TSTP Solution File: NUM924+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM924+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 13:33:13 EDT 2022
% Result : Theorem 0.87s 1.17s
% Output : Refutation 0.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : NUM924+1 : TPTP v8.1.0. Released v5.3.0.
% 0.14/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.36 % Computer : n011.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Wed Jul 6 00:20:52 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.83/1.13 ============================== Prover9 ===============================
% 0.83/1.13 Prover9 (32) version 2009-11A, November 2009.
% 0.83/1.13 Process 11888 was started by sandbox on n011.cluster.edu,
% 0.83/1.13 Wed Jul 6 00:20:53 2022
% 0.83/1.13 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11734_n011.cluster.edu".
% 0.83/1.13 ============================== end of head ===========================
% 0.83/1.13
% 0.83/1.13 ============================== INPUT =================================
% 0.83/1.13
% 0.83/1.13 % Reading from file /tmp/Prover9_11734_n011.cluster.edu
% 0.83/1.13
% 0.83/1.13 set(prolog_style_variables).
% 0.83/1.13 set(auto2).
% 0.83/1.13 % set(auto2) -> set(auto).
% 0.83/1.13 % set(auto) -> set(auto_inference).
% 0.83/1.13 % set(auto) -> set(auto_setup).
% 0.83/1.13 % set(auto_setup) -> set(predicate_elim).
% 0.83/1.13 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.83/1.13 % set(auto) -> set(auto_limits).
% 0.83/1.13 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.83/1.13 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.83/1.13 % set(auto) -> set(auto_denials).
% 0.83/1.13 % set(auto) -> set(auto_process).
% 0.83/1.13 % set(auto2) -> assign(new_constants, 1).
% 0.83/1.13 % set(auto2) -> assign(fold_denial_max, 3).
% 0.83/1.13 % set(auto2) -> assign(max_weight, "200.000").
% 0.83/1.13 % set(auto2) -> assign(max_hours, 1).
% 0.83/1.13 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.83/1.13 % set(auto2) -> assign(max_seconds, 0).
% 0.83/1.13 % set(auto2) -> assign(max_minutes, 5).
% 0.83/1.13 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.83/1.13 % set(auto2) -> set(sort_initial_sos).
% 0.83/1.13 % set(auto2) -> assign(sos_limit, -1).
% 0.83/1.13 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.83/1.13 % set(auto2) -> assign(max_megs, 400).
% 0.83/1.13 % set(auto2) -> assign(stats, some).
% 0.83/1.13 % set(auto2) -> clear(echo_input).
% 0.83/1.13 % set(auto2) -> set(quiet).
% 0.83/1.13 % set(auto2) -> clear(print_initial_clauses).
% 0.83/1.13 % set(auto2) -> clear(print_given).
% 0.83/1.13 assign(lrs_ticks,-1).
% 0.83/1.13 assign(sos_limit,10000).
% 0.83/1.13 assign(order,kbo).
% 0.83/1.13 set(lex_order_vars).
% 0.83/1.13 clear(print_given).
% 0.83/1.13
% 0.83/1.13 % formulas(sos). % not echoed (107 formulas)
% 0.83/1.13
% 0.83/1.13 ============================== end of input ==========================
% 0.83/1.13
% 0.83/1.13 % From the command line: assign(max_seconds, 300).
