0.07/0.12	% Problem    : SLH0538^1 : TPTP v8.2.0. Released v8.2.0.
0.07/0.13	% Command    : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
0.13/0.34	Computer   : n013.cluster.edu
0.13/0.34	Model      : x86_64 x86_64
0.13/0.34	CPUModel   : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	RAMPerCPU  : 8042.1875MB
0.13/0.34	OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 30
0.13/0.34	% DateTime   : Mon Jul  3 05:05:32 EDT 2023
0.13/0.34	% CPUTime    : 
21.13/20.82	% SZS status Theorem
21.13/20.82	% Mode: mode478:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
21.13/20.82	% Inferences: 6426
21.13/20.82	% SZS output start Proof
21.13/20.82	thf(ty_produc2422161461964618553l_real, type, produc2422161461964618553l_real : $tType).
21.13/20.82	thf(ty_nat, type, nat : $tType).
21.13/20.82	thf(ty_num, type, num : $tType).
21.13/20.82	thf(ty_real, type, real : $tType).
21.13/20.82	thf(ty_zero_zero_real, type, zero_zero_real : real).
21.13/20.82	thf(ty_biexp01_well_formed, type, biexp01_well_formed : ((nat>nat)>$o)).
21.13/20.82	thf(ty_r01_r01_to_r01, type, r01_r01_to_r01 : (produc2422161461964618553l_real>nat>nat)).
21.13/20.82	thf(ty_produc3484788084999411615l_real, type, produc3484788084999411615l_real : (produc2422161461964618553l_real>real)).
21.13/20.82	thf(ty_if_nat, type, if_nat : ($o>nat>nat>nat)).
21.13/20.82	thf(ty_produc4511245868158468465l_real, type, produc4511245868158468465l_real : (real>real>produc2422161461964618553l_real)).
21.13/20.82	thf(ty_numeral_numeral_nat, type, numeral_numeral_nat : (num>nat)).
21.13/20.82	thf(ty_produc5828954698716094813l_real, type, produc5828954698716094813l_real : (produc2422161461964618553l_real>real)).
21.13/20.82	thf(ty_bit0, type, bit0 : (num>num)).
21.13/20.82	thf(ty_minus_minus_nat, type, minus_minus_nat : (nat>nat>nat)).
21.13/20.82	thf(ty_dvd_dvd_nat, type, dvd_dvd_nat : (nat>nat>$o)).
21.13/20.82	thf(ty_r1, type, r1 : real).
21.13/20.82	thf(ty_ord_less_real, type, ord_less_real : (real>real>$o)).
21.13/20.82	thf(ty_r2, type, r2 : real).
21.13/20.82	thf(ty_r01_binary_expansion, type, r01_binary_expansion : (real>nat>nat)).
21.13/20.82	thf(ty_one, type, one : num).
21.13/20.82	thf(ty_one_one_nat, type, one_one_nat : nat).
21.13/20.82	thf(ty_one_one_real, type, one_one_real : real).
21.13/20.82	thf(ty_divide_divide_nat, type, divide_divide_nat : (nat>nat>nat)).
21.13/20.82	thf(sP1,plain,sP1 <=> ((ord_less_real @ zero_zero_real) @ r1),introduced(definition,[new_symbols(definition,[sP1])])).
21.13/20.82	thf(sP2,plain,sP2 <=> ((produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ one_one_real) @ zero_zero_real)) = zero_zero_real),introduced(definition,[new_symbols(definition,[sP2])])).
21.13/20.82	thf(sP3,plain,sP3 <=> (![X1:real]:(![X2:real]:(![X3:real]:((((produc4511245868158468465l_real @ r1) @ X1) = ((produc4511245868158468465l_real @ X2) @ X3)) => (~(((r1 = X2) => (~((X1 = X3)))))))))),introduced(definition,[new_symbols(definition,[sP3])])).
21.13/20.82	thf(sP4,plain,sP4 <=> (![X1:real]:(![X2:real]:(![X3:real]:(![X4:real]:((((produc4511245868158468465l_real @ X1) @ X2) = ((produc4511245868158468465l_real @ X3) @ X4)) => (~(((X1 = X3) => (~((X2 = X4))))))))))),introduced(definition,[new_symbols(definition,[sP4])])).
21.13/20.82	thf(sP5,plain,sP5 <=> (![X1:real]:(((produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ one_one_real) @ zero_zero_real)) = X1) => (zero_zero_real = X1))),introduced(definition,[new_symbols(definition,[sP5])])).
21.13/20.82	thf(sP6,plain,sP6 <=> (![X1:real]:((((produc4511245868158468465l_real @ r1) @ r2) = ((produc4511245868158468465l_real @ (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) @ X1)) => (~(((r1 = (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) => (~((r2 = X1)))))))),introduced(definition,[new_symbols(definition,[sP6])])).
21.13/20.82	thf(sP7,plain,sP7 <=> (((produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) @ one_one_real)) = one_one_real) => (one_one_real = one_one_real)),introduced(definition,[new_symbols(definition,[sP7])])).
