0.10/0.12 % Problem : SLH0108^1 : TPTP v8.2.0. Released v8.2.0. 0.10/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s 0.11/0.33 Computer : n013.cluster.edu 0.11/0.33 Model : x86_64 x86_64 0.11/0.33 CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.33 RAMPerCPU : 8042.1875MB 0.11/0.33 OS : Linux 3.10.0-693.el7.x86_64 0.16/0.33 % CPULimit : 30 0.16/0.33 % DateTime : Mon Jul 3 03:28:17 EDT 2023 0.16/0.33 % CPUTime : 12.12/12.44 % SZS status Theorem 12.12/12.44 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0 12.12/12.44 % Inferences: 7 12.12/12.44 % SZS output start Proof 12.12/12.44 thf(ty_nat, type, nat : $tType). 12.12/12.44 thf(ty_real, type, real : $tType). 12.12/12.44 thf(ty_powr_real, type, powr_real : (real>real>real)). 12.12/12.44 thf(ty_power_power_real, type, power_power_real : (real>nat>real)). 12.12/12.44 thf(ty_divide_divide_real, type, divide_divide_real : (real>real>real)). 12.12/12.44 thf(ty_plus_plus_real, type, plus_plus_real : (real>real>real)). 12.12/12.44 thf(ty_semiri5074537144036343181t_real, type, semiri5074537144036343181t_real : (nat>real)). 12.12/12.44 thf(ty_i, type, i : real). 12.12/12.44 thf(ty_zero_zero_nat, type, zero_zero_nat : nat). 12.12/12.44 thf(ty_uminus_uminus_real, type, uminus_uminus_real : (real>real)). 12.12/12.44 thf(ty_i_nom, type, i_nom : (real>nat>real)). 12.12/12.44 thf(ty_one_one_real, type, one_one_real : real). 12.12/12.44 thf(ty_m, type, m : nat). 12.12/12.44 thf(sP1,plain,sP1 <=> (m = zero_zero_nat),introduced(definition,[new_symbols(definition,[sP1])])). 12.12/12.44 thf(sP2,plain,sP2 <=> (![X1:real]:((((power_power_real @ ((plus_plus_real @ one_one_real) @ ((divide_divide_real @ ((i_nom @ i) @ m)) @ (semiri5074537144036343181t_real @ m)))) @ m) = X1) => (X1 = ((power_power_real @ ((plus_plus_real @ one_one_real) @ ((divide_divide_real @ ((i_nom @ i) @ m)) @ (semiri5074537144036343181t_real @ m)))) @ m)))),introduced(definition,[new_symbols(definition,[sP2])])). 12.12/12.44 thf(sP3,plain,sP3 <=> ((((power_power_real @ ((plus_plus_real @ one_one_real) @ ((divide_divide_real @ ((i_nom @ i) @ m)) @ (semiri5074537144036343181t_real @ m)))) @ m) = ((plus_plus_real @ one_one_real) @ i)) => (((plus_plus_real @ one_one_real) @ i) = ((power_power_real @ ((plus_plus_real @ one_one_real) @ ((divide_divide_real @ ((i_nom @ i) @ m)) @ (semiri5074537144036343181t_real @ m)))) @ m))),introduced(definition,[new_symbols(definition,[sP3])])). 12.12/12.44 thf(sP4,plain,sP4 <=> ((~(sP1)) => (((power_power_real @ ((plus_plus_real @ one_one_real) @ ((divide_divide_real @ ((i_nom @ i) @ m)) @ (semiri5074537144036343181t_real @ m)))) @ m) = ((plus_plus_real @ one_one_real) @ i))),introduced(definition,[new_symbols(definition,[sP4])])). 