%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : NUM924^2 : TPTP v8.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n027.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  : 600s
% DateTime : Mon Jul 18 13:57:36 EDT 2022

% Result   : Theorem 6.95s 7.17s
% Output   : Proof 6.95s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUM924^2 : TPTP v8.1.0. Released v5.3.0.
% 0.11/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n027.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34  % CPULimit : 300
% 0.18/0.34  % WCLimit  : 600
% 0.18/0.34  % DateTime : Thu Jul  7 06:28:29 EDT 2022
% 0.18/0.34  % CPUTime  : 
% 6.95/7.17  % SZS status Theorem
% 6.95/7.17  % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 6.95/7.17  % Inferences: 0
% 6.95/7.17  % SZS output start Proof
% 6.95/7.17  thf(ty_int, type, int : $tType).
% 6.95/7.17  thf(ty_nat, type, nat : $tType).
% 6.95/7.17  thf(ty_eigen__2, type, eigen__2 : int).
% 6.95/7.17  thf(ty_s, type, s : int).
% 6.95/7.17  thf(ty_eigen__1, type, eigen__1 : int).
% 6.95/7.17  thf(ty_eigen__0, type, eigen__0 : int).
% 6.95/7.17  thf(ty_bit1, type, bit1 : (int>int)).
% 6.95/7.17  thf(ty_bit0, type, bit0 : (int>int)).
% 6.95/7.17  thf(ty_zcong, type, zcong : (int>int>int>$o)).
% 6.95/7.17  thf(ty_times_times_int, type, times_times_int : (int>int>int)).
% 6.95/7.17  thf(ty_eigen__3, type, eigen__3 : int).
% 6.95/7.17  thf(ty_ord_less_eq_int, type, ord_less_eq_int : (int>int>$o)).
% 6.95/7.17  thf(ty_min, type, min : int).
% 6.95/7.17  thf(ty_t, type, t : int).
% 6.95/7.17  thf(ty_zero_zero_int, type, zero_zero_int : int).
% 6.95/7.17  thf(ty_one_one_int, type, one_one_int : int).
% 6.95/7.17  thf(ty_pls, type, pls : int).
% 6.95/7.17  thf(ty_power_power_int, type, power_power_int : (int>nat>int)).
% 6.95/7.17  thf(ty_plus_plus_int, type, plus_plus_int : (int>int>int)).
% 6.95/7.17  thf(ty_ord_less_int, type, ord_less_int : (int>int>$o)).
% 6.95/7.17  thf(ty_number_number_of_int, type, number_number_of_int : (int>int)).
% 6.95/7.17  thf(ty_s1, type, s1 : int).
% 6.95/7.17  thf(ty_m, type, m : int).
% 6.95/7.17  thf(ty_number_number_of_nat, type, number_number_of_nat : (int>nat)).
% 6.95/7.17  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)).
% 6.95/7.17  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])).
% 6.95/7.17  thf(h1,assumption,(((zcong @ ((power_power_int @ eigen__0) @ (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,[])).
% 6.95/7.17  thf(h2,assumption,(~(((~((((ord_less_eq_int @ zero_zero_int) @ eigen__1) => (~(((ord_less_int @ eigen__1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~((((zcong @ s1) @ eigen__1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))),introduced(assumption,[])).
% 6.95/7.17  thf(h3,assumption,(~((((ord_less_eq_int @ zero_zero_int) @ eigen__1) => (~(((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,[])).
% 6.95/7.17  thf(h4,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,[])).
% 6.95/7.17  thf(h5,assumption,((ord_less_eq_int @ zero_zero_int) @ eigen__1),introduced(assumption,[])).
% 6.95/7.17  thf(h6,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,[])).
% 6.95/7.17  thf(h7,assumption,(~(((~(((~((((ord_less_eq_int @ zero_zero_int) @ eigen__2) => (~(((ord_less_int @ eigen__2) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~((((zcong @ s1) @ eigen__2) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~((![X1:int]:((~(((~((((ord_less_eq_int @ zero_zero_int) @ X1) => (~(((ord_less_int @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~((((zcong @ s1) @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (X1 = eigen__2)))))))),introduced(assumption,[])).