21.13/20.82	thf(sP8,plain,sP8 <=> (r1 = (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2))),introduced(definition,[new_symbols(definition,[sP8])])).
21.13/20.82	thf(sP9,plain,sP9 <=> (![X1:real]:(((produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ one_one_real) @ one_one_real)) = X1) => (one_one_real = X1))),introduced(definition,[new_symbols(definition,[sP9])])).
21.13/20.82	thf(sP10,plain,sP10 <=> (biexp01_well_formed @ (r01_binary_expansion @ (produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ r1) @ r2)))),introduced(definition,[new_symbols(definition,[sP10])])).
21.13/20.82	thf(sP11,plain,sP11 <=> (((ord_less_real @ zero_zero_real) @ (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) => (((ord_less_real @ (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) @ one_one_real) => (biexp01_well_formed @ (r01_binary_expansion @ (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2)))))),introduced(definition,[new_symbols(definition,[sP11])])).
21.13/20.82	thf(sP12,plain,sP12 <=> ((^[X1:nat]:(((if_nat @ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ X1)) @ ((r01_binary_expansion @ (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) @ ((divide_divide_nat @ X1) @ (numeral_numeral_nat @ (bit0 @ one))))) @ ((r01_binary_expansion @ (produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) @ ((divide_divide_nat @ ((minus_minus_nat @ X1) @ one_one_nat)) @ (numeral_numeral_nat @ (bit0 @ one)))))) = (r01_r01_to_r01 @ ((produc4511245868158468465l_real @ r1) @ r2))),introduced(definition,[new_symbols(definition,[sP12])])).
21.13/20.82	thf(sP13,plain,sP13 <=> (![X1:nat>nat]:(![X2:nat>nat]:((X1 = X2) => (X2 = X1)))),introduced(definition,[new_symbols(definition,[sP13])])).
21.13/20.82	thf(sP14,plain,sP14 <=> (((ord_less_real @ (produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) @ one_one_real) => sP10),introduced(definition,[new_symbols(definition,[sP14])])).
21.13/20.82	thf(sP15,plain,sP15 <=> (![X1:nat>nat]:(((r01_r01_to_r01 @ ((produc4511245868158468465l_real @ r1) @ r2)) = X1) => (X1 = (r01_r01_to_r01 @ ((produc4511245868158468465l_real @ r1) @ r2))))),introduced(definition,[new_symbols(definition,[sP15])])).
21.13/20.82	thf(sP16,plain,sP16 <=> (biexp01_well_formed @ (^[X1:nat]:(((if_nat @ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ X1)) @ ((r01_binary_expansion @ (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) @ ((divide_divide_nat @ X1) @ (numeral_numeral_nat @ (bit0 @ one))))) @ ((r01_binary_expansion @ (produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) @ ((divide_divide_nat @ ((minus_minus_nat @ X1) @ one_one_nat)) @ (numeral_numeral_nat @ (bit0 @ one))))))),introduced(definition,[new_symbols(definition,[sP16])])).
21.13/20.82	thf(sP17,plain,sP17 <=> (((produc4511245868158468465l_real @ r1) @ r2) = ((produc4511245868158468465l_real @ (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) @ (produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ r1) @ r2)))),introduced(definition,[new_symbols(definition,[sP17])])).
21.13/20.82	thf(sP18,plain,sP18 <=> (![X1:produc2422161461964618553l_real]:((r01_r01_to_r01 @ X1) = (^[X2:nat]:(((if_nat @ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ X2)) @ ((r01_binary_expansion @ (produc5828954698716094813l_real @ X1)) @ ((divide_divide_nat @ X2) @ (numeral_numeral_nat @ (bit0 @ one))))) @ ((r01_binary_expansion @ (produc3484788084999411615l_real @ X1)) @ ((divide_divide_nat @ ((minus_minus_nat @ X2) @ one_one_nat)) @ (numeral_numeral_nat @ (bit0 @ one)))))))),introduced(definition,[new_symbols(definition,[sP18])])).
21.13/20.82	thf(sP19,plain,sP19 <=> (r2 = (produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ r1) @ r2))),introduced(definition,[new_symbols(definition,[sP19])])).
21.13/20.82	thf(sP20,plain,sP20 <=> (![X1:real]:(![X2:real]:((((produc4511245868158468465l_real @ r1) @ r2) = ((produc4511245868158468465l_real @ X1) @ X2)) => (~(((r1 = X1) => (~((r2 = X2))))))))),introduced(definition,[new_symbols(definition,[sP20])])).
21.13/20.82	thf(sP21,plain,sP21 <=> (sP8 => (~(sP19))),introduced(definition,[new_symbols(definition,[sP21])])).
21.13/20.82	thf(sP22,plain,sP22 <=> (![X1:real]:(![X2:real]:(((produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ one_one_real) @ X1)) = X2) => (X1 = X2)))),introduced(definition,[new_symbols(definition,[sP22])])).
