0.00/0.03	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command    : tptp2X_and_run_prover9 %d %s
0.03/0.23	% Computer   : n119.star.cs.uiowa.edu
0.03/0.23	% Model      : x86_64 x86_64
0.03/0.23	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.03/0.23	% Memory     : 32218.625MB
0.03/0.23	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.03/0.23	% CPULimit   : 300
0.03/0.23	% DateTime   : Sat Jul 14 04:19:09 CDT 2018
0.03/0.23	% CPUTime    : 
0.06/0.56	============================== Prover9 ===============================
0.06/0.56	Prover9 (32) version 2009-11A, November 2009.
0.06/0.56	Process 7756 was started by sandbox on n119.star.cs.uiowa.edu,
0.06/0.56	Sat Jul 14 04:19:10 2018
0.06/0.56	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_7724_n119.star.cs.uiowa.edu".
0.06/0.56	============================== end of head ===========================
0.06/0.56	
0.06/0.56	============================== INPUT =================================
0.06/0.56	
0.06/0.56	% Reading from file /tmp/Prover9_7724_n119.star.cs.uiowa.edu
0.06/0.56	
0.06/0.56	set(prolog_style_variables).
0.06/0.56	set(auto2).
0.06/0.56	    % set(auto2) -> set(auto).
0.06/0.56	    % set(auto) -> set(auto_inference).
0.06/0.56	    % set(auto) -> set(auto_setup).
0.06/0.56	    % set(auto_setup) -> set(predicate_elim).
0.06/0.56	    % set(auto_setup) -> assign(eq_defs, unfold).
0.06/0.56	    % set(auto) -> set(auto_limits).
0.06/0.56	    % set(auto_limits) -> assign(max_weight, "100.000").
0.06/0.56	    % set(auto_limits) -> assign(sos_limit, 20000).
0.06/0.56	    % set(auto) -> set(auto_denials).
0.06/0.56	    % set(auto) -> set(auto_process).
0.06/0.56	    % set(auto2) -> assign(new_constants, 1).
0.06/0.56	    % set(auto2) -> assign(fold_denial_max, 3).
0.06/0.56	    % set(auto2) -> assign(max_weight, "200.000").
0.06/0.56	    % set(auto2) -> assign(max_hours, 1).
0.06/0.56	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.06/0.56	    % set(auto2) -> assign(max_seconds, 0).
0.06/0.56	    % set(auto2) -> assign(max_minutes, 5).
0.06/0.56	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.06/0.56	    % set(auto2) -> set(sort_initial_sos).
0.06/0.56	    % set(auto2) -> assign(sos_limit, -1).
0.06/0.56	    % set(auto2) -> assign(lrs_ticks, 3000).
0.06/0.56	    % set(auto2) -> assign(max_megs, 400).
0.06/0.56	    % set(auto2) -> assign(stats, some).
0.06/0.56	    % set(auto2) -> clear(echo_input).
0.06/0.56	    % set(auto2) -> set(quiet).
0.06/0.56	    % set(auto2) -> clear(print_initial_clauses).
0.06/0.56	    % set(auto2) -> clear(print_given).
0.06/0.56	assign(lrs_ticks,-1).
0.06/0.56	assign(sos_limit,10000).
0.06/0.56	assign(order,kbo).
0.06/0.56	set(lex_order_vars).
0.06/0.56	clear(print_given).
0.06/0.56	
0.06/0.56	% formulas(sos).  % not echoed (153 formulas)
0.06/0.56	
0.06/0.56	============================== end of input ==========================
0.06/0.56	
0.06/0.56	% From the command line: assign(max_seconds, 300).
0.06/0.56	
0.06/0.56	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.06/0.56	
0.06/0.56	% Formulas that are not ordinary clauses:
0.06/0.56	1 (all X_a (linordered_idom(X_a) -> (all A_2 (ord_less(X_a,A_2,zero_zero(X_a)) <-> ord_less(X_a,plus_plus(X_a,A_2,A_2),zero_zero(X_a)))))) # label(fact_44_even__less__0__iff) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	2 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	3 (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].
0.06/0.56	4 (all K pls != bit1(K)) # label(fact_66_rel__simps_I46_J) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	5 (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].
0.06/0.56	6 (all B_1 bit1(ti(int,B_1)) = bit1(B_1)) # label(tsy_c_Int_OBit1_arg1) # label(hypothesis) # label(non_clause).  [assumption].
0.06/0.56	7 (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].
0.06/0.56	8 (all M all N power_power(int,semiring_1_of_nat(int,M),N) = semiring_1_of_nat(int,power_power(nat,M,N))) # label(fact_21_int__power) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	9 (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)))))) <-> zero_zero(X_a) != ti(X_a,Xa) | ti(X_a,Ya) != zero_zero(X_a))))) # label(fact_97_sum__power2__gt__zero__iff) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	10 (all L_1 (bit0(L_1) = pls <-> pls = L_1)) # label(fact_71_rel__simps_I38_J) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	11 (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].
0.06/0.56	12 (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].
0.06/0.56	13 (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) -> 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].
0.06/0.56	14 (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].
0.06/0.56	15 (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].
0.06/0.56	16 (all X all Y all Z plus_plus(int,Y,plus_plus(int,X,Z)) = plus_plus(int,X,plus_plus(int,Y,Z))) # label(fact_46_zadd__left__commute) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	17 (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].
0.06/0.56	18 (all K bit0(K) = plus_plus(int,K,K)) # label(fact_78_Bit0__def) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	19 (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].
0.06/0.56	20 (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))))) <-> zero_zero(X_a) != ti(X_a,A_2))))) # label(fact_95_zero__less__power2) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	21 (all B_1 all B_2 (ord_less(nat,B_1,B_2) <-> ord_less(nat,ti(nat,B_1),B_2))) # label(tsy_c_Orderings_Oord__class_Oless_1_arg1) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	22 (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].
0.06/0.56	23 (all V_1 all V ((ord_less(int,V,pls) -> number_number_of(nat,V_1) = plus_plus(nat,number_number_of(nat,V),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) -> number_number_of(nat,plus_plus(int,V,V_1)) = plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V_1)))))) # label(fact_36_add__nat__number__of) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	24 (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].
