0.04/0.09	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.09	% Command  : tptp2X_and_run_prover9 %d %s
0.08/0.29	% Computer : n011.cluster.edu
0.08/0.29	% Model    : x86_64 x86_64
0.08/0.29	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.08/0.29	% Memory   : 8042.1875MB
0.08/0.29	% OS       : Linux 3.10.0-693.el7.x86_64
0.08/0.29	% CPULimit : 960
0.08/0.29	% WCLimit  : 120
0.08/0.29	% DateTime : Tue Aug  9 02:15:36 EDT 2022
0.08/0.29	% CPUTime  : 
0.73/1.06	============================== Prover9 ===============================
0.73/1.06	Prover9 (32) version 2009-11A, November 2009.
0.73/1.06	Process 18691 was started by sandbox on n011.cluster.edu,
0.73/1.06	Tue Aug  9 02:15:37 2022
0.73/1.06	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_18537_n011.cluster.edu".
0.73/1.06	============================== end of head ===========================
0.73/1.06	
0.73/1.06	============================== INPUT =================================
0.73/1.06	
0.73/1.06	% Reading from file /tmp/Prover9_18537_n011.cluster.edu
0.73/1.06	
0.73/1.06	set(prolog_style_variables).
0.73/1.06	set(auto2).
0.73/1.06	    % set(auto2) -> set(auto).
0.73/1.06	    % set(auto) -> set(auto_inference).
0.73/1.06	    % set(auto) -> set(auto_setup).
0.73/1.06	    % set(auto_setup) -> set(predicate_elim).
0.73/1.06	    % set(auto_setup) -> assign(eq_defs, unfold).
0.73/1.06	    % set(auto) -> set(auto_limits).
0.73/1.06	    % set(auto_limits) -> assign(max_weight, "100.000").
0.73/1.06	    % set(auto_limits) -> assign(sos_limit, 20000).
0.73/1.06	    % set(auto) -> set(auto_denials).
0.73/1.06	    % set(auto) -> set(auto_process).
0.73/1.06	    % set(auto2) -> assign(new_constants, 1).
0.73/1.06	    % set(auto2) -> assign(fold_denial_max, 3).
0.73/1.06	    % set(auto2) -> assign(max_weight, "200.000").
0.73/1.06	    % set(auto2) -> assign(max_hours, 1).
0.73/1.06	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.73/1.06	    % set(auto2) -> assign(max_seconds, 0).
0.73/1.06	    % set(auto2) -> assign(max_minutes, 5).
0.73/1.06	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.73/1.06	    % set(auto2) -> set(sort_initial_sos).
0.73/1.06	    % set(auto2) -> assign(sos_limit, -1).
0.73/1.06	    % set(auto2) -> assign(lrs_ticks, 3000).
0.73/1.06	    % set(auto2) -> assign(max_megs, 400).
0.73/1.06	    % set(auto2) -> assign(stats, some).
0.73/1.06	    % set(auto2) -> clear(echo_input).
0.73/1.06	    % set(auto2) -> set(quiet).
0.73/1.06	    % set(auto2) -> clear(print_initial_clauses).
0.73/1.06	    % set(auto2) -> clear(print_given).
0.73/1.06	assign(lrs_ticks,-1).
0.73/1.06	assign(sos_limit,10000).
0.73/1.06	assign(order,kbo).
0.73/1.06	set(lex_order_vars).
0.73/1.06	clear(print_given).
0.73/1.06	
0.73/1.06	% formulas(sos).  % not echoed (153 formulas)
0.73/1.06	
0.73/1.06	============================== end of input ==========================
0.73/1.06	
0.73/1.06	% From the command line: assign(max_seconds, 960).
0.73/1.06	
0.73/1.06	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.73/1.06	
0.73/1.06	% Formulas that are not ordinary clauses:
0.73/1.06	1 (all B_1 all B_2 all X_a (power(X_a) & semiring_0(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_1_arg2) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	2 (all X_a (linordered_idom(X_a) -> (all A_2 (ord_less(X_a,plus_plus(X_a,A_2,A_2),zero_zero(X_a)) <-> ord_less(X_a,A_2,zero_zero(X_a)))))) # label(fact_44_even__less__0__iff) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	3 (all K_1 (bit0(K_1) = pls <-> pls = K_1)) # label(fact_70_rel__simps_I44_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	4 (all K -ord_less(int,semiring_1_of_nat(int,K),zero_zero(int))) # label(fact_61_int__less__0__conv) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	5 (all K bit1(K) = plus_plus(int,plus_plus(int,one_one(int),K),K)) # label(fact_92_Bit1__def) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	6 (all X_a (number_semiring(X_a) -> number_number_of(X_a,pls) = zero_zero(X_a))) # label(fact_81_semiring__numeral__0__eq__0) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	7 (all Wa all Z_1 (ord_less(int,Wa,plus_plus(int,Z_1,one_one(int))) <-> ord_less(int,Wa,Z_1) | Wa = Z_1)) # label(fact_60_zless__add1__eq) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	8 (all X_a (number_ring(X_a) -> number_number_of(X_a,bit0(bit1(pls))) = plus_plus(X_a,one_one(X_a),one_one(X_a)))) # label(fact_8_one__add__one__is__two) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	9 (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_46_zadd__left__commute) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	10 (all K_1 (ord_less(int,bit1(K_1),pls) <-> ord_less(int,K_1,pls))) # label(fact_51_rel__simps_I12_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	11 (all X_a (number_ring(X_a) -> (all V all W number_number_of(X_a,plus_plus(int,V,W)) = plus_plus(X_a,number_number_of(X_a,V),number_number_of(X_a,W))))) # label(fact_88_add__number__of__eq) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	12 (all Na (zero_zero(int) = semiring_1_of_nat(int,Na) <-> zero_zero(nat) = Na)) # label(fact_27_int__eq__0__conv) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	13 (all L pls != bit1(L)) # label(fact_67_rel__simps_I39_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	14 (all B_1 all B_2 all X_a (power(X_a) & semiring_0(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_1_arg1) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	15 (all B_1 all B_2 all X_a (number_semiring(X_a) -> plus_plus(X_a,B_1,B_2) = ti(X_a,plus_plus(X_a,B_1,B_2)))) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	16 (all X_a (number_ring(X_a) -> number_number_of(X_a,bit1(pls)) = one_one(X_a))) # label(fact_13_numeral__1__eq__1) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	17 (all X_a (linordered_idom(X_a) -> (all Xa all Ya (ti(X_a,Xa) = zero_zero(X_a) & zero_zero(X_a) = ti(X_a,Ya) <-> plus_plus(X_a,power_power(X_a,Xa,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Ya,number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X_a))))) # label(fact_2_sum__power2__eq__zero__iff) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	18 (all X_a (linordered_idom(X_a) -> (all Xa all Ya (ord_less(X_a,zero_zero(X_a),plus_plus(X_a,power_power(X_a,Xa,number_number_of(nat,bit0(bit1(pls)))),power_power(X_a,Ya,number_number_of(nat,bit0(bit1(pls)))))) <-> ti(X_a,Xa) != zero_zero(X_a) | zero_zero(X_a) != ti(X_a,Ya))))) # label(fact_97_sum__power2__gt__zero__iff) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	19 (all Wa (ord_less(int,bit1(Wa),zero_zero(int)) <-> ord_less(int,Wa,zero_zero(int)))) # label(fact_56_bin__less__0__simps_I4_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	20 (all K_1 (ord_less(int,bit0(K_1),pls) <-> ord_less(int,K_1,pls))) # label(fact_54_rel__simps_I10_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	21 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Ya (ord_less(X_a,one_one(X_a),number_number_of(X_a,Ya)) <-> ord_less(int,bit1(pls),Ya))))) # label(fact_63_less__special_I2_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	22 (all B_1 all B_2 (ord_less(nat,B_1,ti(nat,B_2)) <-> ord_less(nat,B_1,B_2))) # label(tsy_c_Orderings_Oord__class_Oless_1_arg2) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	23 (all K bit0(K) = plus_plus(int,K,K)) # label(fact_78_Bit0__def) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	24 (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) -> number_number_of(nat,V) = plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V_1))) & (-ord_less(int,V_1,pls) -> plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V_1)) = number_number_of(nat,plus_plus(int,V,V_1)))))) # label(fact_36_add__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	25 (all K all L bit1(plus_plus(int,K,L)) = plus_plus(int,bit1(K),bit0(L))) # label(fact_90_add__Bit1__Bit0) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	26 (all Z plus_plus(int,plus_plus(int,one_one(int),Z),Z) != zero_zero(int)) # label(fact_93_odd__nonzero) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	27 (all B_1 ti(int,bit1(B_1)) = bit1(B_1)) # label(tsy_c_Int_OBit1_res) # label(hypothesis) # label(non_clause).  [assumption].
