%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM770^1 : 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 : n020.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 02:09:53 PM UTC 2025
% Result : Theorem 0.21s 0.52s
% 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_moref,type,
moref: frac > frac > $o ).
thf(ty_eq,type,
eq: frac > frac > $o ).
thf(ty_y,type,
y: frac ).
thf(ty_mf,type,
mf: frac > frac > frac ).
thf(ty_v,type,
v: frac ).
thf(sP1,plain,
( sP1
<=> ( eq @ ( pf @ y @ v ) @ x ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eq @ v @ ( mf @ x @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( moref @ x @ y )
=> ( eq @ ( pf @ y @ ( mf @ x @ y ) ) @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: frac,X2: frac] :
( ( eq @ ( pf @ y @ X1 ) @ x )
=> ( ( eq @ ( pf @ y @ X2 ) @ x )
=> ( eq @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: frac,X2: frac,X3: frac] :
( ( eq @ ( pf @ X1 @ X2 ) @ x )
=> ( ( eq @ ( pf @ X1 @ X3 ) @ x )
=> ( eq @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: frac,X2: frac,X3: frac,X4: frac] :
( ( eq @ ( pf @ X2 @ X3 ) @ X1 )
=> ( ( eq @ ( pf @ X2 @ X4 ) @ X1 )
=> ( eq @ X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( moref @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: frac] :
( ( moref @ x @ X1 )
=> ( eq @ ( pf @ X1 @ ( mf @ x @ X1 ) ) @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eq @ ( pf @ y @ ( mf @ x @ y ) ) @ x ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP9
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: frac,X2: frac] :
( ( moref @ X1 @ X2 )
=> ( eq @ ( pf @ X2 @ ( mf @ X1 @ X2 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: frac] :
( sP1
=> ( ( eq @ ( pf @ y @ X1 ) @ x )
=> ( eq @ v @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP1
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(satz67e,conjecture,
sP2 ).
thf(h0,negated_conjecture,
~ sP2,
inference(assume_negation,[status(cth)],[satz67e]) ).
thf(1,plain,
( ~ sP10
| ~ sP9
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP13
| ~ sP1
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP12
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP4
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP3
| ~ sP7
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP8
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP5
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP6
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP11
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(satz67c,axiom,
sP11 ).
thf(satz67b,axiom,
sP6 ).
thf(e,axiom,
sP1 ).
thf(m,axiom,
sP7 ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,h0,satz67c,satz67b,e,m]) ).
thf(0,theorem,
sP2,
inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM770^1 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 8 23:01:53 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.21/0.52 % SZS status Theorem
% 0.21/0.52 % Mode: cade22grackle2xfee4
% 0.21/0.52 % Steps: 1639
% 0.21/0.52 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------