TSTP Solution File: NUM926+5 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM926+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 13:33:26 EDT 2022
% Result : Theorem 0.82s 1.13s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM926+5 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jul 7 16:24:57 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.82/1.09 ============================== Prover9 ===============================
% 0.82/1.09 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.09 Process 27409 was started by sandbox on n003.cluster.edu,
% 0.82/1.09 Thu Jul 7 16:24:58 2022
% 0.82/1.09 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_27256_n003.cluster.edu".
% 0.82/1.09 ============================== end of head ===========================
% 0.82/1.09
% 0.82/1.09 ============================== INPUT =================================
% 0.82/1.09
% 0.82/1.09 % Reading from file /tmp/Prover9_27256_n003.cluster.edu
% 0.82/1.09
% 0.82/1.09 set(prolog_style_variables).
% 0.82/1.09 set(auto2).
% 0.82/1.09 % set(auto2) -> set(auto).
% 0.82/1.09 % set(auto) -> set(auto_inference).
% 0.82/1.09 % set(auto) -> set(auto_setup).
% 0.82/1.09 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.09 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.09 % set(auto) -> set(auto_limits).
% 0.82/1.09 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.09 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.09 % set(auto) -> set(auto_denials).
% 0.82/1.09 % set(auto) -> set(auto_process).
% 0.82/1.09 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.09 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.09 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.09 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.09 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.09 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.09 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.09 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.09 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.09 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.09 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.09 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.09 % set(auto2) -> assign(stats, some).
% 0.82/1.09 % set(auto2) -> clear(echo_input).
% 0.82/1.09 % set(auto2) -> set(quiet).
% 0.82/1.09 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.09 % set(auto2) -> clear(print_given).
% 0.82/1.09 assign(lrs_ticks,-1).
% 0.82/1.09 assign(sos_limit,10000).
% 0.82/1.09 assign(order,kbo).
% 0.82/1.09 set(lex_order_vars).
% 0.82/1.09 clear(print_given).
% 0.82/1.09
% 0.82/1.09 % formulas(sos). % not echoed (142 formulas)
% 0.82/1.09
% 0.82/1.09 ============================== end of input ==========================
% 0.82/1.09
% 0.82/1.09 % From the command line: assign(max_seconds, 300).
% 0.82/1.09
% 0.82/1.09 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.09
% 0.82/1.09 % Formulas that are not ordinary clauses:
% 0.82/1.09 1 (all X_a (semiring_1(X_a) -> ti(X_a,one_one(X_a)) = one_one(X_a))) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 2 (all B_1 all B_2 all X_a (comm_semiring_1(X_a) -> plus_plus(X_a,ti(X_a,B_1),B_2) = plus_plus(X_a,B_1,B_2))) # label(tsy_c_Groups_Oplus__class_Oplus_arg1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 3 (all B_1 all B_2 all X_a (comm_semiring_1(X_a) -> plus_plus(X_a,B_1,ti(X_a,B_2)) = plus_plus(X_a,B_1,B_2))) # label(tsy_c_Groups_Oplus__class_Oplus_arg2) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 4 (all B_1 all B_2 all X_a (comm_semiring_1(X_a) -> ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2))) # label(tsy_c_Groups_Oplus__class_Oplus_res) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 5 (all B_1 all B_2 all X_a (monoid_mult(X_a) -> times_times(X_a,ti(X_a,B_1),B_2) = times_times(X_a,B_1,B_2))) # label(tsy_c_Groups_Otimes__class_Otimes_arg1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 6 (all B_1 all B_2 all X_a (monoid_mult(X_a) -> times_times(X_a,B_1,ti(X_a,B_2)) = times_times(X_a,B_1,B_2))) # label(tsy_c_Groups_Otimes__class_Otimes_arg2) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 7 (all B_1 all B_2 all X_a (monoid_mult(X_a) -> ti(X_a,times_times(X_a,B_1,B_2)) = times_times(X_a,B_1,B_2))) # label(tsy_c_Groups_Otimes__class_Otimes_res) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 8 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 9 (all B_1 (zprime(ti(int,B_1)) <-> zprime(B_1))) # label(tsy_c_IntPrimes_Ozprime_arg1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 10 (all B_1 bit0(ti(int,B_1)) = bit0(B_1)) # label(tsy_c_Int_OBit0_arg1) # label(hypothesis) # label(non_clause). [assumption].
% 0.82/1.09 11 (all B_1 ti(int,bit0(B_1)) = bit0(B_1)) # label(tsy_c_Int_OBit0_res) # label(hypothesis) # label(non_clause). [assumption].
% 0.82/1.09 12 (all B_1 bit1(ti(int,B_1)) = bit1(B_1)) # label(tsy_c_Int_OBit1_arg1) # label(hypothesis) # label(non_clause). [assumption].
% 0.82/1.09 13 (all B_1 ti(int,bit1(B_1)) = bit1(B_1)) # label(tsy_c_Int_OBit1_res) # label(hypothesis) # label(non_clause). [assumption].
% 0.82/1.09 14 (all B_1 all X_a (number(X_a) -> number_number_of(X_a,ti(int,B_1)) = number_number_of(X_a,B_1))) # label(tsy_c_Int_Onumber__class_Onumber__of_arg1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 15 (all B_1 all X_a (number(X_a) -> ti(X_a,number_number_of(X_a,B_1)) = number_number_of(X_a,B_1))) # label(tsy_c_Int_Onumber__class_Onumber__of_res) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 16 (all B_1 all B_2 all X_a (number(X_a) & linorder(X_a) -> (ord_less(X_a,ti(X_a,B_1),B_2) <-> ord_less(X_a,B_1,B_2)))) # label(tsy_c_Orderings_Oord__class_Oless_arg1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 17 (all B_1 all B_2 all X_a (number(X_a) & linorder(X_a) -> (ord_less(X_a,B_1,ti(X_a,B_2)) <-> ord_less(X_a,B_1,B_2)))) # label(tsy_c_Orderings_Oord__class_Oless_arg2) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 18 (all B_1 all B_2 all X_a (number(X_a) & linorder(X_a) -> (ord_less_eq(X_a,ti(X_a,B_1),B_2) <-> ord_less_eq(X_a,B_1,B_2)))) # label(tsy_c_Orderings_Oord__class_Oless__eq_arg1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 19 (all B_1 all B_2 all X_a (number(X_a) & linorder(X_a) -> (ord_less_eq(X_a,B_1,ti(X_a,B_2)) <-> ord_less_eq(X_a,B_1,B_2)))) # label(tsy_c_Orderings_Oord__class_Oless__eq_arg2) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 20 (all B_1 all B_2 all X_a (monoid_mult(X_a) -> power_power(X_a,ti(X_a,B_1),B_2) = power_power(X_a,B_1,B_2))) # label(tsy_c_Power_Opower__class_Opower_arg1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 21 (all B_1 all B_2 all X_a (monoid_mult(X_a) -> power_power(X_a,B_1,ti(nat,B_2)) = power_power(X_a,B_1,B_2))) # label(tsy_c_Power_Opower__class_Opower_arg2) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 22 (all B_1 all B_2 all X_a (monoid_mult(X_a) -> ti(X_a,power_power(X_a,B_1,B_2)) = power_power(X_a,B_1,B_2))) # label(tsy_c_Power_Opower__class_Opower_res) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 23 (all B_1 (twoSqu33214720sum2sq(ti(int,B_1)) <-> twoSqu33214720sum2sq(B_1))) # label(tsy_c_TwoSquares__Mirabelle__vsgmegnqdl_Ois__sum2sq_arg1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 24 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].