0.06/0.56	25 (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].
0.06/0.56	26 (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].
0.06/0.56	27 (all L bit1(L) != pls) # label(fact_67_rel__simps_I39_J) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	28 (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].
0.06/0.56	29 (all X_a (semiring_0(X_a) & power(X_a) -> (all W ((zero_zero(nat) = number_number_of(nat,W) -> one_one(X_a) = power_power(X_a,zero_zero(X_a),number_number_of(nat,W))) & (number_number_of(nat,W) != zero_zero(nat) -> power_power(X_a,zero_zero(X_a),number_number_of(nat,W)) = zero_zero(X_a)))))) # label(fact_11_power__0__left__number__of) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	30 (all K_1 all L_1 (bit0(K_1) = bit0(L_1) <-> K_1 = L_1)) # label(fact_43_rel__simps_I48_J) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	31 (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].
0.06/0.56	32 (all Wa (ord_less(int,Wa,zero_zero(int)) <-> ord_less(int,bit0(Wa),zero_zero(int)))) # label(fact_58_bin__less__0__simps_I3_J) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	33 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all Xa all Ya (ord_less(X_a,number_number_of(X_a,Xa),number_number_of(X_a,Ya)) <-> ord_less(int,Xa,Ya))))) # label(fact_18_less__number__of) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	34 (all X all Y (ord_less(int,X,Y) | X = Y | ord_less(int,Y,X))) # label(fact_15_zless__linear) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	35 (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].
0.06/0.56	36 (all X_a (semiring_0(X_a) & power(X_a) -> ti(X_a,zero_zero(X_a)) = zero_zero(X_a))) # label(tsy_c_Groups_Ozero__class_Ozero_2_res) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	37 (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].
0.06/0.56	38 (all Z zero_zero(int) != plus_plus(int,plus_plus(int,one_one(int),Z),Z)) # label(fact_93_odd__nonzero) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	39 (all X_a (number_semiring(X_a) -> zero_zero(X_a) = number_number_of(X_a,pls))) # label(fact_81_semiring__numeral__0__eq__0) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	40 (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].
0.06/0.56	41 (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].
0.06/0.56	42 (all K_1 (ord_less(int,pls,K_1) <-> ord_less(int,pls,bit0(K_1)))) # label(fact_55_rel__simps_I4_J) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	43 (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].
0.06/0.56	44 (all X_a (ring_11004092258visors(X_a) -> (all A_2 (ti(X_a,A_2) = zero_zero(X_a) <-> zero_zero(X_a) = power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))))))) # label(fact_5_zero__eq__power2) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	45 (all K1 all K2 (ord_less(int,bit1(K1),bit1(K2)) <-> ord_less(int,K1,K2))) # label(fact_30_less__int__code_I16_J) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	46 (all X_a (number_ring(X_a) -> zero_zero(X_a) = number_number_of(X_a,pls))) # label(fact_82_number__of__Pls) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	47 (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].
0.06/0.56	48 (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].
0.06/0.56	49 (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].
0.06/0.56	50 (all B_1 bit0(B_1) = ti(int,bit0(B_1))) # label(tsy_c_Int_OBit0_res) # label(hypothesis) # label(non_clause).  [assumption].
0.06/0.56	51 (all X_a (number_semiring(X_a) -> plus_plus(X_a,one_one(X_a),one_one(X_a)) = number_number_of(X_a,bit0(bit1(pls))))) # label(fact_9_semiring__one__add__one__is__two) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	52 (all K_1 (bit0(K_1) = pls <-> K_1 = pls)) # label(fact_70_rel__simps_I44_J) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	53 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Xa (ord_less(int,Xa,pls) <-> ord_less(X_a,number_number_of(X_a,Xa),zero_zero(X_a)))))) # label(fact_49_less__special_I3_J) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	54 (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].
0.06/0.56	55 (all X_a (linordered_idom(X_a) -> (all Xa all Ya (ti(X_a,Ya) = zero_zero(X_a) & zero_zero(X_a) = ti(X_a,Xa) <-> 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))))))))) # label(fact_2_sum__power2__eq__zero__iff) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	56 (all Wa all Z_1 (ord_less(int,Wa,plus_plus(int,Z_1,one_one(int))) <-> ord_less(int,Wa,Z_1) | Z_1 = Wa)) # label(fact_60_zless__add1__eq) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	57 (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].
0.06/0.56	58 (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].
0.06/0.56	59 (all B_1 all B_2 all X_a (number_semiring(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_1_arg2) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	60 (all X_a (linordered_idom(X_a) & number_ring(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].
0.06/0.56	61 (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].
0.06/0.56	62 (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].
0.06/0.56	63 (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].
0.06/0.56	64 (all B_1 bit1(B_1) = ti(int,bit1(B_1))) # label(tsy_c_Int_OBit1_res) # label(hypothesis) # label(non_clause).  [assumption].
0.06/0.56	65 (all B_1 all B_2 all X_a (power(X_a) & semiring_0(X_a) -> power_power(X_a,B_1,B_2) = power_power(X_a,ti(X_a,B_1),B_2))) # label(tsy_c_Power_Opower__class_Opower_1_arg1) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	66 (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].
0.06/0.56	67 (all M all N all Z plus_plus(int,semiring_1_of_nat(int,M),plus_plus(int,semiring_1_of_nat(int,N),Z)) = plus_plus(int,semiring_1_of_nat(int,plus_plus(nat,M,N)),Z)) # label(fact_22_zadd__int__left) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	68 (all B_1 bit0(B_1) = bit0(ti(int,B_1))) # label(tsy_c_Int_OBit0_arg1) # label(hypothesis) # label(non_clause).  [assumption].
