0.03/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command  : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer : n021.cluster.edu
0.12/0.33	% Model    : x86_64 x86_64
0.12/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory   : 8042.1875MB
0.12/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit : 1440
0.12/0.33	% WCLimit  : 180
0.12/0.33	% DateTime : Mon Jul  3 03:33:52 EDT 2023
0.12/0.33	% CPUTime  : 
0.78/1.03	============================== Prover9 ===============================
0.78/1.03	Prover9 (32) version 2009-11A, November 2009.
0.78/1.03	Process 28303 was started by sandbox2 on n021.cluster.edu,
0.78/1.03	Mon Jul  3 03:33:53 2023
0.78/1.03	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1440 -f /tmp/Prover9_28150_n021.cluster.edu".
0.78/1.03	============================== end of head ===========================
0.78/1.03	
0.78/1.03	============================== INPUT =================================
0.78/1.03	
0.78/1.03	% Reading from file /tmp/Prover9_28150_n021.cluster.edu
0.78/1.03	
0.78/1.03	set(prolog_style_variables).
0.78/1.03	set(auto2).
0.78/1.03	    % set(auto2) -> set(auto).
0.78/1.03	    % set(auto) -> set(auto_inference).
0.78/1.03	    % set(auto) -> set(auto_setup).
0.78/1.03	    % set(auto_setup) -> set(predicate_elim).
0.78/1.03	    % set(auto_setup) -> assign(eq_defs, unfold).
0.78/1.03	    % set(auto) -> set(auto_limits).
0.78/1.03	    % set(auto_limits) -> assign(max_weight, "100.000").
0.78/1.03	    % set(auto_limits) -> assign(sos_limit, 20000).
0.78/1.03	    % set(auto) -> set(auto_denials).
0.78/1.03	    % set(auto) -> set(auto_process).
0.78/1.03	    % set(auto2) -> assign(new_constants, 1).
0.78/1.03	    % set(auto2) -> assign(fold_denial_max, 3).
0.78/1.03	    % set(auto2) -> assign(max_weight, "200.000").
0.78/1.03	    % set(auto2) -> assign(max_hours, 1).
0.78/1.03	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.78/1.03	    % set(auto2) -> assign(max_seconds, 0).
0.78/1.03	    % set(auto2) -> assign(max_minutes, 5).
0.78/1.03	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.78/1.03	    % set(auto2) -> set(sort_initial_sos).
0.78/1.03	    % set(auto2) -> assign(sos_limit, -1).
0.78/1.03	    % set(auto2) -> assign(lrs_ticks, 3000).
0.78/1.03	    % set(auto2) -> assign(max_megs, 400).
0.78/1.03	    % set(auto2) -> assign(stats, some).
0.78/1.03	    % set(auto2) -> clear(echo_input).
0.78/1.03	    % set(auto2) -> set(quiet).
0.78/1.03	    % set(auto2) -> clear(print_initial_clauses).
0.78/1.03	    % set(auto2) -> clear(print_given).
0.78/1.03	assign(lrs_ticks,-1).
0.78/1.03	assign(sos_limit,10000).
0.78/1.03	assign(order,kbo).
0.78/1.03	set(lex_order_vars).
0.78/1.03	clear(print_given).
0.78/1.03	
0.78/1.03	% formulas(sos).  % not echoed (124 formulas)
0.78/1.03	
0.78/1.03	============================== end of input ==========================
0.78/1.03	
0.78/1.03	% From the command line: assign(max_seconds, 1440).
0.78/1.03	
0.78/1.03	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.78/1.03	
0.78/1.03	% Formulas that are not ordinary clauses:
0.78/1.03	1 (all K all L (ord_less_int(K,L) <-> ord_less_int(bit1(K),bit0(L)))) # label(fact_117_rel__simps_I16_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.03	2 (all V_3 plus_plus_int(number_number_of_int(V_3),one_one_int) = number_number_of_int(plus_plus_int(V_3,bit1(pls)))) # label(fact_23_add__special_I3_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.03	3 (all K all L (ord_less_eq_int(bit0(K),bit0(L)) <-> ord_less_eq_int(K,L))) # label(fact_57_rel__simps_I31_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.03	4 (all W ord_less_eq_int(W,W)) # label(fact_26_zle__refl) # label(axiom) # label(non_clause).  [assumption].