0.73/1.06	28 (all B_1 all B_2 all X_a (linordered_idom(X_a) -> (ord_less(X_a,B_1,B_2) <-> ord_less(X_a,ti(X_a,B_1),B_2)))) # label(tsy_c_Orderings_Oord__class_Oless_0_arg1) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	29 (all M all N all Z plus_plus(int,semiring_1_of_nat(int,plus_plus(nat,M,N)),Z) = plus_plus(int,semiring_1_of_nat(int,M),plus_plus(int,semiring_1_of_nat(int,N),Z))) # label(fact_22_zadd__int__left) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	30 (all X_a (number_ring(X_a) -> (all A_1 ti(X_a,A_1) = plus_plus(X_a,A_1,number_number_of(X_a,pls))))) # label(fact_85_add__numeral__0__right) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	31 (all B_1 bit0(B_1) = ti(int,bit0(B_1))) # label(tsy_c_Int_OBit0_res) # label(hypothesis) # label(non_clause).  [assumption].
0.73/1.06	32 (all Z plus_plus(int,Z,zero_zero(int)) = Z) # label(fact_79_zadd__0__right) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	33 (all X_a (number_ring(X_a) -> number_number_of(X_a,pls) = zero_zero(X_a))) # label(fact_82_number__of__Pls) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	34 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Ya (ord_less(X_a,zero_zero(X_a),number_number_of(X_a,Ya)) <-> ord_less(int,pls,Ya))))) # label(fact_50_less__special_I1_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	35 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	36 (all Ma all Na (semiring_1_of_nat(int,Ma) = semiring_1_of_nat(int,Na) <-> Na = Ma)) # label(fact_48_int__int__eq) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	37 (all B_1 all B_2 all X_a (linordered_idom(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_0_arg2) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	38 (all X power_power(int,X,number_number_of(nat,bit0(bit0(bit1(pls))))) = power_power(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls))))) # label(fact_10_quartic__square__square) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	39 (all X_a (number_semiring(X_a) -> (all N number_number_of(X_a,semiring_1_of_nat(int,N)) = semiring_1_of_nat(X_a,N)))) # label(fact_94_number__of__int) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	40 (all K all L bit0(K) != bit1(L)) # label(fact_69_rel__simps_I49_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	41 (all L_1 (L_1 = pls <-> bit0(L_1) = pls)) # label(fact_71_rel__simps_I38_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	42 (all X_a (number(X_a) -> (all Wa all Xa (number_number_of(X_a,Wa) = ti(X_a,Xa) <-> ti(X_a,Xa) = number_number_of(X_a,Wa))))) # label(fact_41_number__of__reorient) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	43 (all B_1 all B_2 (ord_less(nat,ti(nat,B_1),B_2) <-> ord_less(nat,B_1,B_2))) # label(tsy_c_Orderings_Oord__class_Oless_1_arg1) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	44 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Xa (ord_less(X_a,number_number_of(X_a,Xa),one_one(X_a)) <-> ord_less(int,Xa,bit1(pls)))))) # label(fact_62_less__special_I4_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	45 (all Z all W plus_plus(int,Z,W) = plus_plus(int,W,Z)) # label(fact_47_zadd__commute) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	46 (all B_1 all X_a (number_semiring(X_a) -> semiring_1_of_nat(X_a,B_1) = ti(X_a,semiring_1_of_nat(X_a,B_1)))) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat_res) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	47 (all X_a (linordered_idom(X_a) -> (all A_2 (ord_less(X_a,zero_zero(X_a),power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls))))) <-> ti(X_a,A_2) != zero_zero(X_a))))) # label(fact_95_zero__less__power2) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	48 (all B_1 all B_2 all X_a (power(X_a) & semiring_0(X_a) -> power_power(X_a,B_1,B_2) = ti(X_a,power_power(X_a,B_1,B_2)))) # label(tsy_c_Power_Opower__class_Opower_1_res) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	49 (all K bit1(K) != pls) # label(fact_66_rel__simps_I46_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	50 (all X_a (zero_neq_one(X_a) & no_zero_divisors(X_a) & mult_zero(X_a) & power(X_a) -> (all A_2 all Wa (zero_zero(nat) != number_number_of(nat,Wa) & ti(X_a,A_2) = zero_zero(X_a) <-> zero_zero(X_a) = power_power(X_a,A_2,number_number_of(nat,Wa)))))) # label(fact_86_power__eq__0__iff__number__of) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	51 (all X_a (power(X_a) & semiring_0(X_a) -> one_one(X_a) = ti(X_a,one_one(X_a)))) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	52 (all K_1 all L_1 (ord_less(int,K_1,L_1) <-> ord_less(int,bit0(K_1),bit0(L_1)))) # label(fact_34_rel__simps_I14_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	53 (all K_1 all L_1 (ord_less(int,bit1(K_1),bit0(L_1)) <-> ord_less(int,K_1,L_1))) # label(fact_53_rel__simps_I16_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	54 (all X_a (power(X_a) & semiring_0(X_a) -> (all W ((number_number_of(nat,W) = zero_zero(nat) -> power_power(X_a,zero_zero(X_a),number_number_of(nat,W)) = one_one(X_a)) & (number_number_of(nat,W) != zero_zero(nat) -> zero_zero(X_a) = power_power(X_a,zero_zero(X_a),number_number_of(nat,W))))))) # label(fact_11_power__0__left__number__of) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	55 (all K all L bit0(plus_plus(int,K,L)) = plus_plus(int,bit0(K),bit0(L))) # label(fact_77_add__Bit0__Bit0) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	56 (all X_a (number_ring(X_a) -> (all V all W all Z plus_plus(X_a,number_number_of(X_a,V),plus_plus(X_a,number_number_of(X_a,W),Z)) = plus_plus(X_a,number_number_of(X_a,plus_plus(int,V,W)),Z)))) # label(fact_87_add__number__of__left) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	57 (all Z1 all Z2 all Z3 plus_plus(int,Z1,plus_plus(int,Z2,Z3)) = plus_plus(int,plus_plus(int,Z1,Z2),Z3)) # label(fact_45_zadd__assoc) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	58 (all K K = plus_plus(int,pls,K)) # label(fact_76_add__Pls) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	59 (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].
0.73/1.06	60 (all K_1 all L_1 (ord_less(int,bit1(K_1),bit1(L_1)) <-> ord_less(int,K_1,L_1))) # label(fact_31_rel__simps_I17_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	61 (all K all I all J (ord_less(int,I,J) -> ord_less(int,plus_plus(int,I,K),plus_plus(int,J,K)))) # label(fact_35_zadd__strict__right__mono) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	62 (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_3_one__power2) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	63 (all M all N semiring_1_of_nat(int,power_power(nat,M,N)) = power_power(int,semiring_1_of_nat(int,M),N)) # label(fact_20_zpower__int) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	64 (all V all W number_number_of(int,plus_plus(int,V,W)) = plus_plus(int,number_number_of(int,V),number_number_of(int,W))) # label(fact_17_plus__numeral__code_I9_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	65 (all X_a (number_ring(X_a) -> (all V all W plus_plus(X_a,number_number_of(X_a,V),number_number_of(X_a,W)) = number_number_of(X_a,plus_plus(int,V,W))))) # label(fact_89_number__of__add) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	66 (all B_1 bit0(ti(int,B_1)) = bit0(B_1)) # label(tsy_c_Int_OBit0_arg1) # label(hypothesis) # label(non_clause).  [assumption].