% 0.82/1.09 25 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].
% 0.82/1.09 26 (all A_1 all B power_power(int,plus_plus(int,A_1,B),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(int,plus_plus(int,power_power(int,A_1,number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),A_1),B)),power_power(int,B,number_number_of(nat,bit0(bit1(pls)))))) # label(fact_7_zadd__power2) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 27 (all A_1 all B power_power(int,plus_plus(int,A_1,B),number_number_of(nat,bit1(bit1(pls)))) = plus_plus(int,plus_plus(int,plus_plus(int,power_power(int,A_1,number_number_of(nat,bit1(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),power_power(int,A_1,number_number_of(nat,bit0(bit1(pls))))),B)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),A_1),power_power(int,B,number_number_of(nat,bit0(bit1(pls)))))),power_power(int,B,number_number_of(nat,bit1(bit1(pls)))))) # label(fact_8_zadd__power3) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 28 (all X_a (number_semiring(X_a) -> (all X_1 all Y_1 power_power(X_a,plus_plus(X_a,X_1,Y_1),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(X_a,plus_plus(X_a,power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Y_1,number_number_of(nat,bit0(bit1(pls))))),times_times(X_a,times_times(X_a,number_number_of(X_a,bit0(bit1(pls))),X_1),Y_1))))) # label(fact_9_power2__sum) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 29 (all X_b (monoid_mult(X_b) & number(X_b) -> (all W power_power(X_b,number_number_of(X_b,W),number_number_of(nat,bit0(bit1(pls)))) = times_times(X_b,number_number_of(X_b,W),number_number_of(X_b,W))))) # label(fact_10_power2__eq__square__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 30 (all A_1 times_times(int,A_1,power_power(int,A_1,number_number_of(nat,bit0(bit1(pls))))) = power_power(int,A_1,number_number_of(nat,bit1(bit1(pls))))) # label(fact_11_cube__square) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 31 (all X_a (semiring_1(X_a) -> power_power(X_a,one_one(X_a),number_number_of(nat,bit0(bit1(pls)))) = one_one(X_a))) # label(fact_12_one__power2) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 32 (all X_a (comm_semiring_1(X_a) -> (all X_1 times_times(X_a,X_1,X_1) = power_power(X_a,X_1,number_number_of(nat,bit0(bit1(pls))))))) # label(fact_13_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 33 (all X_a (monoid_mult(X_a) -> (all A_1 power_power(X_a,A_1,number_number_of(nat,bit0(bit1(pls)))) = times_times(X_a,A_1,A_1)))) # label(fact_14_power2__eq__square) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 34 (all X_a (comm_semiring_1(X_a) -> (all X_1 all N power_power(X_a,X_1,times_times(nat,number_number_of(nat,bit0(bit1(pls))),N)) = times_times(X_a,power_power(X_a,X_1,N),power_power(X_a,X_1,N))))) # label(fact_15_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 35 (all X_a (number_ring(X_a) -> (all W plus_plus(X_a,one_one(X_a),number_number_of(X_a,W)) = number_number_of(X_a,plus_plus(int,bit1(pls),W))))) # label(fact_16_add__special_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 36 (all X_a (number_ring(X_a) -> (all V plus_plus(X_a,number_number_of(X_a,V),one_one(X_a)) = number_number_of(X_a,plus_plus(int,V,bit1(pls)))))) # label(fact_17_add__special_I3_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 37 (all X_a (number_ring(X_a) -> plus_plus(X_a,one_one(X_a),one_one(X_a)) = number_number_of(X_a,bit0(bit1(pls))))) # label(fact_18_one__add__one__is__two) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 38 -(all T_1 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_1)) # label(fact_19__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].
% 0.82/1.09 39 (all W ord_less_eq(int,W,W)) # label(fact_20_zle__refl) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 40 (all Z all W (ord_less_eq(int,Z,W) | ord_less_eq(int,W,Z))) # label(fact_21_zle__linear) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 41 (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_22_zless__le) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 42 (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_23_zless__linear) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 43 (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_24_zle__trans) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 44 (all Z all W (ord_less_eq(int,Z,W) -> (ord_less_eq(int,W,Z) -> Z = W))) # label(fact_25_zle__antisym) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 45 (all X_a (comm_semiring_1(X_a) -> (all X_1 all P all Q power_power(X_a,power_power(X_a,X_1,P),Q) = power_power(X_a,X_1,times_times(nat,P,Q))))) # label(fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 46 (all X_a (comm_semiring_1(X_a) -> (all X_1 power_power(X_a,X_1,one_one(nat)) = ti(X_a,X_1)))) # label(fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 47 (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_28_zpower__zpower) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 48 (all X_a (number(X_a) & linorder(X_a) -> (all V_2 all W_1 (ord_less_eq(X_a,number_number_of(X_a,V_2),number_number_of(X_a,W_1)) <-> -ord_less(X_a,number_number_of(X_a,W_1),number_number_of(X_a,V_2)))))) # label(fact_29_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 49 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_2 all Y_2 (ord_less(X_a,number_number_of(X_a,X_2),number_number_of(X_a,Y_2)) <-> ord_less(int,X_2,Y_2))))) # label(fact_30_less__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 50 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_2 all Y_2 (ord_less_eq(X_a,number_number_of(X_a,X_2),number_number_of(X_a,Y_2)) <-> ord_less_eq(int,X_2,Y_2))))) # label(fact_31_le__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 51 (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_32_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 52 (all X_a (comm_semiring_1(X_a) -> (all X_1 all P all Q times_times(X_a,power_power(X_a,X_1,P),power_power(X_a,X_1,Q)) = power_power(X_a,X_1,plus_plus(nat,P,Q))))) # label(fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 53 (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_34_zpower__zadd__distrib) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 54 (all Z times_times(nat,number_number_of(nat,bit0(bit1(pls))),Z) = plus_plus(nat,Z,Z)) # label(fact_35_nat__mult__2) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 55 (all Z times_times(nat,Z,number_number_of(nat,bit0(bit1(pls)))) = plus_plus(nat,Z,Z)) # label(fact_36_nat__mult__2__right) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 56 (all K1 all K2 (ord_less(int,bit1(K1),bit1(K2)) <-> ord_less(int,K1,K2))) # label(fact_38_less__int__code_I16_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 57 (all K all L (ord_less(int,bit1(K),bit1(L)) <-> ord_less(int,K,L))) # label(fact_39_rel__simps_I17_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 58 (all K1 all K2 (ord_less_eq(int,bit1(K1),bit1(K2)) <-> ord_less_eq(int,K1,K2))) # label(fact_40_less__eq__int__code_I16_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 59 (all K all L (ord_less_eq(int,bit1(K),bit1(L)) <-> ord_less_eq(int,K,L))) # label(fact_41_rel__simps_I34_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 60 (all K1 all K2 (ord_less(int,bit0(K1),bit0(K2)) <-> ord_less(int,K1,K2))) # label(fact_43_less__int__code_I13_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 61 (all K all L (ord_less(int,bit0(K),bit0(L)) <-> ord_less(int,K,L))) # label(fact_44_rel__simps_I14_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 62 (all K1 all K2 (ord_less_eq(int,bit0(K1),bit0(K2)) <-> ord_less_eq(int,K1,K2))) # label(fact_46_less__eq__int__code_I13_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 63 (all K all L (ord_less_eq(int,bit0(K),bit0(L)) <-> ord_less_eq(int,K,L))) # label(fact_47_rel__simps_I31_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 64 (all K all L (ord_less(int,number_number_of(int,K),number_number_of(int,L)) <-> ord_less(int,K,L))) # label(fact_48_less__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 