%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP203^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n004.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 01:47:16 PM UTC 2025
% Result : Theorem 26.18s 26.00s
% Output : Proof 26.18s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_option_game,type,
option_game: $tType ).
thf(ty_fml,type,
fml: $tType ).
thf(ty_produc62062515n_game,type,
produc62062515n_game: $tType ).
thf(ty_option_trm,type,
option_trm: $tType ).
thf(ty_produc799602994n_game,type,
produc799602994n_game: $tType ).
thf(ty_produc1418842292n_game,type,
produc1418842292n_game: $tType ).
thf(ty_char,type,
char: $tType ).
thf(ty_trm,type,
trm: $tType ).
thf(ty_set_variable,type,
set_variable: $tType ).
thf(ty_option_fml,type,
option_fml: $tType ).
thf(ty_uSubst516392818stappt,type,
uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
thf(ty_p,type,
p: char ).
thf(ty_produc1250175341on_fml,type,
produc1250175341on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
thf(ty_theta,type,
theta: trm ).
thf(ty_va,type,
va: 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_if_option_fml,type,
if_option_fml: $o > option_fml > option_fml > option_fml ).
thf(ty_none_fml,type,
none_fml: option_fml ).
thf(ty_bot_bot_set_variable,type,
bot_bot_set_variable: set_variable ).
thf(ty_inf_inf_set_variable,type,
inf_inf_set_variable: set_variable > set_variable > set_variable ).
thf(ty_case_o209804997ml_fml,type,
case_o209804997ml_fml: option_fml > ( fml > option_fml ) > option_fml > option_fml ).
thf(ty_uSubst516392804stappf,type,
uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).
thf(ty_uSubst1408967625substt,type,
uSubst1408967625substt: trm > produc1418842292n_game ).
thf(ty_static_FVF,type,
static_FVF: fml > set_variable ).
thf(ty_produc1615133358on_fml,type,
produc1615133358on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
thf(ty_ua,type,
ua: set_variable ).
thf(ty_the_trm,type,
the_trm: option_trm > trm ).
thf(ty_the_fml,type,
the_fml: option_fml > fml ).
thf(ty_some_fml,type,
some_fml: fml > option_fml ).
thf(ty_pred,type,
pred: char > trm > fml ).
thf(ty_sigma,type,
sigma: produc1418842292n_game ).
thf(sP1,plain,
( sP1
<=> ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
= none_fml ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: set_variable,X2: trm] :
( ( ( produc1250175341on_fml
@ ^ [X3: char > option_trm] :
( produc1615133358on_fml
@ ^ [X4: char > option_trm] :
( produc1420172399on_fml
@ ^ [X5: char > option_fml,X6: char > option_game] : X5 ) )
@ sigma
@ p )
= ( some_fml
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X3: char > option_trm] :
( produc1615133358on_fml
@ ^ [X4: char > option_trm] :
( produc1420172399on_fml
@ ^ [X5: char > option_fml,X6: char > option_game] : X5 ) )
@ sigma
@ p ) ) ) )
=> ( ( ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X3: char > option_trm] :
( produc1615133358on_fml
@ ^ [X4: char > option_trm] :
( produc1420172399on_fml
@ ^ [X5: char > option_fml,X6: char > option_game] : X5 ) )
@ sigma
@ p ) ) )
@ X1 )
!= bot_bot_set_variable )
=> ( ( uSubst516392804stappf @ sigma @ X1 @ ( pred @ p @ X2 ) )
= none_fml ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( 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,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( 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,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: produc1418842292n_game,X2: char,X3: fml,X4: set_variable,X5: trm] :
( ( ( produc1250175341on_fml
@ ^ [X6: char > option_trm] :
( produc1615133358on_fml
@ ^ [X7: char > option_trm] :
( produc1420172399on_fml
@ ^ [X8: char > option_fml,X9: char > option_game] : X8 ) )
@ X1
@ X2 )
= ( some_fml @ X3 ) )
=> ( ( ( inf_inf_set_variable @ ( static_FVF @ X3 ) @ X4 )
!= bot_bot_set_variable )
=> ( ( uSubst516392804stappf @ X1 @ X4 @ ( pred @ X2 @ X5 ) )
= none_fml ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: char,X2: fml,X3: set_variable,X4: trm] :
( ( ( produc1250175341on_fml
@ ^ [X5: char > option_trm] :
( produc1615133358on_fml
@ ^ [X6: char > option_trm] :
( produc1420172399on_fml
@ ^ [X7: char > option_fml,X8: char > option_game] : X7 ) )
@ sigma
@ X1 )
= ( some_fml @ X2 ) )
=> ( ( ( inf_inf_set_variable @ ( static_FVF @ X2 ) @ X3 )
!= bot_bot_set_variable )