0.73/1.06	67 (all K_1 all L_1 (L_1 = K_1 <-> bit0(L_1) = bit0(K_1))) # label(fact_43_rel__simps_I48_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	68 (all Wa (ord_less(int,bit0(Wa),zero_zero(int)) <-> ord_less(int,Wa,zero_zero(int)))) # label(fact_58_bin__less__0__simps_I3_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	69 (all B_1 all B_2 all X_a (power(X_a) & no_zero_divisors(X_a) & zero_neq_one(X_a) & mult_zero(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_0_res) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	70 (all T all A ti(T,A) = ti(T,ti(T,A))) # label(help_ti_idem) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	71 (all B_1 all B_2 all X_a (linord219039673up_add(X_a) -> plus_plus(X_a,B_1,B_2) = ti(X_a,plus_plus(X_a,B_1,B_2)))) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	72 (all B_1 all B_2 all X_a (zero_neq_one(X_a) & no_zero_divisors(X_a) & mult_zero(X_a) & power(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_0_arg1) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	73 (all K all L plus_plus(int,bit0(K),bit1(L)) = bit1(plus_plus(int,K,L))) # label(fact_91_add__Bit0__Bit1) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	74 (all X_a (mult_zero(X_a) & zero_neq_one(X_a) & no_zero_divisors(X_a) & power(X_a) -> zero_zero(X_a) = ti(X_a,zero_zero(X_a)))) # label(tsy_c_Groups_Ozero__class_Ozero_0_res) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	75 (all K_1 all L_1 (bit1(L_1) = bit1(K_1) <-> L_1 = K_1)) # label(fact_42_rel__simps_I51_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	76 (all X_a (power(X_a) & semiring_0(X_a) -> zero_zero(X_a) = ti(X_a,zero_zero(X_a)))) # label(tsy_c_Groups_Ozero__class_Ozero_2_res) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	77 (all B_1 all B_2 all X_a (linord219039673up_add(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_0_arg1) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	78 (all K1 all K2 (ord_less(int,K1,K2) <-> ord_less(int,bit1(K1),bit1(K2)))) # label(fact_30_less__int__code_I16_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	79 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Xa all Ya (ord_less(int,Xa,Ya) <-> ord_less(X_a,number_number_of(X_a,Xa),number_number_of(X_a,Ya)))))) # label(fact_18_less__number__of) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	80 (all X_a (number_semiring(X_a) -> number_number_of(X_a,bit0(bit1(pls))) = plus_plus(X_a,one_one(X_a),one_one(X_a)))) # label(fact_9_semiring__one__add__one__is__two) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	81 (all X_a (linordered_idom(X_a) -> (all A_1 -ord_less(X_a,power_power(X_a,A_1,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X_a))))) # label(fact_96_power2__less__0) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	82 (all M all N plus_plus(int,semiring_1_of_nat(int,M),semiring_1_of_nat(int,N)) = semiring_1_of_nat(int,plus_plus(nat,M,N))) # label(fact_23_zadd__int) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	83 (all X_a (number_ring(X_a) -> (all V number_number_of(X_a,plus_plus(int,V,bit1(pls))) = plus_plus(X_a,number_number_of(X_a,V),one_one(X_a))))) # label(fact_7_add__special_I3_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	84 (all K all L bit1(K) != bit0(L)) # label(fact_68_rel__simps_I50_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	85 (all X_a (ring_11004092258visors(X_a) -> (all A_2 (power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) <-> zero_zero(X_a) = ti(X_a,A_2))))) # label(fact_5_zero__eq__power2) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	86 (all Z plus_plus(int,zero_zero(int),Z) = Z) # label(fact_80_zadd__0) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	87 (all B_1 bit1(B_1) = bit1(ti(int,B_1))) # label(tsy_c_Int_OBit1_arg1) # label(hypothesis) # label(non_clause).  [assumption].
0.73/1.06	88 (all B_1 all X_a (number_semiring(X_a) -> semiring_1_of_nat(X_a,B_1) = semiring_1_of_nat(X_a,ti(nat,B_1)))) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat_arg1) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	89 (all M all N semiring_1_of_nat(int,power_power(nat,M,N)) = power_power(int,semiring_1_of_nat(int,M),N)) # label(fact_21_int__power) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	90 (all X_a (number_ring(X_a) -> zero_zero(X_a) = number_number_of(X_a,pls))) # label(fact_83_semiring__norm_I112_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	91 (all X all Y (ord_less(int,X,Y) | Y = X | ord_less(int,Y,X))) # label(fact_15_zless__linear) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	92 (all K_1 (ord_less(int,pls,bit0(K_1)) <-> ord_less(int,pls,K_1))) # label(fact_55_rel__simps_I4_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	93 (all Z_1 (ord_less(int,Z_1,zero_zero(int)) <-> ord_less(int,plus_plus(int,plus_plus(int,one_one(int),Z_1),Z_1),zero_zero(int)))) # label(fact_64_odd__less__0) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	94 (all X_a (semiring_1(X_a) -> power_power(X_a,zero_zero(X_a),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a))) # label(fact_4_zero__power2) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	95 (all K1 all K2 (ord_less(int,bit1(K1),bit0(K2)) <-> ord_less(int,K1,K2))) # label(fact_52_less__int__code_I15_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	96 (all X_a (number_ring(X_a) -> (all A_1 ti(X_a,A_1) = plus_plus(X_a,number_number_of(X_a,pls),A_1)))) # label(fact_84_add__numeral__0) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	97 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all Xa (ord_less(X_a,number_number_of(X_a,Xa),zero_zero(X_a)) <-> ord_less(int,Xa,pls))))) # label(fact_49_less__special_I3_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	98 (all K plus_plus(int,K,pls) = K) # label(fact_75_add__Pls__right) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	99 (all K1 all K2 (ord_less(int,bit0(K1),bit0(K2)) <-> ord_less(int,K1,K2))) # label(fact_33_less__int__code_I13_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	100 (all X_a (linord219039673up_add(X_a) -> (all A_2 (plus_plus(X_a,A_2,A_2) = zero_zero(X_a) <-> ti(X_a,A_2) = zero_zero(X_a))))) # label(fact_65_double__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	101 (all B_1 all B_2 all X_a (number_semiring(X_a) -> plus_plus(X_a,B_1,B_2) = plus_plus(X_a,ti(X_a,B_1),B_2))) # label(tsy_c_Groups_Oplus__class_Oplus_1_arg1) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	102 (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_6_add__special_I2_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	103 (all X_a (number_ring(X_a) & ring_char_0(X_a) -> (all Xa all Ya (number_number_of(X_a,Xa) = number_number_of(X_a,Ya) <-> Xa = Ya)))) # label(fact_40_eq__number__of) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	104 (all K_1 all L_1 (ord_less(int,K_1,L_1) <-> ord_less(int,number_number_of(int,K_1),number_number_of(int,L_1)))) # label(fact_16_less__number__of__int__code) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	105 (all X_a (number_ring(X_a) -> number_number_of(X_a,bit1(pls)) = one_one(X_a))) # label(fact_12_semiring__norm_I110_J) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	106 (all B_1 all X_a (number(X_a) -> number_number_of(X_a,B_1) = number_number_of(X_a,ti(int,B_1)))) # label(tsy_c_Int_Onumber__class_Onumber__of_arg1) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	107 (all X_a (linord219039673up_add(X_a) -> ti(X_a,zero_zero(X_a)) = zero_zero(X_a))) # label(tsy_c_Groups_Ozero__class_Ozero_1_res) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	108 (all B_1 all B_2 all X_a (linord219039673up_add(X_a) -> plus_plus(X_a,B_1,B_2) = plus_plus(X_a,B_1,ti(X_a,B_2)))) # label(tsy_c_Groups_Oplus__class_Oplus_0_arg2) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	109 (all B_1 all B_2 all X_a (number_semiring(X_a) -> plus_plus(X_a,B_1,B_2) = plus_plus(X_a,B_1,ti(X_a,B_2)))) # label(tsy_c_Groups_Oplus__class_Oplus_1_arg2) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	110 (all B_1 all B_2 all X_a (zero_neq_one(X_a) & no_zero_divisors(X_a) & mult_zero(X_a) & power(X_a) -> power_power(X_a,B_1,B_2) = power_power(X_a,B_1,ti(nat,B_2)))) # label(tsy_c_Power_Opower__class_Opower_0_arg2) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	111 -(power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int)) # label(conj_0) # label(negated_conjecture) # label(non_clause).  [assumption].
0.73/1.06	
0.73/1.06	============================== end of process non-clausal formulas ===
0.73/1.06	
0.73/1.06	============================== PROCESS INITIAL CLAUSES ===============
0.73/1.06	
0.73/1.06	============================== PREDICATE ELIMINATION =================
0.73/1.06	112 power(int) # label(arity_Int_Oint___Power_Opower) # label(axiom).  [assumption].
0.73/1.06	113 -power(A) | -semiring_0(A) | power_power(A,B,ti(nat,C)) = power_power(A,B,C) # label(tsy_c_Power_Opower__class_Opower_1_arg2) # label(axiom).  [clausify(1)].
