0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s 0.12/0.33 Computer : n008.cluster.edu 0.12/0.33 Model : x86_64 x86_64 0.12/0.33 CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 RAMPerCPU : 8042.1875MB 0.12/0.33 OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 960 0.12/0.33 % DateTime : Tue Aug 9 03:19:24 EDT 2022 0.12/0.34 % CPUTime : 19.98/20.09 % SZS status Theorem 19.98/20.09 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1 19.98/20.09 % Inferences: 6 19.98/20.09 % SZS output start Proof 19.98/20.09 thf(ty_int, type, int : $tType). 19.98/20.09 thf(ty_nat, type, nat : $tType). 19.98/20.09 thf(ty_eigen__2, type, eigen__2 : int). 19.98/20.09 thf(ty_s, type, s : int). 19.98/20.09 thf(ty_eigen__1, type, eigen__1 : int). 19.98/20.09 thf(ty_eigen__0, type, eigen__0 : int). 19.98/20.09 thf(ty_bit1, type, bit1 : (int>int)). 19.98/20.09 thf(ty_bit0, type, bit0 : (int>int)). 19.98/20.09 thf(ty_eigen__4, type, eigen__4 : int). 19.98/20.09 thf(ty_eigen__5, type, eigen__5 : int). 19.98/20.09 thf(ty_zcong, type, zcong : (int>int>int>$o)). 19.98/20.09 thf(ty_times_times_int, type, times_times_int : (int>int>int)). 19.98/20.09 thf(ty_eigen__3, type, eigen__3 : int). 19.98/20.09 thf(ty_min, type, min : int). 19.98/20.09 thf(ty_ord_less_eq_int, type, ord_less_eq_int : (int>int>$o)). 19.98/20.09 thf(ty_t, type, t : int). 19.98/20.09 thf(ty_zero_zero_int, type, zero_zero_int : int). 19.98/20.09 thf(ty_one_one_int, type, one_one_int : int). 19.98/20.09 thf(ty_pls, type, pls : int). 19.98/20.09 thf(ty_power_power_int, type, power_power_int : (int>nat>int)). 19.98/20.09 thf(ty_plus_plus_int, type, plus_plus_int : (int>int>int)). 19.98/20.09 thf(ty_ord_less_int, type, ord_less_int : (int>int>$o)). 19.98/20.09 thf(ty_number_number_of_int, type, number_number_of_int : (int>int)). 19.98/20.09 thf(ty_s1, type, s1 : int). 19.98/20.09 thf(ty_m, type, m : int). 19.98/20.09 thf(ty_number_number_of_nat, type, number_number_of_nat : (int>nat)). 19.98/20.09 thf(conj_0,conjecture,((ord_less_int @ ((plus_plus_int @ ((power_power_int @ s) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ one_one_int)) @ zero_zero_int)). 19.98/20.09 thf(h0,negated_conjecture,(~(((ord_less_int @ ((plus_plus_int @ ((power_power_int @ s) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ one_one_int)) @ zero_zero_int))),inference(assume_negation,[status(cth)],[conj_0])). 19.98/20.09 thf(h1,assumption,(~((t = zero_zero_int))),introduced(assumption,[])). 19.98/20.09 thf(h2,assumption,(((plus_plus_int @ ((power_power_int @ s) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ one_one_int) = zero_zero_int),introduced(assumption,[])). 19.98/20.09 thf(h3,assumption,(((plus_plus_int @ ((power_power_int @ s) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ one_one_int) = ((times_times_int @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)) @ eigen__0)),introduced(assumption,[])). 19.98/20.09 thf(h4,assumption,(~(((~(((~(((![X1:int]:((~(((~((((ord_less_eq_int @ zero_zero_int) @ X1) => (~((((zcong @ s1) @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~(((ord_less_int @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (X1 = eigen__1))) => (~((((zcong @ s1) @ eigen__1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~(((ord_less_int @ eigen__1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~(((ord_less_eq_int @ zero_zero_int) @ eigen__1)))))),introduced(assumption,[])). 19.98/20.09 thf(h5,assumption,(~(((~(((![X1:int]:((~(((~((((ord_less_eq_int @ zero_zero_int) @ X1) => (~((((zcong @ s1) @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~(((ord_less_int @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (X1 = eigen__1))) => (~((((zcong @ s1) @ eigen__1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~(((ord_less_int @ eigen__1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))),introduced(assumption,[])). 19.98/20.09 thf(h6,assumption,((ord_less_eq_int @ zero_zero_int) @ eigen__1),introduced(assumption,[])). 19.98/20.09 thf(h7,assumption,(~(((![X1:int]:((~(((~((((ord_less_eq_int @ zero_zero_int) @ X1) => (~((((zcong @ s1) @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~(((ord_less_int @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (X1 = eigen__1))) => (~((((zcong @ s1) @ eigen__1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))),introduced(assumption,[])). 19.98/20.09 thf(h8,assumption,((ord_less_int @ eigen__1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)),introduced(assumption,[])). 