @ ( pf @ ( fr @ x1 @ X1 ) @ ( fr @ x2 @ X1 ) ) @ ( fr @ ( pl @ x1 @ x2 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(satz57a,conjecture,
sP7 ).
thf(h0,negated_conjecture,
~ sP7,
inference(assume_negation,[status(cth)],[satz57a]) ).
thf(1,plain,
( ~ sP3
| ~ sP5
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP8
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP4
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP2
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP6
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(satz38,axiom,
sP6 ).
thf(satz57,axiom,
sP1 ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,satz38,satz57,h0]) ).
thf(0,theorem,
sP7,
inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM747^1 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 22:35:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 21.58/21.78 % SZS status Theorem
% 21.58/21.78 % Mode: cade22grackle2x798d
% 21.58/21.78 % Steps: 58
% 21.58/21.78 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------