0.07/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% Command  : lash -P picomus -M modes -p tstp -t %d %s
0.13/0.33	% Computer : n002.cluster.edu
0.13/0.33	% Model    : x86_64 x86_64
0.13/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory   : 8042.1875MB
0.13/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.33	% CPULimit : 1440
0.13/0.33	% WCLimit  : 180
0.13/0.33	% DateTime : Mon Jul  3 08:14:22 EDT 2023
0.13/0.34	% CPUTime  : 
15.29/15.69	% SZS status Theorem
15.29/15.69	% Mode: cade22sinegrackle2xfaf3
15.29/15.69	% Steps: 3405
15.29/15.69	% SZS output start Proof
15.29/15.69	thf(ty_set_variable_real, type, set_variable_real : $tType).
15.29/15.69	thf(ty_variable, type, variable : $tType).
15.29/15.69	thf(ty_real, type, real : $tType).
15.29/15.69	thf(ty_sigma, type, sigma : produc1418842292n_game).
15.29/15.69	thf(ty_member_variable_real, type, member_variable_real : ((variable>real)>set_variable_real>$o)).
15.29/15.69	thf(ty_i, type, i : denotational_interp).
15.29/15.69	thf(ty_denota1245701238me_sem, type, denota1245701238me_sem : (denotational_interp>game>set_variable_real>set_variable_real)).
15.29/15.69	thf(ty_the_game, type, the_game : (option_game>game)).
15.29/15.69	thf(ty_uminus430703407e_real, type, uminus430703407e_real : (set_variable_real>set_variable_real)).
15.29/15.69	thf(ty_ua, type, ua : set_variable).
15.29/15.69	thf(ty_uSubst516392814stappp, type, uSubst516392814stappp : (produc1418842292n_game>set_variable>game>produc1078154247n_game)).
15.29/15.69	thf(ty_xa, type, xa : set_variable_real).
15.29/15.69	thf(ty_alpha, type, alpha : game).
15.29/15.69	thf(ty_produc293487213n_game, type, produc293487213n_game : (produc1078154247n_game>option_game)).
15.29/15.69	thf(ty_uSubst1599435252djoint, type, uSubst1599435252djoint : (produc1418842292n_game>denotational_interp>(variable>real)>denotational_interp)).
15.29/15.69	thf(ty_omega2, type, omega2 : (variable>real)).
15.29/15.69	thf(ty_nu2, type, nu2 : (variable>real)).
15.29/15.69	thf(sP1,plain,sP1 <=> ((member_variable_real @ nu2) @ (((denota1245701238me_sem @ i) @ (the_game @ (produc293487213n_game @ (((uSubst516392814stappp @ sigma) @ ua) @ alpha)))) @ (uminus430703407e_real @ xa))),introduced(definition,[new_symbols(definition,[sP1])])).
15.29/15.69	thf(sP2,plain,sP2 <=> (((member_variable_real @ nu2) @ (uminus430703407e_real @ (((denota1245701238me_sem @ (((uSubst1599435252djoint @ sigma) @ i) @ omega2)) @ alpha) @ (uminus430703407e_real @ xa)))) = (~(((member_variable_real @ nu2) @ (((denota1245701238me_sem @ (((uSubst1599435252djoint @ sigma) @ i) @ omega2)) @ alpha) @ (uminus430703407e_real @ xa)))))),introduced(definition,[new_symbols(definition,[sP2])])).
15.29/15.69	thf(sP3,plain,sP3 <=> (![X1:variable>real]:(![X2:set_variable_real]:(((member_variable_real @ X1) @ (uminus430703407e_real @ X2)) = (~(((member_variable_real @ X1) @ X2)))))),introduced(definition,[new_symbols(definition,[sP3])])).
15.29/15.69	thf(sP4,plain,sP4 <=> (![X1:set_variable_real]:(((member_variable_real @ nu2) @ (((denota1245701238me_sem @ i) @ (the_game @ (produc293487213n_game @ (((uSubst516392814stappp @ sigma) @ ua) @ alpha)))) @ X1)) = ((member_variable_real @ nu2) @ (((denota1245701238me_sem @ (((uSubst1599435252djoint @ sigma) @ i) @ omega2)) @ alpha) @ X1)))),introduced(definition,[new_symbols(definition,[sP4])])).
15.29/15.69	thf(sP5,plain,sP5 <=> (((member_variable_real @ nu2) @ (uminus430703407e_real @ (((denota1245701238me_sem @ i) @ (the_game @ (produc293487213n_game @ (((uSubst516392814stappp @ sigma) @ ua) @ alpha)))) @ (uminus430703407e_real @ xa)))) = ((member_variable_real @ nu2) @ (uminus430703407e_real @ (((denota1245701238me_sem @ (((uSubst1599435252djoint @ sigma) @ i) @ omega2)) @ alpha) @ (uminus430703407e_real @ xa))))),introduced(definition,[new_symbols(definition,[sP5])])).
15.29/15.69	thf(sP6,plain,sP6 <=> (((member_variable_real @ nu2) @ (uminus430703407e_real @ (((denota1245701238me_sem @ i) @ (the_game @ (produc293487213n_game @ (((uSubst516392814stappp @ sigma) @ ua) @ alpha)))) @ (uminus430703407e_real @ xa)))) = (~(sP1))),introduced(definition,[new_symbols(definition,[sP6])])).