0.73/1.06	114 -power(A) | -semiring_0(A) | power_power(A,ti(A,B),C) = power_power(A,B,C) # label(tsy_c_Power_Opower__class_Opower_1_arg1) # label(axiom).  [clausify(14)].
0.73/1.07	Derived: -semiring_0(int) | power_power(int,A,ti(nat,B)) = power_power(int,A,B).  [resolve(112,a,113,a)].
0.73/1.07	Derived: -semiring_0(int) | power_power(int,ti(int,A),B) = power_power(int,A,B).  [resolve(112,a,114,a)].
0.73/1.07	115 -power(A) | -semiring_0(A) | power_power(A,B,C) = ti(A,power_power(A,B,C)) # label(tsy_c_Power_Opower__class_Opower_1_res) # label(axiom).  [clausify(48)].
0.73/1.07	Derived: -semiring_0(int) | power_power(int,A,B) = ti(int,power_power(int,A,B)).  [resolve(115,a,112,a)].
0.73/1.07	116 -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | -power(A) | number_number_of(nat,B) = zero_zero(nat) | zero_zero(A) != ti(A,C) | zero_zero(A) = power_power(A,C,number_number_of(nat,B)) # label(fact_86_power__eq__0__iff__number__of) # label(axiom).  [clausify(50)].
0.73/1.07	Derived: -zero_neq_one(int) | -no_zero_divisors(int) | -mult_zero(int) | number_number_of(nat,A) = zero_zero(nat) | zero_zero(int) != ti(int,B) | zero_zero(int) = power_power(int,B,number_number_of(nat,A)).  [resolve(116,d,112,a)].
0.73/1.07	117 -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | -power(A) | number_number_of(nat,B) != zero_zero(nat) | zero_zero(A) != power_power(A,C,number_number_of(nat,B)) # label(fact_86_power__eq__0__iff__number__of) # label(axiom).  [clausify(50)].
0.73/1.07	Derived: -zero_neq_one(int) | -no_zero_divisors(int) | -mult_zero(int) | number_number_of(nat,A) != zero_zero(nat) | zero_zero(int) != power_power(int,B,number_number_of(nat,A)).  [resolve(117,d,112,a)].
0.73/1.07	118 -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | -power(A) | zero_zero(A) = ti(A,B) | zero_zero(A) != power_power(A,B,number_number_of(nat,C)) # label(fact_86_power__eq__0__iff__number__of) # label(axiom).  [clausify(50)].
0.73/1.07	Derived: -zero_neq_one(int) | -no_zero_divisors(int) | -mult_zero(int) | zero_zero(int) = ti(int,A) | zero_zero(int) != power_power(int,A,number_number_of(nat,B)).  [resolve(118,d,112,a)].
0.73/1.07	119 -power(A) | -semiring_0(A) | one_one(A) = ti(A,one_one(A)) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom).  [clausify(51)].
0.73/1.07	Derived: -semiring_0(int) | one_one(int) = ti(int,one_one(int)).  [resolve(119,a,112,a)].
0.73/1.07	120 -power(A) | -semiring_0(A) | number_number_of(nat,B) != zero_zero(nat) | one_one(A) = power_power(A,zero_zero(A),number_number_of(nat,B)) # label(fact_11_power__0__left__number__of) # label(axiom).  [clausify(54)].
0.73/1.07	Derived: -semiring_0(int) | number_number_of(nat,A) != zero_zero(nat) | one_one(int) = power_power(int,zero_zero(int),number_number_of(nat,A)).  [resolve(120,a,112,a)].
0.73/1.07	121 -power(A) | -semiring_0(A) | number_number_of(nat,B) = zero_zero(nat) | zero_zero(A) = power_power(A,zero_zero(A),number_number_of(nat,B)) # label(fact_11_power__0__left__number__of) # label(axiom).  [clausify(54)].
0.73/1.07	Derived: -semiring_0(int) | number_number_of(nat,A) = zero_zero(nat) | zero_zero(int) = power_power(int,zero_zero(int),number_number_of(nat,A)).  [resolve(121,a,112,a)].
0.73/1.07	122 -power(A) | -no_zero_divisors(A) | -zero_neq_one(A) | -mult_zero(A) | power_power(A,B,C) = ti(A,power_power(A,B,C)) # label(tsy_c_Power_Opower__class_Opower_0_res) # label(axiom).  [clausify(69)].
0.73/1.07	Derived: -no_zero_divisors(int) | -zero_neq_one(int) | -mult_zero(int) | power_power(int,A,B) = ti(int,power_power(int,A,B)).  [resolve(122,a,112,a)].
0.73/1.07	123 -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | -power(A) | power_power(A,ti(A,B),C) = power_power(A,B,C) # label(tsy_c_Power_Opower__class_Opower_0_arg1) # label(axiom).  [clausify(72)].
0.73/1.07	Derived: -zero_neq_one(int) | -no_zero_divisors(int) | -mult_zero(int) | power_power(int,ti(int,A),B) = power_power(int,A,B).  [resolve(123,d,112,a)].
0.73/1.07	124 -mult_zero(A) | -zero_neq_one(A) | -no_zero_divisors(A) | -power(A) | zero_zero(A) = ti(A,zero_zero(A)) # label(tsy_c_Groups_Ozero__class_Ozero_0_res) # label(axiom).  [clausify(74)].
0.73/1.07	Derived: -mult_zero(int) | -zero_neq_one(int) | -no_zero_divisors(int) | zero_zero(int) = ti(int,zero_zero(int)).  [resolve(124,d,112,a)].
0.73/1.07	125 power(nat) # label(arity_Nat_Onat___Power_Opower) # label(axiom).  [assumption].
0.73/1.07	Derived: -semiring_0(nat) | power_power(nat,A,ti(nat,B)) = power_power(nat,A,B).  [resolve(125,a,113,a)].
0.73/1.07	Derived: -semiring_0(nat) | power_power(nat,ti(nat,A),B) = power_power(nat,A,B).  [resolve(125,a,114,a)].
0.73/1.07	Derived: -semiring_0(nat) | power_power(nat,A,B) = ti(nat,power_power(nat,A,B)).  [resolve(125,a,115,a)].
0.73/1.07	Derived: -zero_neq_one(nat) | -no_zero_divisors(nat) | -mult_zero(nat) | number_number_of(nat,A) = zero_zero(nat) | zero_zero(nat) != ti(nat,B) | zero_zero(nat) = power_power(nat,B,number_number_of(nat,A)).  [resolve(125,a,116,d)].
0.73/1.07	Derived: -zero_neq_one(nat) | -no_zero_divisors(nat) | -mult_zero(nat) | number_number_of(nat,A) != zero_zero(nat) | zero_zero(nat) != power_power(nat,B,number_number_of(nat,A)).  [resolve(125,a,117,d)].
0.73/1.07	Derived: -zero_neq_one(nat) | -no_zero_divisors(nat) | -mult_zero(nat) | zero_zero(nat) = ti(nat,A) | zero_zero(nat) != power_power(nat,A,number_number_of(nat,B)).  [resolve(125,a,118,d)].
0.73/1.07	Derived: -semiring_0(nat) | one_one(nat) = ti(nat,one_one(nat)).  [resolve(125,a,119,a)].
0.73/1.07	Derived: -semiring_0(nat) | number_number_of(nat,A) != zero_zero(nat) | one_one(nat) = power_power(nat,zero_zero(nat),number_number_of(nat,A)).  [resolve(125,a,120,a)].
0.73/1.07	Derived: -semiring_0(nat) | number_number_of(nat,A) = zero_zero(nat) | zero_zero(nat) = power_power(nat,zero_zero(nat),number_number_of(nat,A)).  [resolve(125,a,121,a)].
0.73/1.07	Derived: -no_zero_divisors(nat) | -zero_neq_one(nat) | -mult_zero(nat) | power_power(nat,A,B) = ti(nat,power_power(nat,A,B)).  [resolve(125,a,122,a)].
0.73/1.07	Derived: -zero_neq_one(nat) | -no_zero_divisors(nat) | -mult_zero(nat) | power_power(nat,ti(nat,A),B) = power_power(nat,A,B).  [resolve(125,a,123,d)].
0.73/1.07	Derived: -mult_zero(nat) | -zero_neq_one(nat) | -no_zero_divisors(nat) | zero_zero(nat) = ti(nat,zero_zero(nat)).  [resolve(125,a,124,d)].
0.73/1.07	126 -power(A) | -semiring_0(A) | zero_zero(A) = ti(A,zero_zero(A)) # label(tsy_c_Groups_Ozero__class_Ozero_2_res) # label(axiom).  [clausify(76)].