21.13/20.82	thf(sP23,plain,sP23 <=> ((ord_less_real @ (produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) @ one_one_real),introduced(definition,[new_symbols(definition,[sP23])])).
21.13/20.82	thf(sP24,plain,sP24 <=> (biexp01_well_formed @ (r01_binary_expansion @ (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2)))),introduced(definition,[new_symbols(definition,[sP24])])).
21.13/20.82	thf(sP25,plain,sP25 <=> (![X1:real]:(((produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) @ zero_zero_real)) = X1) => (zero_zero_real = X1))),introduced(definition,[new_symbols(definition,[sP25])])).
21.13/20.82	thf(sP26,plain,sP26 <=> (zero_zero_real = zero_zero_real),introduced(definition,[new_symbols(definition,[sP26])])).
21.13/20.82	thf(sP27,plain,sP27 <=> (![X1:produc2422161461964618553l_real]:(X1 = ((produc4511245868158468465l_real @ (produc5828954698716094813l_real @ X1)) @ (produc3484788084999411615l_real @ X1)))),introduced(definition,[new_symbols(definition,[sP27])])).
21.13/20.82	thf(sP28,plain,sP28 <=> (![X1:real]:(((produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) @ one_one_real)) = X1) => (one_one_real = X1))),introduced(definition,[new_symbols(definition,[sP28])])).
21.13/20.82	thf(sP29,plain,sP29 <=> ((produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) @ zero_zero_real)) = zero_zero_real),introduced(definition,[new_symbols(definition,[sP29])])).
21.13/20.82	thf(sP30,plain,sP30 <=> (![X1:real]:(((ord_less_real @ zero_zero_real) @ X1) => (((ord_less_real @ X1) @ one_one_real) => (biexp01_well_formed @ (r01_binary_expansion @ X1))))),introduced(definition,[new_symbols(definition,[sP30])])).
21.13/20.82	thf(sP31,plain,sP31 <=> (sP17 => (~(sP21))),introduced(definition,[new_symbols(definition,[sP31])])).
21.13/20.82	thf(sP32,plain,sP32 <=> ((ord_less_real @ (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) @ one_one_real),introduced(definition,[new_symbols(definition,[sP32])])).
21.13/20.82	thf(sP33,plain,sP33 <=> ((ord_less_real @ r2) @ one_one_real),introduced(definition,[new_symbols(definition,[sP33])])).
21.13/20.82	thf(sP34,plain,sP34 <=> ((ord_less_real @ zero_zero_real) @ (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2))),introduced(definition,[new_symbols(definition,[sP34])])).
21.13/20.82	thf(sP35,plain,sP35 <=> ((ord_less_real @ zero_zero_real) @ r2),introduced(definition,[new_symbols(definition,[sP35])])).
21.13/20.82	thf(sP36,plain,sP36 <=> (sP2 => sP26),introduced(definition,[new_symbols(definition,[sP36])])).
21.13/20.82	thf(sP37,plain,sP37 <=> (sP32 => sP24),introduced(definition,[new_symbols(definition,[sP37])])).
21.13/20.82	thf(sP38,plain,sP38 <=> (![X1:real]:(![X2:real]:(((produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) @ X1)) = X2) => (X1 = X2)))),introduced(definition,[new_symbols(definition,[sP38])])).
21.13/20.82	thf(sP39,plain,sP39 <=> ((produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ one_one_real) @ one_one_real)) = one_one_real),introduced(definition,[new_symbols(definition,[sP39])])).
21.13/20.82	thf(sP40,plain,sP40 <=> ((ord_less_real @ zero_zero_real) @ (produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ r1) @ r2))),introduced(definition,[new_symbols(definition,[sP40])])).
21.13/20.82	thf(sP41,plain,sP41 <=> ((r01_r01_to_r01 @ ((produc4511245868158468465l_real @ r1) @ r2)) = (^[X1:nat]:(((if_nat @ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ X1)) @ ((r01_binary_expansion @ (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) @ ((divide_divide_nat @ X1) @ (numeral_numeral_nat @ (bit0 @ one))))) @ ((r01_binary_expansion @ (produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) @ ((divide_divide_nat @ ((minus_minus_nat @ X1) @ one_one_nat)) @ (numeral_numeral_nat @ (bit0 @ one))))))),introduced(definition,[new_symbols(definition,[sP41])])).
21.13/20.82	thf(sP42,plain,sP42 <=> (sP40 => sP14),introduced(definition,[new_symbols(definition,[sP42])])).
21.13/20.82	thf(sP43,plain,sP43 <=> (sP41 => sP12),introduced(definition,[new_symbols(definition,[sP43])])).
21.13/20.82	thf(sP44,plain,sP44 <=> (sP39 => (one_one_real = one_one_real)),introduced(definition,[new_symbols(definition,[sP44])])).
21.13/20.82	thf(sP45,plain,sP45 <=> (one_one_real = one_one_real),introduced(definition,[new_symbols(definition,[sP45])])).