12.12/12.44 thf(sP5,plain,sP5 <=> (((powr_real @ ((plus_plus_real @ one_one_real) @ i)) @ (uminus_uminus_real @ one_one_real)) = ((powr_real @ ((power_power_real @ ((plus_plus_real @ one_one_real) @ ((divide_divide_real @ ((i_nom @ i) @ m)) @ (semiri5074537144036343181t_real @ m)))) @ m)) @ (uminus_uminus_real @ one_one_real))),introduced(definition,[new_symbols(definition,[sP5])])). 12.12/12.44 thf(sP6,plain,sP6 <=> (((plus_plus_real @ one_one_real) @ i) = ((power_power_real @ ((plus_plus_real @ one_one_real) @ ((divide_divide_real @ ((i_nom @ i) @ m)) @ (semiri5074537144036343181t_real @ m)))) @ m)),introduced(definition,[new_symbols(definition,[sP6])])). 12.12/12.44 thf(sP7,plain,sP7 <=> (((power_power_real @ ((plus_plus_real @ one_one_real) @ ((divide_divide_real @ ((i_nom @ i) @ m)) @ (semiri5074537144036343181t_real @ m)))) @ m) = ((plus_plus_real @ one_one_real) @ i)),introduced(definition,[new_symbols(definition,[sP7])])). 12.12/12.44 thf(sP8,plain,sP8 <=> (![X1:real]:(![X2:real]:((X1 = X2) => (X2 = X1)))),introduced(definition,[new_symbols(definition,[sP8])])). 12.12/12.44 thf(sP9,plain,sP9 <=> (![X1:nat]:((~((X1 = zero_zero_nat))) => (((power_power_real @ ((plus_plus_real @ one_one_real) @ ((divide_divide_real @ ((i_nom @ i) @ X1)) @ (semiri5074537144036343181t_real @ X1)))) @ X1) = ((plus_plus_real @ one_one_real) @ i)))),introduced(definition,[new_symbols(definition,[sP9])])). 12.12/12.44 thf(sP10,plain,sP10 <=> ((uminus_uminus_real @ one_one_real) = (uminus_uminus_real @ one_one_real)),introduced(definition,[new_symbols(definition,[sP10])])). 12.12/12.44 thf(sP11,plain,sP11 <=> (one_one_real = one_one_real),introduced(definition,[new_symbols(definition,[sP11])])). 12.12/12.44 thf(conj_0,conjecture,sP5). 12.12/12.44 thf(h0,negated_conjecture,(~(sP5)),inference(assume_negation,[status(cth)],[conj_0])). 12.12/12.44 thf(1,plain,(~(sP9) | sP4),inference(all_rule,[status(thm)],[])). 12.12/12.44 thf(2,plain,((~(sP4) | sP1) | sP7),inference(prop_rule,[status(thm)],[])). 12.12/12.44 thf(3,plain,sP11,inference(prop_rule,[status(thm)],[])). 12.12/12.44 thf(4,plain,(sP10 | ~(sP11)),inference(prop_rule,[status(thm)],[])). 12.12/12.44 thf(5,plain,((~(sP3) | ~(sP7)) | sP6),inference(prop_rule,[status(thm)],[])). 12.12/12.44 thf(6,plain,(~(sP2) | sP3),inference(all_rule,[status(thm)],[])). 12.12/12.44 thf(7,plain,(~(sP8) | sP2),inference(all_rule,[status(thm)],[])). 12.12/12.44 thf(8,plain,((sP5 | ~(sP6)) | ~(sP10)),inference(prop_rule,[status(thm)],[])). 12.12/12.44 thf(9,plain,sP8,inference(@eq_sym,[status(thm)],[])). 12.12/12.44 thf(fact_2_i__nom__eff,axiom,sP9). 12.12/12.44 thf(fact_0_that,axiom,(~(sP1))). 12.12/12.44 thf(10,plain,$false,inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,fact_2_i__nom__eff,fact_0_that,h0])). 12.12/12.44 thf(0,theorem,sP5,inference(contra,[status(thm),contra(discharge,[h0])],[10,h0])). 12.12/12.44 % SZS output end Proof 12.12/12.44 EOF