65 (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_49_less__eq__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 66 (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_50_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 67 (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_51_zadd__left__mono) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 68 (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_52_add__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 69 (all K (ord_less_eq(int,bit1(K),pls) <-> ord_less(int,K,pls))) # label(fact_55_rel__simps_I29_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 70 (all K (ord_less(int,pls,bit1(K)) <-> ord_less_eq(int,pls,K))) # label(fact_56_rel__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 71 (all K1 all K2 (ord_less_eq(int,bit1(K1),bit0(K2)) <-> ord_less(int,K1,K2))) # label(fact_57_less__eq__int__code_I15_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 72 (all K all L (ord_less_eq(int,bit1(K),bit0(L)) <-> ord_less(int,K,L))) # label(fact_58_rel__simps_I33_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 73 (all K1 all K2 (ord_less(int,bit0(K1),bit1(K2)) <-> ord_less_eq(int,K1,K2))) # label(fact_59_less__int__code_I14_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 74 (all K all L (ord_less(int,bit0(K),bit1(L)) <-> ord_less_eq(int,K,L))) # label(fact_60_rel__simps_I15_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 75 (all W all Z (ord_less(int,W,Z) -> ord_less_eq(int,plus_plus(int,W,one_one(int)),Z))) # label(fact_61_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 76 (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_62_add1__zle__eq) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 77 (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_63_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 78 (all Y_1 all X_1 (twoSqu33214720sum2sq(X_1) -> (twoSqu33214720sum2sq(Y_1) -> twoSqu33214720sum2sq(times_times(int,X_1,Y_1))))) # label(fact_65_is__mult__sum2sq) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 79 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry times_times(X_a,times_times(X_a,Lx,Ly),times_times(X_a,Rx,Ry)) = times_times(X_a,times_times(X_a,Lx,Rx),times_times(X_a,Ly,Ry))))) # label(fact_66_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 80 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry times_times(X_a,times_times(X_a,Lx,Ly),times_times(X_a,Rx,Ry)) = times_times(X_a,Rx,times_times(X_a,times_times(X_a,Lx,Ly),Ry))))) # label(fact_67_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 81 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry times_times(X_a,times_times(X_a,Lx,Ly),times_times(X_a,Rx,Ry)) = times_times(X_a,Lx,times_times(X_a,Ly,times_times(X_a,Rx,Ry)))))) # label(fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 82 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx times_times(X_a,times_times(X_a,Lx,Ly),Rx) = times_times(X_a,times_times(X_a,Lx,Rx),Ly)))) # label(fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 83 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx times_times(X_a,times_times(X_a,Lx,Ly),Rx) = times_times(X_a,Lx,times_times(X_a,Ly,Rx))))) # label(fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 84 (all X_a (comm_semiring_1(X_a) -> (all Lx all Rx all Ry times_times(X_a,Lx,times_times(X_a,Rx,Ry)) = times_times(X_a,times_times(X_a,Lx,Rx),Ry)))) # label(fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 85 (all X_a (comm_semiring_1(X_a) -> (all Lx all Rx all Ry times_times(X_a,Lx,times_times(X_a,Rx,Ry)) = times_times(X_a,Rx,times_times(X_a,Lx,Ry))))) # label(fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 86 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B times_times(X_a,A_1,B) = times_times(X_a,B,A_1)))) # label(fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 87 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C all D plus_plus(X_a,plus_plus(X_a,A_1,B),plus_plus(X_a,C,D)) = plus_plus(X_a,plus_plus(X_a,A_1,C),plus_plus(X_a,B,D))))) # label(fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 88 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C plus_plus(X_a,plus_plus(X_a,A_1,B),C) = plus_plus(X_a,plus_plus(X_a,A_1,C),B)))) # label(fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 89 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C plus_plus(X_a,plus_plus(X_a,A_1,B),C) = plus_plus(X_a,A_1,plus_plus(X_a,B,C))))) # label(fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 90 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D plus_plus(X_a,A_1,plus_plus(X_a,C,D)) = plus_plus(X_a,plus_plus(X_a,A_1,C),D)))) # label(fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 91 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D plus_plus(X_a,A_1,plus_plus(X_a,C,D)) = plus_plus(X_a,C,plus_plus(X_a,A_1,D))))) # label(fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 92 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C plus_plus(X_a,A_1,C) = plus_plus(X_a,C,A_1)))) # label(fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 93 (all X_a (number_ring(X_a) & ring_char_0(X_a) -> (all X_2 all Y_2 (number_number_of(X_a,X_2) = number_number_of(X_a,Y_2) <-> X_2 = Y_2)))) # label(fact_80_eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 94 (all X_a (number(X_a) -> (all W_1 all X_2 (number_number_of(X_a,W_1) = ti(X_a,X_2) <-> ti(X_a,X_2) = number_number_of(X_a,W_1))))) # label(fact_81_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 95 (all K all L (bit1(K) = bit1(L) <-> K = L)) # label(fact_82_rel__simps_I51_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 96 (all K all L (bit0(K) = bit0(L) <-> K = L)) # label(fact_83_rel__simps_I48_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 97 (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_84_zmult__assoc) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 98 (all Z all W times_times(int,Z,W) = times_times(int,W,Z)) # label(fact_85_zmult__commute) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 99 (all K_1 number_number_of(int,K_1) = K_1) # label(fact_86_number__of__is__id) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 100 (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_87_zadd__assoc) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 101 (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_88_zadd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.10 102 (all Z all W plus_plus(int,Z,W) = plus_plus(int,W,Z)) # label(fact_89_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.10 103 (all K (ord_less(int,bit1(K),pls) <-> ord_less(int,K,pls))) # label(fact_90_rel__simps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.10 104 (all K1 all K2 (ord_less(int,bit1(K1),bit0(K2)) <-> ord_less(int,K1,K2))) # label(fact_91_less__int__code_I15_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.10 105 (all K all L (ord_less(int,bit1(K),bit0(L)) <-> ord_less(int,K,L))) # label(fact_92_rel__simps_I16_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.10 106 (all K (ord_less(int,bit0(K),pls) <-> ord_less(int,K,pls))) # label(fact_93_rel__simps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.10 107 (all K (ord_less(int,pls,bit0(K)) <-> ord_less(int,pls,K))) # label(fact_94_rel__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.10 108 (all K (ord_less_eq(int,pls,bit1(K)) <-> ord_less_eq(int,pls,K))) # label(fact_95_rel__simps_I22_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.10 109 (all K1 all K2 (ord_less_eq(int,bit0(K1),bit1(K2)) <-> ord_less_eq(int,K1,K2))) # label(fact_96_less__eq__int__code_I14_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.10 110 (all K all L (ord_less_eq(int,bit0(K),bit1(L)) <-> ord_less_eq(int,K,L))) # label(fact_97_rel__simps_I32_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.10 111 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.10 112 -(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].