0.73/1.07	Derived: -semiring_0(int) | zero_zero(int) = ti(int,zero_zero(int)).  [resolve(126,a,112,a)].
0.73/1.07	Derived: -semiring_0(nat) | zero_zero(nat) = ti(nat,zero_zero(nat)).  [resolve(126,a,125,a)].
0.73/1.07	127 -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | -power(A) | power_power(A,B,ti(nat,C)) = power_power(A,B,C) # label(tsy_c_Power_Opower__class_Opower_0_arg2) # label(axiom).  [clausify(110)].
0.73/1.07	Derived: -zero_neq_one(int) | -no_zero_divisors(int) | -mult_zero(int) | power_power(int,A,ti(nat,B)) = power_power(int,A,B).  [resolve(127,d,112,a)].
0.73/1.07	Derived: -zero_neq_one(nat) | -no_zero_divisors(nat) | -mult_zero(nat) | power_power(nat,A,ti(nat,B)) = power_power(nat,A,B).  [resolve(127,d,125,a)].
0.73/1.07	128 linordered_idom(int) # label(arity_Int_Oint___Rings_Olinordered__idom) # label(axiom).  [assumption].
0.73/1.07	129 -linordered_idom(A) | -ord_less(A,plus_plus(A,B,B),zero_zero(A)) | ord_less(A,B,zero_zero(A)) # label(fact_44_even__less__0__iff) # label(axiom).  [clausify(2)].
0.73/1.07	130 -linordered_idom(A) | ord_less(A,plus_plus(A,B,B),zero_zero(A)) | -ord_less(A,B,zero_zero(A)) # label(fact_44_even__less__0__iff) # label(axiom).  [clausify(2)].
0.73/1.07	131 -linordered_idom(A) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) | zero_zero(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))))) # label(fact_2_sum__power2__eq__zero__iff) # label(axiom).  [clausify(17)].
0.73/1.07	132 -linordered_idom(A) | zero_zero(A) = ti(A,B) | zero_zero(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))))) # label(fact_2_sum__power2__eq__zero__iff) # label(axiom).  [clausify(17)].
0.73/1.07	133 -linordered_idom(A) | zero_zero(A) = ti(A,B) | zero_zero(A) != plus_plus(A,power_power(A,C,number_number_of(nat,bit0(bit1(pls)))),power_power(A,B,number_number_of(nat,bit0(bit1(pls))))) # label(fact_2_sum__power2__eq__zero__iff) # label(axiom).  [clausify(17)].
0.73/1.07	134 -linordered_idom(A) | -ord_less(A,zero_zero(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)))))) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_97_sum__power2__gt__zero__iff) # label(axiom).  [clausify(18)].
0.73/1.07	135 -linordered_idom(A) | ord_less(A,zero_zero(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)))))) | zero_zero(A) = ti(A,B) # label(fact_97_sum__power2__gt__zero__iff) # label(axiom).  [clausify(18)].
0.73/1.07	136 -linordered_idom(A) | ord_less(A,zero_zero(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)))))) | zero_zero(A) = ti(A,C) # label(fact_97_sum__power2__gt__zero__iff) # label(axiom).  [clausify(18)].
0.73/1.07	137 -number_ring(A) | -linordered_idom(A) | -ord_less(A,one_one(A),number_number_of(A,B)) | ord_less(int,bit1(pls),B) # label(fact_63_less__special_I2_J) # label(axiom).  [clausify(21)].
0.73/1.07	138 -number_ring(A) | -linordered_idom(A) | ord_less(A,one_one(A),number_number_of(A,B)) | -ord_less(int,bit1(pls),B) # label(fact_63_less__special_I2_J) # label(axiom).  [clausify(21)].
0.73/1.07	139 -linordered_idom(A) | -ord_less(A,B,C) | ord_less(A,ti(A,B),C) # label(tsy_c_Orderings_Oord__class_Oless_0_arg1) # label(axiom).  [clausify(28)].
0.73/1.07	140 -linordered_idom(A) | ord_less(A,B,C) | -ord_less(A,ti(A,B),C) # label(tsy_c_Orderings_Oord__class_Oless_0_arg1) # label(axiom).  [clausify(28)].
0.73/1.07	141 -number_ring(A) | -linordered_idom(A) | -ord_less(A,zero_zero(A),number_number_of(A,B)) | ord_less(int,pls,B) # label(fact_50_less__special_I1_J) # label(axiom).  [clausify(34)].
0.73/1.07	142 -number_ring(A) | -linordered_idom(A) | ord_less(A,zero_zero(A),number_number_of(A,B)) | -ord_less(int,pls,B) # label(fact_50_less__special_I1_J) # label(axiom).  [clausify(34)].
0.73/1.07	143 -linordered_idom(A) | -ord_less(A,B,ti(A,C)) | ord_less(A,B,C) # label(tsy_c_Orderings_Oord__class_Oless_0_arg2) # label(axiom).  [clausify(37)].
0.73/1.07	144 -linordered_idom(A) | ord_less(A,B,ti(A,C)) | -ord_less(A,B,C) # label(tsy_c_Orderings_Oord__class_Oless_0_arg2) # label(axiom).  [clausify(37)].
0.73/1.07	145 -number_ring(A) | -linordered_idom(A) | -ord_less(A,number_number_of(A,B),one_one(A)) | ord_less(int,B,bit1(pls)) # label(fact_62_less__special_I4_J) # label(axiom).  [clausify(44)].
0.73/1.07	146 -number_ring(A) | -linordered_idom(A) | ord_less(A,number_number_of(A,B),one_one(A)) | -ord_less(int,B,bit1(pls)) # label(fact_62_less__special_I4_J) # label(axiom).  [clausify(44)].
0.73/1.07	147 -linordered_idom(A) | -ord_less(A,zero_zero(A),power_power(A,B,number_number_of(nat,bit0(bit1(pls))))) | zero_zero(A) != ti(A,B) # label(fact_95_zero__less__power2) # label(axiom).  [clausify(47)].
0.73/1.07	148 -linordered_idom(A) | ord_less(A,zero_zero(A),power_power(A,B,number_number_of(nat,bit0(bit1(pls))))) | zero_zero(A) = ti(A,B) # label(fact_95_zero__less__power2) # label(axiom).  [clausify(47)].
0.73/1.07	Derived: -ord_less(int,plus_plus(int,A,A),zero_zero(int)) | ord_less(int,A,zero_zero(int)).  [resolve(128,a,129,a)].
0.73/1.07	Derived: ord_less(int,plus_plus(int,A,A),zero_zero(int)) | -ord_less(int,A,zero_zero(int)).  [resolve(128,a,130,a)].
0.73/1.07	Derived: zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B) | zero_zero(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))))).  [resolve(128,a,131,a)].
0.73/1.07	Derived: zero_zero(int) = ti(int,A) | zero_zero(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))))).  [resolve(128,a,132,a)].
0.73/1.07	Derived: zero_zero(int) = ti(int,A) | zero_zero(int) != plus_plus(int,power_power(int,B,number_number_of(nat,bit0(bit1(pls)))),power_power(int,A,number_number_of(nat,bit0(bit1(pls))))).  [resolve(128,a,133,a)].
0.73/1.07	Derived: -ord_less(int,zero_zero(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)))))) | zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B).  [resolve(128,a,134,a)].
0.73/1.07	Derived: ord_less(int,zero_zero(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)))))) | zero_zero(int) = ti(int,A).  [resolve(128,a,135,a)].
0.73/1.07	Derived: ord_less(int,zero_zero(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)))))) | zero_zero(int) = ti(int,B).  [resolve(128,a,136,a)].
0.73/1.07	Derived: -number_ring(int) | -ord_less(int,one_one(int),number_number_of(int,A)) | ord_less(int,bit1(pls),A).  [resolve(128,a,137,b)].
0.73/1.07	Derived: -number_ring(int) | ord_less(int,one_one(int),number_number_of(int,A)) | -ord_less(int,bit1(pls),A).  [resolve(128,a,138,b)].
0.73/1.07	Derived: -ord_less(int,A,B) | ord_less(int,ti(int,A),B).  [resolve(128,a,139,a)].
0.73/1.07	Derived: ord_less(int,A,B) | -ord_less(int,ti(int,A),B).  [resolve(128,a,140,a)].
