%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ALG286^5 : 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 : n019.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 01:11:40 PM UTC 2025
% Result : Theorem 4.98s 5.08s
% Output : Proof 4.98s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cZ,type,
cZ: a ).
thf(ty_cR,type,
cR: a > a ).
thf(ty_x,type,
x: a ).
thf(ty_cP,type,
cP: a > a > a ).
thf(ty_u,type,
u: a ).
thf(ty_cL,type,
cL: a > a ).
thf(ty_y,type,
y: a ).
thf(sP1,plain,
( sP1
<=> ( u
= ( cP @ x @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( cL @ ( cP @ x @ y ) )
= x ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( x
= ( cL @ ( cP @ x @ y ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ( cP @ x @ y )
!= cZ )
= ( ( cP @ x @ y )
= ( cP @ ( cL @ ( cP @ x @ y ) ) @ ( cR @ ( cP @ x @ y ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ( cR @ ( cP @ x @ X1 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( cR @ ( cP @ x @ y ) )
= y ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ( cL @ ( cP @ x @ X1 ) )
= x ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( y
= ( cR @ ( cP @ x @ y ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( cP @ x @ y )
= ( cP @ ( cL @ ( cP @ x @ y ) ) @ ( cR @ ( cP @ x @ y ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a] :
( ( X1 != cZ )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( cP @ x @ y )
= cZ ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( u = cZ ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a] :
( ( cR @ ( cP @ ( cP @ x @ y ) @ X1 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> $false ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( cR @ ( cP @ ( cP @ x @ y ) @ u ) )
= u ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(cPU_PAIR_NOT_ZERO_pme,conjecture,
( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ sP5 )
=> ~ sP17 )
=> ~ sP11 )
=> ( sP1
=> ~ sP13 ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ sP5 )
=> ~ sP17 )
=> ~ sP11 )
=> ( sP1
=> ~ sP13 ) ),
inference(assume_negation,[status(cth)],[cPU_PAIR_NOT_ZERO_pme]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ sP5 )
=> ~ sP17 )
=> ~ sP11 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP1
=> ~ sP13 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ sP5 )
=> ~ sP17 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP11,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ sP5 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP17,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP5,
introduced(assumption,[]) ).
thf(h9,assumption,
( ( cL @ cZ )
= cZ ),
introduced(assumption,[]) ).
thf(h10,assumption,
( ( cR @ cZ )
= cZ ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP1,
introduced(assumption,[]) ).
thf(h12,assumption,
sP13,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP7
| sP9
| ~ sP7
| sP15 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP2
| sP3
| ~ sP2
| sP15 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP16
| sP12
| ~ sP1
| ~ sP13 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(4,plain,
~ sP15,
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP10
| ~ sP9
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP4
| ~ sP12
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP14
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP11
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP17
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP8
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP6
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP17
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP5
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h8,h6,h4,h11,h12]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h2,14,h11,h12]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h7,15,h9,h10]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,16,h7,h8]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,17,h5,h6]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,18,h3,h4]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,19,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ sP5 )
=> ~ sP17 )
=> ~ sP11 )
=> ( sP1
=> ~ sP13 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[20,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG286^5 : TPTP v9.2.0. Released v4.0.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 8 23:36:23 EDT 2025
% 0.13/0.35 % CPUTime :
% 4.98/5.08 % SZS status Theorem
% 4.98/5.08 % Mode: cade22grackle2xfee4
% 4.98/5.08 % Steps: 231630
% 4.98/5.08 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------