19.98/20.09 thf(h9,assumption,(![X1:int]:((~(((~((((ord_less_eq_int @ zero_zero_int) @ X1) => (~((((zcong @ s1) @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~(((ord_less_int @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (X1 = eigen__1))),introduced(assumption,[])). 19.98/20.09 thf(h10,assumption,(((zcong @ s1) @ eigen__1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)),introduced(assumption,[])). 19.98/20.09 thf(h11,assumption,(~(((((zcong @ s1) @ s) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)) => (~(((ord_less_int @ s) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))),introduced(assumption,[])). 19.98/20.09 thf(h12,assumption,((ord_less_eq_int @ zero_zero_int) @ s),introduced(assumption,[])). 19.98/20.09 thf(h13,assumption,(((zcong @ s1) @ s) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)),introduced(assumption,[])). 19.98/20.09 thf(h14,assumption,((ord_less_int @ s) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)),introduced(assumption,[])). 19.98/20.09 thf(h15,assumption,(((zcong @ ((power_power_int @ eigen__2) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ (number_number_of_int @ min)) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)),introduced(assumption,[])). 19.98/20.09 tff(pax59, axiom, (p59=>![X126:int]:(fbit0 @ X126)=(fplus_plus_int @ X126 @ X126)), file('', pax59)). 19.98/20.09 tff(pax326, axiom, (p326=>![X13:int, X5:int]:(ftimes_times_int @ (fbit0 @ X13) @ X5)=(fbit0 @ (ftimes_times_int @ X13 @ X5))), file('', pax326)). 19.98/20.09 tff(pax240, axiom, (p240=>![X49:int]:(ftimes_times_int @ fone_one_int @ X49)=(X49)), file('', pax240)). 19.98/20.09 tff(pax194, axiom, (p194=>![X74:int, X75:int]:(fplus_plus_int @ X74 @ X75)=(fplus_plus_int @ X75 @ X74)), file('', pax194)). 19.98/20.09 tff(pax216, axiom, (p216=>(fpls)=(fzero_zero_int)), file('', pax216)). 19.98/20.09 tff(pax115, axiom, (p115=>![X101:int]:(ftimes_times_int @ (fplus_plus_int @ fone_one_int @ fone_one_int) @ (fnumber_number_of_int @ X101))=(fnumber_number_of_int @ (fbit0 @ X101))), file('', pax115)). 19.98/20.09 fof(ax365, axiom, p59, file('', ax365)). 19.98/20.09 fof(ax98, axiom, p326, file('', ax98)). 19.98/20.09 fof(ax184, axiom, p240, file('', ax184)). 19.98/20.09 tff(pax44, axiom, (p44=>(fone_one_int)=(fnumber_number_of_int @ (fbit1 @ fpls))), file('', pax44)). 19.98/20.09 tff(pax274, axiom, (p274=>![X33:int]:(ftimes_times_int @ X33 @ X33)=(fpower_power_int @ X33 @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls))))), file('', pax274)). 19.98/20.09 tff(nax206, axiom, (p206<=ford_less_int @ (fplus_plus_int @ (fpower_power_int @ fs @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls)))) @ fone_one_int) @ fzero_zero_int), file('', nax206)). 19.98/20.09 fof(ax230, axiom, p194, file('', ax230)). 19.98/20.09 fof(ax208, axiom, p216, file('', ax208)). 19.98/20.09 fof(ax218, axiom, ~(p206), file('', ax218)). 19.98/20.09 tff(pax300, axiom, (p300=>(fplus_plus_int @ (fpower_power_int @ fs @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls)))) @ fone_one_int)=(ftimes_times_int @ (fplus_plus_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ fm) @ fone_one_int) @ ft)), file('', pax300)). 19.98/20.09 fof(ax309, axiom, p115, file('', ax309)). 19.98/20.09 fof(ax380, axiom, p44, file('', ax380)). 19.98/20.09 fof(ax150, axiom, p274, file('', ax150)). 19.98/20.09 tff(pax201, axiom, (p201=>![X67:int]:(ftimes_times_int @ X67 @ fzero_zero_int)=(fzero_zero_int)), file('', pax201)). 19.98/20.09 tff(pax341, axiom, (p341=>ford_less_int @ (ftimes_times_int @ (fplus_plus_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ fm) @ fone_one_int) @ ft) @ (ftimes_times_int @ (fplus_plus_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ fm) @ fone_one_int) @ fzero_zero_int)), file('', pax341)). 19.98/20.09 fof(ax124, axiom, p300, file('', ax124)). 19.98/20.09 fof(ax223, axiom, p201, file('', ax223)). 19.98/20.09 fof(ax83, axiom, p341, file('', ax83)). 19.98/20.09 tff(c_0_24, plain, ![X859:int]:(~p59|(fbit0 @ X859)=(fplus_plus_int @ X859 @ X859)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax59])])])). 19.98/20.09 tff(c_0_25, plain, ![X207:int, X208:int]:(~p326|(ftimes_times_int @ (fbit0 @ X207) @ X208)=(fbit0 @ (ftimes_times_int @ X207 @ X208))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax326])])])). 19.98/20.09 tff(c_0_26, plain, ![X401:int]:(~p240|(ftimes_times_int @ fone_one_int @ X401)=(X401)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax240])])])). 