TSTP Solution File: NUM926+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM926+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 13:33:23 EDT 2022
% Result : Theorem 0.76s 1.06s
% Output : Refutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM926+1 : TPTP v8.1.0. Released v5.3.0.
% 0.10/0.13 % 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 : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 5 14:55:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.76/1.04 ============================== Prover9 ===============================
% 0.76/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.76/1.04 Process 31068 was started by sandbox2 on n021.cluster.edu,
% 0.76/1.04 Tue Jul 5 14:55:03 2022
% 0.76/1.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_30908_n021.cluster.edu".
% 0.76/1.04 ============================== end of head ===========================
% 0.76/1.04
% 0.76/1.04 ============================== INPUT =================================
% 0.76/1.04
% 0.76/1.04 % Reading from file /tmp/Prover9_30908_n021.cluster.edu
% 0.76/1.04
% 0.76/1.04 set(prolog_style_variables).
% 0.76/1.04 set(auto2).
% 0.76/1.04 % set(auto2) -> set(auto).
% 0.76/1.04 % set(auto) -> set(auto_inference).
% 0.76/1.04 % set(auto) -> set(auto_setup).
% 0.76/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.76/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.76/1.04 % set(auto) -> set(auto_limits).
% 0.76/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.76/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.76/1.04 % set(auto) -> set(auto_denials).
% 0.76/1.04 % set(auto) -> set(auto_process).
% 0.76/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.76/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.76/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.76/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.76/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.76/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.76/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.76/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.76/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.76/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.76/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.76/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.76/1.04 % set(auto2) -> assign(stats, some).
% 0.76/1.04 % set(auto2) -> clear(echo_input).
% 0.76/1.04 % set(auto2) -> set(quiet).
% 0.76/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.76/1.04 % set(auto2) -> clear(print_given).
% 0.76/1.04 assign(lrs_ticks,-1).
% 0.76/1.04 assign(sos_limit,10000).
% 0.76/1.04 assign(order,kbo).
% 0.76/1.04 set(lex_order_vars).
% 0.76/1.04 clear(print_given).
% 0.76/1.04
% 0.76/1.04 % formulas(sos). % not echoed (124 formulas)
% 0.76/1.04
% 0.76/1.04 ============================== end of input ==========================
% 0.76/1.04
% 0.76/1.04 % From the command line: assign(max_seconds, 300).
% 0.76/1.04
% 0.76/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.76/1.04
% 0.76/1.04 % Formulas that are not ordinary clauses:
% 0.76/1.04 1 t = one_one_int -> (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_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].
% 0.76/1.04 2 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].
% 0.76/1.04 3 (all A_8 all B_4 power_power_int(plus_plus_int(A_8,B_4),number_number_of_nat(bit0(bit1(pls)))) = 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)))))) # label(fact_7_zadd__power2) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 4 (all A_8 all B_4 power_power_int(plus_plus_int(A_8,B_4),number_number_of_nat(bit1(bit1(pls)))) = 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)))))) # label(fact_8_zadd__power3) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 5 (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].
% 0.76/1.04 6 (all X_2 all Y_2 power_power_int(plus_plus_int(X_2,Y_2),number_number_of_nat(bit0(bit1(pls)))) = 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))) # label(fact_10_power2__sum) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 7 (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].
% 0.76/1.04 8 (all W_4 power_power_nat(number_number_of_nat(W_4),number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(number_number_of_nat(W_4),number_number_of_nat(W_4))) # label(fact_12_power2__eq__square__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 9 (all A_8 times_times_int(A_8,power_power_int(A_8,number_number_of_nat(bit0(bit1(pls))))) = power_power_int(A_8,number_number_of_nat(bit1(bit1(pls))))) # label(fact_13_cube__square) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 10 (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].
% 0.76/1.04 11 (all X_7 times_times_nat(X_7,X_7) = power_power_nat(X_7,number_number_of_nat(bit0(bit1(pls))))) # label(fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 12 (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].
% 0.76/1.04 13 (all A_7 power_power_nat(A_7,number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(A_7,A_7)) # label(fact_19_power2__eq__square) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 14 (all X_6 all N power_power_int(X_6,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N)) = times_times_int(power_power_int(X_6,N),power_power_int(X_6,N))) # label(fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 15 (all X_6 all N power_power_nat(X_6,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N)) = times_times_nat(power_power_nat(X_6,N),power_power_nat(X_6,N))) # label(fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 16 (all W_3 plus_plus_int(one_one_int,number_number_of_int(W_3)) = number_number_of_int(plus_plus_int(bit1(pls),W_3))) # label(fact_22_add__special_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 17 (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].
