%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO303^5 : 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 : n005.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 03:23:12 PM UTC 2025
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cS,type,
cS: $i > $o ).
thf(ty_c0,type,
c0: $i ).
thf(ty_a,type,
a: $i ).
thf(ty_b,type,
b: $i ).
thf(ty_cT,type,
cT: $i > $o ).
thf(sP1,plain,
( sP1
<=> ( cT @ c0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] : ( cT @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cT @ a ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cS @ b ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP1
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( cS @ c0 )
=> ! [X1: $i] : ( cS @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( cS @ c0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP3
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] : ( cS @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i > $o] :
( ( X1 @ c0 )
=> ! [X2: $i] : ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(cMIN_QUAN_BUG,conjecture,
( sP10
=> ( ~ ( sP7
=> ~ sP1 )
=> ~ sP8 ) ) ).
thf(h0,negated_conjecture,
~ ( sP10
=> ( ~ ( sP7
=> ~ sP1 )
=> ~ sP8 ) ),
inference(assume_negation,[status(cth)],[cMIN_QUAN_BUG]) ).
thf(h1,assumption,
sP10,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ~ ( sP7
=> ~ sP1 )
=> ~ sP8 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP7
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP8,
introduced(assumption,[]) ).
thf(h5,assumption,
sP7,
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP9
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP6
| ~ sP7
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP10
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP5
| ~ sP1
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP10
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP8
| ~ sP3
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,h1,h5,h6,h4]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,8,h5,h6]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,9,h3,h4]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,10,h1,h2]) ).
thf(0,theorem,
( sP10
=> ( ~ ( sP7
=> ~ sP1 )
=> ~ sP8 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO303^5 : TPTP v9.2.0. Released v4.0.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Oct 9 00:26:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % Mode: cade22grackle2xfee4
% 0.13/0.39 % Steps: 24
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------