0.73/1.07	Derived: -number_ring(int) | -ord_less(int,zero_zero(int),number_number_of(int,A)) | ord_less(int,pls,A).  [resolve(128,a,141,b)].
0.73/1.07	Derived: -number_ring(int) | ord_less(int,zero_zero(int),number_number_of(int,A)) | -ord_less(int,pls,A).  [resolve(128,a,142,b)].
0.73/1.07	Derived: -ord_less(int,A,ti(int,B)) | ord_less(int,A,B).  [resolve(128,a,143,a)].
0.73/1.07	Derived: ord_less(int,A,ti(int,B)) | -ord_less(int,A,B).  [resolve(128,a,144,a)].
0.73/1.07	Derived: -number_ring(int) | -ord_less(int,number_number_of(int,A),one_one(int)) | ord_less(int,A,bit1(pls)).  [resolve(128,a,145,b)].
0.73/1.07	Derived: -number_ring(int) | ord_less(int,number_number_of(int,A),one_one(int)) | -ord_less(int,A,bit1(pls)).  [resolve(128,a,146,b)].
0.73/1.07	Derived: -ord_less(int,zero_zero(int),power_power(int,A,number_number_of(nat,bit0(bit1(pls))))) | zero_zero(int) != ti(int,A).  [resolve(128,a,147,a)].
0.73/1.07	Derived: ord_less(int,zero_zero(int),power_power(int,A,number_number_of(nat,bit0(bit1(pls))))) | zero_zero(int) = ti(int,A).  [resolve(128,a,148,a)].
0.73/1.07	149 -number_ring(A) | -linordered_idom(A) | -ord_less(int,B,C) | ord_less(A,number_number_of(A,B),number_number_of(A,C)) # label(fact_18_less__number__of) # label(axiom).  [clausify(79)].
0.73/1.07	150 -number_ring(A) | -linordered_idom(A) | ord_less(int,B,C) | -ord_less(A,number_number_of(A,B),number_number_of(A,C)) # label(fact_18_less__number__of) # label(axiom).  [clausify(79)].
0.73/1.07	151 -linordered_idom(A) | -ord_less(A,power_power(A,B,number_number_of(nat,bit0(bit1(pls)))),zero_zero(A)) # label(fact_96_power2__less__0) # label(axiom).  [clausify(81)].
0.73/1.07	Derived: -ord_less(int,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))),zero_zero(int)).  [resolve(151,a,128,a)].
0.73/1.07	152 -linordered_idom(A) | -number_ring(A) | -ord_less(A,number_number_of(A,B),zero_zero(A)) | ord_less(int,B,pls) # label(fact_49_less__special_I3_J) # label(axiom).  [clausify(97)].
0.73/1.07	Derived: -number_ring(int) | -ord_less(int,number_number_of(int,A),zero_zero(int)) | ord_less(int,A,pls).  [resolve(152,a,128,a)].
0.73/1.07	153 -linordered_idom(A) | -number_ring(A) | ord_less(A,number_number_of(A,B),zero_zero(A)) | -ord_less(int,B,pls) # label(fact_49_less__special_I3_J) # label(axiom).  [clausify(97)].
0.73/1.07	Derived: -number_ring(int) | ord_less(int,number_number_of(int,A),zero_zero(int)) | -ord_less(int,A,pls).  [resolve(153,a,128,a)].
0.73/1.07	154 number_semiring(nat) # label(arity_Nat_Onat___Int_Onumber__semiring) # label(axiom).  [assumption].
0.73/1.07	155 -number_semiring(A) | number_number_of(A,pls) = zero_zero(A) # label(fact_81_semiring__numeral__0__eq__0) # label(axiom).  [clausify(6)].
0.73/1.07	156 -number_semiring(A) | plus_plus(A,B,C) = ti(A,plus_plus(A,B,C)) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom).  [clausify(15)].
0.73/1.07	Derived: plus_plus(nat,A,B) = ti(nat,plus_plus(nat,A,B)).  [resolve(154,a,156,a)].
0.73/1.07	157 -number_semiring(A) | number_number_of(A,semiring_1_of_nat(int,B)) = semiring_1_of_nat(A,B) # label(fact_94_number__of__int) # label(axiom).  [clausify(39)].
0.73/1.07	Derived: number_number_of(nat,semiring_1_of_nat(int,A)) = semiring_1_of_nat(nat,A).  [resolve(157,a,154,a)].
0.73/1.07	158 -number_semiring(A) | semiring_1_of_nat(A,B) = ti(A,semiring_1_of_nat(A,B)) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat_res) # label(axiom).  [clausify(46)].
0.73/1.07	Derived: semiring_1_of_nat(nat,A) = ti(nat,semiring_1_of_nat(nat,A)).  [resolve(158,a,154,a)].
0.73/1.07	159 -number_semiring(A) | number_number_of(A,bit0(bit1(pls))) = plus_plus(A,one_one(A),one_one(A)) # label(fact_9_semiring__one__add__one__is__two) # label(axiom).  [clausify(80)].
0.80/1.08	Derived: number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)).  [resolve(159,a,154,a)].
0.80/1.08	160 -number_semiring(A) | semiring_1_of_nat(A,ti(nat,B)) = semiring_1_of_nat(A,B) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat_arg1) # label(axiom).  [clausify(88)].
0.80/1.08	Derived: semiring_1_of_nat(nat,ti(nat,A)) = semiring_1_of_nat(nat,A).  [resolve(160,a,154,a)].
0.80/1.08	161 -number_semiring(A) | plus_plus(A,ti(A,B),C) = plus_plus(A,B,C) # label(tsy_c_Groups_Oplus__class_Oplus_1_arg1) # label(axiom).  [clausify(101)].
0.80/1.08	Derived: plus_plus(nat,ti(nat,A),B) = plus_plus(nat,A,B).  [resolve(161,a,154,a)].
0.80/1.08	162 number_semiring(int) # label(arity_Int_Oint___Int_Onumber__semiring) # label(axiom).  [assumption].
0.80/1.08	Derived: number_number_of(int,pls) = zero_zero(int).  [resolve(162,a,155,a)].
0.80/1.08	Derived: plus_plus(int,A,B) = ti(int,plus_plus(int,A,B)).  [resolve(162,a,156,a)].
0.80/1.08	Derived: number_number_of(int,semiring_1_of_nat(int,A)) = semiring_1_of_nat(int,A).  [resolve(162,a,157,a)].
0.80/1.08	Derived: semiring_1_of_nat(int,A) = ti(int,semiring_1_of_nat(int,A)).  [resolve(162,a,158,a)].
0.80/1.08	Derived: number_number_of(int,bit0(bit1(pls))) = plus_plus(int,one_one(int),one_one(int)).  [resolve(162,a,159,a)].
0.80/1.08	Derived: semiring_1_of_nat(int,ti(nat,A)) = semiring_1_of_nat(int,A).  [resolve(162,a,160,a)].
0.80/1.08	Derived: plus_plus(int,ti(int,A),B) = plus_plus(int,A,B).  [resolve(162,a,161,a)].
0.80/1.08	163 -number_semiring(A) | plus_plus(A,B,ti(A,C)) = plus_plus(A,B,C) # label(tsy_c_Groups_Oplus__class_Oplus_1_arg2) # label(axiom).  [clausify(109)].
0.80/1.08	Derived: plus_plus(nat,A,ti(nat,B)) = plus_plus(nat,A,B).  [resolve(163,a,154,a)].
0.80/1.08	Derived: plus_plus(int,A,ti(int,B)) = plus_plus(int,A,B).  [resolve(163,a,162,a)].
0.80/1.08	164 -ring_11004092258visors(A) | zero_zero(A) != power_power(A,B,number_number_of(nat,bit0(bit1(pls)))) | zero_zero(A) = ti(A,B) # label(fact_5_zero__eq__power2) # label(axiom).  [clausify(85)].
0.80/1.08	165 ring_11004092258visors(int) # label(arity_Int_Oint___Rings_Oring__1__no__zero__divisors) # label(axiom).  [assumption].
0.80/1.08	Derived: zero_zero(int) != power_power(int,A,number_number_of(nat,bit0(bit1(pls)))) | zero_zero(int) = ti(int,A).  [resolve(164,a,165,a)].
0.80/1.08	166 -ring_11004092258visors(A) | zero_zero(A) = power_power(A,B,number_number_of(nat,bit0(bit1(pls)))) | zero_zero(A) != ti(A,B) # label(fact_5_zero__eq__power2) # label(axiom).  [clausify(85)].