% 0.76/1.04 18 -(all T 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),T)) # 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].
% 0.76/1.04 19 (all W ord_less_eq_int(W,W)) # label(fact_26_zle__refl) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 20 (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].
% 0.76/1.04 21 (all Z_1 all W_1 (ord_less_int(Z_1,W_1) <-> ord_less_eq_int(Z_1,W_1) & Z_1 != W_1)) # label(fact_28_zless__le) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 22 (all X_1 all Y_1 (ord_less_int(X_1,Y_1) | X_1 = Y_1 | ord_less_int(Y_1,X_1))) # label(fact_29_zless__linear) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 23 (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].
% 0.76/1.04 24 (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].
% 0.76/1.04 25 (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].
% 0.76/1.04 26 (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].
% 0.76/1.04 27 (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].
% 0.76/1.04 28 (all X_4 power_power_nat(X_4,one_one_nat) = X_4) # label(fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 29 (all X_1 all Y_1 all Z power_power_int(power_power_int(X_1,Y_1),Z) = power_power_int(X_1,times_times_nat(Y_1,Z))) # label(fact_36_zpower__zpower) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 30 (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].
% 0.76/1.04 31 (all V_2 all W_1 (ord_less_eq_int(number_number_of_int(V_2),number_number_of_int(W_1)) <-> -ord_less_int(number_number_of_int(W_1),number_number_of_int(V_2)))) # label(fact_38_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 32 (all X_2 all Y_2 (ord_less_int(number_number_of_int(X_2),number_number_of_int(Y_2)) <-> ord_less_int(X_2,Y_2))) # label(fact_39_less__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 33 (all X_2 all Y_2 (ord_less_eq_int(number_number_of_int(X_2),number_number_of_int(Y_2)) <-> ord_less_eq_int(X_2,Y_2))) # label(fact_40_le__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 34 (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].
% 0.76/1.04 35 (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].
% 0.76/1.04 36 (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].
% 0.76/1.04 37 (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].
% 0.76/1.04 38 (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].
% 0.76/1.04 39 (all Z times_times_nat(Z,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(Z,Z)) # label(fact_46_nat__mult__2__right) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 40 (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].
% 0.76/1.04 41 (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].
% 0.76/1.04 42 (all K1 all K2 (ord_less_eq_int(bit1(K1),bit1(K2)) <-> ord_less_eq_int(K1,K2))) # label(fact_50_less__eq__int__code_I16_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 43 (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].
% 0.76/1.04 44 (all K1 all K2 (ord_less_int(bit0(K1),bit0(K2)) <-> ord_less_int(K1,K2))) # label(fact_53_less__int__code_I13_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 45 (all K all L (ord_less_int(bit0(K),bit0(L)) <-> ord_less_int(K,L))) # label(fact_54_rel__simps_I14_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 46 (all K1 all K2 (ord_less_eq_int(bit0(K1),bit0(K2)) <-> ord_less_eq_int(K1,K2))) # label(fact_56_less__eq__int__code_I13_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 47 (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].
% 0.76/1.04 48 (all K all L (ord_less_int(number_number_of_int(K),number_number_of_int(L)) <-> ord_less_int(K,L))) # label(fact_58_less__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 49 (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].
% 0.76/1.04 50 (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].
% 0.76/1.04 51 (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].
% 0.76/1.04 52 (all V_1 all V ((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)) & (-ord_less_int(V,pls) -> (ord_less_int(V_1,pls) -> plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(V)) & (-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)))))) # label(fact_62_add__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 53 (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].
% 0.76/1.04 54 (all K (ord_less_int(pls,bit1(K)) <-> ord_less_eq_int(pls,K))) # label(fact_66_rel__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 55 (all K1 all K2 (ord_less_eq_int(bit1(K1),bit0(K2)) <-> ord_less_int(K1,K2))) # label(fact_67_less__eq__int__code_I15_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 56 (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].
% 0.76/1.04 57 (all K1 all K2 (ord_less_int(bit0(K1),bit1(K2)) <-> ord_less_eq_int(K1,K2))) # label(fact_69_less__int__code_I14_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 58 (all K all L (ord_less_int(bit0(K),bit1(L)) <-> ord_less_eq_int(K,L))) # label(fact_70_rel__simps_I15_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 59 (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].