19.98/20.09 tff(c_0_27, plain, ![X557:int, X558:int]:(~p194|(fplus_plus_int @ X557 @ X558)=(fplus_plus_int @ X558 @ X557)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax194])])])). 19.98/20.09 tff(c_0_28, plain, (~p216|(fpls)=(fzero_zero_int)), inference(fof_nnf,[status(thm)],[pax216])). 19.98/20.09 tff(c_0_29, plain, ![X705:int]:(~p115|(ftimes_times_int @ (fplus_plus_int @ fone_one_int @ fone_one_int) @ (fnumber_number_of_int @ X705))=(fnumber_number_of_int @ (fbit0 @ X705))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax115])])])). 19.98/20.09 thf(c_0_30, plain, ![X1:int]:((fbit0 @ X1)=(fplus_plus_int @ X1 @ X1)|~p59), inference(split_conjunct,[status(thm)],[c_0_24])). 19.98/20.09 thf(c_0_31, plain, (p59), inference(split_conjunct,[status(thm)],[ax365])). 19.98/20.09 thf(c_0_32, plain, ![X2:int, X1:int]:((ftimes_times_int @ (fbit0 @ X1) @ X2)=(fbit0 @ (ftimes_times_int @ X1 @ X2))|~p326), inference(split_conjunct,[status(thm)],[c_0_25])). 19.98/20.09 thf(c_0_33, plain, (p326), inference(split_conjunct,[status(thm)],[ax98])). 19.98/20.09 thf(c_0_34, plain, ![X1:int]:((ftimes_times_int @ fone_one_int @ X1)=(X1)|~p240), inference(split_conjunct,[status(thm)],[c_0_26])). 19.98/20.09 thf(c_0_35, plain, (p240), inference(split_conjunct,[status(thm)],[ax184])). 19.98/20.09 tff(c_0_36, plain, (~p44|(fone_one_int)=(fnumber_number_of_int @ (fbit1 @ fpls))), inference(fof_nnf,[status(thm)],[pax44])). 19.98/20.09 tff(c_0_37, plain, ![X319:int]:(~p274|(ftimes_times_int @ X319 @ X319)=(fpower_power_int @ X319 @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax274])])])). 19.98/20.09 tff(c_0_38, plain, (~ford_less_int @ (fplus_plus_int @ (fpower_power_int @ fs @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls)))) @ fone_one_int) @ fzero_zero_int|p206), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax206])])). 19.98/20.09 thf(c_0_39, plain, ![X2:int, X1:int]:((fplus_plus_int @ X1 @ X2)=(fplus_plus_int @ X2 @ X1)|~p194), inference(split_conjunct,[status(thm)],[c_0_27])). 19.98/20.09 thf(c_0_40, plain, (p194), inference(split_conjunct,[status(thm)],[ax230])). 19.98/20.09 thf(c_0_41, plain, ((fpls)=(fzero_zero_int)|~p216), inference(split_conjunct,[status(thm)],[c_0_28])). 19.98/20.09 thf(c_0_42, plain, (p216), inference(split_conjunct,[status(thm)],[ax208])). 19.98/20.09 fof(c_0_43, plain, ~p206, inference(fof_simplification,[status(thm)],[ax218])). 19.98/20.09 tff(c_0_44, plain, (~p300|(fplus_plus_int @ (fpower_power_int @ fs @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls)))) @ fone_one_int)=(ftimes_times_int @ (fplus_plus_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ fm) @ fone_one_int) @ ft)), inference(fof_nnf,[status(thm)],[pax300])). 19.98/20.09 thf(c_0_45, plain, ![X1:int]:((ftimes_times_int @ (fplus_plus_int @ fone_one_int @ fone_one_int) @ (fnumber_number_of_int @ X1))=(fnumber_number_of_int @ (fbit0 @ X1))|~p115), inference(split_conjunct,[status(thm)],[c_0_29])). 19.98/20.09 thf(c_0_46, plain, ![X1:int]:(fplus_plus_int @ X1 @ X1)=(fbit0 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30, c_0_31])])). 19.98/20.09 thf(c_0_47, plain, ![X2:int, X1:int]:(ftimes_times_int @ (fbit0 @ X1) @ X2)=(fbit0 @ (ftimes_times_int @ X1 @ X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32, c_0_33])])). 19.98/20.09 thf(c_0_48, plain, ![X1:int]:(ftimes_times_int @ fone_one_int @ X1)=(X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34, c_0_35])])). 19.98/20.09 thf(c_0_49, plain, (p115), inference(split_conjunct,[status(thm)],[ax309])). 19.98/20.09 thf(c_0_50, plain, ((fone_one_int)=(fnumber_number_of_int @ (fbit1 @ fpls))|~p44), inference(split_conjunct,[status(thm)],[c_0_36])). 19.98/20.09 thf(c_0_51, plain, (p44), inference(split_conjunct,[status(thm)],[ax380])). 19.98/20.09 thf(c_0_52, plain, ![X1:int]:((ftimes_times_int @ X1 @ X1)=(fpower_power_int @ X1 @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls))))|~p274), inference(split_conjunct,[status(thm)],[c_0_37])). 19.98/20.09 thf(c_0_53, plain, (p274), inference(split_conjunct,[status(thm)],[ax150])). 19.98/20.09 tff(c_0_54, plain, ![X523:int]:(~p201|(ftimes_times_int @ X523 @ fzero_zero_int)=(fzero_zero_int)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax201])])])). 19.98/20.09 thf(c_0_55, plain, (p206|~ford_less_int @ (fplus_plus_int @ (fpower_power_int @ fs @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls)))) @ fone_one_int) @ fzero_zero_int), inference(split_conjunct,[status(thm)],[c_0_38])). 