%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO504^1 : 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 : 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 03:23:46 PM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $o ).
thf(ty_g,type,
g: ( $o > $o > $o ) > $o ).
thf(ty_f,type,
f: ( ( $o > $o > $o ) > $o ) > $o ).
thf(ty_h,type,
h: $o > $o > $o ).
thf(ty_a,type,
a: $o ).
thf(ty_i,type,
i: $o > $o > $o ).
thf(sP1,plain,
( sP1
<=> ( h @ a @ b ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> b ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( i @ a @ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( f @ g ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(claim,conjecture,
( ~ ( ~ ( ~ ( ( sP1
= ( ~ ( a
=> ~ sP2 ) ) )
=> ( sP3
!= ( ~ a
=> sP2 ) ) )
=> ( sP4 != sP3 ) )
=> ~ sP1 )
=> sP4 ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ( sP1
= ( ~ ( a
=> ~ sP2 ) ) )
=> ( sP3
!= ( ~ a
=> sP2 ) ) )
=> ( sP4 != sP3 ) )
=> ~ sP1 )
=> sP4 ),
inference(assume_negation,[status(cth)],[claim]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( ( sP1
= ( ~ ( a
=> ~ sP2 ) ) )
=> ( sP3
!= ( ~ a
=> sP2 ) ) )
=> ( sP4 != sP3 ) )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ( sP1
= ( ~ ( a
=> ~ sP2 ) ) )
=> ( sP3
!= ( ~ a
=> sP2 ) ) )
=> ( sP4 != sP3 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ( sP1
= ( ~ ( a
=> ~ sP2 ) ) )
=> ( sP3
!= ( ~ a
=> sP2 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP4 = sP3,
introduced(assumption,[]) ).
thf(h7,assumption,
( sP1
= ( ~ ( a
=> ~ sP2 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
( sP3
= ( ~ a
=> sP2 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( a
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h11,assumption,
( a
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h12,assumption,
a,
introduced(assumption,[]) ).
thf(h13,assumption,
sP2,
introduced(assumption,[]) ).
thf(h14,assumption,
sP3,
introduced(assumption,[]) ).
thf(h15,assumption,
( ~ a
=> sP2 ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( ~ a
=> sP2 ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP4,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h18,h14,h14,h15,h12,h13,h4,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h18,h2]) ).
thf(2,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h2,h16,h14,h15,h12,h13,h4,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h14,h16]) ).
thf(3,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h14,h15,h12,h13,h4,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h18,h14]),tab_bq(discharge,[h2,h16])],[h6,1,2,h18,h14,h2,h16]) ).
thf(h19,assumption,
~ a,
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(4,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h18,h14,h19,h20,h16,h17,h12,h13,h4,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h18,h2]) ).
thf(5,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h2,h16,h19,h20,h16,h17,h12,h13,h4,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h13,h20]) ).
thf(6,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h19,h20,h16,h17,h12,h13,h4,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h18,h14]),tab_bq(discharge,[h2,h16])],[h6,4,5,h18,h14,h2,h16]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h17,h12,h13,h4,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h19,h20])],[h17,6,h19,h20]) ).
thf(8,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h12,h13,h4,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h14,h15]),tab_bq(discharge,[h16,h17])],[h8,3,7,h14,h15,h16,h17]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h9,8,h12,h13]) ).
thf(10,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h18,h14,h14,h15,h10,h11,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h18,h2]) ).
thf(11,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h2,h16,h14,h15,h10,h11,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h14,h16]) ).
thf(12,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h14,h15,h10,h11,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h18,h14]),tab_bq(discharge,[h2,h16])],[h6,10,11,h18,h14,h2,h16]) ).
thf(13,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h18,h14,h19,h20,h16,h17,h10,h11,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h18,h2]) ).
thf(14,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h2,h16,h19,h20,h16,h17,h10,h11,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h4,h10]) ).
thf(15,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h19,h20,h16,h17,h10,h11,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h18,h14]),tab_bq(discharge,[h2,h16])],[h6,13,14,h18,h14,h2,h16]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h17,h10,h11,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h19,h20])],[h17,15,h19,h20]) ).
thf(17,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h10,h11,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h14,h15]),tab_bq(discharge,[h16,h17])],[h8,12,16,h14,h15,h16,h17]) ).
thf(18,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h4,h9]),tab_bq(discharge,[h10,h11])],[h7,9,17,h4,h9,h10,h11]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,18,h7,h8]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,19,h5,h6]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,20,h3,h4]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,21,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ( sP1
= ( ~ ( a
=> ~ sP2 ) ) )
=> ( sP3
!= ( ~ a
=> sP2 ) ) )
=> ( sP4 != sP3 ) )
=> ~ sP1 )
=> sP4 ),
inference(contra,[status(thm),contra(discharge,[h0])],[22,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO504^1 : TPTP v9.2.0. Released v4.1.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n001.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 01:27:53 EDT 2025
% 0.19/0.34 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % Mode: cade22grackle2xfee4
% 0.19/0.38 % Steps: 0
% 0.19/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------