0.78/1.03	5 (all A_5 all B_2 all C_5 all D_2 plus_plus_int(plus_plus_int(A_5,C_5),plus_plus_int(B_2,D_2)) = plus_plus_int(plus_plus_int(A_5,B_2),plus_plus_int(C_5,D_2))) # label(fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.03	6 (all K1 all K2 (ord_less_int(bit1(K1),bit0(K2)) <-> ord_less_int(K1,K2))) # label(fact_116_less__int__code_I15_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.03	7 (all Lx_1 all Rx_1 all Ry_1 times_times_int(Lx_1,times_times_int(Rx_1,Ry_1)) = times_times_int(times_times_int(Lx_1,Rx_1),Ry_1)) # label(fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.03	8 (all Lx_4 all Ly_2 all Rx_4 all Ry_2 times_times_nat(Lx_4,times_times_nat(Ly_2,times_times_nat(Rx_4,Ry_2))) = times_times_nat(times_times_nat(Lx_4,Ly_2),times_times_nat(Rx_4,Ry_2))) # label(fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.03	9 (all X_2 all Y_2 (ord_less_eq_int(X_2,Y_2) <-> ord_less_eq_int(number_number_of_int(X_2),number_number_of_int(Y_2)))) # label(fact_40_le__number__of) # label(axiom) # label(non_clause).  [assumption].
0.78/1.03	10 (all Z_2 all Z all W_2 all W (ord_less_int(W_2,W) -> (ord_less_eq_int(Z_2,Z) -> ord_less_int(plus_plus_int(W_2,Z_2),plus_plus_int(W,Z))))) # label(fact_41_zadd__zless__mono) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	11 (all K all L (ord_less_int(bit1(K),bit1(L)) <-> ord_less_int(K,L))) # label(fact_49_rel__simps_I17_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	12 (all A_3 all B all C_3 plus_plus_int(A_3,plus_plus_int(B,C_3)) = plus_plus_int(plus_plus_int(A_3,B),C_3)) # label(fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	13 (all W_1 all Z_1 (ord_less_eq_int(plus_plus_int(W_1,one_one_int),Z_1) <-> ord_less_int(W_1,Z_1))) # label(fact_72_add1__zle__eq) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	14 (all K (ord_less_eq_int(bit1(K),pls) <-> ord_less_int(K,pls))) # label(fact_65_rel__simps_I29_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	15 (all Lx_4 all Ly_2 all Rx_4 all Ry_2 times_times_int(Lx_4,times_times_int(Ly_2,times_times_int(Rx_4,Ry_2))) = times_times_int(times_times_int(Lx_4,Ly_2),times_times_int(Rx_4,Ry_2))) # label(fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	16 (all A_6 all B_3 times_times_int(A_6,B_3) = times_times_int(B_3,A_6)) # label(fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	17 (all K all L (ord_less_eq_int(number_number_of_int(K),number_number_of_int(L)) <-> ord_less_eq_int(K,L))) # label(fact_59_less__eq__number__of__int__code) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	18 (all K_1 K_1 = number_number_of_int(K_1)) # label(fact_111_number__of__is__id) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	19 (all Y_1 all X_1 (twoSqu526106917sum2sq(X_1) -> (twoSqu526106917sum2sq(Y_1) -> twoSqu526106917sum2sq(times_times_int(X_1,Y_1))))) # label(fact_75_is__mult__sum2sq) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	20 (all K1 all K2 (ord_less_eq_int(K1,K2) <-> ord_less_int(bit0(K1),bit1(K2)))) # label(fact_69_less__int__code_I14_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	21 (all K (ord_less_int(K,pls) <-> ord_less_int(bit1(K),pls))) # label(fact_115_rel__simps_I12_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	22 (all Z_1 all W_1 (Z_1 != W_1 & ord_less_eq_int(Z_1,W_1) <-> ord_less_int(Z_1,W_1))) # label(fact_28_zless__le) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	23 (all K_1 all I all J (ord_less_int(I,J) -> ord_less_int(plus_plus_int(I,K_1),plus_plus_int(J,K_1)))) # label(fact_60_zadd__strict__right__mono) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	24 (all X_6 all N times_times_nat(power_power_nat(X_6,N),power_power_nat(X_6,N)) = power_power_nat(X_6,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N))) # label(fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	25 (all X_1 all Y_1 (X_1 = Y_1 | ord_less_int(Y_1,X_1) | ord_less_int(X_1,Y_1))) # label(fact_29_zless__linear) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	26 (all K1 all K2 (ord_less_int(K1,K2) <-> ord_less_eq_int(bit1(K1),bit0(K2)))) # label(fact_67_less__eq__int__code_I15_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	