0.06/0.56	69 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Ya (ord_less(int,pls,Ya) <-> ord_less(X_a,zero_zero(X_a),number_number_of(X_a,Ya)))))) # label(fact_50_less__special_I1_J) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	70 (all K all L bit1(L) != bit0(K)) # label(fact_69_rel__simps_I49_J) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	71 (all X_a (linord219039673up_add(X_a) -> (all A_2 (zero_zero(X_a) = ti(X_a,A_2) <-> zero_zero(X_a) = plus_plus(X_a,A_2,A_2))))) # label(fact_65_double__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	72 (all Ma all Na (semiring_1_of_nat(int,Na) = semiring_1_of_nat(int,Ma) <-> Na = Ma)) # label(fact_48_int__int__eq) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	73 (all V all W plus_plus(int,number_number_of(int,V),number_number_of(int,W)) = number_number_of(int,plus_plus(int,V,W))) # label(fact_17_plus__numeral__code_I9_J) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	74 (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].
0.06/0.56	75 (all X_a (power(X_a) & mult_zero(X_a) & zero_neq_one(X_a) & no_zero_divisors(X_a) -> (all A_2 all Wa (zero_zero(X_a) = power_power(X_a,A_2,number_number_of(nat,Wa)) <-> zero_zero(nat) != number_number_of(nat,Wa) & zero_zero(X_a) = ti(X_a,A_2))))) # label(fact_86_power__eq__0__iff__number__of) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	76 (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].
0.06/0.56	77 (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].
0.06/0.56	78 (all M all N power_power(int,semiring_1_of_nat(int,M),N) = semiring_1_of_nat(int,power_power(nat,M,N))) # label(fact_20_zpower__int) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	79 (all B_1 all B_2 all X_a (number_semiring(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_1_arg1) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	80 (all K_1 all L_1 (bit1(K_1) = bit1(L_1) <-> L_1 = K_1)) # label(fact_42_rel__simps_I51_J) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	81 (all Z_1 (ord_less(int,plus_plus(int,plus_plus(int,one_one(int),Z_1),Z_1),zero_zero(int)) <-> ord_less(int,Z_1,zero_zero(int)))) # label(fact_64_odd__less__0) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	82 (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].
0.06/0.56	83 (all X_a (number_ring(X_a) -> number_number_of(X_a,pls) = zero_zero(X_a))) # label(fact_83_semiring__norm_I112_J) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	84 (all K plus_plus(int,K,pls) = K) # label(fact_75_add__Pls__right) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	85 (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) -> power_power(X_a,B_1,B_2) = power_power(X_a,ti(X_a,B_1),B_2))) # label(tsy_c_Power_Opower__class_Opower_0_arg1) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	86 (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].
0.06/0.56	87 (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].
0.06/0.56	88 (all X_a (number(X_a) -> (all Wa all Xa (ti(X_a,Xa) = number_number_of(X_a,Wa) <-> ti(X_a,Xa) = number_number_of(X_a,Wa))))) # label(fact_41_number__of__reorient) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	89 (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].
0.06/0.56	90 (all Z plus_plus(int,Z,zero_zero(int)) = Z) # label(fact_79_zadd__0__right) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	91 (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].
0.06/0.56	92 (all K all L bit1(K) != bit0(L)) # label(fact_68_rel__simps_I50_J) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	93 (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].
0.06/0.56	94 (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].
0.06/0.56	95 (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].
0.06/0.56	96 (all X_a (number_ring(X_a) -> (all W number_number_of(X_a,plus_plus(int,bit1(pls),W)) = plus_plus(X_a,one_one(X_a),number_number_of(X_a,W))))) # label(fact_6_add__special_I2_J) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	97 (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].
0.06/0.56	98 (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].
0.06/0.56	99 (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].
0.06/0.56	100 (all B_1 all B_2 all X_a (linord219039673up_add(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_0_res) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	101 (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].
0.06/0.56	102 (all K_1 all L_1 (ord_less(int,K_1,L_1) <-> ord_less(int,bit1(K_1),bit0(L_1)))) # label(fact_53_rel__simps_I16_J) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	103 (all X_a (linordered_idom(X_a) & number_ring(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].
0.06/0.56	104 (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].
0.06/0.56	105 (all Z Z = plus_plus(int,zero_zero(int),Z)) # label(fact_80_zadd__0) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	106 (all K plus_plus(int,pls,K) = K) # label(fact_76_add__Pls) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	107 (all T all A ti(T,A) = ti(T,ti(T,A))) # label(help_ti_idem) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	108 (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_8_one__add__one__is__two) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	109 (all X_a (ring_char_0(X_a) & number_ring(X_a) -> (all Xa all Ya (number_number_of(X_a,Ya) = number_number_of(X_a,Xa) <-> Ya = Xa)))) # label(fact_40_eq__number__of) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	110 (all X power_power(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls)))) = power_power(int,X,number_number_of(nat,bit0(bit0(bit1(pls)))))) # label(fact_10_quartic__square__square) # label(axiom) # label(non_clause).  [assumption].
0.06/0.56	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].
0.06/0.56	
0.06/0.56	============================== end of process non-clausal formulas ===
0.06/0.56	
0.06/0.56	============================== PROCESS INITIAL CLAUSES ===============
0.06/0.56	
0.06/0.56	============================== PREDICATE ELIMINATION =================
0.06/0.56	112 linordered_idom(int) # label(arity_Int_Oint___Rings_Olinordered__idom) # label(axiom).  [assumption].
0.06/0.56	113 -linordered_idom(A) | -ord_less(A,B,zero_zero(A)) | ord_less(A,plus_plus(A,B,B),zero_zero(A)) # label(fact_44_even__less__0__iff) # label(axiom).  [clausify(1)].
0.06/0.56	114 -linordered_idom(A) | ord_less(A,B,zero_zero(A)) | -ord_less(A,plus_plus(A,B,B),zero_zero(A)) # label(fact_44_even__less__0__iff) # label(axiom).  [clausify(1)].
0.06/0.56	115 -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)))))) | ti(A,B) != zero_zero(A) | ti(A,C) != zero_zero(A) # label(fact_97_sum__power2__gt__zero__iff) # label(axiom).  [clausify(9)].
0.06/0.56	116 -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)))))) | ti(A,B) = zero_zero(A) # label(fact_97_sum__power2__gt__zero__iff) # label(axiom).  [clausify(9)].