% 0.83/1.13
% 0.83/1.13 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.83/1.13
% 0.83/1.13 % Formulas that are not ordinary clauses:
% 0.83/1.13 1 t = zero_zero_int -> plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = zero_zero_int # label(fact_4_calculation_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 2 (all X all Y -ord_less_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))))),zero_zero_int)) # label(fact_7_not__sum__power2__lt__zero) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 3 (all X_1 all Y_1 (ord_less_int(zero_zero_int,plus_plus_int(power_power_int(X_1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y_1,number_number_of_nat(bit0(bit1(pls)))))) <-> X_1 != zero_zero_int | Y_1 != zero_zero_int)) # label(fact_8_sum__power2__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 4 (all X_1 all Y_1 (plus_plus_int(power_power_int(X_1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y_1,number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int <-> X_1 = zero_zero_int & Y_1 = zero_zero_int)) # label(fact_9_sum__power2__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 5 (all A_2 -ord_less_int(power_power_int(A_2,number_number_of_nat(bit0(bit1(pls)))),zero_zero_int)) # label(fact_10_power2__less__0) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 6 (all A_1 (ord_less_int(zero_zero_int,power_power_int(A_1,number_number_of_nat(bit0(bit1(pls))))) <-> A_1 != zero_zero_int)) # label(fact_11_zero__less__power2) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 7 (all A_1 (power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int <-> A_1 = zero_zero_int)) # label(fact_16_zero__eq__power2) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 8 (all W_6 plus_plus_int(one_one_int,number_number_of_int(W_6)) = number_number_of_int(plus_plus_int(bit1(pls),W_6))) # label(fact_17_add__special_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 9 (all V_13 plus_plus_int(number_number_of_int(V_13),one_one_int) = number_number_of_int(plus_plus_int(V_13,bit1(pls)))) # label(fact_18_add__special_I3_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 10 -(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_20__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].
% 0.83/1.13 11 (all W ord_less_eq_int(W,W)) # label(fact_23_zle__refl) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 12 (all K_1 number_number_of_int(K_1) = K_1) # label(fact_24_number__of__is__id) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 13 (all Z all W times_times_int(Z,W) = times_times_int(W,Z)) # label(fact_25_zmult__commute) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 14 (all Z all W (ord_less_eq_int(Z,W) | ord_less_eq_int(W,Z))) # label(fact_26_zle__linear) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 15 (all V_2 all W times_times_int(number_number_of_int(V_2),number_number_of_int(W)) = number_number_of_int(times_times_int(V_2,W))) # label(fact_27_times__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 16 (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_28_less__eq__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 17 (all X_1 all Y_1 (ord_less_eq_int(number_number_of_int(X_1),number_number_of_int(Y_1)) <-> ord_less_eq_int(X_1,Y_1))) # label(fact_29_le__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 18 (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_30_zmult__assoc) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 19 (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_31_zle__trans) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 20 (all Z all W (ord_less_eq_int(Z,W) -> (ord_less_eq_int(W,Z) -> Z = W))) # label(fact_32_zle__antisym) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 21 (all X all Y all Z power_power_int(X,plus_plus_nat(Y,Z)) = times_times_int(power_power_int(X,Y),power_power_int(X,Z))) # label(fact_33_zpower__zadd__distrib) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 22 (all K1 all K2 (ord_less_eq_int(bit1(K1),bit1(K2)) <-> ord_less_eq_int(K1,K2))) # label(fact_34_less__eq__int__code_I16_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 23 (all K all L (ord_less_eq_int(bit1(K),bit1(L)) <-> ord_less_eq_int(K,L))) # label(fact_35_rel__simps_I34_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 24 (all K1 all K2 (ord_less_eq_int(bit0(K1),bit0(K2)) <-> ord_less_eq_int(K1,K2))) # label(fact_37_less__eq__int__code_I13_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 25 (all K all L (ord_less_eq_int(bit0(K),bit0(L)) <-> ord_less_eq_int(K,L))) # label(fact_38_rel__simps_I31_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 26 (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_39_zless__le) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 27 (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_40_zadd__left__mono) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 28 (all V_7 (number_number_of_nat(V_7) = zero_zero_nat <-> ord_less_eq_int(V_7,pls))) # label(fact_41_eq__number__of__0) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 29 (all V_7 (zero_zero_nat = number_number_of_nat(V_7) <-> ord_less_eq_int(V_7,pls))) # label(fact_42_eq__0__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.13 30 (all V_12 all V_11 (ord_less_eq_int(pls,V_11) -> (ord_less_eq_int(pls,V_12) -> times_times_nat(number_number_of_nat(V_11),number_number_of_nat(V_12)) = number_number_of_nat(times_times_int(V_11,V_12))))) # label(fact_43_semiring__mult__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 31 (all V_12 all V_11 (ord_less_eq_int(pls,V_11) -> (ord_less_eq_int(pls,V_12) -> times_times_int(number_number_of_int(V_11),number_number_of_int(V_12)) = number_number_of_int(times_times_int(V_11,V_12))))) # label(fact_44_semiring__mult__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 32 (all V_10 all W_5 all Z_3 times_times_int(number_number_of_int(V_10),times_times_int(number_number_of_int(W_5),Z_3)) = times_times_int(number_number_of_int(times_times_int(V_10,W_5)),Z_3)) # label(fact_45_mult__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 33 (all V_9 all W_4 times_times_int(number_number_of_int(V_9),number_number_of_int(W_4)) = number_number_of_int(times_times_int(V_9,W_4))) # label(fact_46_arith__simps_I32_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 34 (all V_8 all W_3 number_number_of_int(times_times_int(V_8,W_3)) = times_times_int(number_number_of_int(V_8),number_number_of_int(W_3))) # label(fact_47_number__of__mult) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 35 (all X_1 all Y_1 (ord_less_eq_int(plus_plus_int(times_times_int(X_1,X_1),times_times_int(Y_1,Y_1)),zero_zero_int) <-> X_1 = zero_zero_int & Y_1 = zero_zero_int)) # label(fact_48_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 36 (all X_2 all Y_2 ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(X_2,X_2),times_times_int(Y_2,Y_2)))) # label(fact_49_sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 37 (all X_1 (ord_less_eq_int(number_number_of_int(X_1),zero_zero_int) <-> ord_less_eq_int(X_1,pls))) # label(fact_50_le__special_I3_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 38 (all Y_1 (ord_less_eq_int(zero_zero_int,number_number_of_int(Y_1)) <-> ord_less_eq_int(pls,Y_1))) # label(fact_51_le__special_I1_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 39 (all V_7 (ord_less_nat(zero_zero_nat,number_number_of_nat(V_7)) <-> ord_less_int(pls,V_7))) # label(fact_52_less__0__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 40 (all V_7 all W_1 (ord_less_eq_int(number_number_of_int(V_7),number_number_of_int(W_1)) <-> -ord_less_int(number_number_of_int(W_1),number_number_of_int(V_7)))) # label(fact_53_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 41 (all V_7 all W_1 (ord_less_eq_nat(number_number_of_nat(V_7),number_number_of_nat(W_1)) <-> -ord_less_nat(number_number_of_nat(W_1),number_number_of_nat(V_7)))) # label(fact_54_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 42 (all K (ord_less_eq_int(pls,bit1(K)) <-> ord_less_eq_int(pls,K))) # label(fact_55_rel__simps_I22_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 43 (all K1 all K2 (ord_less_eq_int(bit0(K1),bit1(K2)) <-> ord_less_eq_int(K1,K2))) # label(fact_56_less__eq__int__code_I14_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 44 (all K all L (ord_less_eq_int(bit0(K),bit1(L)) <-> ord_less_eq_int(K,L))) # label(fact_57_rel__simps_I32_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 45 (all K (ord_less_eq_int(bit0(K),pls) <-> ord_less_eq_int(K,pls))) # label(fact_58_rel__simps_I27_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 46 (all K (ord_less_eq_int(pls,bit0(K)) <-> ord_less_eq_int(pls,K))) # label(fact_59_rel__simps_I21_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 47 (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_60_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 48 (all X_1 (ord_less_eq_int(number_number_of_int(X_1),one_one_int) <-> ord_less_eq_int(X_1,bit1(pls)))) # label(fact_63_le__special_I4_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 49 (all Y_1 (ord_less_eq_int(one_one_int,number_number_of_int(Y_1)) <-> ord_less_eq_int(bit1(pls),Y_1))) # label(fact_64_le__special_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 50 (all W times_times_int(pls,W) = pls) # label(fact_66_mult__Pls) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 51 (all K_1 all L_1 times_times_int(bit0(K_1),L_1) = bit0(times_times_int(K_1,L_1))) # label(fact_67_mult__Bit0) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 52 (all K all L (ord_less_int(number_number_of_int(K),number_number_of_int(L)) <-> ord_less_int(K,L))) # label(fact_68_less__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 53 (all Z times_times_int(Z,one_one_int) = Z) # label(fact_69_zmult__1__right) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 54 (all Z times_times_int(one_one_int,Z) = Z) # label(fact_70_zmult__1) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 55 (all V_2 all W plus_plus_int(number_number_of_int(V_2),number_number_of_int(W)) = number_number_of_int(plus_plus_int(V_2,W))) # label(fact_71_plus__numeral__code_I9_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 56 (all Z1 all Z2 all W times_times_int(plus_plus_int(Z1,Z2),W) = plus_plus_int(times_times_int(Z1,W),times_times_int(Z2,W))) # label(fact_72_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 57 (all W all Z1 all Z2 times_times_int(W,plus_plus_int(Z1,Z2)) = plus_plus_int(times_times_int(W,Z1),times_times_int(W,Z2))) # label(fact_73_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 58 (all K (ord_less_eq_int(bit1(K),pls) <-> ord_less_int(K,pls))) # label(fact_74_rel__simps_I29_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 59 (all K (ord_less_int(pls,bit1(K)) <-> ord_less_eq_int(pls,K))) # label(fact_75_rel__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 60 (all K1 all K2 (ord_less_eq_int(bit1(K1),bit0(K2)) <-> ord_less_int(K1,K2))) # label(fact_76_less__eq__int__code_I15_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 61 (all K all L (ord_less_eq_int(bit1(K),bit0(L)) <-> ord_less_int(K,L))) # label(fact_77_rel__simps_I33_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 62 (all K1 all K2 (ord_less_int(bit0(K1),bit1(K2)) <-> ord_less_eq_int(K1,K2))) # label(fact_78_less__int__code_I14_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 63 (all K all L (ord_less_int(bit0(K),bit1(L)) <-> ord_less_eq_int(K,L))) # label(fact_79_rel__simps_I15_J) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 64 (all V_7 all V_6 (ord_less_nat(number_number_of_nat(V_7),number_number_of_nat(V_6)) <-> (ord_less_int(V_7,V_6) -> ord_less_int(pls,V_6)) & ord_less_int(V_7,V_6))) # label(fact_80_less__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 65 (all Z_1 (ord_less_eq_int(one_one_int,Z_1) <-> ord_less_int(zero_zero_int,Z_1))) # label(fact_81_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 66 (all W all Z (ord_less_int(W,Z) -> ord_less_eq_int(plus_plus_int(W,one_one_int),Z))) # label(fact_84_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 67 (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_85_add1__zle__eq) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 68 (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_86_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 69 (all V_5 all V_4 (ord_less_eq_int(pls,V_4) -> (ord_less_eq_int(pls,V_5) -> plus_plus_int(number_number_of_int(V_4),number_number_of_int(V_5)) = number_number_of_int(plus_plus_int(V_4,V_5))))) # label(fact_87_semiring__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 