27 (all Lx_6 all Ly_4 all Rx_6 all Ry_4 times_times_nat(times_times_nat(Lx_6,Rx_6),times_times_nat(Ly_4,Ry_4)) = times_times_nat(times_times_nat(Lx_6,Ly_4),times_times_nat(Rx_6,Ry_4))) # label(fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	28 (all X_1 all Y_1 all Z plus_plus_int(X_1,plus_plus_int(Y_1,Z)) = plus_plus_int(Y_1,plus_plus_int(X_1,Z))) # label(fact_113_zadd__left__commute) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	29 (all X_2 all Y_2 (ord_less_int(X_2,Y_2) <-> ord_less_int(number_number_of_int(X_2),number_number_of_int(Y_2)))) # label(fact_39_less__number__of) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	30 (all V_2 all W_1 (-ord_less_int(number_number_of_int(W_1),number_number_of_int(V_2)) <-> ord_less_eq_int(number_number_of_int(V_2),number_number_of_int(W_1)))) # label(fact_38_le__number__of__eq__not__less) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	31 (all X_4 power_power_int(X_4,one_one_nat) = X_4) # label(fact_34_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	32 (all W_1 all Z_1 (ord_less_int(W_1,plus_plus_int(Z_1,one_one_int)) <-> ord_less_eq_int(W_1,Z_1))) # label(fact_73_zle__add1__eq__le) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	33 (all A_8 all B_4 plus_plus_int(plus_plus_int(power_power_int(A_8,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),A_8),B_4)),power_power_int(B_4,number_number_of_nat(bit0(bit1(pls))))) = power_power_int(plus_plus_int(A_8,B_4),number_number_of_nat(bit0(bit1(pls))))) # label(fact_7_zadd__power2) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	34 (all A_2 all C_2 all D_1 plus_plus_int(plus_plus_int(A_2,C_2),D_1) = plus_plus_int(A_2,plus_plus_int(C_2,D_1))) # label(fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	35 (all Lx_2 all Ly all Rx_2 times_times_int(Lx_2,times_times_int(Ly,Rx_2)) = times_times_int(times_times_int(Lx_2,Ly),Rx_2)) # label(fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	36 (all X_6 all N times_times_int(power_power_int(X_6,N),power_power_int(X_6,N)) = power_power_int(X_6,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N))) # label(fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	37 (all X_4 X_4 = power_power_nat(X_4,one_one_nat)) # label(fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	38 ord_less_int(one_one_int,t) -> (exists X exists Y plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) # label(fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	39 (all K all L (ord_less_int(K,L) <-> ord_less_int(number_number_of_int(K),number_number_of_int(L)))) # label(fact_58_less__number__of__int__code) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	40 (all K_1 all I all J (ord_less_eq_int(I,J) -> ord_less_eq_int(plus_plus_int(K_1,I),plus_plus_int(K_1,J)))) # label(fact_61_zadd__left__mono) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	41 (all Lx all Rx all Ry times_times_int(Lx,times_times_int(Rx,Ry)) = times_times_int(Rx,times_times_int(Lx,Ry))) # label(fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	42 (all Lx_6 all Ly_4 all Rx_6 all Ry_4 times_times_int(times_times_int(Lx_6,Rx_6),times_times_int(Ly_4,Ry_4)) = times_times_int(times_times_int(Lx_6,Ly_4),times_times_int(Rx_6,Ry_4))) # label(fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	43 (all X_2 all Y_2 (number_number_of_int(Y_2) = number_number_of_int(X_2) <-> Y_2 = X_2)) # label(fact_104_eq__number__of) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	44 (all A all C plus_plus_int(C,A) = plus_plus_int(A,C)) # label(fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	45 (all V_2 all W_1 (ord_less_eq_nat(number_number_of_nat(V_2),number_number_of_nat(W_1)) <-> -ord_less_nat(number_number_of_nat(W_1),number_number_of_nat(V_2)))) # label(fact_37_le__number__of__eq__not__less) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	46 (all Z1 all Z2 all Z3 plus_plus_int(Z1,plus_plus_int(Z2,Z3)) = plus_plus_int(plus_plus_int(Z1,Z2),Z3)) # label(fact_112_zadd__assoc) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	47 (all K1 all K2 (ord_less_int(K1,K2) <-> ord_less_int(bit0(K1),bit0(K2)))) # label(fact_53_less__int__code_I13_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	