0.06/0.56	117 -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)))))) | ti(A,C) = zero_zero(A) # label(fact_97_sum__power2__gt__zero__iff) # label(axiom).  [clausify(9)].
0.06/0.56	118 -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(19)].
0.06/0.56	119 -linordered_idom(A) | -ord_less(A,zero_zero(A),power_power(A,B,number_number_of(nat,bit0(bit1(pls))))) | ti(A,B) != zero_zero(A) # label(fact_95_zero__less__power2) # label(axiom).  [clausify(20)].
0.06/0.56	120 -linordered_idom(A) | ord_less(A,zero_zero(A),power_power(A,B,number_number_of(nat,bit0(bit1(pls))))) | ti(A,B) = zero_zero(A) # label(fact_95_zero__less__power2) # label(axiom).  [clausify(20)].
0.06/0.56	121 -linordered_idom(A) | -number_ring(A) | -ord_less(A,number_number_of(A,B),number_number_of(A,C)) | ord_less(int,B,C) # label(fact_18_less__number__of) # label(axiom).  [clausify(33)].
0.06/0.56	122 -linordered_idom(A) | -number_ring(A) | ord_less(A,number_number_of(A,B),number_number_of(A,C)) | -ord_less(int,B,C) # label(fact_18_less__number__of) # label(axiom).  [clausify(33)].
0.06/0.56	123 -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(43)].
0.06/0.56	124 -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(43)].
0.06/0.56	125 -number_ring(A) | -linordered_idom(A) | -ord_less(int,B,pls) | ord_less(A,number_number_of(A,B),zero_zero(A)) # label(fact_49_less__special_I3_J) # label(axiom).  [clausify(53)].
0.06/0.56	126 -number_ring(A) | -linordered_idom(A) | ord_less(int,B,pls) | -ord_less(A,number_number_of(A,B),zero_zero(A)) # label(fact_49_less__special_I3_J) # label(axiom).  [clausify(53)].
0.06/0.56	127 -linordered_idom(A) | ti(A,B) != zero_zero(A) | ti(A,C) != 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))))) = zero_zero(A) # label(fact_2_sum__power2__eq__zero__iff) # label(axiom).  [clausify(55)].
0.06/0.56	128 -linordered_idom(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))))) != zero_zero(A) # label(fact_2_sum__power2__eq__zero__iff) # label(axiom).  [clausify(55)].
0.06/0.56	129 -linordered_idom(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))))) != zero_zero(A) # label(fact_2_sum__power2__eq__zero__iff) # label(axiom).  [clausify(55)].
0.06/0.56	130 -linordered_idom(A) | -number_ring(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(60)].
0.06/0.56	131 -linordered_idom(A) | -number_ring(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(60)].
0.06/0.56	132 -number_ring(A) | -linordered_idom(A) | -ord_less(int,pls,B) | ord_less(A,zero_zero(A),number_number_of(A,B)) # label(fact_50_less__special_I1_J) # label(axiom).  [clausify(69)].
0.06/0.56	133 -number_ring(A) | -linordered_idom(A) | ord_less(int,pls,B) | -ord_less(A,zero_zero(A),number_number_of(A,B)) # label(fact_50_less__special_I1_J) # label(axiom).  [clausify(69)].
0.06/0.56	134 -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(74)].
0.06/0.56	135 -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(74)].
0.06/0.56	Derived: -ord_less(int,A,zero_zero(int)) | ord_less(int,plus_plus(int,A,A),zero_zero(int)).  [resolve(112,a,113,a)].
0.06/0.56	Derived: ord_less(int,A,zero_zero(int)) | -ord_less(int,plus_plus(int,A,A),zero_zero(int)).  [resolve(112,a,114,a)].
0.06/0.56	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)))))) | ti(int,A) != zero_zero(int) | ti(int,B) != zero_zero(int).  [resolve(112,a,115,a)].
0.06/0.56	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)))))) | ti(int,A) = zero_zero(int).  [resolve(112,a,116,a)].
0.06/0.56	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)))))) | ti(int,B) = zero_zero(int).  [resolve(112,a,117,a)].
0.06/0.56	Derived: -ord_less(int,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))),zero_zero(int)).  [resolve(112,a,118,a)].
0.06/0.56	Derived: -ord_less(int,zero_zero(int),power_power(int,A,number_number_of(nat,bit0(bit1(pls))))) | ti(int,A) != zero_zero(int).  [resolve(112,a,119,a)].
0.06/0.56	Derived: ord_less(int,zero_zero(int),power_power(int,A,number_number_of(nat,bit0(bit1(pls))))) | ti(int,A) = zero_zero(int).  [resolve(112,a,120,a)].
0.06/0.56	Derived: -ord_less(int,A,ti(int,B)) | ord_less(int,A,B).  [resolve(112,a,123,a)].
0.06/0.56	Derived: ord_less(int,A,ti(int,B)) | -ord_less(int,A,B).  [resolve(112,a,124,a)].
0.06/0.56	Derived: -number_ring(int) | -ord_less(int,A,pls) | ord_less(int,number_number_of(int,A),zero_zero(int)).  [resolve(112,a,125,b)].
0.06/0.56	Derived: -number_ring(int) | ord_less(int,A,pls) | -ord_less(int,number_number_of(int,A),zero_zero(int)).  [resolve(112,a,126,b)].
0.06/0.56	Derived: ti(int,A) != zero_zero(int) | ti(int,B) != 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))))) = zero_zero(int).  [resolve(112,a,127,a)].
0.06/0.56	Derived: 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))))) != zero_zero(int).  [resolve(112,a,128,a)].
0.06/0.56	Derived: 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))))) != zero_zero(int).  [resolve(112,a,129,a)].
0.06/0.56	Derived: -number_ring(int) | -ord_less(int,one_one(int),number_number_of(int,A)) | ord_less(int,bit1(pls),A).  [resolve(112,a,130,a)].
0.06/0.56	Derived: -number_ring(int) | ord_less(int,one_one(int),number_number_of(int,A)) | -ord_less(int,bit1(pls),A).  [resolve(112,a,131,a)].