% 0.82/1.10
% 0.82/1.10 ============================== end of process non-clausal formulas ===
% 0.82/1.10
% 0.82/1.10 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.10
% 0.82/1.10 ============================== PREDICATE ELIMINATION =================
% 0.82/1.10 113 semiring_1(int) # label(arity_Int_Oint___Rings_Osemiring__1) # label(axiom). [assumption].
% 0.82/1.10 114 -semiring_1(A) | ti(A,one_one(A)) = one_one(A) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom). [clausify(1)].
% 0.82/1.10 115 -semiring_1(A) | power_power(A,one_one(A),number_number_of(nat,bit0(bit1(pls)))) = one_one(A) # label(fact_12_one__power2) # label(axiom). [clausify(31)].
% 0.82/1.10 Derived: ti(int,one_one(int)) = one_one(int). [resolve(113,a,114,a)].
% 0.82/1.10 Derived: power_power(int,one_one(int),number_number_of(nat,bit0(bit1(pls)))) = one_one(int). [resolve(113,a,115,a)].
% 0.82/1.10 116 semiring_1(nat) # label(arity_Nat_Onat___Rings_Osemiring__1) # label(axiom). [assumption].
% 0.82/1.10 Derived: ti(nat,one_one(nat)) = one_one(nat). [resolve(116,a,114,a)].
% 0.82/1.10 Derived: power_power(nat,one_one(nat),number_number_of(nat,bit0(bit1(pls)))) = one_one(nat). [resolve(116,a,115,a)].
% 0.82/1.10 117 comm_semiring_1(int) # label(arity_Int_Oint___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 0.82/1.10 118 -comm_semiring_1(A) | plus_plus(A,ti(A,B),C) = plus_plus(A,B,C) # label(tsy_c_Groups_Oplus__class_Oplus_arg1) # label(axiom). [clausify(2)].
% 0.82/1.10 119 -comm_semiring_1(A) | plus_plus(A,B,ti(A,C)) = plus_plus(A,B,C) # label(tsy_c_Groups_Oplus__class_Oplus_arg2) # label(axiom). [clausify(3)].
% 0.82/1.10 120 -comm_semiring_1(A) | plus_plus(A,B,C) = ti(A,plus_plus(A,B,C)) # label(tsy_c_Groups_Oplus__class_Oplus_res) # label(axiom). [clausify(4)].
% 0.82/1.10 121 -comm_semiring_1(A) | power_power(A,B,number_number_of(nat,bit0(bit1(pls)))) = times_times(A,B,B) # label(fact_13_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) # label(axiom). [clausify(32)].
% 0.82/1.10 122 -comm_semiring_1(A) | power_power(A,B,times_times(nat,number_number_of(nat,bit0(bit1(pls))),C)) = times_times(A,power_power(A,B,C),power_power(A,B,C)) # label(fact_15_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) # label(axiom). [clausify(34)].
% 0.82/1.10 123 -comm_semiring_1(A) | power_power(A,power_power(A,B,C),D) = power_power(A,B,times_times(nat,C,D)) # label(fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom). [clausify(45)].
% 0.82/1.10 124 -comm_semiring_1(A) | power_power(A,B,one_one(nat)) = ti(A,B) # label(fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom). [clausify(46)].
% 0.82/1.10 125 -comm_semiring_1(A) | power_power(A,B,plus_plus(nat,C,D)) = times_times(A,power_power(A,B,C),power_power(A,B,D)) # label(fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom). [clausify(52)].
% 0.82/1.10 126 -comm_semiring_1(A) | times_times(A,times_times(A,B,C),times_times(A,D,E)) = times_times(A,times_times(A,B,D),times_times(A,C,E)) # label(fact_66_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom). [clausify(79)].
% 0.82/1.10 127 -comm_semiring_1(A) | times_times(A,times_times(A,B,C),times_times(A,D,E)) = times_times(A,D,times_times(A,times_times(A,B,C),E)) # label(fact_67_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom). [clausify(80)].
% 0.82/1.10 128 -comm_semiring_1(A) | times_times(A,times_times(A,B,C),times_times(A,D,E)) = times_times(A,B,times_times(A,C,times_times(A,D,E))) # label(fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom). [clausify(81)].
% 0.82/1.10 129 -comm_semiring_1(A) | times_times(A,times_times(A,B,C),D) = times_times(A,times_times(A,B,D),C) # label(fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom). [clausify(82)].
% 0.82/1.10 130 -comm_semiring_1(A) | times_times(A,times_times(A,B,C),D) = times_times(A,B,times_times(A,C,D)) # label(fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom). [clausify(83)].
% 0.82/1.10 131 -comm_semiring_1(A) | times_times(A,times_times(A,B,C),D) = times_times(A,B,times_times(A,C,D)) # label(fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom). [clausify(84)].
% 0.82/1.10 132 -comm_semiring_1(A) | times_times(A,B,times_times(A,C,D)) = times_times(A,C,times_times(A,B,D)) # label(fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom). [clausify(85)].
% 0.82/1.10 133 -comm_semiring_1(A) | times_times(A,B,C) = times_times(A,C,B) # label(fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom). [clausify(86)].
% 0.82/1.10 134 -comm_semiring_1(A) | plus_plus(A,plus_plus(A,B,C),plus_plus(A,D,E)) = plus_plus(A,plus_plus(A,B,D),plus_plus(A,C,E)) # label(fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom). [clausify(87)].
% 0.82/1.10 135 -comm_semiring_1(A) | plus_plus(A,plus_plus(A,B,C),D) = plus_plus(A,plus_plus(A,B,D),C) # label(fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom). [clausify(88)].
% 0.82/1.10 136 -comm_semiring_1(A) | plus_plus(A,plus_plus(A,B,C),D) = plus_plus(A,B,plus_plus(A,C,D)) # label(fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom). [clausify(89)].
% 0.82/1.10 137 -comm_semiring_1(A) | plus_plus(A,plus_plus(A,B,C),D) = plus_plus(A,B,plus_plus(A,C,D)) # label(fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom). [clausify(90)].
% 0.82/1.10 138 -comm_semiring_1(A) | plus_plus(A,B,plus_plus(A,C,D)) = plus_plus(A,C,plus_plus(A,B,D)) # label(fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom). [clausify(91)].
% 0.82/1.10 139 -comm_semiring_1(A) | plus_plus(A,B,C) = plus_plus(A,C,B) # label(fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom). [clausify(92)].
% 0.82/1.10 Derived: plus_plus(int,ti(int,A),B) = plus_plus(int,A,B). [resolve(117,a,118,a)].