=> ( ( uSubst516392804stappf @ sigma @ X3 @ ( pred @ X1 @ X4 ) )
= none_fml ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ sP4
=> ( ( 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 )
= ( some_fml
@ ( 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,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: option_fml] :
( ( X1 != none_fml )
=> ( X1
= ( some_fml @ ( the_fml @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: fml,X2: set_variable,X3: trm] :
( ( ( produc1250175341on_fml
@ ^ [X4: char > option_trm] :
( produc1615133358on_fml
@ ^ [X5: char > option_trm] :
( produc1420172399on_fml
@ ^ [X6: char > option_fml,X7: char > option_game] : X6 ) )
@ sigma
@ p )
= ( some_fml @ X1 ) )
=> ( ( ( inf_inf_set_variable @ ( static_FVF @ X1 ) @ X2 )
!= bot_bot_set_variable )
=> ( ( uSubst516392804stappf @ sigma @ X2 @ ( pred @ p @ X3 ) )
= none_fml ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: trm] :
( ( ( 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 )
= ( some_fml
@ ( 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 ) ) ) )
=> ( ~ sP3
=> ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ X1 ) )
= none_fml ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ sP3
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( ( 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 )
= ( some_fml
@ ( 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 ) ) ) )
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( 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 )
= ( some_fml
@ ( 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,[sP14])]) ).
thf(conj_0,conjecture,
sP4 ).
thf(h0,negated_conjecture,
~ sP4,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
( ( uSubst516392804stappf @ sigma @ ua @ ( 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(assumption,[]) ).
thf(h2,assumption,
sP4,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP3
=> ( ( uSubst516392804stappf @ sigma @ ua @ ( 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(assumption,[]) ).
thf(h4,assumption,
~ ( ~ sP3
=> ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
= none_fml ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP3,
introduced(assumption,[]) ).
thf(h6,assumption,
( ( uSubst516392804stappf @ sigma @ ua @ ( 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(assumption,[]) ).
thf(h7,assumption,
~ ( sP3
=> ( ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
@ ^ [X1: fml] :
( if_option_fml
@ ( ( inf_inf_set_variable @ ( static_FVF @ X1 ) @ va )
= bot_bot_set_variable )
@ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ X1 )
@ none_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 @ ( 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(assumption,[]) ).
thf(h8,assumption,
~ ( ~ sP3
=> ( ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
@ ^ [X1: fml] :
( if_option_fml
@ ( ( inf_inf_set_variable @ ( static_FVF @ X1 ) @ va )
= bot_bot_set_variable )
@ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ X1 )
@ none_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(assumption,[]) ).
thf(h9,assumption,
( ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
@ ^ [X1: fml] :
( if_option_fml
@ ( ( inf_inf_set_variable @ ( static_FVF @ X1 ) @ va )
= bot_bot_set_variable )
@ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ X1 )
@ none_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 @ ( 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(assumption,[]) ).
thf(h10,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h11,assumption,
sP8,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h13,assumption,
( none_fml
!= ( 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(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h13,h10,h5,h9,h7,h5,h6,h3,h1,h0])],[h5,h12]) ).
thf(fact_8__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_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_092_060close_062,axiom,
~ ( ~ sP3
=> ( none_fml
= ( 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 ) ) ) ) ) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h5,h9,h7,h5,h6,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[fact_8__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_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_092_060close_062,1,h12,h13]) ).