21.13/20.82	thf(sP46,plain,sP46 <=> (![X1:real]:(![X2:real]:(![X3:real]:(((produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ X1) @ X2)) = X3) => (X2 = X3))))),introduced(definition,[new_symbols(definition,[sP46])])).
21.13/20.82	thf(sP47,plain,sP47 <=> (sP29 => sP26),introduced(definition,[new_symbols(definition,[sP47])])).
21.13/20.82	thf(sP48,plain,sP48 <=> (![X1:real]:(![X2:real]:((produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ X1) @ X2)) = X2))),introduced(definition,[new_symbols(definition,[sP48])])).
21.13/20.82	thf(sP49,plain,sP49 <=> ((produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) @ one_one_real)) = one_one_real),introduced(definition,[new_symbols(definition,[sP49])])).
21.13/20.82	thf(sP50,plain,sP50 <=> ((ord_less_real @ r1) @ one_one_real),introduced(definition,[new_symbols(definition,[sP50])])).
21.13/20.82	thf(sP51,plain,sP51 <=> (![X1:real]:((produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ (produc5828954698716094813l_real @ ((produc4511245868158468465l_real @ r1) @ r2))) @ X1)) = X1)),introduced(definition,[new_symbols(definition,[sP51])])).
21.13/20.82	thf(sP52,plain,sP52 <=> (biexp01_well_formed @ (r01_r01_to_r01 @ ((produc4511245868158468465l_real @ r1) @ r2))),introduced(definition,[new_symbols(definition,[sP52])])).
21.13/20.82	thf(sP53,plain,sP53 <=> (![X1:real]:((produc3484788084999411615l_real @ ((produc4511245868158468465l_real @ one_one_real) @ X1)) = X1)),introduced(definition,[new_symbols(definition,[sP53])])).
21.13/20.82	thf(sP54,plain,sP54 <=> (r01_r01_to_r01 = (^[X1:produc2422161461964618553l_real]:(^[X2:nat]:(((if_nat @ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ X2)) @ ((r01_binary_expansion @ (produc5828954698716094813l_real @ X1)) @ ((divide_divide_nat @ X2) @ (numeral_numeral_nat @ (bit0 @ one))))) @ ((r01_binary_expansion @ (produc3484788084999411615l_real @ X1)) @ ((divide_divide_nat @ ((minus_minus_nat @ X2) @ one_one_nat)) @ (numeral_numeral_nat @ (bit0 @ one)))))))),introduced(definition,[new_symbols(definition,[sP54])])).
21.13/20.82	thf(conj_0,conjecture,sP52).
21.13/20.82	thf(h0,negated_conjecture,(~(sP52)),inference(assume_negation,[status(cth)],[conj_0])).
21.13/20.82	thf(h1,assumption,(~(sP24)),introduced(assumption,[])).
21.13/20.82	thf(h2,assumption,(sP10 => sP16),introduced(assumption,[])).
21.13/20.82	thf(h3,assumption,(~(sP35)),introduced(assumption,[])).
21.13/20.82	thf(h4,assumption,(sP33 => (biexp01_well_formed @ (r01_binary_expansion @ r2))),introduced(assumption,[])).
21.13/20.82	thf(h5,assumption,(~(sP1)),introduced(assumption,[])).
21.13/20.82	thf(h6,assumption,(sP50 => (biexp01_well_formed @ (r01_binary_expansion @ r1))),introduced(assumption,[])).
21.13/20.82	thf(fact_1_assms_I1_J,axiom,sP1).
21.13/20.82	thf(1,plain,$false,inference(tab_conflict,[status(thm),assumptions([h5,h3,h1,h0])],[fact_1_assms_I1_J,h5])).
21.13/20.82	thf(h7,assumption,(~(sP50)),introduced(assumption,[])).
21.13/20.82	thf(h8,assumption,(biexp01_well_formed @ (r01_binary_expansion @ r1)),introduced(assumption,[])).
21.13/20.82	thf(fact_3_assms_I2_J,axiom,sP50).
21.13/20.82	thf(2,plain,$false,inference(tab_conflict,[status(thm),assumptions([h7,h6,h3,h1,h0])],[fact_3_assms_I2_J,h7])).
21.13/20.82	thf(fact_0_assms_I3_J,axiom,sP35).
21.13/20.82	thf(3,plain,$false,inference(tab_conflict,[status(thm),assumptions([h8,h6,h3,h1,h0])],[fact_0_assms_I3_J,h3])).
21.13/20.82	thf(4,plain,$false,inference(tab_imp,[status(thm),assumptions([h6,h3,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,2,3,h7,h8])).
21.13/20.82	thf(fact_4__092_060open_062_092_060lbrakk_0620_A_060_Ar1_059_Ar1_A_060_A1_092_060rbrakk_062_A_092_060Longrightarrow_062_Abiexp01__well__formed_A_Ir01__binary__expansion_H_Ar1_J_092_060close_062,axiom,(sP1 => (sP50 => (biexp01_well_formed @ (r01_binary_expansion @ r1))))).