% 6.95/7.17  thf(h8,assumption,(~(((~((((ord_less_eq_int @ zero_zero_int) @ eigen__2) => (~(((ord_less_int @ eigen__2) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~((((zcong @ s1) @ eigen__2) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))),introduced(assumption,[])).
% 6.95/7.17  thf(h9,assumption,(![X1:int]:((~(((~((((ord_less_eq_int @ zero_zero_int) @ X1) => (~(((ord_less_int @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~((((zcong @ s1) @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (X1 = eigen__2))),introduced(assumption,[])).
% 6.95/7.17  thf(h10,assumption,(~((((ord_less_eq_int @ zero_zero_int) @ eigen__2) => (~(((ord_less_int @ eigen__2) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))),introduced(assumption,[])).
% 6.95/7.17  thf(h11,assumption,(((zcong @ s1) @ eigen__2) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)),introduced(assumption,[])).
% 6.95/7.17  thf(h12,assumption,((ord_less_eq_int @ zero_zero_int) @ eigen__2),introduced(assumption,[])).
% 6.95/7.17  thf(h13,assumption,((ord_less_int @ eigen__2) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)),introduced(assumption,[])).
% 6.95/7.17  thf(h14,assumption,(~((((ord_less_eq_int @ zero_zero_int) @ s) => (~(((ord_less_int @ s) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))),introduced(assumption,[])).
% 6.95/7.17  thf(h15,assumption,(((zcong @ s1) @ s) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)),introduced(assumption,[])).
% 6.95/7.17  thf(h16,assumption,((ord_less_eq_int @ zero_zero_int) @ s),introduced(assumption,[])).
% 6.95/7.17  thf(h17,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,[])).
% 6.95/7.17  thf(h18,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,[])).
% 6.95/7.17  thf(h19,assumption,(~((t = zero_zero_int))),introduced(assumption,[])).
% 6.95/7.17  thf(h20,assumption,(((plus_plus_int @ ((power_power_int @ s) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ one_one_int) = zero_zero_int),introduced(assumption,[])).
% 6.95/7.17  thf(pax84, axiom, (p84=>![X50:int, X51:int]:(fplus_plus_int @ X50 @ X51)=(fplus_plus_int @ X51 @ X50)), file('<stdin>', pax84)).
% 6.95/7.17  thf(pax137, axiom, (p137=>![X26:int]:(fpower_power_int @ X26 @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls))))=(ftimes_times_int @ X26 @ X26)), file('<stdin>', pax137)).
% 6.95/7.17  thf(pax112, axiom, (p112=>(fpls)=(fzero_zero_int)), file('<stdin>', pax112)).
% 6.95/7.17  thf(pax2, axiom, (p2=>(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('<stdin>', pax2)).
% 6.95/7.17  thf(ax142, axiom, p84, file('<stdin>', ax142)).
% 6.95/7.17  thf(ax89, axiom, p137, file('<stdin>', ax89)).
% 6.95/7.17  thf(pax214, axiom, (p214=>![X1:int]:(ftimes_times_int @ X1 @ fzero_zero_int)=(fzero_zero_int)), file('<stdin>', pax214)).
% 6.95/7.17  thf(ax114, axiom, p112, file('<stdin>', ax114)).
% 6.95/7.17  thf(pax96, axiom, (p96=>![X45:int, X27:int]:~(ford_less_int @ (fplus_plus_int @ (ftimes_times_int @ X45 @ X45) @ (ftimes_times_int @ X27 @ X27)) @ fzero_zero_int)), file('<stdin>', pax96)).
% 6.95/7.17  thf(pax53, axiom, (p53=>![X58:int]:(ftimes_times_int @ X58 @ fone_one_int)=(X58)), file('<stdin>', pax53)).
% 6.95/7.17  thf(pax1, axiom, (p1=>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('<stdin>', pax1)).
% 6.95/7.17  thf(ax224, axiom, p2, file('<stdin>', ax224)).
% 6.95/7.17  thf(ax12, axiom, p214, file('<stdin>', ax12)).
% 6.95/7.17  thf(ax130, axiom, p96, file('<stdin>', ax130)).
% 6.95/7.17  thf(ax173, axiom, p53, file('<stdin>', ax173)).
