%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO502^1 : TPTP v9.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n025.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 03:23:46 PM UTC 2025
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $i ).
thf(ty_f,type,
f: $i > $i ).
thf(ty_a,type,
a: $i ).
thf(ty_g,type,
g: $i > $i ).
thf(sP1,plain,
( sP1
<=> ( ( f @ a )
= ( g @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( g @ b )
= ( g @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( a = b ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( f @ b )
= ( g @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( f @ a )
= ( f @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( b = a ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> $false ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(claim,conjecture,
( ~ ( sP3
=> ~ sP1 )
=> sP4 ) ).
thf(h0,negated_conjecture,
~ ( ~ ( sP3
=> ~ sP1 )
=> sP4 ),
inference(assume_negation,[status(cth)],[claim]) ).
thf(h1,assumption,
~ ( sP3
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h3,assumption,
sP3,
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| sP6
| ~ sP3
| sP7 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(2,plain,
~ sP7,
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( sP2
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP5
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP1
| sP4
| ~ sP5
| ~ sP2 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h4,h1,h2,h0])],[1,2,3,4,5,h3,h4,h2]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,6,h3,h4]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,7,h1,h2]) ).
thf(0,theorem,
( ~ ( sP3
=> ~ sP1 )
=> sP4 ),
inference(contra,[status(thm),contra(discharge,[h0])],[8,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SYO502^1 : TPTP v9.2.0. Released v4.1.0.
% 0.14/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n025.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Oct 9 00:47:53 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % Mode: cade22grackle2xfee4
% 0.14/0.40 % Steps: 45
% 0.14/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------