21.13/20.82	thf(5,plain,$false,inference(tab_imp,[status(thm),assumptions([h3,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_4__092_060open_062_092_060lbrakk_0620_A_060_Ar1_059_Ar1_A_060_A1_092_060rbrakk_062_A_092_060Longrightarrow_062_Abiexp01__well__formed_A_Ir01__binary__expansion_H_Ar1_J_092_060close_062,1,4,h5,h6])).
21.13/20.82	thf(h9,assumption,(~(sP33)),introduced(assumption,[])).
21.13/20.82	thf(h10,assumption,(biexp01_well_formed @ (r01_binary_expansion @ r2)),introduced(assumption,[])).
21.13/20.82	thf(6,plain,$false,inference(tab_conflict,[status(thm),assumptions([h5,h9,h4,h1,h0])],[fact_1_assms_I1_J,h5])).
21.13/20.82	thf(7,plain,$false,inference(tab_conflict,[status(thm),assumptions([h7,h6,h9,h4,h1,h0])],[fact_3_assms_I2_J,h7])).
21.13/20.82	thf(fact_2_assms_I4_J,axiom,sP33).
21.13/20.82	thf(8,plain,$false,inference(tab_conflict,[status(thm),assumptions([h8,h6,h9,h4,h1,h0])],[fact_2_assms_I4_J,h9])).
21.13/20.82	thf(9,plain,$false,inference(tab_imp,[status(thm),assumptions([h6,h9,h4,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,7,8,h7,h8])).
21.13/20.82	thf(10,plain,$false,inference(tab_imp,[status(thm),assumptions([h9,h4,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_4__092_060open_062_092_060lbrakk_0620_A_060_Ar1_059_Ar1_A_060_A1_092_060rbrakk_062_A_092_060Longrightarrow_062_Abiexp01__well__formed_A_Ir01__binary__expansion_H_Ar1_J_092_060close_062,6,9,h5,h6])).
21.13/20.82	thf(11,plain,$false,inference(tab_conflict,[status(thm),assumptions([h5,h10,h4,h1,h0])],[fact_1_assms_I1_J,h5])).
21.13/20.82	thf(12,plain,$false,inference(tab_conflict,[status(thm),assumptions([h7,h6,h10,h4,h1,h0])],[fact_3_assms_I2_J,h7])).
21.13/20.82	thf(13,plain,(((~(sP1) | sP34) | ~(sP26)) | ~(sP8)),inference(mating_rule,[status(thm)],[])).
21.13/20.82	thf(14,plain,(((~(sP50) | sP32) | ~(sP8)) | ~(sP45)),inference(mating_rule,[status(thm)],[])).
21.13/20.82	thf(15,plain,(~(sP25) | sP47),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(16,plain,((~(sP47) | ~(sP29)) | sP26),inference(prop_rule,[status(thm)],[])).
21.13/20.82	thf(17,plain,(~(sP28) | sP7),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(18,plain,((~(sP7) | ~(sP49)) | sP45),inference(prop_rule,[status(thm)],[])).
21.13/20.82	thf(19,plain,(sP21 | sP8),inference(prop_rule,[status(thm)],[])).
21.13/20.82	thf(20,plain,(~(sP38) | sP25),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(21,plain,(~(sP38) | sP28),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(22,plain,(~(sP51) | sP29),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(23,plain,(~(sP51) | sP49),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(24,plain,(~(sP20) | sP6),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(25,plain,(~(sP6) | sP31),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(26,plain,((~(sP31) | ~(sP17)) | ~(sP21)),inference(prop_rule,[status(thm)],[])).
21.13/20.82	thf(27,plain,(~(sP3) | sP20),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(28,plain,((~(sP11) | ~(sP34)) | sP37),inference(prop_rule,[status(thm)],[])).
21.13/20.82	thf(29,plain,((~(sP37) | ~(sP32)) | sP24),inference(prop_rule,[status(thm)],[])).
21.13/20.82	thf(30,plain,(~(sP46) | sP38),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(31,plain,(~(sP48) | sP51),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(32,plain,(~(sP27) | sP17),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(33,plain,(~(sP30) | sP11),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(34,plain,(~(sP4) | sP3),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(fact_364_snd__eqD,axiom,sP46).
21.13/20.82	thf(fact_362_snd__conv,axiom,sP48).
21.13/20.82	thf(fact_358_surjective__pairing,axiom,sP27).
21.13/20.82	thf(fact_19_r01__binary__expansion__well__formed,axiom,sP30).
21.13/20.82	thf(fact_16_Pair__inject,axiom,sP4).
21.13/20.82	thf(35,plain,$false,inference(prop_unsat,[status(thm),assumptions([h8,h6,h10,h4,h1,h0])],[13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,h1,fact_364_snd__eqD,fact_362_snd__conv,fact_358_surjective__pairing,fact_19_r01__binary__expansion__well__formed,fact_16_Pair__inject,fact_3_assms_I2_J,fact_1_assms_I1_J])).