19.98/20.09 thf(c_0_56, plain, ![X2:int, X1:int]:(fplus_plus_int @ X1 @ X2)=(fplus_plus_int @ X2 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_40])])). 19.98/20.09 thf(c_0_57, plain, (fzero_zero_int)=(fpls), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_42])])). 19.98/20.09 thf(c_0_58, plain, (~p206), inference(split_conjunct,[status(thm)],[c_0_43])). 19.98/20.09 tff(c_0_59, plain, (~p341|ford_less_int @ (ftimes_times_int @ (fplus_plus_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ fm) @ fone_one_int) @ ft) @ (ftimes_times_int @ (fplus_plus_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ fm) @ fone_one_int) @ fzero_zero_int)), inference(fof_nnf,[status(thm)],[pax341])). 19.98/20.09 thf(c_0_60, plain, ((fplus_plus_int @ (fpower_power_int @ fs @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls)))) @ fone_one_int)=(ftimes_times_int @ (fplus_plus_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ fm) @ fone_one_int) @ ft)|~p300), inference(split_conjunct,[status(thm)],[c_0_44])). 19.98/20.09 thf(c_0_61, plain, ![X1:int]:(fnumber_number_of_int @ (fbit0 @ X1))=(fbit0 @ (fnumber_number_of_int @ X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_46]), c_0_47]), c_0_48]), c_0_49])])). 19.98/20.09 thf(c_0_62, plain, (fnumber_number_of_int @ (fbit1 @ fpls))=(fone_one_int), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50, c_0_51])])). 19.98/20.09 thf(c_0_63, plain, ![X1:int]:(ftimes_times_int @ X1 @ X1)=(fpower_power_int @ X1 @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52, c_0_53])])). 19.98/20.09 thf(c_0_64, plain, (p300), inference(split_conjunct,[status(thm)],[ax124])). 19.98/20.09 thf(c_0_65, plain, ![X1:int]:((ftimes_times_int @ X1 @ fzero_zero_int)=(fzero_zero_int)|~p201), inference(split_conjunct,[status(thm)],[c_0_54])). 19.98/20.09 thf(c_0_66, plain, (p201), inference(split_conjunct,[status(thm)],[ax223])). 19.98/20.09 thf(c_0_67, plain, ~ford_less_int @ (fplus_plus_int @ fone_one_int @ (fpower_power_int @ fs @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls))))) @ fpls, inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55, c_0_56]), c_0_57]), c_0_58])). 19.98/20.09 thf(c_0_68, plain, (ford_less_int @ (ftimes_times_int @ (fplus_plus_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ fm) @ fone_one_int) @ ft) @ (ftimes_times_int @ (fplus_plus_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ fm) @ fone_one_int) @ fzero_zero_int)|~p341), inference(split_conjunct,[status(thm)],[c_0_59])). 19.98/20.09 thf(c_0_69, plain, (ftimes_times_int @ (fplus_plus_int @ fone_one_int @ (fbit0 @ (fbit0 @ fm))) @ ft)=(fplus_plus_int @ fone_one_int @ (ftimes_times_int @ fs @ fs)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60, c_0_61]), c_0_61]), c_0_62]), c_0_47]), c_0_47]), c_0_48]), c_0_56]), c_0_56]), c_0_63]), c_0_64])])). 19.98/20.09 thf(c_0_70, plain, ![X1:int]:(ftimes_times_int @ X1 @ fpls)=(fpls), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65, c_0_57]), c_0_57]), c_0_66])])). 19.98/20.09 thf(c_0_71, plain, (p341), inference(split_conjunct,[status(thm)],[ax83])). 19.98/20.09 thf(c_0_72, plain, ~ford_less_int @ (fplus_plus_int @ fone_one_int @ (ftimes_times_int @ fs @ fs)) @ fpls, inference(rw,[status(thm)],[c_0_67, c_0_63])). 19.98/20.09 thf(c_0_73, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68, c_0_61]), c_0_61]), c_0_62]), c_0_47]), c_0_47]), c_0_48]), c_0_56]), c_0_69]), c_0_61]), c_0_61]), c_0_62]), c_0_47]), c_0_47]), c_0_48]), c_0_56]), c_0_57]), c_0_70]), c_0_71])]), c_0_72]), ['proof']). 19.98/20.09 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h15,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h4,h3,h1,h0])],[])). 19.98/20.09 thf(fact_444__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_,axiom,(~((![X1:int]:(~((((zcong @ ((power_power_int @ X1) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ (number_number_of_int @ min)) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)))))))). 19.98/20.09 thf(2,plain,$false,inference(tab_negall,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h4,h3,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__2)],[fact_444__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_,1,h15])). 19.98/20.09 thf(3,plain,$false,inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h4,h3,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,2,h13,h14])). 19.98/20.09 thf(fact_272_s0p,axiom,(~(((~(((((zcong @ s1) @ s) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)) => (~(((ord_less_int @ s) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~(((ord_less_eq_int @ zero_zero_int) @ s))))))). 