70 (all V_5 all V_4 (ord_less_eq_int(pls,V_4) -> (ord_less_eq_int(pls,V_5) -> plus_plus_nat(number_number_of_nat(V_4),number_number_of_nat(V_5)) = number_number_of_nat(plus_plus_int(V_4,V_5))))) # label(fact_88_semiring__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.83/1.14 71 (all V_3 all V_2 ((ord_less_int(V_2,pls) -> plus_plus_nat(number_number_of_nat(V_2),number_number_of_nat(V_3)) = number_number_of_nat(V_3)) & (-ord_less_int(V_2,pls) -> (ord_less_int(V_3,pls) -> plus_plus_nat(number_number_of_nat(V_2),number_number_of_nat(V_3)) = number_number_of_nat(V_2)) & (-ord_less_int(V_3,pls) -> plus_plus_nat(number_number_of_nat(V_2),number_number_of_nat(V_3)) = number_number_of_nat(plus_plus_int(V_2,V_3)))))) # label(fact_89_add__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.15 72 (all Z (ord_less_eq_int(zero_zero_int,Z) -> ord_less_int(zero_zero_int,plus_plus_int(one_one_int,Z)))) # label(fact_90_le__imp__0__less) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.15 73 (all X_1 all Y_1 (number_number_of_int(X_1) = number_number_of_int(Y_1) <-> X_1 = Y_1)) # label(fact_91_eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.15 74 (all W_1 all X_1 (number_number_of_nat(W_1) = X_1 <-> X_1 = number_number_of_nat(W_1))) # label(fact_92_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.15 75 (all W_1 all X_1 (number_number_of_int(W_1) = X_1 <-> X_1 = number_number_of_int(W_1))) # label(fact_93_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.15 76 (all K all L (bit1(K) = bit1(L) <-> K = L)) # label(fact_94_rel__simps_I51_J) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.15 77 (all K all L (bit0(K) = bit0(L) <-> K = L)) # label(fact_95_rel__simps_I48_J) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.15 78 (all X all Y (ord_less_int(X,Y) | X = Y | ord_less_int(Y,X))) # label(fact_96_zless__linear) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.15 79 (all X_1 all Y_1 (plus_plus_int(times_times_int(X_1,X_1),times_times_int(Y_1,Y_1)) = zero_zero_int <-> X_1 = zero_zero_int & Y_1 = zero_zero_int)) # label(fact_97_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.15 80 (all A all B_1 all V_1 times_times_int(plus_plus_int(A,B_1),number_number_of_int(V_1)) = plus_plus_int(times_times_int(A,number_number_of_int(V_1)),times_times_int(B_1,number_number_of_int(V_1)))) # label(fact_98_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.15 81 (all A all B_1 all V_1 times_times_nat(plus_plus_nat(A,B_1),number_number_of_nat(V_1)) = plus_plus_nat(times_times_nat(A,number_number_of_nat(V_1)),times_times_nat(B_1,number_number_of_nat(V_1)))) # label(fact_99_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.15 82 (all V all B all C times_times_int(number_number_of_int(V),plus_plus_int(B,C)) = plus_plus_int(times_times_int(number_number_of_int(V),B),times_times_int(number_number_of_int(V),C))) # label(fact_100_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.15 83 (all V all B all C times_times_nat(number_number_of_nat(V),plus_plus_nat(B,C)) = plus_plus_nat(times_times_nat(number_number_of_nat(V),B),times_times_nat(number_number_of_nat(V),C))) # label(fact_101_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.15 84 (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_102_zadd__assoc) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.15 85 (all X all Y all Z plus_plus_int(X,plus_plus_int(Y,Z)) = plus_plus_int(Y,plus_plus_int(X,Z))) # label(fact_103_zadd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.15 86 (all Z all W plus_plus_int(Z,W) = plus_plus_int(W,Z)) # label(fact_104_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.15
% 0.87/1.15 ============================== end of process non-clausal formulas ===
% 0.87/1.15
% 0.87/1.15 ============================== PROCESS INITIAL CLAUSES ===============
% 0.87/1.15
% 0.87/1.15 ============================== PREDICATE ELIMINATION =================
% 0.87/1.15
% 0.87/1.15 ============================== end predicate elimination =============
% 0.87/1.15
% 0.87/1.15 Auto_denials: (non-Horn, no changes).