0.06/0.56	Derived: -number_ring(int) | -ord_less(int,pls,A) | ord_less(int,zero_zero(int),number_number_of(int,A)).  [resolve(112,a,132,b)].
0.06/0.56	Derived: -number_ring(int) | ord_less(int,pls,A) | -ord_less(int,zero_zero(int),number_number_of(int,A)).  [resolve(112,a,133,b)].
0.06/0.56	Derived: -ord_less(int,A,B) | ord_less(int,ti(int,A),B).  [resolve(112,a,134,a)].
0.06/0.56	Derived: ord_less(int,A,B) | -ord_less(int,ti(int,A),B).  [resolve(112,a,135,a)].
0.06/0.56	136 -linordered_idom(A) | -number_ring(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(103)].
0.06/0.56	Derived: -number_ring(int) | -ord_less(int,number_number_of(int,A),one_one(int)) | ord_less(int,A,bit1(pls)).  [resolve(136,a,112,a)].
0.06/0.56	137 -linordered_idom(A) | -number_ring(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(103)].
0.06/0.56	Derived: -number_ring(int) | ord_less(int,number_number_of(int,A),one_one(int)) | -ord_less(int,A,bit1(pls)).  [resolve(137,a,112,a)].
0.06/0.57	138 power(int) # label(arity_Int_Oint___Power_Opower) # label(axiom).  [assumption].
0.06/0.57	139 -power(A) | -semiring_0(A) | one_one(A) = ti(A,one_one(A)) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom).  [clausify(3)].
0.06/0.57	Derived: -semiring_0(int) | one_one(int) = ti(int,one_one(int)).  [resolve(138,a,139,a)].
0.06/0.57	140 -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | -power(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(13)].
0.06/0.57	Derived: -zero_neq_one(int) | -no_zero_divisors(int) | -mult_zero(int) | power_power(int,A,B) = ti(int,power_power(int,A,B)).  [resolve(140,d,138,a)].
0.06/0.57	141 -mult_zero(A) | -zero_neq_one(A) | -no_zero_divisors(A) | -power(A) | ti(A,zero_zero(A)) = zero_zero(A) # label(tsy_c_Groups_Ozero__class_Ozero_0_res) # label(axiom).  [clausify(14)].
0.06/0.57	Derived: -mult_zero(int) | -zero_neq_one(int) | -no_zero_divisors(int) | ti(int,zero_zero(int)) = zero_zero(int).  [resolve(141,d,138,a)].
0.06/0.57	142 power(nat) # label(arity_Nat_Onat___Power_Opower) # label(axiom).  [assumption].
0.06/0.57	Derived: -semiring_0(nat) | one_one(nat) = ti(nat,one_one(nat)).  [resolve(142,a,139,a)].
0.06/0.57	Derived: -zero_neq_one(nat) | -no_zero_divisors(nat) | -mult_zero(nat) | power_power(nat,A,B) = ti(nat,power_power(nat,A,B)).  [resolve(142,a,140,d)].
0.06/0.57	Derived: -mult_zero(nat) | -zero_neq_one(nat) | -no_zero_divisors(nat) | ti(nat,zero_zero(nat)) = zero_zero(nat).  [resolve(142,a,141,d)].
0.06/0.57	143 -semiring_0(A) | -power(A) | number_number_of(nat,B) != zero_zero(nat) | power_power(A,zero_zero(A),number_number_of(nat,B)) = one_one(A) # label(fact_11_power__0__left__number__of) # label(axiom).  [clausify(29)].
0.06/0.57	Derived: -semiring_0(int) | number_number_of(nat,A) != zero_zero(nat) | power_power(int,zero_zero(int),number_number_of(nat,A)) = one_one(int).  [resolve(143,b,138,a)].
0.06/0.57	Derived: -semiring_0(nat) | number_number_of(nat,A) != zero_zero(nat) | power_power(nat,zero_zero(nat),number_number_of(nat,A)) = one_one(nat).  [resolve(143,b,142,a)].
0.06/0.57	144 -semiring_0(A) | -power(A) | number_number_of(nat,B) = zero_zero(nat) | power_power(A,zero_zero(A),number_number_of(nat,B)) = zero_zero(A) # label(fact_11_power__0__left__number__of) # label(axiom).  [clausify(29)].
0.06/0.57	Derived: -semiring_0(int) | number_number_of(nat,A) = zero_zero(nat) | power_power(int,zero_zero(int),number_number_of(nat,A)) = zero_zero(int).  [resolve(144,b,138,a)].
0.06/0.57	Derived: -semiring_0(nat) | number_number_of(nat,A) = zero_zero(nat) | power_power(nat,zero_zero(nat),number_number_of(nat,A)) = zero_zero(nat).  [resolve(144,b,142,a)].
0.06/0.57	145 -semiring_0(A) | -power(A) | ti(A,zero_zero(A)) = zero_zero(A) # label(tsy_c_Groups_Ozero__class_Ozero_2_res) # label(axiom).  [clausify(36)].
0.06/0.57	Derived: -semiring_0(int) | ti(int,zero_zero(int)) = zero_zero(int).  [resolve(145,b,138,a)].
0.06/0.57	Derived: -semiring_0(nat) | ti(nat,zero_zero(nat)) = zero_zero(nat).  [resolve(145,b,142,a)].
0.06/0.57	146 -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(49)].
0.06/0.57	Derived: -semiring_0(int) | power_power(int,A,ti(nat,B)) = power_power(int,A,B).  [resolve(146,a,138,a)].
0.06/0.57	Derived: -semiring_0(nat) | power_power(nat,A,ti(nat,B)) = power_power(nat,A,B).  [resolve(146,a,142,a)].
0.06/0.57	147 -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(65)].
0.06/0.57	Derived: -semiring_0(int) | power_power(int,ti(int,A),B) = power_power(int,A,B).  [resolve(147,a,138,a)].
0.06/0.57	Derived: -semiring_0(nat) | power_power(nat,ti(nat,A),B) = power_power(nat,A,B).  [resolve(147,a,142,a)].