% 0.82/1.10 Derived: plus_plus(int,A,ti(int,B)) = plus_plus(int,A,B). [resolve(117,a,119,a)].
% 0.82/1.10 Derived: plus_plus(int,A,B) = ti(int,plus_plus(int,A,B)). [resolve(117,a,120,a)].
% 0.82/1.10 Derived: power_power(int,A,number_number_of(nat,bit0(bit1(pls)))) = times_times(int,A,A). [resolve(117,a,121,a)].
% 0.82/1.10 Derived: power_power(int,A,times_times(nat,number_number_of(nat,bit0(bit1(pls))),B)) = times_times(int,power_power(int,A,B),power_power(int,A,B)). [resolve(117,a,122,a)].
% 0.82/1.10 Derived: power_power(int,power_power(int,A,B),C) = power_power(int,A,times_times(nat,B,C)). [resolve(117,a,123,a)].
% 0.82/1.10 Derived: power_power(int,A,one_one(nat)) = ti(int,A). [resolve(117,a,124,a)].
% 0.82/1.10 Derived: power_power(int,A,plus_plus(nat,B,C)) = times_times(int,power_power(int,A,B),power_power(int,A,C)). [resolve(117,a,125,a)].
% 0.82/1.10 Derived: times_times(int,times_times(int,A,B),times_times(int,C,D)) = times_times(int,times_times(int,A,C),times_times(int,B,D)). [resolve(117,a,126,a)].
% 0.82/1.10 Derived: times_times(int,times_times(int,A,B),times_times(int,C,D)) = times_times(int,C,times_times(int,times_times(int,A,B),D)). [resolve(117,a,127,a)].
% 0.82/1.10 Derived: times_times(int,times_times(int,A,B),times_times(int,C,D)) = times_times(int,A,times_times(int,B,times_times(int,C,D))). [resolve(117,a,128,a)].
% 0.82/1.10 Derived: times_times(int,times_times(int,A,B),C) = times_times(int,times_times(int,A,C),B). [resolve(117,a,129,a)].
% 0.82/1.10 Derived: times_times(int,times_times(int,A,B),C) = times_times(int,A,times_times(int,B,C)). [resolve(117,a,130,a)].
% 0.82/1.10 Derived: times_times(int,A,times_times(int,B,C)) = times_times(int,B,times_times(int,A,C)). [resolve(117,a,132,a)].
% 0.82/1.10 Derived: times_times(int,A,B) = times_times(int,B,A). [resolve(117,a,133,a)].
% 0.82/1.10 Derived: 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)). [resolve(117,a,134,a)].
% 0.82/1.10 Derived: plus_plus(int,plus_plus(int,A,B),C) = plus_plus(int,plus_plus(int,A,C),B). [resolve(117,a,135,a)].
% 0.82/1.10 Derived: plus_plus(int,plus_plus(int,A,B),C) = plus_plus(int,A,plus_plus(int,B,C)). [resolve(117,a,136,a)].
% 0.82/1.10 Derived: plus_plus(int,A,plus_plus(int,B,C)) = plus_plus(int,B,plus_plus(int,A,C)). [resolve(117,a,138,a)].
% 0.82/1.10 Derived: plus_plus(int,A,B) = plus_plus(int,B,A). [resolve(117,a,139,a)].
% 0.82/1.10 140 comm_semiring_1(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 0.82/1.10 Derived: plus_plus(nat,ti(nat,A),B) = plus_plus(nat,A,B). [resolve(140,a,118,a)].
% 0.82/1.10 Derived: plus_plus(nat,A,ti(nat,B)) = plus_plus(nat,A,B). [resolve(140,a,119,a)].
% 0.82/1.10 Derived: plus_plus(nat,A,B) = ti(nat,plus_plus(nat,A,B)). [resolve(140,a,120,a)].
% 0.82/1.10 Derived: power_power(nat,A,number_number_of(nat,bit0(bit1(pls)))) = times_times(nat,A,A). [resolve(140,a,121,a)].
% 0.82/1.10 Derived: power_power(nat,A,times_times(nat,number_number_of(nat,bit0(bit1(pls))),B)) = times_times(nat,power_power(nat,A,B),power_power(nat,A,B)). [resolve(140,a,122,a)].
% 0.82/1.10 Derived: power_power(nat,power_power(nat,A,B),C) = power_power(nat,A,times_times(nat,B,C)). [resolve(140,a,123,a)].
% 0.82/1.10 Derived: power_power(nat,A,one_one(nat)) = ti(nat,A). [resolve(140,a,124,a)].
% 0.82/1.10 Derived: power_power(nat,A,plus_plus(nat,B,C)) = times_times(nat,power_power(nat,A,B),power_power(nat,A,C)). [resolve(140,a,125,a)].
% 0.82/1.10 Derived: times_times(nat,times_times(nat,A,B),times_times(nat,C,D)) = times_times(nat,times_times(nat,A,C),times_times(nat,B,D)). [resolve(140,a,126,a)].
% 0.82/1.10 Derived: times_times(nat,times_times(nat,A,B),times_times(nat,C,D)) = times_times(nat,C,times_times(nat,times_times(nat,A,B),D)). [resolve(140,a,127,a)].
% 0.82/1.10 Derived: times_times(nat,times_times(nat,A,B),times_times(nat,C,D)) = times_times(nat,A,times_times(nat,B,times_times(nat,C,D))). [resolve(140,a,128,a)].
% 0.82/1.10 Derived: times_times(nat,times_times(nat,A,B),C) = times_times(nat,times_times(nat,A,C),B). [resolve(140,a,129,a)].
% 0.82/1.10 Derived: times_times(nat,times_times(nat,A,B),C) = times_times(nat,A,times_times(nat,B,C)). [resolve(140,a,130,a)].
% 0.82/1.10 Derived: times_times(nat,A,times_times(nat,B,C)) = times_times(nat,B,times_times(nat,A,C)). [resolve(140,a,132,a)].
% 0.82/1.10 Derived: times_times(nat,A,B) = times_times(nat,B,A). [resolve(140,a,133,a)].
% 0.82/1.10 Derived: 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)). [resolve(140,a,134,a)].
% 0.82/1.10 Derived: plus_plus(nat,plus_plus(nat,A,B),C) = plus_plus(nat,plus_plus(nat,A,C),B). [resolve(140,a,135,a)].
% 0.82/1.10 Derived: plus_plus(nat,plus_plus(nat,A,B),C) = plus_plus(nat,A,plus_plus(nat,B,C)). [resolve(140,a,136,a)].
% 0.82/1.10 Derived: plus_plus(nat,A,plus_plus(nat,B,C)) = plus_plus(nat,B,plus_plus(nat,A,C)). [resolve(140,a,138,a)].
% 0.82/1.10 Derived: plus_plus(nat,A,B) = plus_plus(nat,B,A). [resolve(140,a,139,a)].
% 0.82/1.10 141 monoid_mult(int) # label(arity_Int_Oint___Groups_Omonoid__mult) # label(axiom). [assumption].
% 0.82/1.10 142 -monoid_mult(A) | times_times(A,ti(A,B),C) = times_times(A,B,C) # label(tsy_c_Groups_Otimes__class_Otimes_arg1) # label(axiom). [clausify(5)].