48 (all Lx_5 all Ly_3 all Rx_5 all Ry_3 times_times_nat(times_times_nat(Lx_5,Ly_3),times_times_nat(Rx_5,Ry_3)) = times_times_nat(Rx_5,times_times_nat(times_times_nat(Lx_5,Ly_3),Ry_3))) # label(fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	49 (all X_5 all P_1 all Q_1 power_power_nat(power_power_nat(X_5,P_1),Q_1) = power_power_nat(X_5,times_times_nat(P_1,Q_1))) # label(fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	50 (all X_7 power_power_nat(X_7,number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(X_7,X_7)) # label(fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	51 (all A_8 all B_4 plus_plus_int(plus_plus_int(plus_plus_int(power_power_int(A_8,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(A_8,number_number_of_nat(bit0(bit1(pls))))),B_4)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),A_8),power_power_int(B_4,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(B_4,number_number_of_nat(bit1(bit1(pls))))) = power_power_int(plus_plus_int(A_8,B_4),number_number_of_nat(bit1(bit1(pls))))) # label(fact_8_zadd__power3) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	52 (all K1 all K2 (ord_less_eq_int(K1,K2) <-> ord_less_eq_int(bit0(K1),bit0(K2)))) # label(fact_56_less__eq__int__code_I13_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	53 (all K1 all K2 (ord_less_int(bit1(K1),bit1(K2)) <-> ord_less_int(K1,K2))) # label(fact_48_less__int__code_I16_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	54 (all W_3 number_number_of_int(plus_plus_int(bit1(pls),W_3)) = plus_plus_int(one_one_int,number_number_of_int(W_3))) # label(fact_22_add__special_I2_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	55 (all K all L (ord_less_eq_int(bit0(K),bit1(L)) <-> ord_less_eq_int(K,L))) # label(fact_122_rel__simps_I32_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	56 (all K all L (bit1(L) = bit1(K) <-> L = K)) # label(fact_107_rel__simps_I51_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	57 -(all T times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),T) != plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int)) # label(fact_25__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_) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	58 (all Lx_3 all Ly_1 all Rx_3 times_times_int(times_times_int(Lx_3,Rx_3),Ly_1) = times_times_int(times_times_int(Lx_3,Ly_1),Rx_3)) # label(fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	59 (all K1 all K2 (ord_less_eq_int(K1,K2) <-> ord_less_eq_int(bit1(K1),bit1(K2)))) # label(fact_50_less__eq__int__code_I16_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	60 (all X_3 all P all Q times_times_int(power_power_int(X_3,P),power_power_int(X_3,Q)) = power_power_int(X_3,plus_plus_nat(P,Q))) # label(fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	61 (all Z plus_plus_nat(Z,Z) = times_times_nat(Z,number_number_of_nat(bit0(bit1(pls))))) # label(fact_46_nat__mult__2__right) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	62 (all A_8 power_power_int(A_8,number_number_of_nat(bit1(bit1(pls)))) = times_times_int(A_8,power_power_int(A_8,number_number_of_nat(bit0(bit1(pls)))))) # label(fact_13_cube__square) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	63 (all V_1 all V ((-ord_less_int(V,pls) -> (ord_less_int(V_1,pls) -> number_number_of_nat(V) = plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1))) & (-ord_less_int(V_1,pls) -> plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(plus_plus_int(V,V_1)))) & (ord_less_int(V,pls) -> plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(V_1)))) # label(fact_62_add__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	64 (all K (ord_less_eq_int(pls,K) <-> ord_less_int(pls,bit1(K)))) # label(fact_66_rel__simps_I5_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	65 (all Z all W (ord_less_eq_int(Z,W) | ord_less_eq_int(W,Z))) # label(fact_27_zle__linear) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	66 (all X_2 all Y_2 