0.06/0.57	148 -power(A) | -mult_zero(A) | -zero_neq_one(A) | -no_zero_divisors(A) | power_power(A,B,number_number_of(nat,C)) != zero_zero(A) | number_number_of(nat,C) != zero_zero(nat) # label(fact_86_power__eq__0__iff__number__of) # label(axiom).  [clausify(75)].
0.06/0.57	Derived: -mult_zero(int) | -zero_neq_one(int) | -no_zero_divisors(int) | power_power(int,A,number_number_of(nat,B)) != zero_zero(int) | number_number_of(nat,B) != zero_zero(nat).  [resolve(148,a,138,a)].
0.06/0.57	Derived: -mult_zero(nat) | -zero_neq_one(nat) | -no_zero_divisors(nat) | power_power(nat,A,number_number_of(nat,B)) != zero_zero(nat) | number_number_of(nat,B) != zero_zero(nat).  [resolve(148,a,142,a)].
0.06/0.57	149 -power(A) | -mult_zero(A) | -zero_neq_one(A) | -no_zero_divisors(A) | power_power(A,B,number_number_of(nat,C)) != zero_zero(A) | ti(A,B) = zero_zero(A) # label(fact_86_power__eq__0__iff__number__of) # label(axiom).  [clausify(75)].
0.06/0.57	Derived: -mult_zero(int) | -zero_neq_one(int) | -no_zero_divisors(int) | power_power(int,A,number_number_of(nat,B)) != zero_zero(int) | ti(int,A) = zero_zero(int).  [resolve(149,a,138,a)].
0.06/0.57	Derived: -mult_zero(nat) | -zero_neq_one(nat) | -no_zero_divisors(nat) | power_power(nat,A,number_number_of(nat,B)) != zero_zero(nat) | ti(nat,A) = zero_zero(nat).  [resolve(149,a,142,a)].
0.06/0.57	150 -power(A) | -mult_zero(A) | -zero_neq_one(A) | -no_zero_divisors(A) | power_power(A,B,number_number_of(nat,C)) = zero_zero(A) | number_number_of(nat,C) = zero_zero(nat) | ti(A,B) != zero_zero(A) # label(fact_86_power__eq__0__iff__number__of) # label(axiom).  [clausify(75)].
0.06/0.57	Derived: -mult_zero(int) | -zero_neq_one(int) | -no_zero_divisors(int) | power_power(int,A,number_number_of(nat,B)) = zero_zero(int) | number_number_of(nat,B) = zero_zero(nat) | ti(int,A) != zero_zero(int).  [resolve(150,a,138,a)].
0.06/0.57	Derived: -mult_zero(nat) | -zero_neq_one(nat) | -no_zero_divisors(nat) | power_power(nat,A,number_number_of(nat,B)) = zero_zero(nat) | number_number_of(nat,B) = zero_zero(nat) | ti(nat,A) != zero_zero(nat).  [resolve(150,a,142,a)].
0.06/0.57	151 -power(A) | -no_zero_divisors(A) | -zero_neq_one(A) | -mult_zero(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(85)].
0.06/0.57	Derived: -no_zero_divisors(int) | -zero_neq_one(int) | -mult_zero(int) | power_power(int,ti(int,A),B) = power_power(int,A,B).  [resolve(151,a,138,a)].
0.06/0.57	Derived: -no_zero_divisors(nat) | -zero_neq_one(nat) | -mult_zero(nat) | power_power(nat,ti(nat,A),B) = power_power(nat,A,B).  [resolve(151,a,142,a)].
0.06/0.57	152 -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(101)].
0.06/0.57	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(152,d,138,a)].
0.06/0.57	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(152,d,142,a)].
0.06/0.57	153 -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(104)].
0.06/0.57	Derived: -semiring_0(int) | power_power(int,A,B) = ti(int,power_power(int,A,B)).  [resolve(153,a,138,a)].
0.06/0.57	Derived: -semiring_0(nat) | power_power(nat,A,B) = ti(nat,power_power(nat,A,B)).  [resolve(153,a,142,a)].
0.06/0.57	154 number(nat) # label(arity_Nat_Onat___Int_Onumber) # label(axiom).  [assumption].
0.06/0.57	155 -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(5)].
0.06/0.57	Derived: number_number_of(nat,A) = ti(nat,number_number_of(nat,A)).  [resolve(154,a,155,a)].
0.06/0.57	156 number(int) # label(arity_Int_Oint___Int_Onumber) # label(axiom).  [assumption].
0.06/0.57	Derived: number_number_of(int,A) = ti(int,number_number_of(int,A)).  [resolve(156,a,155,a)].
0.06/0.57	157 -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(87)].
0.06/0.57	Derived: number_number_of(nat,ti(int,A)) = number_number_of(nat,A).  [resolve(157,a,154,a)].
0.06/0.57	Derived: number_number_of(int,ti(int,A)) = number_number_of(int,A).  [resolve(157,a,156,a)].
0.06/0.57	158 number_semiring(nat) # label(arity_Nat_Onat___Int_Onumber__semiring) # label(axiom).  [assumption].
0.06/0.57	159 -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(11)].
0.06/0.57	Derived: number_number_of(nat,semiring_1_of_nat(int,A)) = semiring_1_of_nat(nat,A).  [resolve(158,a,159,a)].
0.06/0.57	160 -number_semiring(A) | number_number_of(A,pls) = zero_zero(A) # label(fact_81_semiring__numeral__0__eq__0) # label(axiom).  [clausify(39)].
0.06/0.57	161 -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(51)].
0.06/0.57	162 -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(57)].
0.06/0.57	Derived: semiring_1_of_nat(nat,A) = ti(nat,semiring_1_of_nat(nat,A)).  [resolve(162,a,158,a)].
0.06/0.57	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(59)].
0.06/0.57	Derived: plus_plus(nat,A,ti(nat,B)) = plus_plus(nat,A,B).  [resolve(163,a,158,a)].
0.06/0.57	164 -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(79)].
0.06/0.57	Derived: plus_plus(nat,ti(nat,A),B) = plus_plus(nat,A,B).  [resolve(164,a,158,a)].
0.06/0.57	165 number_semiring(int) # label(arity_Int_Oint___Int_Onumber__semiring) # label(axiom).  [assumption].
