TSTP Solution File: ITP204^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP204^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n014.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 Aug 31 04:02:53 EDT 2023
% Result : Theorem 22.34s 22.66s
% Output : Proof 22.34s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_produc62062515n_game,type,
produc62062515n_game: $tType ).
thf(ty_trm,type,
trm: $tType ).
thf(ty_produc799602994n_game,type,
produc799602994n_game: $tType ).
thf(ty_variable,type,
variable: $tType ).
thf(ty_produc1418842292n_game,type,
produc1418842292n_game: $tType ).
thf(ty_set_variable,type,
set_variable: $tType ).
thf(ty_option_game,type,
option_game: $tType ).
thf(ty_option_fml,type,
option_fml: $tType ).
thf(ty_option_trm,type,
option_trm: $tType ).
thf(ty_fml,type,
fml: $tType ).
thf(ty_char,type,
char: $tType ).
thf(ty_bot_bot_set_variable,type,
bot_bot_set_variable: set_variable ).
thf(ty_the_trm,type,
the_trm: option_trm > trm ).
thf(ty_uSubst516392818stappt,type,
uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
thf(ty_member_variable,type,
member_variable: variable > set_variable > $o ).
thf(ty_pred,type,
pred: char > trm > fml ).
thf(ty_produc1615133358on_fml,type,
produc1615133358on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
thf(ty_uSubst516392804stappf,type,
uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).
thf(ty_va,type,
va: set_variable ).
thf(ty_none_fml,type,
none_fml: option_fml ).
thf(ty_produc1250175341on_fml,type,
produc1250175341on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
thf(ty_sigma,type,
sigma: produc1418842292n_game ).
thf(ty_theta,type,
theta: trm ).
thf(ty_eigen__0,type,
eigen__0: set_variable > set_variable > variable ).
thf(ty_p,type,
p: char ).
thf(ty_uSubst1408967625substt,type,
uSubst1408967625substt: trm > produc1418842292n_game ).
thf(ty_the_fml,type,
the_fml: option_fml > fml ).
thf(ty_vv,type,
vv: set_variable > set_variable > variable ).
thf(ty_static_FVF,type,
static_FVF: fml > set_variable ).
thf(ty_produc1420172399on_fml,type,
produc1420172399on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
thf(ty_vva,type,
vva: set_variable > set_variable > variable ).
thf(ty_inf_inf_set_variable,type,
inf_inf_set_variable: set_variable > set_variable > set_variable ).
thf(sP1,plain,
( sP1
<=> ( ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p )
= none_fml ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) )
@ va )
= bot_bot_set_variable )
=> ( ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) )
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( sP2
=> ~ ( ( ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) )
@ va )
!= bot_bot_set_variable )
=> ( none_fml
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) )
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
= none_fml ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) )
= none_fml ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP2
=> ~ ( ( ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) )
@ va )
!= bot_bot_set_variable )
=> ( none_fml
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) )
@ va )
= bot_bot_set_variable ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(conj_0,conjecture,
( sP5
=> sP1 ) ).
thf(h0,negated_conjecture,
~ ( sP5
=> sP1 ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
sP5,
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h3,assumption,
! [X1: set_variable,X2: set_variable] :
~ ( ( ( ( inf_inf_set_variable @ X1 @ X2 )
= bot_bot_set_variable )
=> ! [X3: variable] :
( ( member_variable @ X3 @ X1 )
=> ! [X4: variable] :
( ( member_variable @ X4 @ X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ( ( ( inf_inf_set_variable @ X1 @ X2 )
!= bot_bot_set_variable )
=> ~ ( ~ ( ( member_variable @ ( vv @ X2 @ X1 ) @ X1 )
=> ~ ( member_variable @ ( eigen__0 @ X2 @ X1 ) @ X2 ) )
=> ( ( vv @ X2 @ X1 )
!= ( eigen__0 @ X2 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
( sP9
=> ! [X1: variable] :
( ( member_variable @ X1
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X2: char > option_trm] :
( produc1615133358on_fml
@ ^ [X3: char > option_trm] :
( produc1420172399on_fml
@ ^ [X4: char > option_fml,X5: char > option_game] : X4 ) )
@ sigma
@ p ) ) ) )
=> ! [X2: variable] :
( ( member_variable @ X2 @ va )
=> ( X1 != X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
( ~ sP9
=> ~ ( ~ ( ( member_variable
@ ( vv @ va
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) )
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) )
=> ~ ( member_variable
@ ( vva @ va
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) )
@ va ) )
=> ( ( vv @ va
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) )
!= ( vva @ va
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP9,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| sP6 ),
inference(symeq,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| ~ sP9
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP7
| ~ sP6
| ~ sP5 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(4,plain,
( sP8
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| ~ sP8
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(fact_3__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_A_092_060Longrightarrow_062_ASPreds_A_092_060sigma_062_Ap_A_061_Aundeff_092_060close_062,axiom,
sP3 ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h7,h4,h5,h3,h1,h2,h0])],[1,2,3,4,5,h1,h2,fact_3__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_A_092_060Longrightarrow_062_ASPreds_A_092_060sigma_062_Ap_A_061_Aundeff_092_060close_062,h6,h7]) ).