% 0.87/1.15
% 0.87/1.15 Term ordering decisions:
% 0.87/1.15 Function symbol KB weights: pls=1. zero_zero_int=1. one_one_int=1. zero_zero_nat=1. m=1. one_one_nat=1. t=1. s=1. c1=1. times_times_int=1. plus_plus_int=1. power_power_int=1. plus_plus_nat=1. times_times_nat=1. power_power_nat=1. number_number_of_int=1. bit1=1. bit0=1. number_number_of_nat=1.
% 0.87/1.15
% 0.87/1.15 ============================== end of process initial clauses ========
% 0.87/1.15
% 0.87/1.15 ============================== CLAUSES FOR SEARCH ====================
% 0.87/1.15
% 0.87/1.15 ============================== end of clauses for search =============
% 0.87/1.17
% 0.87/1.17 ============================== SEARCH ================================
% 0.87/1.17
% 0.87/1.17 % Starting search at 0.03 seconds.
% 0.87/1.17
% 0.87/1.17 ============================== PROOF =================================
% 0.87/1.17 % SZS status Theorem
% 0.87/1.17 % SZS output start Refutation
% 0.87/1.17
% 0.87/1.17 % Proof 1 at 0.05 (+ 0.00) seconds.
% 0.87/1.17 % Length of proof is 34.
% 0.87/1.17 % Level of proof is 6.
% 0.87/1.17 % Maximum clause weight is 23.000.
% 0.87/1.17 % Given clauses 79.
% 0.87/1.17
% 0.87/1.17 4 (all X_1 all Y_1 (plus_plus_int(power_power_int(X_1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y_1,number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int <-> X_1 = zero_zero_int & Y_1 = zero_zero_int)) # label(fact_9_sum__power2__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.17 12 (all K_1 number_number_of_int(K_1) = K_1) # label(fact_24_number__of__is__id) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.17 13 (all Z all W times_times_int(Z,W) = times_times_int(W,Z)) # label(fact_25_zmult__commute) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.17 50 (all W times_times_int(pls,W) = pls) # label(fact_66_mult__Pls) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.17 56 (all Z1 all Z2 all W times_times_int(plus_plus_int(Z1,Z2),W) = plus_plus_int(times_times_int(Z1,W),times_times_int(Z2,W))) # label(fact_72_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.17 86 (all Z all W plus_plus_int(Z,W) = plus_plus_int(W,Z)) # label(fact_104_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 0.87/1.17 89 ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)) # label(fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) # label(axiom). [assumption].
% 0.87/1.17 90 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_3_t) # label(axiom). [assumption].
% 0.87/1.17 91 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). [copy(90),flip(a)].
% 0.87/1.17 107 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))))) = zero_zero_int | A != zero_zero_int | B != zero_zero_int # label(fact_9_sum__power2__eq__zero__iff) # label(axiom). [clausify(4)].
% 0.87/1.17 108 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))))) = zero_zero_int | zero_zero_int != A | zero_zero_int != B. [copy(107),flip(b),flip(c)].
% 0.87/1.17 117 power_power_int(zero_zero_int,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int # label(fact_15_zero__power2) # label(axiom). [assumption].
% 0.87/1.17 130 number_number_of_int(A) = A # label(fact_24_number__of__is__id) # label(axiom). [clausify(12)].
% 0.87/1.17 131 times_times_int(A,B) = times_times_int(B,A) # label(fact_25_zmult__commute) # label(axiom). [clausify(13)].
% 0.87/1.17 201 plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))) # label(fact_65_nat__1__add__1) # label(axiom). [assumption].
% 0.87/1.17 202 number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat). [copy(201),flip(a)].
% 0.87/1.17 203 times_times_int(pls,A) = pls # label(fact_66_mult__Pls) # label(axiom). [clausify(50)].