19.98/20.09 thf(4,plain,$false,inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h4,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[fact_272_s0p,3,h11,h12])). 19.98/20.09 thf(5,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h4,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,4,h9,h10])). 19.98/20.09 thf(6,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,5,h7,h8])). 19.98/20.09 thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,6,h5,h6])). 19.98/20.09 thf(fact_282__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1,axiom,(~((![X1:int]:((~(((~(((![X2:int]:((~(((~((((ord_less_eq_int @ zero_zero_int) @ X2) => (~((((zcong @ s1) @ X2) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~(((ord_less_int @ X2) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (X2 = X1))) => (~((((zcong @ s1) @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~(((ord_less_int @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~(((ord_less_eq_int @ zero_zero_int) @ X1)))))))). 19.98/20.09 thf(8,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[fact_282__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1,7,h4])). 19.98/20.09 thf(fact_30__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_,axiom,(~((![X1:int]:(~((((plus_plus_int @ ((power_power_int @ s) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ one_one_int) = ((times_times_int @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)) @ X1)))))))). 19.98/20.09 thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[fact_30__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_,8,h3])). 19.98/20.09 thf(h16,assumption,(((plus_plus_int @ ((power_power_int @ s) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ one_one_int) = ((times_times_int @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)) @ eigen__3)),introduced(assumption,[])). 19.98/20.09 thf(h17,assumption,(~(((~(((~(((![X1:int]:((~(((~((((ord_less_eq_int @ zero_zero_int) @ X1) => (~((((zcong @ s1) @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~(((ord_less_int @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (X1 = eigen__4))) => (~((((zcong @ s1) @ eigen__4) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~(((ord_less_int @ eigen__4) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~(((ord_less_eq_int @ zero_zero_int) @ eigen__4)))))),introduced(assumption,[])). 19.98/20.09 thf(h18,assumption,(~(((~(((![X1:int]:((~(((~((((ord_less_eq_int @ zero_zero_int) @ X1) => (~((((zcong @ s1) @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~(((ord_less_int @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (X1 = eigen__4))) => (~((((zcong @ s1) @ eigen__4) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~(((ord_less_int @ eigen__4) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))),introduced(assumption,[])). 19.98/20.09 thf(h19,assumption,((ord_less_eq_int @ zero_zero_int) @ eigen__4),introduced(assumption,[])). 19.98/20.09 thf(h20,assumption,(~(((![X1:int]:((~(((~((((ord_less_eq_int @ zero_zero_int) @ X1) => (~((((zcong @ s1) @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~(((ord_less_int @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (X1 = eigen__4))) => (~((((zcong @ s1) @ eigen__4) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))),introduced(assumption,[])). 19.98/20.09 thf(h21,assumption,((ord_less_int @ eigen__4) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)),introduced(assumption,[])). 19.98/20.09 thf(h22,assumption,(![X1:int]:((~(((~((((ord_less_eq_int @ zero_zero_int) @ X1) => (~((((zcong @ s1) @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~(((ord_less_int @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (X1 = eigen__4))),introduced(assumption,[])). 19.98/20.09 thf(h23,assumption,(((zcong @ s1) @ eigen__4) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)),introduced(assumption,[])). 19.98/20.09 thf(h24,assumption,(((zcong @ ((power_power_int @ eigen__5) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ (number_number_of_int @ min)) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)),introduced(assumption,[])). 19.98/20.09 tff(pax59, axiom, (p59=>![X126:int]:(fbit0 @ X126)=(fplus_plus_int @ X126 @ X126)), file('', pax59)). 19.98/20.09 tff(pax326, axiom, (p326=>![X13:int, X5:int]:(ftimes_times_int @ (fbit0 @ X13) @ X5)=(fbit0 @ (ftimes_times_int @ X13 @ X5))), file('', pax326)). 