plus_plus_int(plus_plus_int(power_power_int(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y_2,number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X_2),Y_2)) = power_power_int(plus_plus_int(X_2,Y_2),number_number_of_nat(bit0(bit1(pls))))) # label(fact_10_power2__sum) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	67 (all A_5 all B_2 all C_5 all D_2 plus_plus_nat(plus_plus_nat(A_5,B_2),plus_plus_nat(C_5,D_2)) = plus_plus_nat(plus_plus_nat(A_5,C_5),plus_plus_nat(B_2,D_2))) # label(fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	68 (all X_2 all Y_2 power_power_nat(plus_plus_nat(X_2,Y_2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(plus_plus_nat(power_power_nat(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(Y_2,number_number_of_nat(bit0(bit1(pls))))),times_times_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls))),X_2),Y_2))) # label(fact_9_power2__sum) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	69 (all Lx_3 all Ly_1 all Rx_3 times_times_nat(times_times_nat(Lx_3,Rx_3),Ly_1) = times_times_nat(times_times_nat(Lx_3,Ly_1),Rx_3)) # label(fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	70 (all K all L (ord_less_eq_int(bit1(K),bit1(L)) <-> ord_less_eq_int(K,L))) # label(fact_51_rel__simps_I34_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	71 (all K (ord_less_eq_int(pls,bit1(K)) <-> ord_less_eq_int(pls,K))) # label(fact_120_rel__simps_I22_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	72 (all K all L (ord_less_eq_int(bit1(K),bit0(L)) <-> ord_less_int(K,L))) # label(fact_68_rel__simps_I33_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	73 (all K (ord_less_int(K,pls) <-> ord_less_int(bit0(K),pls))) # label(fact_118_rel__simps_I10_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	74 (all K all L (bit0(K) = bit0(L) <-> K = L)) # label(fact_108_rel__simps_I48_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	75 (all A_7 power_power_int(A_7,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(A_7,A_7)) # label(fact_18_power2__eq__square) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	76 (all A_7 times_times_nat(A_7,A_7) = power_power_nat(A_7,number_number_of_nat(bit0(bit1(pls))))) # label(fact_19_power2__eq__square) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	77 (all W all Z (ord_less_int(W,Z) -> ord_less_eq_int(plus_plus_int(W,one_one_int),Z))) # label(fact_71_zless__imp__add1__zle) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	78 (all W_1 all X_2 (X_2 = number_number_of_nat(W_1) <-> number_number_of_nat(W_1) = X_2)) # label(fact_105_number__of__reorient) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	79 (all A all C plus_plus_nat(C,A) = plus_plus_nat(A,C)) # label(fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	80 (all W_1 all X_2 (number_number_of_int(W_1) = X_2 <-> X_2 = number_number_of_int(W_1))) # label(fact_106_number__of__reorient) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	81 (all K1 all K2 (ord_less_eq_int(K1,K2) <-> ord_less_eq_int(bit0(K1),bit1(K2)))) # label(fact_121_less__eq__int__code_I14_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	82 (all A_3 all B all C_3 plus_plus_nat(A_3,plus_plus_nat(B,C_3)) = plus_plus_nat(plus_plus_nat(A_3,B),C_3)) # label(fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	83 (all Z times_times_nat(number_number_of_nat(bit0(bit1(pls))),Z) = plus_plus_nat(Z,Z)) # label(fact_45_nat__mult__2) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	84 (all X_1 all Y_1 all Z power_power_int(X_1,plus_plus_nat(Y_1,Z)) = times_times_int(power_power_int(X_1,Y_1),power_power_int(X_1,Z))) # label(fact_44_zpower__zadd__distrib) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	85 (all K all L (ord_less_int(K,L) <-> ord_less_int(bit0(K),bit0(L)))) # label(fact_54_rel__simps_I14_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	86 (all K all L (ord_less_eq_int(K,L) <-> ord_less_int(bit0(K),bit1(L)))) # label(fact_70_rel__simps_I15_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	87 (all X_1 all Y_1 all Z power_power_int(X_1,times_times_nat(Y_1,Z)) = power_power_int(power_power_int(X_1,Y_1),Z)) # label(fact_36_zpower__zpower) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	88 (all X_5 all P_1 all Q_1 