thf(3,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h13,h11,h5,h9,h7,h5,h6,h3,h1,h0])],[h5,h12]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h5,h9,h7,h5,h6,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[fact_8__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_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_092_060close_062,3,h12,h13]) ).
thf(fact_9_f9,axiom,
( sP4
=> sP8 ) ).
thf(5,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h9,h7,h5,h6,h3,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[fact_9_f9,2,4,h10,h11]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h3,h1,h0]),tab_negimp(discharge,[h5,h9])],[h7,5,h5,h9]) ).
thf(h14,assumption,
( ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
@ ^ [X1: fml] :
( if_option_fml
@ ( ( inf_inf_set_variable @ ( static_FVF @ X1 ) @ va )
= bot_bot_set_variable )
@ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ X1 )
@ none_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(assumption,[]) ).
thf(7,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h13,h10,h12,h14,h8,h5,h6,h3,h1,h0])],[h5,h12]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h12,h14,h8,h5,h6,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[fact_8__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_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_092_060close_062,7,h12,h13]) ).
thf(fact_26__092_060open_062usubstappf_A_092_060sigma_062_AU_A_IPred_Ap_A_092_060theta_062_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_092_060close_062,axiom,
~ sP8 ).
thf(9,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h13,h11,h12,h14,h8,h5,h6,h3,h1,h0])],[h11,fact_26__092_060open_062usubstappf_A_092_060sigma_062_AU_A_IPred_Ap_A_092_060theta_062_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_092_060close_062]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h14,h8,h5,h6,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[fact_8__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_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_092_060close_062,9,h12,h13]) ).
thf(11,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h12,h14,h8,h5,h6,h3,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[fact_9_f9,8,10,h10,h11]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h5,h6,h3,h1,h0]),tab_negimp(discharge,[h12,h14])],[h8,11,h12,h14]) ).
thf(fact_10__092_060open_062_Icase_ASPreds_A_092_060sigma_062_Ap_Aof_ANone_A_092_060Rightarrow_062_AAfml_A_IPred_Ap_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_124_ASome_Af_A_092_060Rightarrow_062_Aif_AFVF_Af_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_Af_Aelse_Aundeff_J_A_092_060noteq_062_A_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_092_060close_062,axiom,
( ( sP3
=> ( ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
@ ^ [X1: fml] :
( if_option_fml
@ ( ( inf_inf_set_variable @ ( static_FVF @ X1 ) @ va )
= bot_bot_set_variable )
@ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ X1 )
@ none_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 @ ( 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 ) ) ) ) )
=> ~ ( ~ sP3
=> ( ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
@ ^ [X1: fml] :
( if_option_fml
@ ( ( inf_inf_set_variable @ ( static_FVF @ X1 ) @ va )
= bot_bot_set_variable )
@ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ X1 )
@ none_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 ) ) ) ).
thf(13,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h3,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[fact_10__092_060open_062_Icase_ASPreds_A_092_060sigma_062_Ap_Aof_ANone_A_092_060Rightarrow_062_AAfml_A_IPred_Ap_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_124_ASome_Af_A_092_060Rightarrow_062_Aif_AFVF_Af_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_Af_Aelse_Aundeff_J_A_092_060noteq_062_A_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_092_060close_062,6,12,h7,h8]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,13,h5,h6]) ).
thf(h15,assumption,
( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
!= none_fml ),
introduced(assumption,[]) ).
thf(15,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h13,h10,h5,h9,h7,h12,h15,h4,h1,h0])],[h5,h12]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h5,h9,h7,h12,h15,h4,h1,h0]),tab_negimp(discharge,[h12,h13])],[fact_8__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_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_092_060close_062,15,h12,h13]) ).
thf(17,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h13,h11,h5,h9,h7,h12,h15,h4,h1,h0])],[h5,h12]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h5,h9,h7,h12,h15,h4,h1,h0]),tab_negimp(discharge,[h12,h13])],[fact_8__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_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_092_060close_062,17,h12,h13]) ).
thf(19,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h9,h7,h12,h15,h4,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[fact_9_f9,16,18,h10,h11]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h12,h15,h4,h1,h0]),tab_negimp(discharge,[h5,h9])],[h7,19,h5,h9]) ).