% 0.87/1.17 204 times_times_int(A,pls) = pls. [copy(203),rewrite([131(2)])].
% 0.87/1.17 212 plus_plus_int(times_times_int(A,B),times_times_int(C,B)) = times_times_int(plus_plus_int(A,C),B) # label(fact_72_zadd__zmult__distrib) # label(axiom). [clausify(56)].
% 0.87/1.17 213 plus_plus_int(times_times_int(A,B),times_times_int(B,C)) = times_times_int(B,plus_plus_int(A,C)). [copy(212),rewrite([131(2),131(5)])].
% 0.87/1.17 261 plus_plus_int(A,B) = plus_plus_int(B,A) # label(fact_104_zadd__commute) # label(axiom). [clausify(86)].
% 0.87/1.17 262 zero_zero_int = number_number_of_int(pls) # label(fact_105_zero__is__num__zero) # label(axiom). [assumption].
% 0.87/1.17 263 zero_zero_int = pls. [copy(262),rewrite([130(3)])].
% 0.87/1.17 264 -ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int) # label(conj_0) # label(negated_conjecture). [assumption].
% 0.87/1.17 265 -ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),pls). [copy(264),rewrite([202(5),261(7),263(8)])].
% 0.87/1.17 266 ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))). [back_rewrite(89),rewrite([130(5),131(6),261(8),131(10),130(15),131(16),261(18),263(19),131(20)])].
% 0.87/1.17 268 plus_plus_int(power_power_int(A,plus_plus_nat(one_one_nat,one_one_nat)),power_power_int(A,plus_plus_nat(one_one_nat,one_one_nat))) = pls | pls != A. [factor(108,b,c),rewrite([202(4),202(8),263(10),263(12)])].
% 0.87/1.17 273 times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) = plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))). [back_rewrite(91),rewrite([130(5),131(6),261(8),131(10),202(15),261(17)])].
% 0.87/1.17 278 power_power_int(pls,plus_plus_nat(one_one_nat,one_one_nat)) = pls. [back_rewrite(117),rewrite([263(1),202(5),263(6)])].
% 0.87/1.17 307 ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))). [back_rewrite(266),rewrite([273(10)])].
% 0.87/1.17 360 times_times_int(pls,plus_plus_int(A,B)) = plus_plus_int(pls,pls). [para(204(a,1),213(a,1,1)),rewrite([131(3),204(3),261(5)]),flip(a)].
% 0.87/1.17 365 ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),plus_plus_int(pls,pls)). [back_rewrite(307),rewrite([360(17)])].
% 0.87/1.17 464 plus_plus_int(pls,pls) = pls. [resolve(268,b,263,a(flip)),rewrite([263(1),278(5),263(2),278(6)])].
% 0.87/1.17 465 $F. [back_rewrite(365),rewrite([464(10)]),unit_del(a,265)].
% 0.87/1.17
% 0.87/1.17 % SZS output end Refutation
% 0.87/1.17 ============================== end of proof ==========================
% 0.87/1.17
% 0.87/1.17 ============================== STATISTICS ============================
% 0.87/1.17
% 0.87/1.17 Given=79. Generated=650. Kept=317. proofs=1.
% 0.87/1.17 Usable=78. Sos=191. Demods=48. Limbo=1, Disabled=201. Hints=0.
% 0.87/1.17 Megabytes=0.50.
% 0.87/1.17 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.87/1.17
% 0.87/1.17 ============================== end of statistics =====================
% 0.87/1.17
% 0.87/1.17 ============================== end of search =========================
% 0.87/1.17
% 0.87/1.17 THEOREM PROVED
% 0.87/1.17 % SZS status Theorem
% 0.87/1.17
% 0.87/1.17 Exiting with 1 proof.
% 0.87/1.17
% 0.87/1.17 Process 11888 exit (max_proofs) Wed Jul 6 00:20:53 2022
% 0.87/1.17 Prover9 interrupted
%------------------------------------------------------------------------------