0.80/1.08	Derived: zero_zero(int) = power_power(int,A,number_number_of(nat,bit0(bit1(pls)))) | zero_zero(int) != ti(int,A).  [resolve(166,a,165,a)].
0.80/1.08	167 -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(59)].
0.80/1.08	168 number(nat) # label(arity_Nat_Onat___Int_Onumber) # label(axiom).  [assumption].
0.80/1.08	Derived: number_number_of(nat,A) = ti(nat,number_number_of(nat,A)).  [resolve(167,a,168,a)].
0.80/1.08	169 number(int) # label(arity_Int_Oint___Int_Onumber) # label(axiom).  [assumption].
0.80/1.08	Derived: number_number_of(int,A) = ti(int,number_number_of(int,A)).  [resolve(169,a,167,a)].
0.80/1.08	170 -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(106)].
0.80/1.08	Derived: number_number_of(nat,ti(int,A)) = number_number_of(nat,A).  [resolve(170,a,168,a)].
0.80/1.08	Derived: number_number_of(int,ti(int,A)) = number_number_of(int,A).  [resolve(170,a,169,a)].
0.80/1.08	171 -linord219039673up_add(A) | plus_plus(A,B,C) = ti(A,plus_plus(A,B,C)) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom).  [clausify(71)].
0.80/1.08	172 linord219039673up_add(int) # label(arity_Int_Oint___Groups_Olinordered__ab__group__add) # label(axiom).  [assumption].
0.80/1.08	173 -linord219039673up_add(A) | plus_plus(A,ti(A,B),C) = plus_plus(A,B,C) # label(tsy_c_Groups_Oplus__class_Oplus_0_arg1) # label(axiom).  [clausify(77)].
0.80/1.08	174 -linord219039673up_add(A) | zero_zero(A) != plus_plus(A,B,B) | zero_zero(A) = ti(A,B) # label(fact_65_double__eq__0__iff) # label(axiom).  [clausify(100)].
0.80/1.08	Derived: zero_zero(int) != plus_plus(int,A,A) | zero_zero(int) = ti(int,A).  [resolve(174,a,172,a)].
0.97/1.32	175 -linord219039673up_add(A) | zero_zero(A) = plus_plus(A,B,B) | zero_zero(A) != ti(A,B) # label(fact_65_double__eq__0__iff) # label(axiom).  [clausify(100)].
0.97/1.32	Derived: zero_zero(int) = plus_plus(int,A,A) | zero_zero(int) != ti(int,A).  [resolve(175,a,172,a)].
0.97/1.32	176 -linord219039673up_add(A) | zero_zero(A) = ti(A,zero_zero(A)) # label(tsy_c_Groups_Ozero__class_Ozero_1_res) # label(axiom).  [clausify(107)].
0.97/1.32	Derived: zero_zero(int) = ti(int,zero_zero(int)).  [resolve(176,a,172,a)].
0.97/1.32	177 -linord219039673up_add(A) | plus_plus(A,B,ti(A,C)) = plus_plus(A,B,C) # label(tsy_c_Groups_Oplus__class_Oplus_0_arg2) # label(axiom).  [clausify(108)].
0.97/1.32	178 semiring_1(int) # label(arity_Int_Oint___Rings_Osemiring__1) # label(axiom).  [assumption].
0.97/1.32	179 -semiring_1(A) | one_one(A) = power_power(A,one_one(A),number_number_of(nat,bit0(bit1(pls)))) # label(fact_3_one__power2) # label(axiom).  [clausify(62)].
0.97/1.32	180 -semiring_1(A) | zero_zero(A) = power_power(A,zero_zero(A),number_number_of(nat,bit0(bit1(pls)))) # label(fact_4_zero__power2) # label(axiom).  [clausify(94)].
0.97/1.32	Derived: one_one(int) = power_power(int,one_one(int),number_number_of(nat,bit0(bit1(pls)))).  [resolve(178,a,179,a)].
0.97/1.32	Derived: zero_zero(int) = power_power(int,zero_zero(int),number_number_of(nat,bit0(bit1(pls)))).  [resolve(178,a,180,a)].
0.97/1.32	181 semiring_1(nat) # label(arity_Nat_Onat___Rings_Osemiring__1) # label(axiom).  [assumption].
0.97/1.32	Derived: one_one(nat) = power_power(nat,one_one(nat),number_number_of(nat,bit0(bit1(pls)))).  [resolve(181,a,179,a)].
0.97/1.32	Derived: zero_zero(nat) = power_power(nat,zero_zero(nat),number_number_of(nat,bit0(bit1(pls)))).  [resolve(181,a,180,a)].
0.97/1.32	182 ring_char_0(int) # label(arity_Int_Oint___Int_Oring__char__0) # label(axiom).  [assumption].
0.97/1.32	183 -number_ring(A) | -ring_char_0(A) | number_number_of(A,B) != number_number_of(A,C) | B = C # label(fact_40_eq__number__of) # label(axiom).  [clausify(103)].
0.97/1.32	184 -number_ring(A) | -ring_char_0(A) | number_number_of(A,B) = number_number_of(A,C) | B != C # label(fact_40_eq__number__of) # label(axiom).  [clausify(103)].
0.97/1.32	Derived: -number_ring(int) | number_number_of(int,A) != number_number_of(int,B) | A = B.  [resolve(182,a,183,b)].
0.97/1.32	Derived: -number_ring(int) | number_number_of(int,A) = number_number_of(int,B) | A != B.  [resolve(182,a,184,b)].
0.97/1.32	
0.97/1.32	============================== end predicate elimination =============
0.97/1.32	
0.97/1.32	Auto_denials:  (non-Horn, no changes).
0.97/1.32	
0.97/1.32	Term ordering decisions:
0.97/1.32	Function symbol KB weights:  int=1. nat=1. pls=1. n=1. t=1. number_number_of=1. ti=1. semiring_1_of_nat=1. zero_zero=1. bit1=1. bit0=1. one_one=1. undefined=1. plus_plus=1. power_power=1.
0.97/1.32	
0.97/1.32	============================== end of process initial clauses ========
0.97/1.32	
0.97/1.32	============================== CLAUSES FOR SEARCH ====================
0.97/1.32	
0.97/1.32	============================== end of clauses for search =============
0.97/1.32	
0.97/1.32	============================== SEARCH ================================
0.97/1.32	
0.97/1.32	% Starting search at 0.05 seconds.
0.97/1.32	
0.97/1.32	============================== PROOF =================================
0.97/1.32	% SZS status Theorem
0.97/1.32	% SZS output start Refutation
0.97/1.32	
0.97/1.32	% Proof 1 at 0.26 (+ 0.01) seconds.
0.97/1.32	% Length of proof is 48.
0.97/1.32	% Level of proof is 7.
0.97/1.32	% Maximum clause weight is 36.000.
0.97/1.32	% Given clauses 270.
0.97/1.32	
0.97/1.32	5 (all K bit1(K) = plus_plus(int,plus_plus(int,one_one(int),K),K)) # label(fact_92_Bit1__def) # label(axiom) # label(non_clause).  [assumption].
0.97/1.32	23 (all K bit0(K) = plus_plus(int,K,K)) # label(fact_78_Bit0__def) # label(axiom) # label(non_clause).  [assumption].
0.97/1.32	32 (all Z plus_plus(int,Z,zero_zero(int)) = Z) # label(fact_79_zadd__0__right) # label(axiom) # label(non_clause).  [assumption].
0.97/1.32	34 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Ya (ord_less(X_a,zero_zero(X_a),number_number_of(X_a,Ya)) <-> ord_less(int,pls,Ya))))) # label(fact_50_less__special_I1_J) # label(axiom) # label(non_clause).  [assumption].
0.97/1.32	45 (all Z all W plus_plus(int,Z,W) = plus_plus(int,W,Z)) # label(fact_47_zadd__commute) # label(axiom) # label(non_clause).  [assumption].
0.97/1.32	50 (all X_a (zero_neq_one(X_a) & no_zero_divisors(X_a) & mult_zero(X_a) & power(X_a) -> (all A_2 all Wa (zero_zero(nat) != number_number_of(nat,Wa) & ti(X_a,A_2) = zero_zero(X_a) <-> zero_zero(X_a) = power_power(X_a,A_2,number_number_of(nat,Wa)))))) # label(fact_86_power__eq__0__iff__number__of) # label(axiom) # label(non_clause).  [assumption].
0.97/1.32	61 (all K all I all J (ord_less(int,I,J) -> ord_less(int,plus_plus(int,I,K),plus_plus(int,J,K)))) # label(fact_35_zadd__strict__right__mono) # label(axiom) # label(non_clause).  [assumption].