% 0.76/1.04 60 (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].
% 0.76/1.04 61 (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].
% 0.76/1.04 62 (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].
% 0.76/1.04 63 (all Lx_6 all Ly_4 all Rx_6 all Ry_4 times_times_int(times_times_int(Lx_6,Ly_4),times_times_int(Rx_6,Ry_4)) = times_times_int(times_times_int(Lx_6,Rx_6),times_times_int(Ly_4,Ry_4))) # label(fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 64 (all Lx_6 all Ly_4 all Rx_6 all Ry_4 times_times_nat(times_times_nat(Lx_6,Ly_4),times_times_nat(Rx_6,Ry_4)) = times_times_nat(times_times_nat(Lx_6,Rx_6),times_times_nat(Ly_4,Ry_4))) # label(fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 65 (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].
% 0.76/1.04 66 (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].
% 0.76/1.04 67 (all Lx_4 all Ly_2 all Rx_4 all Ry_2 times_times_int(times_times_int(Lx_4,Ly_2),times_times_int(Rx_4,Ry_2)) = times_times_int(Lx_4,times_times_int(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].
% 0.76/1.04 68 (all Lx_4 all Ly_2 all Rx_4 all Ry_2 times_times_nat(times_times_nat(Lx_4,Ly_2),times_times_nat(Rx_4,Ry_2)) = times_times_nat(Lx_4,times_times_nat(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].
% 0.76/1.04 69 (all Lx_3 all Ly_1 all Rx_3 times_times_int(times_times_int(Lx_3,Ly_1),Rx_3) = times_times_int(times_times_int(Lx_3,Rx_3),Ly_1)) # label(fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 70 (all Lx_3 all Ly_1 all Rx_3 times_times_nat(times_times_nat(Lx_3,Ly_1),Rx_3) = times_times_nat(times_times_nat(Lx_3,Rx_3),Ly_1)) # label(fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 71 (all Lx_2 all Ly all Rx_2 times_times_int(times_times_int(Lx_2,Ly),Rx_2) = times_times_int(Lx_2,times_times_int(Ly,Rx_2))) # label(fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 72 (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].
% 0.76/1.04 73 (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].
% 0.76/1.04 74 (all Lx_1 all Rx_1 all Ry_1 times_times_nat(Lx_1,times_times_nat(Rx_1,Ry_1)) = times_times_nat(times_times_nat(Lx_1,Rx_1),Ry_1)) # label(fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 75 (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].
% 0.76/1.04 76 (all Lx all Rx all Ry times_times_nat(Lx,times_times_nat(Rx,Ry)) = times_times_nat(Rx,times_times_nat(Lx,Ry))) # label(fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 77 (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].
% 0.76/1.04 78 (all A_6 all B_3 times_times_nat(A_6,B_3) = times_times_nat(B_3,A_6)) # label(fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 79 (all A_5 all B_2 all C_5 all D_2 plus_plus_int(plus_plus_int(A_5,B_2),plus_plus_int(C_5,D_2)) = plus_plus_int(plus_plus_int(A_5,C_5),plus_plus_int(B_2,D_2))) # label(fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 80 (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].
% 0.76/1.04 81 (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].
% 0.76/1.04 82 (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].
% 0.76/1.04 83 (all A_3 all B all C_3 plus_plus_int(plus_plus_int(A_3,B),C_3) = plus_plus_int(A_3,plus_plus_int(B,C_3))) # label(fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 84 (all A_3 all B all C_3 plus_plus_nat(plus_plus_nat(A_3,B),C_3) = plus_plus_nat(A_3,plus_plus_nat(B,C_3))) # label(fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 85 (all A_2 all C_2 all D_1 plus_plus_int(A_2,plus_plus_int(C_2,D_1)) = plus_plus_int(plus_plus_int(A_2,C_2),D_1)) # label(fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 86 (all A_2 all C_2 all D_1 plus_plus_nat(A_2,plus_plus_nat(C_2,D_1)) = plus_plus_nat(plus_plus_nat(A_2,C_2),D_1)) # label(fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 87 (all A_1 all C_1 all D plus_plus_int(A_1,plus_plus_int(C_1,D)) = plus_plus_int(C_1,plus_plus_int(A_1,D))) # label(fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 88 (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].
