%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO291^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n028.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 03:23:10 PM UTC 2025
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cQ,type,
cQ: $i > $o ).
thf(ty_cR,type,
cR: $i > $o ).
thf(ty_x,type,
x: $i ).
thf(ty_y,type,
y: $i ).
thf(ty_f,type,
f: $i > $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i > $o] : ( X1 @ y ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> $false ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(cTEST3,conjecture,
( sP1
=> ~ ( ~ ( ( cR @ x )
=> ~ ( cR @ ( f @ x ) ) )
=> ~ ( cQ @ y ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP1
=> ~ ( ~ ( ( cR @ x )
=> ~ ( cR @ ( f @ x ) ) )
=> ~ ( cQ @ y ) ) ),
inference(assume_negation,[status(cth)],[cTEST3]) ).
thf(h1,assumption,
sP1,
introduced(assumption,[]) ).
thf(h2,assumption,
( ~ ( ( cR @ x )
=> ~ ( cR @ ( f @ x ) ) )
=> ~ ( cQ @ y ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP1
| ~ sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h2,h0])],[1,2,h1]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,3,h1,h2]) ).
thf(0,theorem,
( sP1
=> ~ ( ~ ( ( cR @ x )
=> ~ ( cR @ ( f @ x ) ) )
=> ~ ( cQ @ y ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[4,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYO291^5 : TPTP v9.2.0. Released v4.0.0.
% 0.04/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n028.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 : Thu Oct 9 00:58:53 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % Mode: cade22grackle2xfee4
% 0.21/0.40 % Steps: 35
% 0.21/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------