0.06/0.57	Derived: number_number_of(int,semiring_1_of_nat(int,A)) = semiring_1_of_nat(int,A).  [resolve(165,a,159,a)].
0.06/0.57	Derived: number_number_of(int,pls) = zero_zero(int).  [resolve(165,a,160,a)].
0.06/0.57	Derived: number_number_of(int,bit0(bit1(pls))) = plus_plus(int,one_one(int),one_one(int)).  [resolve(165,a,161,a)].
0.06/0.57	Derived: semiring_1_of_nat(int,A) = ti(int,semiring_1_of_nat(int,A)).  [resolve(165,a,162,a)].
0.06/0.57	Derived: plus_plus(int,A,ti(int,B)) = plus_plus(int,A,B).  [resolve(165,a,163,a)].
0.06/0.57	Derived: plus_plus(int,ti(int,A),B) = plus_plus(int,A,B).  [resolve(165,a,164,a)].
0.06/0.57	166 -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(89)].
0.06/0.57	Derived: semiring_1_of_nat(nat,ti(nat,A)) = semiring_1_of_nat(nat,A).  [resolve(166,a,158,a)].
0.06/0.57	Derived: semiring_1_of_nat(int,ti(nat,A)) = semiring_1_of_nat(int,A).  [resolve(166,a,165,a)].
0.06/0.57	167 -number_semiring(A) | ti(A,plus_plus(A,B,C)) = plus_plus(A,B,C) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom).  [clausify(93)].
0.06/0.57	Derived: ti(nat,plus_plus(nat,A,B)) = plus_plus(nat,A,B).  [resolve(167,a,158,a)].
0.06/0.57	Derived: ti(int,plus_plus(int,A,B)) = plus_plus(int,A,B).  [resolve(167,a,165,a)].
0.06/0.57	168 -semiring_1(A) | power_power(A,one_one(A),number_number_of(nat,bit0(bit1(pls)))) = one_one(A) # label(fact_3_one__power2) # label(axiom).  [clausify(22)].
0.06/0.57	169 semiring_1(int) # label(arity_Int_Oint___Rings_Osemiring__1) # label(axiom).  [assumption].
0.06/0.57	Derived: power_power(int,one_one(int),number_number_of(nat,bit0(bit1(pls)))) = one_one(int).  [resolve(168,a,169,a)].
0.06/0.57	170 -semiring_1(A) | power_power(A,zero_zero(A),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(A) # label(fact_4_zero__power2) # label(axiom).  [clausify(31)].
0.06/0.57	Derived: power_power(int,zero_zero(int),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int).  [resolve(170,a,169,a)].
0.06/0.57	171 semiring_1(nat) # label(arity_Nat_Onat___Rings_Osemiring__1) # label(axiom).  [assumption].
0.06/0.57	Derived: power_power(nat,one_one(nat),number_number_of(nat,bit0(bit1(pls)))) = one_one(nat).  [resolve(171,a,168,a)].
0.06/0.57	Derived: power_power(nat,zero_zero(nat),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(nat).  [resolve(171,a,170,a)].
0.06/0.57	172 -ring_char_0(A) | -number_ring(A) | number_number_of(A,B) != number_number_of(A,C) | B = C # label(fact_40_eq__number__of) # label(axiom).  [clausify(109)].
0.06/0.57	173 ring_char_0(int) # label(arity_Int_Oint___Int_Oring__char__0) # label(axiom).  [assumption].
0.06/0.57	Derived: -number_ring(int) | number_number_of(int,A) != number_number_of(int,B) | A = B.  [resolve(172,a,173,a)].
0.06/0.57	174 -ring_char_0(A) | -number_ring(A) | number_number_of(A,B) = number_number_of(A,C) | B != C # label(fact_40_eq__number__of) # label(axiom).  [clausify(109)].
0.06/0.57	Derived: -number_ring(int) | number_number_of(int,A) = number_number_of(int,B) | A != B.  [resolve(174,a,173,a)].
2.30/2.59	175 -linord219039673up_add(A) | ti(A,B) != zero_zero(A) | plus_plus(A,B,B) = zero_zero(A) # label(fact_65_double__eq__0__iff) # label(axiom).  [clausify(71)].
2.30/2.59	176 linord219039673up_add(int) # label(arity_Int_Oint___Groups_Olinordered__ab__group__add) # label(axiom).  [assumption].
2.30/2.59	Derived: ti(int,A) != zero_zero(int) | plus_plus(int,A,A) = zero_zero(int).  [resolve(175,a,176,a)].
2.30/2.59	177 -linord219039673up_add(A) | ti(A,B) = zero_zero(A) | plus_plus(A,B,B) != zero_zero(A) # label(fact_65_double__eq__0__iff) # label(axiom).  [clausify(71)].
2.30/2.59	Derived: ti(int,A) = zero_zero(int) | plus_plus(int,A,A) != zero_zero(int).  [resolve(177,a,176,a)].
2.30/2.59	178 -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(91)].
2.30/2.59	179 -linord219039673up_add(A) | ti(A,zero_zero(A)) = zero_zero(A) # label(tsy_c_Groups_Ozero__class_Ozero_1_res) # label(axiom).  [clausify(95)].
2.30/2.59	Derived: ti(int,zero_zero(int)) = zero_zero(int).  [resolve(179,a,176,a)].
2.30/2.59	180 -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(99)].
2.30/2.59	181 -linord219039673up_add(A) | ti(A,plus_plus(A,B,C)) = plus_plus(A,B,C) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom).  [clausify(100)].
2.30/2.59	182 ring_11004092258visors(int) # label(arity_Int_Oint___Rings_Oring__1__no__zero__divisors) # label(axiom).  [assumption].
2.30/2.59	183 -ring_11004092258visors(A) | ti(A,B) != zero_zero(A) | power_power(A,B,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(A) # label(fact_5_zero__eq__power2) # label(axiom).  [clausify(44)].