19.98/20.09 tff(pax240, axiom, (p240=>![X49:int]:(ftimes_times_int @ fone_one_int @ X49)=(X49)), file('', pax240)). 19.98/20.09 tff(pax194, axiom, (p194=>![X74:int, X75:int]:(fplus_plus_int @ X74 @ X75)=(fplus_plus_int @ X75 @ X74)), file('', pax194)). 19.98/20.09 tff(pax274, axiom, (p274=>![X33:int]:(ftimes_times_int @ X33 @ X33)=(fpower_power_int @ X33 @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls))))), file('', pax274)). 19.98/20.09 tff(pax216, axiom, (p216=>(fpls)=(fzero_zero_int)), file('', pax216)). 19.98/20.09 tff(pax115, axiom, (p115=>![X101:int]:(ftimes_times_int @ (fplus_plus_int @ fone_one_int @ fone_one_int) @ (fnumber_number_of_int @ X101))=(fnumber_number_of_int @ (fbit0 @ X101))), file('', pax115)). 19.98/20.09 fof(ax377, axiom, p59, file('', ax377)). 19.98/20.09 fof(ax110, axiom, p326, file('', ax110)). 19.98/20.09 fof(ax196, axiom, p240, file('', ax196)). 19.98/20.09 tff(pax44, axiom, (p44=>(fone_one_int)=(fnumber_number_of_int @ (fbit1 @ fpls))), file('', pax44)). 19.98/20.09 tff(pax432, axiom, (p432=>(fplus_plus_int @ (fpower_power_int @ fs @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls)))) @ fone_one_int)=(fzero_zero_int)), file('', pax432)). 19.98/20.09 fof(ax242, axiom, p194, file('', ax242)). 19.98/20.09 fof(ax162, axiom, p274, file('', ax162)). 19.98/20.09 fof(ax220, axiom, p216, file('', ax220)). 19.98/20.09 tff(pax300, axiom, (p300=>(fplus_plus_int @ (fpower_power_int @ fs @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls)))) @ fone_one_int)=(ftimes_times_int @ (fplus_plus_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ fm) @ fone_one_int) @ ft)), file('', pax300)). 19.98/20.09 fof(ax321, axiom, p115, file('', ax321)). 19.98/20.09 fof(ax392, axiom, p44, file('', ax392)). 19.98/20.09 fof(ax111, axiom, p432, file('', ax111)). 19.98/20.09 tff(pax201, axiom, (p201=>![X67:int]:(ftimes_times_int @ X67 @ fzero_zero_int)=(fzero_zero_int)), file('', pax201)). 19.98/20.09 tff(nax26, axiom, (p26<=ford_less_int @ fpls @ fzero_zero_int), file('', nax26)). 19.98/20.09 fof(ax410, axiom, ~(p26), file('', ax410)). 19.98/20.09 tff(pax341, axiom, (p341=>ford_less_int @ (ftimes_times_int @ (fplus_plus_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ fm) @ fone_one_int) @ ft) @ (ftimes_times_int @ (fplus_plus_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ fm) @ fone_one_int) @ fzero_zero_int)), file('', pax341)). 19.98/20.09 fof(ax136, axiom, p300, file('', ax136)). 19.98/20.09 fof(ax235, axiom, p201, file('', ax235)). 19.98/20.09 fof(ax95, axiom, p341, file('', ax95)). 19.98/20.09 tff(c_0_26, plain, ![X867:int]:(~p59|(fbit0 @ X867)=(fplus_plus_int @ X867 @ X867)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax59])])])). 19.98/20.09 tff(c_0_27, plain, ![X215:int, X216:int]:(~p326|(ftimes_times_int @ (fbit0 @ X215) @ X216)=(fbit0 @ (ftimes_times_int @ X215 @ X216))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax326])])])). 19.98/20.09 tff(c_0_28, plain, ![X409:int]:(~p240|(ftimes_times_int @ fone_one_int @ X409)=(X409)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax240])])])). 19.98/20.09 tff(c_0_29, plain, ![X565:int, X566:int]:(~p194|(fplus_plus_int @ X565 @ X566)=(fplus_plus_int @ X566 @ X565)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax194])])])). 19.98/20.09 tff(c_0_30, plain, ![X327:int]:(~p274|(ftimes_times_int @ X327 @ X327)=(fpower_power_int @ X327 @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax274])])])). 19.98/20.09 tff(c_0_31, plain, (~p216|(fpls)=(fzero_zero_int)), inference(fof_nnf,[status(thm)],[pax216])). 19.98/20.09 tff(c_0_32, plain, ![X713:int]:(~p115|(ftimes_times_int @ (fplus_plus_int @ fone_one_int @ fone_one_int) @ (fnumber_number_of_int @ X713))=(fnumber_number_of_int @ (fbit0 @ X713))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax115])])])). 19.98/20.09 thf(c_0_33, plain, ![X1:int]:((fbit0 @ X1)=(fplus_plus_int @ X1 @ X1)|~p59), inference(split_conjunct,[status(thm)],[c_0_26])). 19.98/20.09 thf(c_0_34, plain, (p59), inference(split_conjunct,[status(thm)],[ax377])). 19.98/20.09 thf(c_0_35, plain, ![X2:int, X1:int]:((ftimes_times_int @ (fbit0 @ X1) @ X2)=(fbit0 @ (ftimes_times_int @ X1 @ X2))|~p326), inference(split_conjunct,[status(thm)],[c_0_27])). 19.98/20.09 thf(c_0_36, plain, (p326), inference(split_conjunct,[status(thm)],[ax110])). 19.98/20.09 thf(c_0_37, plain, ![X1:int]:((ftimes_times_int @ fone_one_int @ X1)=(X1)|~p240), inference(split_conjunct,[status(thm)],[c_0_28])). 