power_power_int(power_power_int(X_5,P_1),Q_1) = power_power_int(X_5,times_times_nat(P_1,Q_1))) # label(fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	89 (all A_4 all B_1 all C_4 plus_plus_int(plus_plus_int(A_4,B_1),C_4) = plus_plus_int(plus_plus_int(A_4,C_4),B_1)) # label(fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	90 (all A_6 all B_3 times_times_nat(B_3,A_6) = times_times_nat(A_6,B_3)) # label(fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	91 (all A_1 all C_1 all D plus_plus_int(C_1,plus_plus_int(A_1,D)) = plus_plus_int(A_1,plus_plus_int(C_1,D))) # label(fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	92 (all Lx_1 all Rx_1 all Ry_1 times_times_nat(times_times_nat(Lx_1,Rx_1),Ry_1) = times_times_nat(Lx_1,times_times_nat(Rx_1,Ry_1))) # label(fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	93 (all W_4 times_times_nat(number_number_of_nat(W_4),number_number_of_nat(W_4)) = power_power_nat(number_number_of_nat(W_4),number_number_of_nat(bit0(bit1(pls))))) # label(fact_12_power2__eq__square__number__of) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	94 (all Z all W times_times_int(Z,W) = times_times_int(W,Z)) # label(fact_110_zmult__commute) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	95 (all Lx all Rx all Ry times_times_nat(Rx,times_times_nat(Lx,Ry)) = times_times_nat(Lx,times_times_nat(Rx,Ry))) # label(fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	96 (all X_3 all P all Q times_times_nat(power_power_nat(X_3,P),power_power_nat(X_3,Q)) = power_power_nat(X_3,plus_plus_nat(P,Q))) # label(fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	97 (all K_1 all I all J (ord_less_eq_int(I,J) -> (ord_less_eq_int(J,K_1) -> ord_less_eq_int(I,K_1)))) # label(fact_30_zle__trans) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	98 (all Lx_2 all Ly all Rx_2 times_times_nat(times_times_nat(Lx_2,Ly),Rx_2) = times_times_nat(Lx_2,times_times_nat(Ly,Rx_2))) # label(fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	99 (all Lx_5 all Ly_3 all Rx_5 all Ry_3 times_times_int(times_times_int(Lx_5,Ly_3),times_times_int(Rx_5,Ry_3)) = times_times_int(Rx_5,times_times_int(times_times_int(Lx_5,Ly_3),Ry_3))) # label(fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.04	100 (all A_4 all B_1 all C_4 plus_plus_nat(plus_plus_nat(A_4,B_1),C_4) = plus_plus_nat(plus_plus_nat(A_4,C_4),B_1)) # label(fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	101 one_one_int = t -> (exists X exists Y plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls)))))) # label(fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	102 (all X_7 times_times_int(X_7,X_7) = power_power_int(X_7,number_number_of_nat(bit0(bit1(pls))))) # label(fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	103 (all A_2 all C_2 all D_1 plus_plus_nat(plus_plus_nat(A_2,C_2),D_1) = plus_plus_nat(A_2,plus_plus_nat(C_2,D_1))) # label(fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	104 (all Z1 all Z2 all Z3 times_times_int(Z1,times_times_int(Z2,Z3)) = times_times_int(times_times_int(Z1,Z2),Z3)) # label(fact_109_zmult__assoc) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	105 (all W_4 power_power_int(number_number_of_int(W_4),number_number_of_nat(bit0(bit1(pls)))) = times_times_int(number_number_of_int(W_4),number_number_of_int(W_4))) # label(fact_11_power2__eq__square__number__of) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	106 (all A_1 all C_1 all D plus_plus_nat(A_1,plus_plus_nat(C_1,D)) = plus_plus_nat(C_1,plus_plus_nat(A_1,D))) # label(fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	107 (all Z all W plus_plus_int(Z,W) = plus_plus_int(W,Z)) # label(fact_114_zadd__commute) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	108 (all K (ord_less_int(pls,K) <-> ord_less_int(pls,bit0(K)))) # label(fact_119_rel__simps_I4_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	109 (all Z all W (ord_less_eq_int(Z,W) -> (ord_less_eq_int(W,Z) -> Z = W))) # label(fact_31_zle__antisym) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	110 -(exists X exists Y plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) # label(conj_0) # label(negated_conjecture) # label(non_clause).  [assumption].
