%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ALG287^5 : 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 : n008.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 74.92s 74.48s
% Output : Proof 74.92s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_v,type,
v: a ).
thf(ty_cR,type,
cR: a > a ).
thf(ty_x,type,
x: a ).
thf(ty_cP,type,
cP: a > a > a ).
thf(ty_cZ,type,
cZ: a ).
thf(ty_u,type,
u: a ).
thf(ty_cL,type,
cL: a > a ).
thf(ty_y,type,
y: a ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( X1 != cZ )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( v = u ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( u = v ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( cR @ ( cP @ y @ v ) )
= v ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( x = y )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( cL @ ( cP @ y @ v ) )
= x ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( cR @ ( cP @ x @ u ) )
= ( cR @ ( cP @ y @ v ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ( cL @ ( cP @ y @ X1 ) )
= y ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( cR @ ( cP @ ( cP @ x @ u ) @ ( cR @ ( cP @ x @ u ) ) ) )
= ( cR @ ( cP @ x @ u ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( cR @ ( cP @ y @ v ) )
= u ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( ( cP @ x @ u )
= ( cP @ y @ v ) )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( cL @ ( cP @ y @ v ) )
= y ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP1
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( cR @ ( cP @ ( cP @ x @ u ) @ ( cL @ ( cP @ x @ u ) ) ) )
= ( cL @ ( cP @ x @ u ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a] :
( ( cL @ ( cP @ x @ X1 ) )
= x ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( cL @ ( cP @ x @ u ) )
= x ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ sP13 )
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( cR @ ( cP @ x @ u ) )
= u ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: a] :
( ( cR @ ( cP @ x @ X1 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: a] :
( ( cR @ ( cP @ y @ X1 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( cP @ x @ u )
= ( cP @ y @ v ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: a] :
( ( cR @ ( cP @ ( cP @ x @ u ) @ X1 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( cL @ ( cP @ x @ u ) )
= ( cL @ ( cP @ y @ v ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(cPU_P_INJ_pme,conjecture,
sP16 ).
thf(h0,negated_conjecture,
~ sP16,
inference(assume_negation,[status(cth)],[cPU_P_INJ_pme]) ).
thf(1,plain,
( ~ sP4
| sP2
| ~ sP4
| ~ sP11 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP15
| sP9
| ~ sP6
| ~ sP15 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP10
| sP11
| ~ sP7
| ~ sP22 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP17
| sP6
| ~ sP27
| ~ sP19 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP23
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP18
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP24
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP8
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( sP7
| ~ sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP27
| ~ sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP26
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP26
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP2
| sP3 ),
inference(symeq,[status(thm)],[]) ).
thf(14,plain,
( ~ sP12
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP13
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP12
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP13
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP12
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( sP21
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP20
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( sP20
| ~ sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( sP1
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP5
| ~ sP9
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( sP14
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( sP14
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( sP16
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( sP16
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,h0]) ).
thf(0,theorem,
sP16,
inference(contra,[status(thm),contra(discharge,[h0])],[28,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : ALG287^5 : TPTP v9.2.0. Released v4.0.0.
% 0.07/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n008.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 : Wed Oct 8 23:33:38 EDT 2025
% 0.14/0.36 % CPUTime :
% 74.92/74.48 % SZS status Theorem
% 74.92/74.48 % Mode: cade22grackle2x34cb
% 74.92/74.48 % Steps: 228971
% 74.92/74.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------