% 6.95/7.17  thf(ax225, axiom, p1, file('<stdin>', ax225)).
% 6.95/7.17  thf(c_0_16, plain, ![X383:int, X384:int]:(~p84|(fplus_plus_int @ X383 @ X384)=(fplus_plus_int @ X384 @ X383)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax84])])])).
% 6.95/7.17  thf(c_0_17, plain, ![X275:int]:(~p137|(fpower_power_int @ X275 @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls))))=(ftimes_times_int @ X275 @ X275)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax137])])])).
% 6.95/7.17  thf(c_0_18, plain, (~p112|(fpls)=(fzero_zero_int)), inference(fof_nnf,[status(thm)],[pax112])).
% 6.95/7.17  thf(c_0_19, plain, (~p2|(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)],[pax2])).
% 6.95/7.18  thf(c_0_20, plain, ![X2:int, X1:int]:((fplus_plus_int @ X1 @ X2)=(fplus_plus_int @ X2 @ X1)|~p84), inference(split_conjunct,[status(thm)],[c_0_16])).
% 6.95/7.18  thf(c_0_21, plain, p84, inference(split_conjunct,[status(thm)],[ax142])).
% 6.95/7.18  thf(c_0_22, plain, ![X1:int]:((fpower_power_int @ X1 @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls))))=(ftimes_times_int @ X1 @ X1)|~p137), inference(split_conjunct,[status(thm)],[c_0_17])).
% 6.95/7.18  thf(c_0_23, plain, p137, inference(split_conjunct,[status(thm)],[ax89])).
% 6.95/7.18  thf(c_0_24, plain, ![X107:int]:(~p214|(ftimes_times_int @ X107 @ fzero_zero_int)=(fzero_zero_int)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax214])])])).
% 6.95/7.18  thf(c_0_25, plain, ((fpls)=(fzero_zero_int)|~p112), inference(split_conjunct,[status(thm)],[c_0_18])).
% 6.95/7.18  thf(c_0_26, plain, p112, inference(split_conjunct,[status(thm)],[ax114])).
% 6.95/7.18  thf(c_0_27, plain, ![X347:int, X348:int]:(~p96|~ford_less_int @ (fplus_plus_int @ (ftimes_times_int @ X347 @ X347) @ (ftimes_times_int @ X348 @ X348)) @ fzero_zero_int), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax96])])])])).
% 6.95/7.18  thf(c_0_28, plain, ![X467:int]:(~p53|(ftimes_times_int @ X467 @ fone_one_int)=(X467)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax53])])])).
% 6.95/7.18  thf(c_0_29, plain, (~p1|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)],[pax1])).
% 6.95/7.18  thf(c_0_30, 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)|~p2), inference(split_conjunct,[status(thm)],[c_0_19])).
% 6.95/7.18  thf(c_0_31, 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_20, c_0_21])])).
% 6.95/7.18  thf(c_0_32, plain, ![X1:int]:(fpower_power_int @ X1 @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls))))=(ftimes_times_int @ X1 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22, c_0_23])])).
% 6.95/7.18  thf(c_0_33, plain, p2, inference(split_conjunct,[status(thm)],[ax224])).
% 6.95/7.18  thf(c_0_34, plain, ![X1:int]:((ftimes_times_int @ X1 @ fzero_zero_int)=(fzero_zero_int)|~p214), inference(split_conjunct,[status(thm)],[c_0_24])).
% 6.95/7.18  thf(c_0_35, plain, (fzero_zero_int)=(fpls), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25, c_0_26])])).
% 6.95/7.18  thf(c_0_36, plain, p214, inference(split_conjunct,[status(thm)],[ax12])).
% 6.95/7.18  thf(c_0_37, plain, ![X1:int, X2:int]:(~p96|~ford_less_int @ (fplus_plus_int @ (ftimes_times_int @ X1 @ X1) @ (ftimes_times_int @ X2 @ X2)) @ fzero_zero_int), inference(split_conjunct,[status(thm)],[c_0_27])).
% 6.95/7.18  thf(c_0_38, plain, p96, inference(split_conjunct,[status(thm)],[ax130])).
% 6.95/7.18  thf(c_0_39, plain, ![X1:int]:((ftimes_times_int @ X1 @ fone_one_int)=(X1)|~p53), inference(split_conjunct,[status(thm)],[c_0_28])).