thf(21,plain,
( ~ sP6
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP10
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP2
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP11
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP13
| ~ sP14
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP12
| sP3
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP5
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP9
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP7
| sP4
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(fact_133_option_Oexhaust__sel,axiom,
sP9 ).
thf(fact_32_usubstappf__pred2,axiom,
sP5 ).
thf(fact_1_Pred_Oprems_I2_J,axiom,
~ sP1 ).
thf(30,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h13,h10,h12,h14,h8,h12,h15,h4,h1,h0])],[21,22,23,24,25,26,27,28,29,fact_133_option_Oexhaust__sel,fact_32_usubstappf__pred2,h10,h12,fact_1_Pred_Oprems_I2_J]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h12,h14,h8,h12,h15,h4,h1,h0]),tab_negimp(discharge,[h12,h13])],[fact_8__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_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_092_060close_062,30,h12,h13]) ).
thf(32,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h13,h11,h12,h14,h8,h12,h15,h4,h1,h0])],[h11,fact_26__092_060open_062usubstappf_A_092_060sigma_062_AU_A_IPred_Ap_A_092_060theta_062_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_092_060close_062]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h14,h8,h12,h15,h4,h1,h0]),tab_negimp(discharge,[h12,h13])],[fact_8__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_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_092_060close_062,32,h12,h13]) ).
thf(34,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h12,h14,h8,h12,h15,h4,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[fact_9_f9,31,33,h10,h11]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h12,h15,h4,h1,h0]),tab_negimp(discharge,[h12,h14])],[h8,34,h12,h14]) ).
thf(36,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h12,h15,h4,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[fact_10__092_060open_062_Icase_ASPreds_A_092_060sigma_062_Ap_Aof_ANone_A_092_060Rightarrow_062_AAfml_A_IPred_Ap_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_124_ASome_Af_A_092_060Rightarrow_062_Aif_AFVF_Af_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_Af_Aelse_Aundeff_J_A_092_060noteq_062_A_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_092_060close_062,20,35,h7,h8]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h1,h0]),tab_negimp(discharge,[h12,h15])],[h4,36,h12,h15]) ).
thf(fact_28_calculation_I1_J,axiom,
( ( sP3
=> ( ( uSubst516392804stappf @ sigma @ ua @ ( 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 ) ) ) ) )
=> ~ ( ~ sP3
=> ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
= none_fml ) ) ) ).
thf(38,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_28_calculation_I1_J,14,37,h3,h4]) ).
thf(39,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h13,h10,h5,h9,h7,h5,h6,h3,h2,h0])],[h5,h12]) ).
thf(40,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h5,h9,h7,h5,h6,h3,h2,h0]),tab_negimp(discharge,[h12,h13])],[fact_8__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_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_092_060close_062,39,h12,h13]) ).
thf(41,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h13,h11,h5,h9,h7,h5,h6,h3,h2,h0])],[h5,h12]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h5,h9,h7,h5,h6,h3,h2,h0]),tab_negimp(discharge,[h12,h13])],[fact_8__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_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_092_060close_062,41,h12,h13]) ).
thf(43,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h9,h7,h5,h6,h3,h2,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[fact_9_f9,40,42,h10,h11]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h3,h2,h0]),tab_negimp(discharge,[h5,h9])],[h7,43,h5,h9]) ).
thf(45,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h13,h10,h12,h14,h8,h5,h6,h3,h2,h0])],[h5,h12]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h12,h14,h8,h5,h6,h3,h2,h0]),tab_negimp(discharge,[h12,h13])],[fact_8__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_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_092_060close_062,45,h12,h13]) ).
thf(47,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h13,h11,h12,h14,h8,h5,h6,h3,h2,h0])],[h11,fact_26__092_060open_062usubstappf_A_092_060sigma_062_AU_A_IPred_Ap_A_092_060theta_062_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_092_060close_062]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h14,h8,h5,h6,h3,h2,h0]),tab_negimp(discharge,[h12,h13])],[fact_8__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_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_092_060close_062,47,h12,h13]) ).