0.78/1.06	
0.78/1.06	============================== end of process non-clausal formulas ===
0.78/1.06	
0.78/1.06	============================== PROCESS INITIAL CLAUSES ===============
0.78/1.06	
0.78/1.06	============================== PREDICATE ELIMINATION =================
0.78/1.06	
0.78/1.06	============================== end predicate elimination =============
0.78/1.06	
0.78/1.06	Auto_denials:  (non-Horn, no changes).
0.78/1.06	
0.78/1.06	Term ordering decisions:
0.78/1.06	Function symbol KB weights:  pls=1. one_one_int=1. one_one_nat=1. m=1. t=1. s=1. c1=1. c2=1. c3=1. c4=1. c5=1. plus_plus_int=1. times_times_int=1. times_times_nat=1. power_power_int=1. plus_plus_nat=1. power_power_nat=1. bit1=1. bit0=1. number_number_of_nat=1. number_number_of_int=1.
0.78/1.06	
0.78/1.06	============================== end of process initial clauses ========
0.78/1.06	
0.78/1.06	============================== CLAUSES FOR SEARCH ====================
0.78/1.06	
0.78/1.06	============================== end of clauses for search =============
0.78/1.06	
0.78/1.06	============================== SEARCH ================================
0.78/1.06	
0.78/1.06	% Starting search at 0.04 seconds.
0.78/1.06	
0.78/1.06	============================== PROOF =================================
0.78/1.06	% SZS status Theorem
0.78/1.06	% SZS output start Refutation
0.78/1.06	
0.78/1.06	% Proof 1 at 0.04 (+ 0.00) seconds.
0.78/1.06	% Length of proof is 25.
0.78/1.06	% Level of proof is 6.
0.78/1.06	% Maximum clause weight is 25.000.
0.78/1.06	% Given clauses 45.
0.78/1.06	
0.78/1.06	16 (all A_6 all B_3 times_times_int(A_6,B_3) = times_times_int(B_3,A_6)) # label(fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	18 (all K_1 K_1 = number_number_of_int(K_1)) # label(fact_111_number__of__is__id) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	22 (all Z_1 all W_1 (Z_1 != W_1 & ord_less_eq_int(Z_1,W_1) <-> ord_less_int(Z_1,W_1))) # label(fact_28_zless__le) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	38 ord_less_int(one_one_int,t) -> (exists X exists Y plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) # label(fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	44 (all A all C plus_plus_int(C,A) = plus_plus_int(A,C)) # label(fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	101 one_one_int = t -> (exists X exists Y plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls)))))) # label(fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	110 -(exists X exists Y plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) # label(conj_0) # label(negated_conjecture) # label(non_clause).  [assumption].
0.78/1.06	135 times_times_int(A,B) = times_times_int(B,A) # label(fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom).  [clausify(16)].
0.78/1.06	136 number_number_of_int(A) = A # label(fact_111_number__of__is__id) # label(axiom).  [clausify(18)].
0.78/1.06	142 A = B | -ord_less_eq_int(A,B) | ord_less_int(A,B) # label(fact_28_zless__le) # label(axiom).  [clausify(22)].
0.78/1.06	159 plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))) # label(fact_24_one__add__one__is__two) # label(axiom).  [assumption].
0.78/1.06	160 bit0(bit1(pls)) = plus_plus_int(one_one_int,one_one_int).  [copy(159),rewrite([136(7)]),flip(a)].
