0.11/0.12	% Problem  : SLH0050^1 : TPTP v8.2.0. Released v8.2.0.
0.11/0.12	% Command  : lash -P picomus -M modes -p tstp -t %d %s
0.13/0.33	% Computer : n003.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 : 30
0.13/0.33	% WCLimit  : 30
0.13/0.33	% DateTime : Mon Jul  3 03:24:45 EDT 2023
0.13/0.33	% CPUTime  : 
0.19/0.53	% SZS status Theorem
0.19/0.53	% Mode: cade22sinegrackle2x6978
0.19/0.53	% Steps: 0
0.19/0.53	% SZS output start Proof
0.19/0.53	thf(ty_probab4737552673497767871pace_a, type, probab4737552673497767871pace_a : $tType).
0.19/0.53	thf(ty_quasi_borel_a, type, quasi_borel_a : $tType).
0.19/0.53	thf(ty_sigma_measure_real, type, sigma_measure_real : $tType).
0.19/0.53	thf(ty_produc6543235832880896358e_real, type, produc6543235832880896358e_real : $tType).
0.19/0.53	thf(ty_a, type, a : $tType).
0.19/0.53	thf(ty_real, type, real : $tType).
0.19/0.53	thf(ty_produc725540845905733987e_real, type, produc725540845905733987e_real : $tType).
0.19/0.53	thf(ty_eigen__0, type, eigen__0 : (real>a)).
0.19/0.53	thf(ty_probab701741629625904796prob_a, type, probab701741629625904796prob_a : (quasi_borel_a>(real>a)>sigma_measure_real>$o)).
0.19/0.53	thf(ty_y, type, y : quasi_borel_a).
0.19/0.53	thf(ty_produc623176010801490259e_real, type, produc623176010801490259e_real : ((real>a)>sigma_measure_real>produc725540845905733987e_real)).
0.19/0.53	thf(ty_mu, type, mu : sigma_measure_real).
0.19/0.53	thf(ty_alpha, type, alpha : (real>a)).
0.19/0.53	thf(ty_s, type, s : probab4737552673497767871pace_a).
0.19/0.53	thf(ty_produc4145838808978236886e_real, type, produc4145838808978236886e_real : (quasi_borel_a>produc725540845905733987e_real>produc6543235832880896358e_real)).
0.19/0.53	thf(ty_probab8173042092732894328pace_a, type, probab8173042092732894328pace_a : (produc6543235832880896358e_real>probab4737552673497767871pace_a)).
0.19/0.53	thf(ty_eigen__1, type, eigen__1 : sigma_measure_real).
0.19/0.53	thf(sP1,plain,sP1 <=> (((probab701741629625904796prob_a @ y) @ alpha) @ mu),introduced(definition,[new_symbols(definition,[sP1])])).
0.19/0.53	thf(conj_0,conjecture,sP1).
0.19/0.53	thf(h0,negated_conjecture,(~(sP1)),inference(assume_negation,[status(cth)],[conj_0])).
0.19/0.53	thf(h1,assumption,(~((![X1:sigma_measure_real]:((((probab701741629625904796prob_a @ y) @ eigen__0) @ X1) => (~((s = (probab8173042092732894328pace_a @ ((produc4145838808978236886e_real @ y) @ ((produc623176010801490259e_real @ eigen__0) @ X1)))))))))),introduced(assumption,[])).
0.19/0.53	thf(h2,assumption,(~(((((probab701741629625904796prob_a @ y) @ eigen__0) @ eigen__1) => (~((s = (probab8173042092732894328pace_a @ ((produc4145838808978236886e_real @ y) @ ((produc623176010801490259e_real @ eigen__0) @ eigen__1))))))))),introduced(assumption,[])).
0.19/0.53	thf(h3,assumption,(((probab701741629625904796prob_a @ y) @ eigen__0) @ eigen__1),introduced(assumption,[])).
0.19/0.53	thf(h4,assumption,(s = (probab8173042092732894328pace_a @ ((produc4145838808978236886e_real @ y) @ ((produc623176010801490259e_real @ eigen__0) @ eigen__1)))),introduced(assumption,[])).
0.19/0.53	thf(fact_0_hs_I1_J,axiom,sP1).
0.19/0.53	thf(1,plain,$false,inference(tab_conflict,[status(thm),assumptions([h3,h4,h2,h1,h0])],[fact_0_hs_I1_J,h0])).
0.19/0.53	thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,1,h3,h4])).
0.19/0.53	thf(3,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,2,h2])).
0.19/0.53	thf(fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060alpha_062_A_092_060mu_062_O_A_092_060lbrakk_062qbs__prob_AY_A_092_060alpha_062_A_092_060mu_062_059_As_A_061_Aqbs__prob__space_A_IY_M_A_092_060alpha_062_M_A_092_060mu_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,(~((![X1:real>a]:(![X2:sigma_measure_real]:((((probab701741629625904796prob_a @ y) @ X1) @ X2) => (~((s = (probab8173042092732894328pace_a @ ((produc4145838808978236886e_real @ y) @ ((produc623176010801490259e_real @ X1) @ X2)))))))))))).
0.19/0.53	thf(4,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060alpha_062_A_092_060mu_062_O_A_092_060lbrakk_062qbs__prob_AY_A_092_060alpha_062_A_092_060mu_062_059_As_A_061_Aqbs__prob__space_A_IY_M_A_092_060alpha_062_M_A_092_060mu_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,3,h1])).
0.19/0.53	thf(0,theorem,sP1,inference(contra,[status(thm),contra(discharge,[h0])],[4,h0])).
0.19/0.53	% SZS output end Proof
0.19/0.53	EOF