% 0.76/1.04 89 (all A all C plus_plus_int(A,C) = plus_plus_int(C,A)) # label(fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 90 (all A all C plus_plus_nat(A,C) = plus_plus_nat(C,A)) # label(fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 91 (all X_2 all Y_2 (number_number_of_int(X_2) = number_number_of_int(Y_2) <-> X_2 = Y_2)) # label(fact_104_eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 92 (all W_1 all X_2 (number_number_of_nat(W_1) = X_2 <-> X_2 = number_number_of_nat(W_1))) # label(fact_105_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 93 (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].
% 0.76/1.04 94 (all K all L (bit1(K) = bit1(L) <-> K = L)) # label(fact_107_rel__simps_I51_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 95 (all K all L (bit0(K) = bit0(L) <-> K = L)) # label(fact_108_rel__simps_I48_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 96 (all Z1 all Z2 all Z3 times_times_int(times_times_int(Z1,Z2),Z3) = times_times_int(Z1,times_times_int(Z2,Z3))) # label(fact_109_zmult__assoc) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.04 97 (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].
% 0.76/1.06 98 (all K_1 number_number_of_int(K_1) = K_1) # label(fact_111_number__of__is__id) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 99 (all Z1 all Z2 all Z3 plus_plus_int(plus_plus_int(Z1,Z2),Z3) = plus_plus_int(Z1,plus_plus_int(Z2,Z3))) # label(fact_112_zadd__assoc) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 100 (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].
% 0.76/1.06 101 (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].
% 0.76/1.06 102 (all K (ord_less_int(bit1(K),pls) <-> ord_less_int(K,pls))) # label(fact_115_rel__simps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 103 (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].
% 0.76/1.06 104 (all K all L (ord_less_int(bit1(K),bit0(L)) <-> ord_less_int(K,L))) # label(fact_117_rel__simps_I16_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 105 (all K (ord_less_int(bit0(K),pls) <-> ord_less_int(K,pls))) # label(fact_118_rel__simps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 106 (all K (ord_less_int(pls,bit0(K)) <-> ord_less_int(pls,K))) # label(fact_119_rel__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 107 (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].
% 0.76/1.06 108 (all K1 all K2 (ord_less_eq_int(bit0(K1),bit1(K2)) <-> ord_less_eq_int(K1,K2))) # label(fact_121_less__eq__int__code_I14_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 109 (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].
% 0.76/1.06 110 -(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].
% 0.76/1.06
% 0.76/1.06 ============================== end of process non-clausal formulas ===
% 0.76/1.06
% 0.76/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.76/1.06
% 0.76/1.06 ============================== PREDICATE ELIMINATION =================
% 0.76/1.06
% 0.76/1.06 ============================== end predicate elimination =============
% 0.76/1.06
% 0.76/1.06 Auto_denials: (non-Horn, no changes).
% 0.76/1.06
% 0.76/1.06 Term ordering decisions:
% 0.76/1.06 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.
% 0.76/1.06 % back CAC tautology: 220 plus_plus_nat(plus_plus_nat(A,B),C) = plus_plus_nat(plus_plus_nat(A,C),B) # label(fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom). [clausify(82)].
% 0.76/1.06 % back CAC tautology: 219 plus_plus_int(plus_plus_int(A,B),C) = plus_plus_int(plus_plus_int(A,C),B) # label(fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom). [clausify(81)].
% 0.76/1.06 % back CAC tautology: 218 plus_plus_nat(plus_plus_nat(A,B),plus_plus_nat(C,D)) = plus_plus_nat(plus_plus_nat(A,C),plus_plus_nat(B,D)) # label(fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom). [clausify(80)].
% 0.76/1.06 % back CAC tautology: 217 plus_plus_int(plus_plus_int(A,B),plus_plus_int(C,D)) = plus_plus_int(plus_plus_int(A,C),plus_plus_int(B,D)) # label(fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom). [clausify(79)].
% 0.76/1.06
% 0.76/1.06 ============================== end of process initial clauses ========
% 0.76/1.06
% 0.76/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.76/1.06
% 0.76/1.06 ============================== end of clauses for search =============
% 0.76/1.06
% 0.76/1.06 ============================== SEARCH ================================
% 0.76/1.06
% 0.76/1.06 % Starting search at 0.04 seconds.