% 0.82/1.10 143 -monoid_mult(A) | times_times(A,B,ti(A,C)) = times_times(A,B,C) # label(tsy_c_Groups_Otimes__class_Otimes_arg2) # label(axiom). [clausify(6)].
% 0.82/1.10 144 -monoid_mult(A) | times_times(A,B,C) = ti(A,times_times(A,B,C)) # label(tsy_c_Groups_Otimes__class_Otimes_res) # label(axiom). [clausify(7)].
% 0.82/1.10 145 -monoid_mult(A) | power_power(A,ti(A,B),C) = power_power(A,B,C) # label(tsy_c_Power_Opower__class_Opower_arg1) # label(axiom). [clausify(20)].
% 0.82/1.10 146 -monoid_mult(A) | power_power(A,B,ti(nat,C)) = power_power(A,B,C) # label(tsy_c_Power_Opower__class_Opower_arg2) # label(axiom). [clausify(21)].
% 0.82/1.10 147 -monoid_mult(A) | power_power(A,B,C) = ti(A,power_power(A,B,C)) # label(tsy_c_Power_Opower__class_Opower_res) # label(axiom). [clausify(22)].
% 0.82/1.10 148 -monoid_mult(A) | -number(A) | power_power(A,number_number_of(A,B),number_number_of(nat,bit0(bit1(pls)))) = times_times(A,number_number_of(A,B),number_number_of(A,B)) # label(fact_10_power2__eq__square__number__of) # label(axiom). [clausify(29)].
% 0.82/1.10 149 -monoid_mult(A) | power_power(A,B,number_number_of(nat,bit0(bit1(pls)))) = times_times(A,B,B) # label(fact_14_power2__eq__square) # label(axiom). [clausify(33)].
% 0.82/1.10 Derived: times_times(int,ti(int,A),B) = times_times(int,A,B). [resolve(141,a,142,a)].
% 0.82/1.10 Derived: times_times(int,A,ti(int,B)) = times_times(int,A,B). [resolve(141,a,143,a)].
% 0.82/1.10 Derived: times_times(int,A,B) = ti(int,times_times(int,A,B)). [resolve(141,a,144,a)].
% 0.82/1.10 Derived: power_power(int,ti(int,A),B) = power_power(int,A,B). [resolve(141,a,145,a)].
% 0.82/1.10 Derived: power_power(int,A,ti(nat,B)) = power_power(int,A,B). [resolve(141,a,146,a)].
% 0.82/1.10 Derived: power_power(int,A,B) = ti(int,power_power(int,A,B)). [resolve(141,a,147,a)].
% 0.82/1.10 150 monoid_mult(nat) # label(arity_Nat_Onat___Groups_Omonoid__mult) # label(axiom). [assumption].
% 0.82/1.10 Derived: times_times(nat,ti(nat,A),B) = times_times(nat,A,B). [resolve(150,a,142,a)].
% 0.82/1.10 Derived: times_times(nat,A,ti(nat,B)) = times_times(nat,A,B). [resolve(150,a,143,a)].
% 0.82/1.10 Derived: times_times(nat,A,B) = ti(nat,times_times(nat,A,B)). [resolve(150,a,144,a)].
% 0.82/1.10 Derived: power_power(nat,ti(nat,A),B) = power_power(nat,A,B). [resolve(150,a,145,a)].
% 0.82/1.10 Derived: power_power(nat,A,ti(nat,B)) = power_power(nat,A,B). [resolve(150,a,146,a)].
% 0.82/1.10 Derived: power_power(nat,A,B) = ti(nat,power_power(nat,A,B)). [resolve(150,a,147,a)].
% 0.82/1.10 151 number(int) # label(arity_Int_Oint___Int_Onumber) # label(axiom). [assumption].
% 0.82/1.10 152 -number(A) | number_number_of(A,ti(int,B)) = number_number_of(A,B) # label(tsy_c_Int_Onumber__class_Onumber__of_arg1) # label(axiom). [clausify(14)].
% 0.82/1.10 153 -number(A) | number_number_of(A,B) = ti(A,number_number_of(A,B)) # label(tsy_c_Int_Onumber__class_Onumber__of_res) # label(axiom). [clausify(15)].
% 0.82/1.10 154 -number(A) | -linorder(A) | -ord_less(A,ti(A,B),C) | ord_less(A,B,C) # label(tsy_c_Orderings_Oord__class_Oless_arg1) # label(axiom). [clausify(16)].
% 0.82/1.10 155 -number(A) | -linorder(A) | ord_less(A,ti(A,B),C) | -ord_less(A,B,C) # label(tsy_c_Orderings_Oord__class_Oless_arg1) # label(axiom). [clausify(16)].
% 0.82/1.10 156 -number(A) | -linorder(A) | -ord_less(A,B,ti(A,C)) | ord_less(A,B,C) # label(tsy_c_Orderings_Oord__class_Oless_arg2) # label(axiom). [clausify(17)].
% 0.82/1.10 157 -number(A) | -linorder(A) | ord_less(A,B,ti(A,C)) | -ord_less(A,B,C) # label(tsy_c_Orderings_Oord__class_Oless_arg2) # label(axiom). [clausify(17)].
% 0.82/1.10 158 -number(A) | -linorder(A) | -ord_less_eq(A,ti(A,B),C) | ord_less_eq(A,B,C) # label(tsy_c_Orderings_Oord__class_Oless__eq_arg1) # label(axiom). [clausify(18)].
% 0.82/1.10 159 -number(A) | -linorder(A) | ord_less_eq(A,ti(A,B),C) | -ord_less_eq(A,B,C) # label(tsy_c_Orderings_Oord__class_Oless__eq_arg1) # label(axiom). [clausify(18)].
% 0.82/1.10 160 -number(A) | -linorder(A) | -ord_less_eq(A,B,ti(A,C)) | ord_less_eq(A,B,C) # label(tsy_c_Orderings_Oord__class_Oless__eq_arg2) # label(axiom). [clausify(19)].
% 0.82/1.11 161 -number(A) | -linorder(A) | ord_less_eq(A,B,ti(A,C)) | -ord_less_eq(A,B,C) # label(tsy_c_Orderings_Oord__class_Oless__eq_arg2) # label(axiom). [clausify(19)].
% 0.82/1.11 162 -number(A) | -linorder(A) | -ord_less_eq(A,number_number_of(A,B),number_number_of(A,C)) | -ord_less(A,number_number_of(A,C),number_number_of(A,B)) # label(fact_29_le__number__of__eq__not__less) # label(axiom). [clausify(48)].
% 0.82/1.11 163 -number(A) | -linorder(A) | ord_less_eq(A,number_number_of(A,B),number_number_of(A,C)) | ord_less(A,number_number_of(A,C),number_number_of(A,B)) # label(fact_29_le__number__of__eq__not__less) # label(axiom). [clausify(48)].
% 0.82/1.11 Derived: number_number_of(int,ti(int,A)) = number_number_of(int,A). [resolve(151,a,152,a)].
% 0.82/1.11 Derived: number_number_of(int,A) = ti(int,number_number_of(int,A)). [resolve(151,a,153,a)].