0.97/1.32	96 (all X_a (number_ring(X_a) -> (all A_1 ti(X_a,A_1) = plus_plus(X_a,number_number_of(X_a,pls),A_1)))) # label(fact_84_add__numeral__0) # label(axiom) # label(non_clause).  [assumption].
0.97/1.32	111 -(power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int)) # label(conj_0) # label(negated_conjecture) # label(non_clause).  [assumption].
0.97/1.32	112 power(int) # label(arity_Int_Oint___Power_Opower) # label(axiom).  [assumption].
0.97/1.32	118 -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | -power(A) | zero_zero(A) = ti(A,B) | zero_zero(A) != power_power(A,B,number_number_of(nat,C)) # label(fact_86_power__eq__0__iff__number__of) # label(axiom).  [clausify(50)].
0.97/1.32	128 linordered_idom(int) # label(arity_Int_Oint___Rings_Olinordered__idom) # label(axiom).  [assumption].
0.97/1.32	142 -number_ring(A) | -linordered_idom(A) | ord_less(A,zero_zero(A),number_number_of(A,B)) | -ord_less(int,pls,B) # label(fact_50_less__special_I1_J) # label(axiom).  [clausify(34)].
0.97/1.32	189 bit1(A) = plus_plus(int,plus_plus(int,one_one(int),A),A) # label(fact_92_Bit1__def) # label(axiom).  [clausify(5)].
0.97/1.32	217 zero_zero(int) != one_one(int) # label(fact_74_int__0__neq__1) # label(axiom).  [assumption].
0.97/1.32	218 one_one(int) != zero_zero(int).  [copy(217),flip(a)].
0.97/1.32	219 bit0(A) = plus_plus(int,A,A) # label(fact_78_Bit0__def) # label(axiom).  [clausify(23)].
0.97/1.32	239 pls = zero_zero(int) # label(fact_73_Pls__def) # label(axiom).  [assumption].
0.97/1.32	243 plus_plus(int,A,zero_zero(int)) = A # label(fact_79_zadd__0__right) # label(axiom).  [clausify(32)].
0.97/1.32	252 -ord_less(int,pls,pls) # label(fact_32_rel__simps_I2_J) # label(axiom).  [assumption].
0.97/1.32	253 -ord_less(int,zero_zero(int),zero_zero(int)).  [copy(252),rewrite([239(2),239(4)])].
0.97/1.32	254 no_zero_divisors(int) # label(arity_Int_Oint___Rings_Ono__zero__divisors) # label(axiom).  [assumption].
0.97/1.32	267 plus_plus(int,A,B) = plus_plus(int,B,A) # label(fact_47_zadd__commute) # label(axiom).  [clausify(45)].
0.97/1.32	292 -ord_less(int,A,B) | ord_less(int,plus_plus(int,A,C),plus_plus(int,B,C)) # label(fact_35_zadd__strict__right__mono) # label(axiom).  [clausify(61)].
0.97/1.32	313 number_ring(int) # label(arity_Int_Oint___Int_Onumber__ring) # label(axiom).  [assumption].
0.97/1.32	319 ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) # label(fact_0_n1pos) # label(axiom).  [assumption].
0.97/1.32	330 zero_neq_one(int) # label(arity_Int_Oint___Rings_Ozero__neq__one) # label(axiom).  [assumption].
0.97/1.32	331 zero_zero(int) = number_number_of(int,pls) # label(fact_19_zero__is__num__zero) # label(axiom).  [assumption].
0.97/1.32	332 number_number_of(int,zero_zero(int)) = zero_zero(int).  [copy(331),rewrite([239(4)]),flip(a)].
0.97/1.32	340 mult_zero(int) # label(arity_Int_Oint___Rings_Omult__zero) # label(axiom).  [assumption].
0.97/1.32	358 -number_ring(A) | plus_plus(A,number_number_of(A,pls),B) = ti(A,B) # label(fact_84_add__numeral__0) # label(axiom).  [clausify(96)].
0.97/1.32	359 -number_ring(A) | plus_plus(A,number_number_of(A,zero_zero(int)),B) = ti(A,B).  [copy(358),rewrite([239(2)])].
0.97/1.32	370 zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) # label(conj_0) # label(negated_conjecture).  [clausify(111)].
0.97/1.32	371 power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,plus_plus(int,plus_plus(int,zero_zero(int),plus_plus(int,zero_zero(int),one_one(int))),plus_plus(int,zero_zero(int),plus_plus(int,zero_zero(int),one_one(int)))))) = zero_zero(int).  [copy(370),rewrite([239(12),189(14),267(18),267(21),219(22)]),flip(a)].
0.97/1.32	382 -zero_neq_one(int) | -no_zero_divisors(int) | -mult_zero(int) | zero_zero(int) = ti(int,A) | zero_zero(int) != power_power(int,A,number_number_of(nat,B)).  [resolve(118,d,112,a)].
0.97/1.32	383 ti(int,A) = zero_zero(int) | power_power(int,A,number_number_of(nat,B)) != zero_zero(int).  [copy(382),flip(d),flip(e),unit_del(a,330),unit_del(b,254),unit_del(c,340)].
0.97/1.32	439 -number_ring(int) | ord_less(int,zero_zero(int),number_number_of(int,A)) | -ord_less(int,pls,A).  [resolve(128,a,142,b)].
0.97/1.32	440 ord_less(int,zero_zero(int),number_number_of(int,A)) | -ord_less(int,zero_zero(int),A).  [copy(439),rewrite([239(10)]),unit_del(a,313)].
0.97/1.32	506 one_one(int) = c_0.  [new_symbol(218)].
0.97/1.32	534 power_power(int,plus_plus(int,c_0,semiring_1_of_nat(int,n)),number_number_of(nat,plus_plus(int,c_0,c_0))) = zero_zero(int).  [back_rewrite(371),rewrite([506(4),506(17),267(17),243(17),267(14),243(14),506(18),267(18),243(18),267(15),243(15)])].
0.97/1.32	548 ord_less(int,zero_zero(int),plus_plus(int,c_0,semiring_1_of_nat(int,n))).  [back_rewrite(319),rewrite([506(6)])].
0.97/1.32	623 ti(int,A) = A.  [resolve(359,a,313,a),rewrite([332(5),267(4),243(4)]),flip(a)].
0.97/1.32	635 zero_zero(int) = A | power_power(int,A,number_number_of(nat,B)) != zero_zero(int).  [back_rewrite(383),rewrite([623(2)]),flip(a)].
0.97/1.32	809 ord_less(int,zero_zero(int),number_number_of(int,plus_plus(int,c_0,semiring_1_of_nat(int,n)))).  [resolve(548,a,440,b)].
0.97/1.32	1448 ord_less(int,A,plus_plus(int,A,number_number_of(int,plus_plus(int,c_0,semiring_1_of_nat(int,n))))).  [resolve(809,a,292,a),rewrite([267(5),243(5),267(11)])].
0.97/1.32	1777 plus_plus(int,c_0,semiring_1_of_nat(int,n)) = zero_zero(int).  [resolve(635,b,534,a),flip(a)].
0.97/1.32	1785 ord_less(int,A,A).  [back_rewrite(1448),rewrite([1777(9),332(6),243(5)])].
0.97/1.32	1786 $F.  [resolve(1785,a,253,a)].
0.97/1.32	
0.97/1.32	% SZS output end Refutation
0.97/1.32	============================== end of proof ==========================
0.97/1.32	
0.97/1.32	============================== STATISTICS ============================
0.97/1.32	
0.97/1.32	Given=270. Generated=5104. Kept=1455. proofs=1.
0.97/1.32	Usable=239. Sos=958. Demods=87. Limbo=8, Disabled=526. Hints=0.
0.97/1.32	Megabytes=2.12.
0.97/1.32	User_CPU=0.26, System_CPU=0.01, Wall_clock=0.
0.97/1.32	
0.97/1.32	============================== end of statistics =====================
0.97/1.32	
0.97/1.32	============================== end of search =========================
0.97/1.32	
0.97/1.32	THEOREM PROVED
0.97/1.32	% SZS status Theorem
0.97/1.32	
0.97/1.32	Exiting with 1 proof.
0.97/1.32	
0.97/1.32	Process 18691 exit (max_proofs) Tue Aug  9 02:15:37 2022
0.97/1.32	Prover9 interrupted
0.97/1.32	EOF