thf(fact_2__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Aundeff_092_060close_062,axiom,
~ ( sP9
=> sP7 ) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[fact_2__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Aundeff_092_060close_062,6,h6,h7]) ).
thf(fact_15_f10,axiom,
~ ( ( sP9
=> ! [X1: variable] :
( ( member_variable @ X1
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X2: char > option_trm] :
( produc1615133358on_fml
@ ^ [X3: char > option_trm] :
( produc1420172399on_fml
@ ^ [X4: char > option_fml,X5: char > option_game] : X4 ) )
@ sigma
@ p ) ) ) )
=> ! [X2: variable] :
( ( member_variable @ X2 @ va )
=> ( X1 != X2 ) ) ) )
=> ~ ( ~ sP9
=> ~ ( ~ ( ( member_variable
@ ( vv @ va
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) )
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) )
=> ~ ( member_variable
@ ( vva @ va
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) )
@ va ) )
=> ( ( vv @ va
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) )
!= ( vva @ va
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) ) ) ) ) ) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h1,h2,h0]),tab_negimp(discharge,[h4,h5])],[fact_15_f10,7,h4,h5]) ).
thf(fact_30__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062vva_O_A_092_060forall_062V_AVa_O_A_IV_A_092_060inter_062_AVa_A_092_060noteq_062_A_123_125_A_092_060or_062_A_I_092_060forall_062v_O_Av_A_092_060notin_062_AV_A_092_060or_062_A_I_092_060forall_062va_O_Ava_A_092_060notin_062_AVa_A_092_060or_062_Av_A_092_060noteq_062_Ava_J_J_J_A_092_060and_062_A_IV_A_092_060inter_062_AVa_A_061_A_123_125_A_092_060or_062_Avv_AVa_AV_A_092_060in_062_AV_A_092_060and_062_Avva_AVa_AV_A_092_060in_062_AVa_A_092_060and_062_Avv_AVa_AV_A_061_Avva_AVa_AV_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
~ ! [X1: set_variable > set_variable > variable] :
~ ! [X2: set_variable,X3: set_variable] :
~ ( ( ( ( inf_inf_set_variable @ X2 @ X3 )
= bot_bot_set_variable )
=> ! [X4: variable] :
( ( member_variable @ X4 @ X2 )
=> ! [X5: variable] :
( ( member_variable @ X5 @ X3 )
=> ( X4 != X5 ) ) ) )
=> ~ ( ( ( inf_inf_set_variable @ X2 @ X3 )
!= bot_bot_set_variable )
=> ~ ( ~ ( ( member_variable @ ( vv @ X3 @ X2 ) @ X2 )
=> ~ ( member_variable @ ( X1 @ X3 @ X2 ) @ X3 ) )
=> ( ( vv @ X3 @ X2 )
!= ( X1 @ X3 @ X2 ) ) ) ) ) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[fact_30__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062vva_O_A_092_060forall_062V_AVa_O_A_IV_A_092_060inter_062_AVa_A_092_060noteq_062_A_123_125_A_092_060or_062_A_I_092_060forall_062v_O_Av_A_092_060notin_062_AV_A_092_060or_062_A_I_092_060forall_062va_O_Ava_A_092_060notin_062_AVa_A_092_060or_062_Av_A_092_060noteq_062_Ava_J_J_J_A_092_060and_062_A_IV_A_092_060inter_062_AVa_A_061_A_123_125_A_092_060or_062_Avv_AVa_AV_A_092_060in_062_AV_A_092_060and_062_Avva_AVa_AV_A_092_060in_062_AVa_A_092_060and_062_Avv_AVa_AV_A_061_Avva_AVa_AV_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,8,h3]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,9,h1,h2]) ).
thf(0,theorem,
( sP5
=> sP1 ),
inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP204^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n014.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 : Sun Aug 27 13:18:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 22.34/22.66 % SZS status Theorem
% 22.34/22.66 % Mode: cade22sinegrackle2xfaf3
% 22.34/22.66 % Steps: 1384
% 22.34/22.66 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------