thf(49,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h12,h14,h8,h5,h6,h3,h2,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[fact_9_f9,46,48,h10,h11]) ).
thf(50,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h5,h6,h3,h2,h0]),tab_negimp(discharge,[h12,h14])],[h8,49,h12,h14]) ).
thf(51,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h3,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[fact_10__092_060open_062_Icase_ASPreds_A_092_060sigma_062_Ap_Aof_ANone_A_092_060Rightarrow_062_AAfml_A_IPred_Ap_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_124_ASome_Af_A_092_060Rightarrow_062_Aif_AFVF_Af_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_Af_Aelse_Aundeff_J_A_092_060noteq_062_A_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_092_060close_062,44,50,h7,h8]) ).
thf(52,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,51,h5,h6]) ).
thf(53,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h13,h10,h5,h9,h7,h12,h15,h4,h2,h0])],[h5,h12]) ).
thf(54,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h5,h9,h7,h12,h15,h4,h2,h0]),tab_negimp(discharge,[h12,h13])],[fact_8__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_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_092_060close_062,53,h12,h13]) ).
thf(55,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h13,h11,h5,h9,h7,h12,h15,h4,h2,h0])],[h5,h12]) ).
thf(56,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h5,h9,h7,h12,h15,h4,h2,h0]),tab_negimp(discharge,[h12,h13])],[fact_8__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_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_092_060close_062,55,h12,h13]) ).
thf(57,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h9,h7,h12,h15,h4,h2,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[fact_9_f9,54,56,h10,h11]) ).
thf(58,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h12,h15,h4,h2,h0]),tab_negimp(discharge,[h5,h9])],[h7,57,h5,h9]) ).
thf(59,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h13,h10,h12,h14,h8,h12,h15,h4,h2,h0])],[h2,h10]) ).
thf(60,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h12,h14,h8,h12,h15,h4,h2,h0]),tab_negimp(discharge,[h12,h13])],[fact_8__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_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_092_060close_062,59,h12,h13]) ).
thf(61,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h13,h11,h12,h14,h8,h12,h15,h4,h2,h0])],[h11,fact_26__092_060open_062usubstappf_A_092_060sigma_062_AU_A_IPred_Ap_A_092_060theta_062_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_092_060close_062]) ).
thf(62,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h14,h8,h12,h15,h4,h2,h0]),tab_negimp(discharge,[h12,h13])],[fact_8__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_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_092_060close_062,61,h12,h13]) ).
thf(63,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h12,h14,h8,h12,h15,h4,h2,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[fact_9_f9,60,62,h10,h11]) ).
thf(64,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h12,h15,h4,h2,h0]),tab_negimp(discharge,[h12,h14])],[h8,63,h12,h14]) ).
thf(65,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h12,h15,h4,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[fact_10__092_060open_062_Icase_ASPreds_A_092_060sigma_062_Ap_Aof_ANone_A_092_060Rightarrow_062_AAfml_A_IPred_Ap_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_124_ASome_Af_A_092_060Rightarrow_062_Aif_AFVF_Af_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_Af_Aelse_Aundeff_J_A_092_060noteq_062_A_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_092_060close_062,58,64,h7,h8]) ).
thf(66,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h0]),tab_negimp(discharge,[h12,h15])],[h4,65,h12,h15]) ).
thf(67,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_28_calculation_I1_J,52,66,h3,h4]) ).
thf(fact_29_calculation_I2_J,axiom,
( ( ( uSubst516392804stappf @ sigma @ ua @ ( 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 ) ) ) )
=> sP4 ) ).
thf(68,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_29_calculation_I2_J,38,67,h1,h2]) ).
thf(0,theorem,
sP4,
inference(contra,[status(thm),contra(discharge,[h0])],[68,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP203^1 : TPTP v9.2.0. Released v7.5.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 17:52:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 26.18/26.00 % SZS status Theorem
% 26.18/26.00 % Mode: mode94:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=3.:SINE_DEPTH=0
% 26.18/26.00 % Inferences: 159
% 26.18/26.00 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------