% 0.82/1.11 Derived: -linorder(int) | -ord_less(int,ti(int,A),B) | ord_less(int,A,B). [resolve(151,a,154,a)].
% 0.82/1.11 Derived: -linorder(int) | ord_less(int,ti(int,A),B) | -ord_less(int,A,B). [resolve(151,a,155,a)].
% 0.82/1.11 Derived: -linorder(int) | -ord_less(int,A,ti(int,B)) | ord_less(int,A,B). [resolve(151,a,156,a)].
% 0.82/1.11 Derived: -linorder(int) | ord_less(int,A,ti(int,B)) | -ord_less(int,A,B). [resolve(151,a,157,a)].
% 0.82/1.11 Derived: -linorder(int) | -ord_less_eq(int,ti(int,A),B) | ord_less_eq(int,A,B). [resolve(151,a,158,a)].
% 0.82/1.11 Derived: -linorder(int) | ord_less_eq(int,ti(int,A),B) | -ord_less_eq(int,A,B). [resolve(151,a,159,a)].
% 0.82/1.11 Derived: -linorder(int) | -ord_less_eq(int,A,ti(int,B)) | ord_less_eq(int,A,B). [resolve(151,a,160,a)].
% 0.82/1.11 Derived: -linorder(int) | ord_less_eq(int,A,ti(int,B)) | -ord_less_eq(int,A,B). [resolve(151,a,161,a)].
% 0.82/1.11 Derived: -linorder(int) | -ord_less_eq(int,number_number_of(int,A),number_number_of(int,B)) | -ord_less(int,number_number_of(int,B),number_number_of(int,A)). [resolve(151,a,162,a)].
% 0.82/1.11 Derived: -linorder(int) | ord_less_eq(int,number_number_of(int,A),number_number_of(int,B)) | ord_less(int,number_number_of(int,B),number_number_of(int,A)). [resolve(151,a,163,a)].
% 0.82/1.11 164 number(nat) # label(arity_Nat_Onat___Int_Onumber) # label(axiom). [assumption].
% 0.82/1.11 Derived: number_number_of(nat,ti(int,A)) = number_number_of(nat,A). [resolve(164,a,152,a)].
% 0.82/1.11 Derived: number_number_of(nat,A) = ti(nat,number_number_of(nat,A)). [resolve(164,a,153,a)].
% 0.82/1.11 Derived: -linorder(nat) | -ord_less(nat,ti(nat,A),B) | ord_less(nat,A,B). [resolve(164,a,154,a)].
% 0.82/1.11 Derived: -linorder(nat) | ord_less(nat,ti(nat,A),B) | -ord_less(nat,A,B). [resolve(164,a,155,a)].
% 0.82/1.11 Derived: -linorder(nat) | -ord_less(nat,A,ti(nat,B)) | ord_less(nat,A,B). [resolve(164,a,156,a)].
% 0.82/1.11 Derived: -linorder(nat) | ord_less(nat,A,ti(nat,B)) | -ord_less(nat,A,B). [resolve(164,a,157,a)].
% 0.82/1.11 Derived: -linorder(nat) | -ord_less_eq(nat,ti(nat,A),B) | ord_less_eq(nat,A,B). [resolve(164,a,158,a)].
% 0.82/1.11 Derived: -linorder(nat) | ord_less_eq(nat,ti(nat,A),B) | -ord_less_eq(nat,A,B). [resolve(164,a,159,a)].
% 0.82/1.11 Derived: -linorder(nat) | -ord_less_eq(nat,A,ti(nat,B)) | ord_less_eq(nat,A,B). [resolve(164,a,160,a)].
% 0.82/1.11 Derived: -linorder(nat) | ord_less_eq(nat,A,ti(nat,B)) | -ord_less_eq(nat,A,B). [resolve(164,a,161,a)].
% 0.82/1.11 Derived: -linorder(nat) | -ord_less_eq(nat,number_number_of(nat,A),number_number_of(nat,B)) | -ord_less(nat,number_number_of(nat,B),number_number_of(nat,A)). [resolve(164,a,162,a)].
% 0.82/1.11 Derived: -linorder(nat) | ord_less_eq(nat,number_number_of(nat,A),number_number_of(nat,B)) | ord_less(nat,number_number_of(nat,B),number_number_of(nat,A)). [resolve(164,a,163,a)].
% 0.82/1.11 165 number_semiring(int) # label(arity_Int_Oint___Int_Onumber__semiring) # label(axiom). [assumption].
% 0.82/1.11 166 -number_semiring(A) | power_power(A,plus_plus(A,B,C),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(A,plus_plus(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),power_power(A,C,number_number_of(nat,bit0(bit1(pls))))),times_times(A,times_times(A,number_number_of(A,bit0(bit1(pls))),B),C)) # label(fact_9_power2__sum) # label(axiom). [clausify(28)].
% 0.82/1.11 Derived: power_power(int,plus_plus(int,A,B),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(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))))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),A),B)). [resolve(165,a,166,a)].
% 0.82/1.13 167 number_semiring(nat) # label(arity_Nat_Onat___Int_Onumber__semiring) # label(axiom). [assumption].
% 0.82/1.13 Derived: power_power(nat,plus_plus(nat,A,B),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(nat,plus_plus(nat,power_power(nat,A,number_number_of(nat,bit0(bit1(pls)))),power_power(nat,B,number_number_of(nat,bit0(bit1(pls))))),times_times(nat,times_times(nat,number_number_of(nat,bit0(bit1(pls))),A),B)). [resolve(167,a,166,a)].
% 0.82/1.13 168 number_ring(int) # label(arity_Int_Oint___Int_Onumber__ring) # label(axiom). [assumption].
% 0.82/1.13 169 -number_ring(A) | number_number_of(A,plus_plus(int,bit1(pls),B)) = plus_plus(A,one_one(A),number_number_of(A,B)) # label(fact_16_add__special_I2_J) # label(axiom). [clausify(35)].
% 0.82/1.13 170 -number_ring(A) | number_number_of(A,plus_plus(int,B,bit1(pls))) = plus_plus(A,number_number_of(A,B),one_one(A)) # label(fact_17_add__special_I3_J) # label(axiom). [clausify(36)].
% 0.82/1.13 171 -number_ring(A) | number_number_of(A,bit0(bit1(pls))) = plus_plus(A,one_one(A),one_one(A)) # label(fact_18_one__add__one__is__two) # label(axiom). [clausify(37)].
% 0.82/1.13 172 -number_ring(A) | -linordered_idom(A) | -ord_less(A,number_number_of(A,B),number_number_of(A,C)) | ord_less(int,B,C) # label(fact_30_less__number__of) # label(axiom). [clausify(49)].
% 0.82/1.13 173 -number_ring(A) | -linordered_idom(A) | ord_less(A,number_number_of(A,B),number_number_of(A,C)) | -ord_less(int,B,C) # label(fact_30_less__number__of) # label(axiom). [clausify(49)].
% 0.82/1.13 174 -number_ring(A) | -linordered_idom(A) | -ord_less_eq(A,number_number_of(A,B),number_number_of(A,C)) | ord_less_eq(int,B,C) # label(fact_31_le__number__of) # label(axiom). [clausify(50)].