% 6.95/7.18  thf(c_0_40, plain, p53, inference(split_conjunct,[status(thm)],[ax173])).
% 6.95/7.18  thf(c_0_41, 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)|~p1), inference(split_conjunct,[status(thm)],[c_0_29])).
% 6.95/7.18  thf(c_0_42, plain, (ftimes_times_int @ (fplus_plus_int @ fone_one_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ 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)],[c_0_30, c_0_31]), c_0_32]), c_0_31]), c_0_33])])).
% 6.95/7.18  thf(c_0_43, 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_34, c_0_35]), c_0_35]), c_0_36])])).
% 6.95/7.18  thf(c_0_44, plain, p1, inference(split_conjunct,[status(thm)],[ax225])).
% 6.95/7.18  thf(c_0_45, plain, ![X1:int, X2:int]:~ford_less_int @ (fplus_plus_int @ (ftimes_times_int @ X1 @ X1) @ (ftimes_times_int @ X2 @ X2)) @ fpls, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37, c_0_38]), c_0_35])])).
% 6.95/7.18  thf(c_0_46, plain, ![X1:int]:(ftimes_times_int @ X1 @ fone_one_int)=(X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_40])])).
% 6.95/7.18  thf(c_0_47, plain, ford_less_int @ (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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_31]), c_0_42]), c_0_31]), c_0_35]), c_0_43]), c_0_44])])).
% 6.95/7.18  thf(c_0_48, plain, ![X1:int]:~ford_less_int @ (fplus_plus_int @ fone_one_int @ (ftimes_times_int @ X1 @ X1)) @ fpls, inference(spm,[status(thm)],[c_0_45, c_0_46])).
% 6.95/7.18  thf(c_0_49, plain, ($false), inference(sr,[status(thm)],[c_0_47, c_0_48]), ['proof']).
% 6.95/7.18  thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h19,h18,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0])],[])).
% 6.95/7.18  thf(pax84, axiom, (p84=>![X52:int, X53:int]:(fplus_plus_int @ X52 @ X53)=(fplus_plus_int @ X53 @ X52)), file('<stdin>', pax84)).
% 6.95/7.18  thf(pax137, axiom, (p137=>![X28:int]:(fpower_power_int @ X28 @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls))))=(ftimes_times_int @ X28 @ X28)), file('<stdin>', pax137)).
% 6.95/7.18  thf(pax112, axiom, (p112=>(fpls)=(fzero_zero_int)), file('<stdin>', pax112)).
% 6.95/7.18  thf(pax228, axiom, (p228=>(fplus_plus_int @ (fpower_power_int @ fs @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls)))) @ fone_one_int)=(fzero_zero_int)), file('<stdin>', pax228)).
% 6.95/7.18  thf(ax154, axiom, p84, file('<stdin>', ax154)).
% 6.95/7.18  thf(ax101, axiom, p137, file('<stdin>', ax101)).
% 6.95/7.18  thf(ax126, axiom, p112, file('<stdin>', ax126)).
% 6.95/7.18  thf(pax2, axiom, (p2=>(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('<stdin>', pax2)).
% 6.95/7.18  thf(ax235, axiom, p228, file('<stdin>', ax235)).
% 6.95/7.18  thf(pax214, axiom, (p214=>![X4:int]:(ftimes_times_int @ X4 @ fzero_zero_int)=(fzero_zero_int)), file('<stdin>', pax214)).
% 6.95/7.18  thf(nax114, axiom, (p114<=ford_less_int @ fpls @ fpls), file('<stdin>', nax114)).
% 6.95/7.18  thf(ax124, axiom, ~(p114), file('<stdin>', ax124)).
% 6.95/7.18  thf(pax1, axiom, (p1=>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('<stdin>', pax1)).
% 6.95/7.18  thf(ax236, axiom, p2, file('<stdin>', ax236)).
% 6.95/7.18  thf(ax24, axiom, p214, file('<stdin>', ax24)).
% 6.95/7.18  thf(ax237, axiom, p1, file('<stdin>', ax237)).