21.13/20.82	thf(36,plain,$false,inference(tab_imp,[status(thm),assumptions([h6,h10,h4,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,12,35,h7,h8])).
21.13/20.82	thf(37,plain,$false,inference(tab_imp,[status(thm),assumptions([h10,h4,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_4__092_060open_062_092_060lbrakk_0620_A_060_Ar1_059_Ar1_A_060_A1_092_060rbrakk_062_A_092_060Longrightarrow_062_Abiexp01__well__formed_A_Ir01__binary__expansion_H_Ar1_J_092_060close_062,11,36,h5,h6])).
21.13/20.82	thf(38,plain,$false,inference(tab_imp,[status(thm),assumptions([h4,h1,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h4,10,37,h9,h10])).
21.13/20.82	thf(fact_5__092_060open_062_092_060lbrakk_0620_A_060_Ar2_059_Ar2_A_060_A1_092_060rbrakk_062_A_092_060Longrightarrow_062_Abiexp01__well__formed_A_Ir01__binary__expansion_H_Ar2_J_092_060close_062,axiom,(sP35 => (sP33 => (biexp01_well_formed @ (r01_binary_expansion @ r2))))).
21.13/20.82	thf(39,plain,$false,inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_5__092_060open_062_092_060lbrakk_0620_A_060_Ar2_059_Ar2_A_060_A1_092_060rbrakk_062_A_092_060Longrightarrow_062_Abiexp01__well__formed_A_Ir01__binary__expansion_H_Ar2_J_092_060close_062,5,38,h3,h4])).
21.13/20.82	thf(h11,assumption,(~(sP10)),introduced(assumption,[])).
21.13/20.82	thf(h12,assumption,sP16,introduced(assumption,[])).
21.13/20.82	thf(40,plain,$false,inference(tab_conflict,[status(thm),assumptions([h5,h3,h11,h2,h0])],[fact_1_assms_I1_J,h5])).
21.13/20.82	thf(41,plain,$false,inference(tab_conflict,[status(thm),assumptions([h7,h6,h3,h11,h2,h0])],[fact_3_assms_I2_J,h7])).
21.13/20.82	thf(42,plain,$false,inference(tab_conflict,[status(thm),assumptions([h8,h6,h3,h11,h2,h0])],[fact_0_assms_I3_J,h3])).
21.13/20.82	thf(43,plain,$false,inference(tab_imp,[status(thm),assumptions([h6,h3,h11,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,41,42,h7,h8])).
21.13/20.82	thf(44,plain,$false,inference(tab_imp,[status(thm),assumptions([h3,h11,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_4__092_060open_062_092_060lbrakk_0620_A_060_Ar1_059_Ar1_A_060_A1_092_060rbrakk_062_A_092_060Longrightarrow_062_Abiexp01__well__formed_A_Ir01__binary__expansion_H_Ar1_J_092_060close_062,40,43,h5,h6])).
21.13/20.82	thf(45,plain,$false,inference(tab_conflict,[status(thm),assumptions([h5,h9,h4,h11,h2,h0])],[fact_1_assms_I1_J,h5])).
21.13/20.82	thf(46,plain,$false,inference(tab_conflict,[status(thm),assumptions([h7,h6,h9,h4,h11,h2,h0])],[fact_3_assms_I2_J,h7])).
21.13/20.82	thf(47,plain,$false,inference(tab_conflict,[status(thm),assumptions([h8,h6,h9,h4,h11,h2,h0])],[fact_2_assms_I4_J,h9])).
21.13/20.82	thf(48,plain,$false,inference(tab_imp,[status(thm),assumptions([h6,h9,h4,h11,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,46,47,h7,h8])).
21.13/20.82	thf(49,plain,$false,inference(tab_imp,[status(thm),assumptions([h9,h4,h11,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_4__092_060open_062_092_060lbrakk_0620_A_060_Ar1_059_Ar1_A_060_A1_092_060rbrakk_062_A_092_060Longrightarrow_062_Abiexp01__well__formed_A_Ir01__binary__expansion_H_Ar1_J_092_060close_062,45,48,h5,h6])).
21.13/20.82	thf(50,plain,$false,inference(tab_conflict,[status(thm),assumptions([h5,h10,h4,h11,h2,h0])],[fact_1_assms_I1_J,h5])).
21.13/20.82	thf(51,plain,$false,inference(tab_conflict,[status(thm),assumptions([h7,h6,h10,h4,h11,h2,h0])],[fact_3_assms_I2_J,h7])).
21.13/20.82	thf(52,plain,(((~(sP35) | sP40) | ~(sP26)) | ~(sP19)),inference(mating_rule,[status(thm)],[])).
21.13/20.82	thf(53,plain,(((~(sP33) | sP23) | ~(sP19)) | ~(sP45)),inference(mating_rule,[status(thm)],[])).
21.13/20.82	thf(54,plain,(~(sP53) | sP2),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(55,plain,(~(sP53) | sP39),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(56,plain,(sP21 | sP19),inference(prop_rule,[status(thm)],[])).