% 0.76/1.06
% 0.76/1.06 ============================== PROOF =================================
% 0.76/1.06 % SZS status Theorem
% 0.76/1.06 % SZS output start Refutation
% 0.76/1.06
% 0.76/1.06 % Proof 1 at 0.04 (+ 0.00) seconds.
% 0.76/1.06 % Length of proof is 23.
% 0.76/1.06 % Level of proof is 4.
% 0.76/1.06 % Maximum clause weight is 26.000.
% 0.76/1.06 % Given clauses 6.
% 0.76/1.06
% 0.76/1.06 1 t = one_one_int -> (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_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].
% 0.76/1.06 2 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].
% 0.76/1.06 21 (all Z_1 all W_1 (ord_less_int(Z_1,W_1) <-> ord_less_eq_int(Z_1,W_1) & Z_1 != W_1)) # label(fact_28_zless__le) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 77 (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].
% 0.76/1.06 89 (all A all C plus_plus_int(A,C) = plus_plus_int(C,A)) # label(fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 98 (all K_1 number_number_of_int(K_1) = K_1) # label(fact_111_number__of__is__id) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 110 -(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].
% 0.76/1.06 111 ord_less_eq_int(one_one_int,t) # label(fact_0_tpos) # label(axiom). [assumption].
% 0.76/1.06 112 t != one_one_int | plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = 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))))) # 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(1)].
% 0.76/1.06 113 t != one_one_int | 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). [copy(112),flip(b)].
% 0.76/1.06 114 -ord_less_int(one_one_int,t) | plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(power_power_int(c3,number_number_of_nat(bit0(bit1(pls)))),power_power_int(c4,number_number_of_nat(bit0(bit1(pls))))) # 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(2)].
% 0.76/1.06 115 -ord_less_int(one_one_int,t) | plus_plus_int(power_power_int(c3,number_number_of_nat(bit0(bit1(pls)))),power_power_int(c4,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). [copy(114),flip(b)].
% 0.76/1.06 147 ord_less_int(A,B) | -ord_less_eq_int(A,B) | B = A # label(fact_28_zless__le) # label(axiom). [clausify(21)].
% 0.76/1.06 170 plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))) # label(fact_47_nat__1__add__1) # label(axiom). [assumption].
% 0.76/1.06 171 number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat). [copy(170),flip(a)].
% 0.76/1.06 215 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(77)].
% 0.76/1.06 227 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(89)].
% 0.76/1.06 237 number_number_of_int(A) = A # label(fact_111_number__of__is__id) # label(axiom). [clausify(98)].
% 0.76/1.06 253 plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) != 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))))) # label(conj_0) # label(negated_conjecture). [clausify(110)].
% 0.76/1.06 254 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(bit0(bit1(pls))))). [copy(253),rewrite([237(5),215(6),227(8),171(12),171(16)]),flip(a)].
% 0.76/1.06 270 -ord_less_int(one_one_int,t). [back_rewrite(115),rewrite([171(8),171(13),237(19),215(20),227(22)]),unit_del(b,254)].
% 0.76/1.06 271 t != one_one_int. [back_rewrite(113),rewrite([171(8),171(13),237(19),215(20),227(22)]),unit_del(b,254)].
% 0.76/1.06 286 $F. [resolve(147,b,111,a),unit_del(a,270),unit_del(b,271)].
% 0.76/1.06
% 0.76/1.06 % SZS output end Refutation
% 0.76/1.06 ============================== end of proof ==========================
% 0.76/1.06
% 0.76/1.06 ============================== STATISTICS ============================
% 0.76/1.06
% 0.76/1.06 Given=6. Generated=215. Kept=152. proofs=1.
% 0.76/1.06 Usable=6. Sos=90. Demods=27. Limbo=0, Disabled=215. Hints=0.
% 0.76/1.06 Megabytes=0.38.
% 0.76/1.06 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.76/1.06
% 0.76/1.06 ============================== end of statistics =====================
% 0.76/1.06
% 0.76/1.06 ============================== end of search =========================
% 0.76/1.06
% 0.76/1.06 THEOREM PROVED
% 0.76/1.06 % SZS status Theorem
% 0.76/1.06
% 0.76/1.06 Exiting with 1 proof.
% 0.76/1.06
% 0.76/1.06 Process 31068 exit (max_proofs) Tue Jul 5 14:55:03 2022
% 0.76/1.06 Prover9 interrupted
%------------------------------------------------------------------------------