% 6.95/7.18  thf(c_0_16, plain, ![X407:int, X408:int]:(~p84|(fplus_plus_int @ X407 @ X408)=(fplus_plus_int @ X408 @ X407)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax84])])])).
% 6.95/7.18  thf(c_0_17, plain, ![X299:int]:(~p137|(fpower_power_int @ X299 @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls))))=(ftimes_times_int @ X299 @ X299)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax137])])])).
% 6.95/7.18  thf(c_0_18, plain, (~p112|(fpls)=(fzero_zero_int)), inference(fof_nnf,[status(thm)],[pax112])).
% 6.95/7.18  thf(c_0_19, plain, (~p228|(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)],[pax228])).
% 6.95/7.18  thf(c_0_20, plain, ![X3:int, X1:int]:((fplus_plus_int @ X1 @ X3)=(fplus_plus_int @ X3 @ X1)|~p84), inference(split_conjunct,[status(thm)],[c_0_16])).
% 6.95/7.18  thf(c_0_21, plain, p84, inference(split_conjunct,[status(thm)],[ax154])).
% 6.95/7.18  thf(c_0_22, plain, ![X1:int]:((fpower_power_int @ X1 @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls))))=(ftimes_times_int @ X1 @ X1)|~p137), inference(split_conjunct,[status(thm)],[c_0_17])).
% 6.95/7.18  thf(c_0_23, plain, p137, inference(split_conjunct,[status(thm)],[ax101])).
% 6.95/7.18  thf(c_0_24, plain, ((fpls)=(fzero_zero_int)|~p112), inference(split_conjunct,[status(thm)],[c_0_18])).
% 6.95/7.18  thf(c_0_25, plain, p112, inference(split_conjunct,[status(thm)],[ax126])).
% 6.95/7.18  thf(c_0_26, plain, (~p2|(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)],[pax2])).
% 6.95/7.18  thf(c_0_27, plain, ((fplus_plus_int @ (fpower_power_int @ fs @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls)))) @ fone_one_int)=(fzero_zero_int)|~p228), inference(split_conjunct,[status(thm)],[c_0_19])).
% 6.95/7.18  thf(c_0_28, plain, ![X3:int, X1:int]:(fplus_plus_int @ X1 @ X3)=(fplus_plus_int @ X3 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21])])).
% 6.95/7.18  thf(c_0_29, plain, ![X1:int]:(fpower_power_int @ X1 @ (fnumber_number_of_nat @ (fbit0 @ (fbit1 @ fpls))))=(ftimes_times_int @ X1 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22, c_0_23])])).
% 6.95/7.18  thf(c_0_30, plain, (fzero_zero_int)=(fpls), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_25])])).
% 6.95/7.18  thf(c_0_31, plain, p228, inference(split_conjunct,[status(thm)],[ax235])).
% 6.95/7.18  thf(c_0_32, plain, ![X131:int]:(~p214|(ftimes_times_int @ X131 @ fzero_zero_int)=(fzero_zero_int)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax214])])])).
% 6.95/7.18  thf(c_0_33, plain, (~ford_less_int @ fpls @ fpls|p114), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax114])])).
% 6.95/7.18  thf(c_0_34, plain, ~p114, inference(fof_simplification,[status(thm)],[ax124])).
% 6.95/7.18  thf(c_0_35, plain, (~p1|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)],[pax1])).
% 6.95/7.18  thf(c_0_36, 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)|~p2), inference(split_conjunct,[status(thm)],[c_0_26])).
% 6.95/7.18  thf(c_0_37, 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_27, c_0_28]), c_0_29]), c_0_30]), c_0_31])])).
% 6.95/7.18  thf(c_0_38, plain, p2, inference(split_conjunct,[status(thm)],[ax236])).
% 6.95/7.18  thf(c_0_39, plain, ![X1:int]:((ftimes_times_int @ X1 @ fzero_zero_int)=(fzero_zero_int)|~p214), inference(split_conjunct,[status(thm)],[c_0_32])).
% 6.95/7.18  thf(c_0_40, plain, p214, inference(split_conjunct,[status(thm)],[ax24])).
% 6.95/7.18  thf(c_0_41, plain, (p114|~ford_less_int @ fpls @ fpls), inference(split_conjunct,[status(thm)],[c_0_33])).
