%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP202^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n007.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 01:45:25 PM UTC 2025
% Result : Theorem 21.75s 21.92s
% Output : Proof 21.75s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_option_trm,type,
option_trm: $tType ).
thf(ty_produc1418842292n_game,type,
produc1418842292n_game: $tType ).
thf(ty_char,type,
char: $tType ).
thf(ty_produc62062515n_game,type,
produc62062515n_game: $tType ).
thf(ty_produc799602994n_game,type,
produc799602994n_game: $tType ).
thf(ty_option_fml,type,
option_fml: $tType ).
thf(ty_option_game,type,
option_game: $tType ).
thf(ty_set_variable,type,
set_variable: $tType ).
thf(ty_trm,type,
trm: $tType ).
thf(ty_static_FVT,type,
static_FVT: trm > set_variable ).
thf(ty_v,type,
v: set_variable ).
thf(ty_const,type,
const: char > trm ).
thf(ty_produc1231571704on_trm,type,
produc1231571704on_trm: ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc62062515n_game > char > option_trm ).
thf(ty_produc1036610745on_trm,type,
produc1036610745on_trm: ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > produc799602994n_game > char > option_trm ).
thf(ty_u,type,
u: set_variable ).
thf(ty_bot_bot_set_variable,type,
bot_bot_set_variable: set_variable ).
thf(ty_f,type,
f: char ).
thf(ty_uSubst516392818stappt,type,
uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
thf(ty_sigma,type,
sigma: produc1418842292n_game ).
thf(ty_none_trm,type,
none_trm: option_trm ).
thf(ty_the_trm,type,
the_trm: option_trm > trm ).
thf(ty_uSubst1559070963pconst,type,
uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm ).
thf(ty_inf_inf_set_variable,type,
inf_inf_set_variable: set_variable > set_variable > set_variable ).
thf(ty_some_trm,type,
some_trm: trm > option_trm ).
thf(ty_produc866613687on_trm,type,
produc866613687on_trm: ( ( char > option_trm ) > produc62062515n_game > char > option_trm ) > produc1418842292n_game > char > option_trm ).
thf(sP1,plain,
( sP1
<=> ( ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f ) ) )
@ u )
= bot_bot_set_variable ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f ) ) )
= ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f )
!= none_trm )
=> ~ ( ( sP1
=> ( ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f ) ) )
= ( uSubst1559070963pconst @ sigma @ u @ f ) ) )
=> ~ ( ~ sP1
=> ( none_trm
= ( uSubst1559070963pconst @ sigma @ u @ f ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f )
= ( uSubst516392818stappt @ sigma @ u @ ( const @ f ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f )
!= none_trm )
=> ( ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f ) ) )
@ v )
= bot_bot_set_variable ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( sP1
=> ( ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f ) ) )
= ( uSubst1559070963pconst @ sigma @ u @ f ) ) )
=> ~ ( ~ sP1
=> ( none_trm
= ( uSubst1559070963pconst @ sigma @ u @ f ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: option_trm] :
( ( X1 != none_trm )
=> ( X1
= ( some_trm @ ( the_trm @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( inf_inf_set_variable
@ ( static_FVT
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f ) ) )
@ v )
= bot_bot_set_variable ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: set_variable,X2: char] :
( ( uSubst516392818stappt @ sigma @ X1 @ ( const @ X2 ) )
= ( uSubst1559070963pconst @ sigma @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP1
=> ( ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f ) ) )
= ( uSubst1559070963pconst @ sigma @ u @ f ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f ) ) )
= ( uSubst1559070963pconst @ sigma @ u @ f ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f )
!= none_trm )
=> ~ ( ( sP8
=> ( ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f ) ) )
= ( uSubst1559070963pconst @ sigma @ v @ f ) ) )
=> ~ ( ~ sP8
=> ( none_trm
= ( uSubst1559070963pconst @ sigma @ v @ f ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( uSubst1559070963pconst @ sigma @ u @ f )
= ( uSubst516392818stappt @ sigma @ u @ ( const @ f ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f )
= ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( some_trm
@ ( the_trm
@ ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f ) ) )
= ( uSubst1559070963pconst @ sigma @ v @ f ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP8
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: produc1418842292n_game,X2: set_variable,X3: char] :
( ( uSubst516392818stappt @ X1 @ X2 @ ( const @ X3 ) )
= ( uSubst1559070963pconst @ X1 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f )
!= none_trm )
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP16
=> ~ ( ~ sP8
=> ( none_trm
= ( uSubst1559070963pconst @ sigma @ v @ f ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f )
!= none_trm )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( uSubst516392818stappt @ sigma @ u @ ( const @ f ) )
= ( uSubst1559070963pconst @ sigma @ u @ f ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: char] :
( ( uSubst516392818stappt @ sigma @ u @ ( const @ X1 ) )
= ( uSubst1559070963pconst @ sigma @ u @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( produc866613687on_trm
@ ^ [X1: char > option_trm] :
( produc1231571704on_trm
@ ^ [X2: char > option_trm] :
( produc1036610745on_trm
@ ^ [X3: char > option_fml,X4: char > option_game] : X1 ) )
@ sigma
@ f )
= none_trm ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( uSubst516392818stappt @ sigma @ u @ ( const @ f ) )
= ( uSubst1559070963pconst @ sigma @ v @ f ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(conj_0,conjecture,
( ~ sP23
=> sP24 ) ).
thf(h0,negated_conjecture,
~ ( ~ sP23
=> sP24 ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
~ sP23,
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP24,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP11
| sP4
| ~ sP2
| ~ sP13 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP14
| sP24
| ~ sP4
| ~ sP15 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP21
| sP13 ),
inference(symeq,[status(thm)],[]) ).
thf(4,plain,
( ~ sP14
| sP2 ),
inference(symeq,[status(thm)],[]) ).
thf(5,plain,
( ~ sP10
| ~ sP1
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP16
| ~ sP8
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP22
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP18
| sP23
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP6
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP19
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP9
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP7
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP3
| sP23
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP12
| sP23
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP17
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP5
| sP23
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP20
| sP23
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(fact_118_option_Oexhaust__sel,axiom,
sP7 ).
thf(fact_10__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AU_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AU_Af_092_060close_062,axiom,
sP3 ).
thf(fact_9__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AV_Af_092_060close_062,axiom,
sP12 ).
thf(fact_7_usubstappt_Osimps_I3_J,axiom,
sP17 ).
thf(fact_4__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062,axiom,
sP5 ).
thf(fact_3_f3,axiom,
sP20 ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,h1,h2,fact_118_option_Oexhaust__sel,fact_10__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AU_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AU_Af_092_060close_062,fact_9__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_A_Iif_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_AAterm_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_Aelse_Aundeft_J_A_061_Ausappconst_A_092_060sigma_062_AV_Af_092_060close_062,fact_7_usubstappt_Osimps_I3_J,fact_4__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062,fact_3_f3]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,18,h1,h2]) ).
thf(0,theorem,
( ~ sP23
=> sP24 ),
inference(contra,[status(thm),contra(discharge,[h0])],[19,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : ITP202^1 : TPTP v9.2.0. Released v7.5.0.
% 0.08/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Oct 8 17:57:23 EDT 2025
% 0.11/0.34 % CPUTime :
% 21.75/21.92 % SZS status Theorem
% 21.75/21.92 % Mode: cade22sinegrackle2xfaf3
% 21.75/21.92 % Steps: 8846
% 21.75/21.92 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------