21.13/20.82	thf(57,plain,((~(sP42) | ~(sP40)) | sP14),inference(prop_rule,[status(thm)],[])).
21.13/20.82	thf(58,plain,((~(sP14) | ~(sP23)) | sP10),inference(prop_rule,[status(thm)],[])).
21.13/20.82	thf(59,plain,(~(sP22) | sP9),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(60,plain,(~(sP9) | sP44),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(61,plain,((~(sP44) | ~(sP39)) | sP45),inference(prop_rule,[status(thm)],[])).
21.13/20.82	thf(62,plain,(~(sP22) | sP5),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(63,plain,(~(sP5) | sP36),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(64,plain,((~(sP36) | ~(sP2)) | sP26),inference(prop_rule,[status(thm)],[])).
21.13/20.82	thf(65,plain,(~(sP46) | sP22),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(66,plain,(~(sP48) | sP53),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(67,plain,(~(sP27) | sP17),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(68,plain,(~(sP30) | sP42),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(69,plain,(~(sP4) | sP3),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(70,plain,(~(sP3) | sP20),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(71,plain,(~(sP20) | sP6),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(72,plain,(~(sP6) | sP31),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(73,plain,((~(sP31) | ~(sP17)) | ~(sP21)),inference(prop_rule,[status(thm)],[])).
21.13/20.82	thf(74,plain,$false,inference(prop_unsat,[status(thm),assumptions([h8,h6,h10,h4,h11,h2,h0])],[52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,h11,fact_364_snd__eqD,fact_362_snd__conv,fact_358_surjective__pairing,fact_19_r01__binary__expansion__well__formed,fact_16_Pair__inject,fact_2_assms_I4_J,fact_0_assms_I3_J])).
21.13/20.82	thf(75,plain,$false,inference(tab_imp,[status(thm),assumptions([h6,h10,h4,h11,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,51,74,h7,h8])).
21.13/20.82	thf(76,plain,$false,inference(tab_imp,[status(thm),assumptions([h10,h4,h11,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_4__092_060open_062_092_060lbrakk_0620_A_060_Ar1_059_Ar1_A_060_A1_092_060rbrakk_062_A_092_060Longrightarrow_062_Abiexp01__well__formed_A_Ir01__binary__expansion_H_Ar1_J_092_060close_062,50,75,h5,h6])).
21.13/20.82	thf(77,plain,$false,inference(tab_imp,[status(thm),assumptions([h4,h11,h2,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h4,49,76,h9,h10])).
21.13/20.82	thf(78,plain,$false,inference(tab_imp,[status(thm),assumptions([h11,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_5__092_060open_062_092_060lbrakk_0620_A_060_Ar2_059_Ar2_A_060_A1_092_060rbrakk_062_A_092_060Longrightarrow_062_Abiexp01__well__formed_A_Ir01__binary__expansion_H_Ar2_J_092_060close_062,44,77,h3,h4])).
21.13/20.82	thf(79,plain,$false,inference(tab_conflict,[status(thm),assumptions([h5,h3,h12,h2,h0])],[fact_1_assms_I1_J,h5])).
21.13/20.82	thf(80,plain,$false,inference(tab_conflict,[status(thm),assumptions([h7,h6,h3,h12,h2,h0])],[fact_3_assms_I2_J,h7])).
21.13/20.82	thf(81,plain,$false,inference(tab_conflict,[status(thm),assumptions([h8,h6,h3,h12,h2,h0])],[fact_0_assms_I3_J,h3])).
21.13/20.82	thf(82,plain,$false,inference(tab_imp,[status(thm),assumptions([h6,h3,h12,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,80,81,h7,h8])).
21.13/20.82	thf(83,plain,$false,inference(tab_imp,[status(thm),assumptions([h3,h12,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_4__092_060open_062_092_060lbrakk_0620_A_060_Ar1_059_Ar1_A_060_A1_092_060rbrakk_062_A_092_060Longrightarrow_062_Abiexp01__well__formed_A_Ir01__binary__expansion_H_Ar1_J_092_060close_062,79,82,h5,h6])).
21.13/20.82	thf(84,plain,$false,inference(tab_conflict,[status(thm),assumptions([h5,h9,h4,h12,h2,h0])],[fact_1_assms_I1_J,h5])).
21.13/20.82	thf(85,plain,$false,inference(tab_conflict,[status(thm),assumptions([h7,h6,h9,h4,h12,h2,h0])],[fact_3_assms_I2_J,h7])).
21.13/20.82	thf(86,plain,$false,inference(tab_conflict,[status(thm),assumptions([h8,h6,h9,h4,h12,h2,h0])],[fact_2_assms_I4_J,h9])).
21.13/20.82	thf(87,plain,$false,inference(tab_imp,[status(thm),assumptions([h6,h9,h4,h12,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,85,86,h7,h8])).