% 6.95/7.18  thf(c_0_42, plain, ~p114, inference(split_conjunct,[status(thm)],[c_0_34])).
% 6.95/7.18  thf(c_0_43, 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)|~p1), inference(split_conjunct,[status(thm)],[c_0_35])).
% 6.95/7.18  thf(c_0_44, plain, (ftimes_times_int @ (fplus_plus_int @ fone_one_int @ (ftimes_times_int @ (fnumber_number_of_int @ (fbit0 @ (fbit0 @ (fbit1 @ fpls)))) @ 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)],[c_0_36, c_0_28]), c_0_28]), c_0_29]), c_0_37]), c_0_38])])).
% 6.95/7.18  thf(c_0_45, 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_39, c_0_30]), c_0_30]), c_0_40])])).
% 6.95/7.18  thf(c_0_46, plain, p1, inference(split_conjunct,[status(thm)],[ax237])).
% 6.95/7.18  thf(c_0_47, plain, ~ford_less_int @ fpls @ fpls, inference(sr,[status(thm)],[c_0_41, c_0_42])).
% 6.95/7.18  thf(c_0_48, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43, c_0_28]), c_0_44]), c_0_28]), c_0_30]), c_0_45]), c_0_46])]), c_0_47]), ['proof']).
% 6.95/7.18  thf(2,plain,$false,inference(eprover,[status(thm),assumptions([h20,h18,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0])],[])).
% 6.95/7.18  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))).
% 6.95/7.18  thf(3,plain,$false,inference(tab_imp,[status(thm),assumptions([h18,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_imp(discharge,[h19]),tab_imp(discharge,[h20])],[fact_4_calculation_I2_J,1,2,h19,h20])).
% 6.95/7.18  thf(fact_30__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_,axiom,(~((![X1:int]:(~((((plus_plus_int @ ((power_power_int @ s) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ one_one_int) = ((times_times_int @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)) @ X1)))))))).
% 6.95/7.18  thf(4,plain,$false,inference(tab_negall,[status(thm),assumptions([h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h18]),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_,3,h18])).
% 6.95/7.18  thf(5,plain,$false,inference(tab_negimp,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h14,4,h16,h17])).
% 6.95/7.18  thf(fact_272_s0p,axiom,(~(((~((((ord_less_eq_int @ zero_zero_int) @ s) => (~(((ord_less_int @ s) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~((((zcong @ s1) @ s) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)))))))).
% 6.95/7.18  thf(6,plain,$false,inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[fact_272_s0p,5,h14,h15])).
% 6.95/7.18  thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,6,h12,h13])).
% 6.95/7.18  thf(8,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,7,h10,h11])).
% 6.95/7.18  thf(9,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,8,h8,h9])).
% 6.95/7.18  thf(fact_282__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1,axiom,(~((![X1:int]:((~(((~((((ord_less_eq_int @ zero_zero_int) @ X1) => (~(((ord_less_int @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~((((zcong @ s1) @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~((![X2:int]:((~(((~((((ord_less_eq_int @ zero_zero_int) @ X2) => (~(((ord_less_int @ X2) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~((((zcong @ s1) @ X2) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (X2 = X1)))))))))).
% 6.95/7.18  thf(10,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[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_091s1,9,h7])).
% 6.95/7.18  thf(11,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,10,h5,h6])).
% 6.95/7.18  thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,11,h3,h4])).
% 6.95/7.18  thf(fact_283__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_,axiom,(~((![X1:int]:((~((((ord_less_eq_int @ zero_zero_int) @ X1) => (~(((ord_less_int @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))) => (~((((zcong @ s1) @ X1) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int))))))))).
% 6.95/7.18  thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[fact_283__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_,12,h2])).
% 6.95/7.18  thf(fact_444__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_,axiom,(~((![X1:int]:(~((((zcong @ ((power_power_int @ X1) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ (number_number_of_int @ min)) @ ((plus_plus_int @ ((times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls))))) @ m)) @ one_one_int)))))))).
% 6.95/7.18  thf(14,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_444__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_,13,h1])).
% 6.95/7.18  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])],[14,h0])).
% 6.95/7.18  % SZS output end Proof
%------------------------------------------------------------------------------