% 0.82/1.13 175 -number_ring(A) | -linordered_idom(A) | ord_less_eq(A,number_number_of(A,B),number_number_of(A,C)) | -ord_less_eq(int,B,C) # label(fact_31_le__number__of) # label(axiom). [clausify(50)].
% 0.82/1.13 176 -number_ring(A) | -ring_char_0(A) | number_number_of(A,B) != number_number_of(A,C) | B = C # label(fact_80_eq__number__of) # label(axiom). [clausify(93)].
% 0.82/1.13 177 -number_ring(A) | -ring_char_0(A) | number_number_of(A,B) = number_number_of(A,C) | B != C # label(fact_80_eq__number__of) # label(axiom). [clausify(93)].
% 0.82/1.13 Derived: number_number_of(int,plus_plus(int,bit1(pls),A)) = plus_plus(int,one_one(int),number_number_of(int,A)). [resolve(168,a,169,a)].
% 0.82/1.13 Derived: number_number_of(int,plus_plus(int,A,bit1(pls))) = plus_plus(int,number_number_of(int,A),one_one(int)). [resolve(168,a,170,a)].
% 0.82/1.13 Derived: number_number_of(int,bit0(bit1(pls))) = plus_plus(int,one_one(int),one_one(int)). [resolve(168,a,171,a)].
% 0.82/1.13 Derived: -linordered_idom(int) | -ord_less(int,number_number_of(int,A),number_number_of(int,B)) | ord_less(int,A,B). [resolve(168,a,172,a)].
% 0.82/1.13 Derived: -linordered_idom(int) | ord_less(int,number_number_of(int,A),number_number_of(int,B)) | -ord_less(int,A,B). [resolve(168,a,173,a)].
% 0.82/1.13 Derived: -linordered_idom(int) | -ord_less_eq(int,number_number_of(int,A),number_number_of(int,B)) | ord_less_eq(int,A,B). [resolve(168,a,174,a)].
% 0.82/1.13 Derived: -linordered_idom(int) | ord_less_eq(int,number_number_of(int,A),number_number_of(int,B)) | -ord_less_eq(int,A,B). [resolve(168,a,175,a)].
% 0.82/1.13 Derived: -ring_char_0(int) | number_number_of(int,A) != number_number_of(int,B) | A = B. [resolve(168,a,176,a)].
% 0.82/1.13 Derived: -ring_char_0(int) | number_number_of(int,A) = number_number_of(int,B) | A != B. [resolve(168,a,177,a)].
% 0.82/1.13
% 0.82/1.13 ============================== end predicate elimination =============
% 0.82/1.13
% 0.82/1.13 Auto_denials: (non-Horn, no changes).
% 0.82/1.13
% 0.82/1.13 Term ordering decisions:
% 0.82/1.13 Function symbol KB weights: int=1. nat=1. pls=1. m=1. t=1. s=1. c1=1. c2=1. c3=1. c4=1. c5=1. number_number_of=1. ti=1. bit1=1. bit0=1. one_one=1. undefined=1. times_times=1. plus_plus=1. power_power=1.
% 0.82/1.13
% 0.82/1.13 ============================== end of process initial clauses ========
% 0.82/1.13
% 0.82/1.13 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.13
% 0.82/1.13 ============================== end of clauses for search =============
% 0.82/1.13
% 0.82/1.13 ============================== SEARCH ================================
% 0.82/1.13
% 0.82/1.13 % Starting search at 0.06 seconds.
% 0.82/1.13
% 0.82/1.13 ============================== PROOF =================================
% 0.82/1.13 % SZS status Theorem
% 0.82/1.13 % SZS output start Refutation
% 0.82/1.13
% 0.82/1.13 % Proof 1 at 0.06 (+ 0.00) seconds.
% 0.82/1.13 % Length of proof is 19.
% 0.82/1.13 % Level of proof is 4.
% 0.82/1.13 % Maximum clause weight is 37.000.
% 0.82/1.13 % Given clauses 8.
% 0.82/1.13
% 0.82/1.13 24 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].
% 0.82/1.13 25 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].
% 0.82/1.13 41 (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_22_zless__le) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 98 (all Z all W times_times(int,Z,W) = times_times(int,W,Z)) # label(fact_85_zmult__commute) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 99 (all K_1 number_number_of(int,K_1) = K_1) # label(fact_86_number__of__is__id) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 102 (all Z all W plus_plus(int,Z,W) = plus_plus(int,W,Z)) # label(fact_89_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 112 -(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].
% 0.82/1.13 194 ord_less_eq(int,one_one(int),t) # label(fact_0_tpos) # label(axiom). [assumption].
% 0.82/1.13 195 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_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(24)].
% 0.82/1.13 196 -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)) # 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(25)].
% 0.82/1.13 214 ord_less(int,A,B) | -ord_less_eq(int,A,B) | B = A # label(fact_22_zless__le) # label(axiom). [clausify(41)].
% 0.82/1.13 267 times_times(int,A,B) = times_times(int,B,A) # label(fact_85_zmult__commute) # label(axiom). [clausify(98)].
% 0.82/1.13 268 number_number_of(int,A) = A # label(fact_86_number__of__is__id) # label(axiom). [clausify(99)].
% 0.82/1.13 271 plus_plus(int,A,B) = plus_plus(int,B,A) # label(fact_89_zadd__commute) # label(axiom). [clausify(102)].
% 0.82/1.13 289 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(112)].
% 0.82/1.13 290 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,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))). [copy(289),rewrite([268(24),267(24),271(27)])].
% 0.82/1.13 423 -ord_less(int,one_one(int),t). [back_rewrite(196),rewrite([268(31),267(31),271(34)]),unit_del(b,290)].
% 0.82/1.13 424 one_one(int) != t. [back_rewrite(195),rewrite([268(30),267(30),271(33)]),unit_del(b,290)].
% 0.82/1.13 442 $F. [resolve(214,b,194,a),flip(b),unit_del(a,423),unit_del(b,424)].
% 0.82/1.13
% 0.82/1.13 % SZS output end Refutation
% 0.82/1.13 ============================== end of proof ==========================
% 0.82/1.13
% 0.82/1.13 ============================== STATISTICS ============================
% 0.82/1.13
% 0.82/1.13 Given=8. Generated=263. Kept=189. proofs=1.
% 0.82/1.13 Usable=8. Sos=128. Demods=37. Limbo=0, Disabled=327. Hints=0.
% 0.82/1.13 Megabytes=0.52.
% 0.82/1.13 User_CPU=0.06, System_CPU=0.00, Wall_clock=0.
% 0.82/1.13
% 0.82/1.13 ============================== end of statistics =====================
% 0.82/1.13
% 0.82/1.13 ============================== end of search =========================
% 0.82/1.13
% 0.82/1.13 THEOREM PROVED
% 0.82/1.13 % SZS status Theorem
% 0.82/1.13
% 0.82/1.13 Exiting with 1 proof.
% 0.82/1.13
% 0.82/1.13 Process 27409 exit (max_proofs) Thu Jul 7 16:24:58 2022
% 0.82/1.13 Prover9 interrupted
%------------------------------------------------------------------------------