19.98/20.09 thf(c_0_38, plain, (p240), inference(split_conjunct,[status(thm)],[ax196])). 19.98/20.09 tff(c_0_39, plain, (~p44|(fone_one_int)=(fnumber_number_of_int @ (fbit1 @ fpls))), inference(fof_nnf,[status(thm)],[pax44])). 19.98/20.09 tff(c_0_40, plain, (~p432|(fplus_plus_int @ (fpower_power_int @ fs @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls)))) @ fone_one_int)=(fzero_zero_int)), inference(fof_nnf,[status(thm)],[pax432])). 19.98/20.09 thf(c_0_41, plain, ![X2:int, X1:int]:((fplus_plus_int @ X1 @ X2)=(fplus_plus_int @ X2 @ X1)|~p194), inference(split_conjunct,[status(thm)],[c_0_29])). 19.98/20.09 thf(c_0_42, plain, (p194), inference(split_conjunct,[status(thm)],[ax242])). 19.98/20.09 thf(c_0_43, plain, ![X1:int]:((ftimes_times_int @ X1 @ X1)=(fpower_power_int @ X1 @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls))))|~p274), inference(split_conjunct,[status(thm)],[c_0_30])). 19.98/20.09 thf(c_0_44, plain, (p274), inference(split_conjunct,[status(thm)],[ax162])). 19.98/20.09 thf(c_0_45, plain, ((fpls)=(fzero_zero_int)|~p216), inference(split_conjunct,[status(thm)],[c_0_31])). 19.98/20.09 thf(c_0_46, plain, (p216), inference(split_conjunct,[status(thm)],[ax220])). 19.98/20.09 tff(c_0_47, plain, (~p300|(fplus_plus_int @ (fpower_power_int @ fs @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls)))) @ fone_one_int)=(ftimes_times_int @ (fplus_plus_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ fm) @ fone_one_int) @ ft)), inference(fof_nnf,[status(thm)],[pax300])). 19.98/20.09 thf(c_0_48, plain, ![X1:int]:((ftimes_times_int @ (fplus_plus_int @ fone_one_int @ fone_one_int) @ (fnumber_number_of_int @ X1))=(fnumber_number_of_int @ (fbit0 @ X1))|~p115), inference(split_conjunct,[status(thm)],[c_0_32])). 19.98/20.09 thf(c_0_49, plain, ![X1:int]:(fplus_plus_int @ X1 @ X1)=(fbit0 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33, c_0_34])])). 19.98/20.09 thf(c_0_50, plain, ![X2:int, X1:int]:(ftimes_times_int @ (fbit0 @ X1) @ X2)=(fbit0 @ (ftimes_times_int @ X1 @ X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35, c_0_36])])). 19.98/20.09 thf(c_0_51, plain, ![X1:int]:(ftimes_times_int @ fone_one_int @ X1)=(X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37, c_0_38])])). 19.98/20.09 thf(c_0_52, plain, (p115), inference(split_conjunct,[status(thm)],[ax321])). 19.98/20.09 thf(c_0_53, plain, ((fone_one_int)=(fnumber_number_of_int @ (fbit1 @ fpls))|~p44), inference(split_conjunct,[status(thm)],[c_0_39])). 19.98/20.09 thf(c_0_54, plain, (p44), inference(split_conjunct,[status(thm)],[ax392])). 19.98/20.09 thf(c_0_55, plain, ((fplus_plus_int @ (fpower_power_int @ fs @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls)))) @ fone_one_int)=(fzero_zero_int)|~p432), inference(split_conjunct,[status(thm)],[c_0_40])). 19.98/20.09 thf(c_0_56, plain, ![X2:int, X1:int]:(fplus_plus_int @ X1 @ X2)=(fplus_plus_int @ X2 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_42])])). 19.98/20.09 thf(c_0_57, plain, ![X1:int]:(ftimes_times_int @ X1 @ X1)=(fpower_power_int @ X1 @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43, c_0_44])])). 19.98/20.09 thf(c_0_58, plain, (fzero_zero_int)=(fpls), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_46])])). 19.98/20.09 thf(c_0_59, plain, (p432), inference(split_conjunct,[status(thm)],[ax111])). 19.98/20.09 tff(c_0_60, plain, ![X531:int]:(~p201|(ftimes_times_int @ X531 @ fzero_zero_int)=(fzero_zero_int)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax201])])])). 19.98/20.09 tff(c_0_61, plain, (~ford_less_int @ fpls @ fzero_zero_int|p26), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax26])])). 19.98/20.09 fof(c_0_62, plain, ~p26, inference(fof_simplification,[status(thm)],[ax410])). 19.98/20.09 tff(c_0_63, plain, (~p341|ford_less_int @ (ftimes_times_int @ (fplus_plus_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ fm) @ fone_one_int) @ ft) @ (ftimes_times_int @ (fplus_plus_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ fm) @ fone_one_int) @ fzero_zero_int)), inference(fof_nnf,[status(thm)],[pax341])). 19.98/20.09 thf(c_0_64, plain, ((fplus_plus_int @ (fpower_power_int @ fs @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls)))) @ fone_one_int)=(ftimes_times_int @ (fplus_plus_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ fm) @ fone_one_int) @ ft)|~p300), inference(split_conjunct,[status(thm)],[c_0_47])). 19.98/20.09 thf(c_0_65, plain, ![X1:int]:(fnumber_number_of_int @ (fbit0 @ X1))=(fbit0 @ (fnumber_number_of_int @ X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48, c_0_49]), c_0_50]), c_0_51]), c_0_52])])). 