21.13/20.82	thf(88,plain,$false,inference(tab_imp,[status(thm),assumptions([h9,h4,h12,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_4__092_060open_062_092_060lbrakk_0620_A_060_Ar1_059_Ar1_A_060_A1_092_060rbrakk_062_A_092_060Longrightarrow_062_Abiexp01__well__formed_A_Ir01__binary__expansion_H_Ar1_J_092_060close_062,84,87,h5,h6])).
21.13/20.82	thf(89,plain,$false,inference(tab_conflict,[status(thm),assumptions([h5,h10,h4,h12,h2,h0])],[fact_1_assms_I1_J,h5])).
21.13/20.82	thf(90,plain,$false,inference(tab_conflict,[status(thm),assumptions([h7,h6,h10,h4,h12,h2,h0])],[fact_3_assms_I2_J,h7])).
21.13/20.82	thf(91,plain,((~(sP43) | ~(sP41)) | sP12),inference(prop_rule,[status(thm)],[])).
21.13/20.82	thf(92,plain,(~(sP15) | sP43),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(93,plain,(~(sP13) | sP15),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(94,plain,sP13,inference(@eq_sym,[status(thm)],[])).
21.13/20.82	thf(95,plain,((~(sP16) | sP52) | ~(sP12)),inference(mating_rule,[status(thm)],[])).
21.13/20.82	thf(96,plain,(~(sP18) | sP41),inference(all_rule,[status(thm)],[])).
21.13/20.82	thf(97,plain,(~(sP54) | sP18),inference(prop_rule,[status(thm)],[])).
21.13/20.82	thf(fact_387_r01__r01__to__r01_H__def,axiom,sP54).
21.13/20.82	thf(98,plain,$false,inference(prop_unsat,[status(thm),assumptions([h8,h6,h10,h4,h12,h2,h0])],[91,92,93,94,95,96,97,h0,h12,fact_387_r01__r01__to__r01_H__def])).
21.13/20.82	thf(99,plain,$false,inference(tab_imp,[status(thm),assumptions([h6,h10,h4,h12,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,90,98,h7,h8])).
21.13/20.82	thf(100,plain,$false,inference(tab_imp,[status(thm),assumptions([h10,h4,h12,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_4__092_060open_062_092_060lbrakk_0620_A_060_Ar1_059_Ar1_A_060_A1_092_060rbrakk_062_A_092_060Longrightarrow_062_Abiexp01__well__formed_A_Ir01__binary__expansion_H_Ar1_J_092_060close_062,89,99,h5,h6])).
21.13/20.82	thf(101,plain,$false,inference(tab_imp,[status(thm),assumptions([h4,h12,h2,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h4,88,100,h9,h10])).
21.13/20.82	thf(102,plain,$false,inference(tab_imp,[status(thm),assumptions([h12,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_5__092_060open_062_092_060lbrakk_0620_A_060_Ar2_059_Ar2_A_060_A1_092_060rbrakk_062_A_092_060Longrightarrow_062_Abiexp01__well__formed_A_Ir01__binary__expansion_H_Ar2_J_092_060close_062,83,101,h3,h4])).
21.13/20.82	thf(103,plain,$false,inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h12])],[h2,78,102,h11,h12])).
21.13/20.82	thf(fact_392__092_060open_062_092_060lbrakk_062biexp01__well__formed_A_Ir01__binary__expansion_H_A_Ifst_A_Ir1_M_Ar2_J_J_J_059_Abiexp01__well__formed_A_Ir01__binary__expansion_H_A_Isnd_A_Ir1_M_Ar2_J_J_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Abiexp01__well__formed_A_I_092_060lambda_062n_O_Aif_Aeven_An_Athen_Ar01__binary__expansion_H_A_Ifst_A_Ir1_M_Ar2_J_J_A_In_Adiv_A2_J_Aelse_Ar01__binary__expansion_H_A_Isnd_A_Ir1_M_Ar2_J_J_A_I_In_A_N_A1_J_Adiv_A2_J_J_092_060close_062,axiom,(sP24 => (sP10 => sP16))).
21.13/20.82	thf(104,plain,$false,inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_392__092_060open_062_092_060lbrakk_062biexp01__well__formed_A_Ir01__binary__expansion_H_A_Ifst_A_Ir1_M_Ar2_J_J_J_059_Abiexp01__well__formed_A_Ir01__binary__expansion_H_A_Isnd_A_Ir1_M_Ar2_J_J_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Abiexp01__well__formed_A_I_092_060lambda_062n_O_Aif_Aeven_An_Athen_Ar01__binary__expansion_H_A_Ifst_A_Ir1_M_Ar2_J_J_A_In_Adiv_A2_J_Aelse_Ar01__binary__expansion_H_A_Isnd_A_Ir1_M_Ar2_J_J_A_I_In_A_N_A1_J_Adiv_A2_J_J_092_060close_062,39,103,h1,h2])).
21.13/20.82	thf(0,theorem,sP52,inference(contra,[status(thm),contra(discharge,[h0])],[104,h0])).
21.13/20.82	% SZS output end Proof
21.13/20.82	EOF