%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO258^5 : 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 : n001.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 03:23:07 PM UTC 2025
% Result : Theorem 0.17s 0.40s
% Output : Proof 0.17s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cQ,type,
cQ: $i > ( $i > $o ) > $o ).
thf(ty_cP,type,
cP: $i > $i > $o ).
thf(ty_a,type,
a: $i ).
thf(ty_b,type,
b: $i ).
thf(sP1,plain,
( sP1
<=> $false ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ( ~ ! [X3: $i] :
( ( cP @ X2 @ X3 )
=> ~ ( cQ @ X3 @ X1 ) )
=> ~ ( X1 @ a ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(cBLEDSOE_FENG_6,conjecture,
( ~ ( ( cP @ a @ b )
=> ~ ! [X1: $i > $o] : ( cQ @ b @ X1 ) )
=> ~ sP2 ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ( cP @ a @ b )
=> ~ ! [X1: $i > $o] : ( cQ @ b @ X1 ) )
=> ~ sP2 ),
inference(assume_negation,[status(cth)],[cBLEDSOE_FENG_6]) ).
thf(h1,assumption,
~ ( ( cP @ a @ b )
=> ~ ! [X1: $i > $o] : ( cQ @ b @ X1 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP2,
introduced(assumption,[]) ).
thf(h3,assumption,
cP @ a @ b,
introduced(assumption,[]) ).
thf(h4,assumption,
! [X1: $i > $o] : ( cQ @ b @ X1 ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
~ sP1,
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h4,h1,h2,h0])],[1,2,h2]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,3,h3,h4]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,4,h1,h2]) ).
thf(0,theorem,
( ~ ( ( cP @ a @ b )
=> ~ ! [X1: $i > $o] : ( cQ @ b @ X1 ) )
=> ~ sP2 ),
inference(contra,[status(thm),contra(discharge,[h0])],[5,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYO258^5 : TPTP v9.2.0. Released v4.0.0.
% 0.06/0.11 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.32 % Computer : n001.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Oct 9 01:01:23 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.17/0.40 % SZS status Theorem
% 0.17/0.40 % Mode: cade22grackle2xfee4
% 0.17/0.40 % Steps: 173
% 0.17/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------