0.78/1.06	172 -ord_less_int(one_one_int,t) | plus_plus_int(power_power_int(c1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(c2,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) # label(fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) # label(axiom).  [clausify(38)].
0.78/1.06	173 -ord_less_int(one_one_int,t) | plus_plus_int(power_power_int(c1,number_number_of_nat(plus_plus_int(one_one_int,one_one_int))),power_power_int(c2,number_number_of_nat(plus_plus_int(one_one_int,one_one_int)))) = plus_plus_int(times_times_int(m,bit0(plus_plus_int(one_one_int,one_one_int))),one_one_int).  [copy(172),rewrite([160(7),160(13),160(19),136(21),135(22)])].
0.78/1.06	184 plus_plus_int(A,B) = plus_plus_int(B,A) # label(fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom).  [clausify(44)].
0.78/1.06	199 ord_less_eq_int(one_one_int,t) # label(fact_0_tpos) # label(axiom).  [assumption].
0.78/1.06	265 t != one_one_int | plus_plus_int(power_power_int(c4,number_number_of_nat(bit0(bit1(pls)))),power_power_int(c5,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) # label(fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) # label(axiom).  [clausify(101)].
0.78/1.06	266 t != one_one_int | plus_plus_int(power_power_int(c4,number_number_of_nat(plus_plus_int(one_one_int,one_one_int))),power_power_int(c5,number_number_of_nat(plus_plus_int(one_one_int,one_one_int)))) = plus_plus_int(one_one_int,times_times_int(m,bit0(plus_plus_int(one_one_int,one_one_int)))).  [copy(265),rewrite([160(7),160(13),160(19),136(21),135(22),184(24)])].
0.78/1.06	268 number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat) # label(fact_47_nat__1__add__1) # label(axiom).  [assumption].
0.78/1.06	269 number_number_of_nat(plus_plus_int(one_one_int,one_one_int)) = plus_plus_nat(one_one_nat,one_one_nat).  [copy(268),rewrite([160(3)])].
0.78/1.06	279 plus_plus_int(power_power_int(A,number_number_of_nat(bit0(bit1(pls)))),power_power_int(B,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) # label(conj_0) # label(negated_conjecture).  [clausify(110)].
0.78/1.06	280 plus_plus_int(power_power_int(A,plus_plus_nat(one_one_nat,one_one_nat)),power_power_int(B,plus_plus_nat(one_one_nat,one_one_nat))) != plus_plus_int(one_one_int,times_times_int(m,bit0(plus_plus_int(one_one_int,one_one_int)))).  [copy(279),rewrite([160(3),269(4),160(7),269(8),160(12),136(14),135(15),184(17)])].
0.78/1.06	287 -ord_less_int(one_one_int,t).  [back_rewrite(173),rewrite([269(8),269(13),184(22)]),unit_del(b,280)].
0.78/1.06	292 t != one_one_int.  [back_rewrite(266),rewrite([269(8),269(13)]),unit_del(b,280)].
0.78/1.06	345 $F.  [resolve(199,a,142,b),flip(a),unit_del(a,292),unit_del(b,287)].
0.78/1.06	
0.78/1.06	% SZS output end Refutation
0.78/1.06	============================== end of proof ==========================
0.78/1.06	
0.78/1.06	============================== STATISTICS ============================
0.78/1.06	
0.78/1.06	Given=45. Generated=317. Kept=172. proofs=1.
0.78/1.06	Usable=44. Sos=93. Demods=28. Limbo=2, Disabled=192. Hints=0.
0.78/1.06	Megabytes=0.41.
0.78/1.06	User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
0.78/1.06	
0.78/1.06	============================== end of statistics =====================
0.78/1.06	
0.78/1.06	============================== end of search =========================
0.78/1.06	
0.78/1.06	THEOREM PROVED
0.78/1.06	% SZS status Theorem
0.78/1.06	
0.78/1.06	Exiting with 1 proof.
0.78/1.06	
0.78/1.06	Process 28303 exit (max_proofs) Mon Jul  3 03:33:53 2023
0.78/1.06	Prover9 interrupted
0.78/1.06	EOF