19.98/20.09 thf(c_0_66, plain, (fnumber_number_of_int @ (fbit1 @ fpls))=(fone_one_int), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53, c_0_54])])). 19.98/20.09 thf(c_0_67, plain, (fplus_plus_int @ fone_one_int @ (ftimes_times_int @ fs @ fs))=(fpls), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55, c_0_56]), c_0_57]), c_0_58]), c_0_59])])). 19.98/20.09 thf(c_0_68, plain, (p300), inference(split_conjunct,[status(thm)],[ax136])). 19.98/20.09 thf(c_0_69, plain, ![X1:int]:((ftimes_times_int @ X1 @ fzero_zero_int)=(fzero_zero_int)|~p201), inference(split_conjunct,[status(thm)],[c_0_60])). 19.98/20.09 thf(c_0_70, plain, (p201), inference(split_conjunct,[status(thm)],[ax235])). 19.98/20.09 thf(c_0_71, plain, (p26|~ford_less_int @ fpls @ fzero_zero_int), inference(split_conjunct,[status(thm)],[c_0_61])). 19.98/20.09 thf(c_0_72, plain, (~p26), inference(split_conjunct,[status(thm)],[c_0_62])). 19.98/20.09 thf(c_0_73, plain, (ford_less_int @ (ftimes_times_int @ (fplus_plus_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ fm) @ fone_one_int) @ ft) @ (ftimes_times_int @ (fplus_plus_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ fm) @ fone_one_int) @ fzero_zero_int)|~p341), inference(split_conjunct,[status(thm)],[c_0_63])). 19.98/20.09 thf(c_0_74, plain, (ftimes_times_int @ (fplus_plus_int @ fone_one_int @ (fbit0 @ (fbit0 @ fm))) @ ft)=(fpls), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64, c_0_65]), c_0_65]), c_0_66]), c_0_50]), c_0_50]), c_0_51]), c_0_56]), c_0_56]), c_0_57]), c_0_67]), c_0_68])])). 19.98/20.09 thf(c_0_75, plain, ![X1:int]:(ftimes_times_int @ X1 @ fpls)=(fpls), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69, c_0_58]), c_0_58]), c_0_70])])). 19.98/20.09 thf(c_0_76, plain, (p341), inference(split_conjunct,[status(thm)],[ax95])). 19.98/20.09 thf(c_0_77, plain, ~ford_less_int @ fpls @ fpls, inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_71, c_0_58]), c_0_72])). 19.98/20.09 thf(c_0_78, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73, c_0_65]), c_0_65]), c_0_66]), c_0_50]), c_0_50]), c_0_51]), c_0_56]), c_0_74]), c_0_65]), c_0_65]), c_0_66]), c_0_50]), c_0_50]), c_0_51]), c_0_56]), c_0_58]), c_0_75]), c_0_76])]), c_0_77]), ['proof']). 19.98/20.09 thf(10,plain,$false,inference(eprover,[status(thm),assumptions([h24,h13,h14,h11,h12,h22,h23,h20,h21,h18,h19,h17,h16,h2,h0])],[])). 19.98/20.09 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h13,h14,h11,h12,h22,h23,h20,h21,h18,h19,h17,h16,h2,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__5)],[fact_444__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_,10,h24])). 19.98/20.09 thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h11,h12,h22,h23,h20,h21,h18,h19,h17,h16,h2,h0]),tab_negimp(discharge,[h13,h14])],[h11,11,h13,h14])). 19.98/20.09 thf(13,plain,$false,inference(tab_negimp,[status(thm),assumptions([h22,h23,h20,h21,h18,h19,h17,h16,h2,h0]),tab_negimp(discharge,[h11,h12])],[fact_272_s0p,12,h11,h12])). 19.98/20.09 thf(14,plain,$false,inference(tab_negimp,[status(thm),assumptions([h20,h21,h18,h19,h17,h16,h2,h0]),tab_negimp(discharge,[h22,h23])],[h20,13,h22,h23])). 19.98/20.09 thf(15,plain,$false,inference(tab_negimp,[status(thm),assumptions([h18,h19,h17,h16,h2,h0]),tab_negimp(discharge,[h20,h21])],[h18,14,h20,h21])). 19.98/20.09 thf(16,plain,$false,inference(tab_negimp,[status(thm),assumptions([h17,h16,h2,h0]),tab_negimp(discharge,[h18,h19])],[h17,15,h18,h19])). 19.98/20.09 thf(17,plain,$false,inference(tab_negall,[status(thm),assumptions([h16,h2,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__4)],[fact_282__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1,16,h17])). 19.98/20.09 thf(18,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__3)],[fact_30__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_,17,h16])). 19.98/20.09 thf(fact_4_calculation_I2_J,axiom,((t = zero_zero_int) => (((plus_plus_int @ ((power_power_int @ s) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ one_one_int) = zero_zero_int))). 19.98/20.09 thf(19,plain,$false,inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_4_calculation_I2_J,9,18,h1,h2])). 19.98/20.09 thf(0,theorem,((ord_less_int @ ((plus_plus_int @ ((power_power_int @ s) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ one_one_int)) @ zero_zero_int),inference(contra,[status(thm),contra(discharge,[h0])],[19,h0])). 19.98/20.09 % SZS output end Proof 20.01/20.09 EOF