15.29/15.69	thf(sP7,plain,sP7 <=> (sP1 = ((member_variable_real @ nu2) @ (((denota1245701238me_sem @ (((uSubst1599435252djoint @ sigma) @ i) @ omega2)) @ alpha) @ (uminus430703407e_real @ xa)))),introduced(definition,[new_symbols(definition,[sP7])])).
15.29/15.69	thf(sP8,plain,sP8 <=> (![X1:set_variable_real]:(((member_variable_real @ nu2) @ (uminus430703407e_real @ X1)) = (~(((member_variable_real @ nu2) @ X1))))),introduced(definition,[new_symbols(definition,[sP8])])).
15.29/15.69	thf(sP9,plain,sP9 <=> ((member_variable_real @ nu2) @ (uminus430703407e_real @ (((denota1245701238me_sem @ i) @ (the_game @ (produc293487213n_game @ (((uSubst516392814stappp @ sigma) @ ua) @ alpha)))) @ (uminus430703407e_real @ xa)))),introduced(definition,[new_symbols(definition,[sP9])])).
15.29/15.69	thf(sP10,plain,sP10 <=> ((member_variable_real @ nu2) @ (uminus430703407e_real @ (((denota1245701238me_sem @ (((uSubst1599435252djoint @ sigma) @ i) @ omega2)) @ alpha) @ (uminus430703407e_real @ xa)))),introduced(definition,[new_symbols(definition,[sP10])])).
15.29/15.69	thf(sP11,plain,sP11 <=> ((member_variable_real @ nu2) @ (((denota1245701238me_sem @ (((uSubst1599435252djoint @ sigma) @ i) @ omega2)) @ alpha) @ (uminus430703407e_real @ xa))),introduced(definition,[new_symbols(definition,[sP11])])).
15.29/15.69	thf(conj_0,conjecture,sP5).
15.29/15.69	thf(h0,negated_conjecture,(~(sP5)),inference(assume_negation,[status(cth)],[conj_0])).
15.29/15.69	thf(1,plain,((~(sP2) | ~(sP10)) | ~(sP11)),inference(prop_rule,[status(thm)],[])).
15.29/15.69	thf(2,plain,((~(sP2) | sP10) | sP11),inference(prop_rule,[status(thm)],[])).
15.29/15.69	thf(3,plain,((~(sP6) | ~(sP9)) | ~(sP1)),inference(prop_rule,[status(thm)],[])).
15.29/15.69	thf(4,plain,((~(sP6) | sP9) | sP1),inference(prop_rule,[status(thm)],[])).
15.29/15.69	thf(5,plain,((~(sP7) | ~(sP1)) | sP11),inference(prop_rule,[status(thm)],[])).
15.29/15.69	thf(6,plain,((~(sP7) | sP1) | ~(sP11)),inference(prop_rule,[status(thm)],[])).
15.29/15.69	thf(7,plain,(~(sP8) | sP2),inference(all_rule,[status(thm)],[])).
15.29/15.69	thf(8,plain,(~(sP8) | sP6),inference(all_rule,[status(thm)],[])).
15.29/15.69	thf(9,plain,(~(sP4) | sP7),inference(all_rule,[status(thm)],[])).
15.29/15.69	thf(10,plain,((sP5 | ~(sP9)) | ~(sP10)),inference(prop_rule,[status(thm)],[])).
15.29/15.69	thf(11,plain,((sP5 | sP9) | sP10),inference(prop_rule,[status(thm)],[])).
15.29/15.69	thf(12,plain,(~(sP3) | sP8),inference(all_rule,[status(thm)],[])).
15.29/15.69	thf(fact_0__092_060open_062_092_060And_062X_O_A_I_092_060nu_062_A_092_060in_062_Agame__sem_AI_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_J_AX_J_A_061_A_I_092_060nu_062_A_092_060in_062_Agame__sem_A_IUSubst__Mirabelle__vidvnmlwwz_Oadjoint_A_092_060sigma_062_AI_A_092_060omega_062_J_A_092_060alpha_062_AX_J_092_060close_062,axiom,sP4).
15.29/15.69	thf(fact_13_Compl__iff,axiom,sP3).
15.29/15.69	thf(13,plain,$false,inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h0,fact_0__092_060open_062_092_060And_062X_O_A_I_092_060nu_062_A_092_060in_062_Agame__sem_AI_A_Ithe_A_Isnd_A_Iusubstappp_A_092_060sigma_062_AU_A_092_060alpha_062_J_J_J_AX_J_A_061_A_I_092_060nu_062_A_092_060in_062_Agame__sem_A_IUSubst__Mirabelle__vidvnmlwwz_Oadjoint_A_092_060sigma_062_AI_A_092_060omega_062_J_A_092_060alpha_062_AX_J_092_060close_062,fact_13_Compl__iff])).
15.29/15.69	thf(0,theorem,sP5,inference(contra,[status(thm),contra(discharge,[h0])],[13,h0])).
15.29/15.69	% SZS output end Proof
15.29/15.69	EOF