2.30/2.59	184 -ring_11004092258visors(A) | ti(A,B) = zero_zero(A) | power_power(A,B,number_number_of(nat,bit0(bit1(pls)))) != zero_zero(A) # label(fact_5_zero__eq__power2) # label(axiom).  [clausify(44)].
2.30/2.59	Derived: ti(int,A) != zero_zero(int) | power_power(int,A,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int).  [resolve(182,a,183,a)].
2.30/2.59	Derived: ti(int,A) = zero_zero(int) | power_power(int,A,number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int).  [resolve(182,a,184,a)].
2.30/2.59	
2.30/2.59	============================== end predicate elimination =============
2.30/2.59	
2.30/2.59	Auto_denials:  (non-Horn, no changes).
2.30/2.59	
2.30/2.59	Term ordering decisions:
2.30/2.59	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.
2.30/2.59	
2.30/2.59	============================== end of process initial clauses ========
2.30/2.59	
2.30/2.59	============================== CLAUSES FOR SEARCH ====================
2.30/2.59	
2.30/2.59	============================== end of clauses for search =============
2.30/2.59	
2.30/2.59	============================== SEARCH ================================
2.30/2.59	
2.30/2.59	% Starting search at 0.04 seconds.
2.30/2.59	
2.30/2.59	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 38 (0.00 of 0.48 sec).
2.30/2.59	
2.30/2.59	Low Water (keep): wt=67.000, iters=3381
2.30/2.59	
2.30/2.59	Low Water (keep): wt=63.000, iters=3384
2.30/2.59	
2.30/2.59	Low Water (keep): wt=57.000, iters=3407
2.30/2.59	
2.30/2.59	Low Water (keep): wt=55.000, iters=3361
2.30/2.59	
2.30/2.59	Low Water (keep): wt=51.000, iters=3429
2.30/2.59	
2.30/2.59	Low Water (keep): wt=50.000, iters=3342
2.30/2.59	
2.30/2.59	Low Water (keep): wt=44.000, iters=3359
2.30/2.59	
2.30/2.59	Low Water (keep): wt=40.000, iters=3342
2.30/2.59	
2.30/2.59	Low Water (keep): wt=39.000, iters=3400
2.30/2.59	
2.30/2.59	Low Water (keep): wt=38.000, iters=3361
2.30/2.59	
2.30/2.59	Low Water (keep): wt=37.000, iters=3358
2.30/2.59	
2.30/2.59	Low Water (keep): wt=36.000, iters=3396
2.30/2.59	
2.30/2.59	Low Water (keep): wt=35.000, iters=3335
2.30/2.59	
2.30/2.59	Low Water (keep): wt=34.000, iters=3358
2.30/2.59	
2.30/2.59	============================== PROOF =================================
2.30/2.59	% SZS status Theorem
2.30/2.59	% SZS output start Refutation
2.30/2.59	
2.30/2.59	% Proof 1 at 2.02 (+ 0.03) seconds.
2.30/2.59	% Length of proof is 55.
2.30/2.59	% Level of proof is 8.
2.30/2.59	% Maximum clause weight is 36.000.
2.30/2.59	% Given clauses 912.
2.30/2.59	
2.30/2.59	12 (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].
2.30/2.59	18 (all K bit0(K) = plus_plus(int,K,K)) # label(fact_78_Bit0__def) # label(axiom) # label(non_clause).  [assumption].
2.30/2.59	24 (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].
2.30/2.59	40 (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].
2.30/2.59	45 (all K1 all K2 (ord_less(int,bit1(K1),bit1(K2)) <-> ord_less(int,K1,K2))) # label(fact_30_less__int__code_I16_J) # label(axiom) # label(non_clause).  [assumption].
2.30/2.59	63 (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].
2.30/2.59	75 (all X_a (power(X_a) & mult_zero(X_a) & zero_neq_one(X_a) & no_zero_divisors(X_a) -> (all A_2 all Wa (zero_zero(X_a) = power_power(X_a,A_2,number_number_of(nat,Wa)) <-> zero_zero(nat) != number_number_of(nat,Wa) & zero_zero(X_a) = ti(X_a,A_2))))) # label(fact_86_power__eq__0__iff__number__of) # label(axiom) # label(non_clause).  [assumption].
2.30/2.59	90 (all Z plus_plus(int,Z,zero_zero(int)) = Z) # label(fact_79_zadd__0__right) # label(axiom) # label(non_clause).  [assumption].
2.30/2.59	93 (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].
2.30/2.59	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].
2.30/2.59	138 power(int) # label(arity_Int_Oint___Power_Opower) # label(axiom).  [assumption].
2.30/2.59	149 -power(A) | -mult_zero(A) | -zero_neq_one(A) | -no_zero_divisors(A) | power_power(A,B,number_number_of(nat,C)) != zero_zero(A) | ti(A,B) = zero_zero(A) # label(fact_86_power__eq__0__iff__number__of) # label(axiom).  [clausify(75)].
2.30/2.59	165 number_semiring(int) # label(arity_Int_Oint___Int_Onumber__semiring) # label(axiom).  [assumption].
2.30/2.59	167 -number_semiring(A) | ti(A,plus_plus(A,B,C)) = plus_plus(A,B,C) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom).  [clausify(93)].
2.30/2.59	201 one_one(int) != zero_zero(int) # label(fact_74_int__0__neq__1) # label(axiom).  [assumption].
2.30/2.59	204 bit1(A) = plus_plus(int,plus_plus(int,one_one(int),A),A) # label(fact_92_Bit1__def) # label(axiom).  [clausify(12)].
2.30/2.59	206 zero_neq_one(int) # label(arity_Int_Oint___Rings_Ozero__neq__one) # label(axiom).  [assumption].
2.30/2.59	213 mult_zero(int) # label(arity_Int_Oint___Rings_Omult__zero) # label(axiom).  [assumption].
2.30/2.59	214 bit0(A) = plus_plus(int,A,A) # label(fact_78_Bit0__def) # label(axiom).  [clausify(18)].
2.30/2.59	225 plus_plus(int,plus_plus(int,A,B),C) = plus_plus(int,A,plus_plus(int,B,C)) # label(fact_45_zadd__assoc) # label(axiom).  [clausify(24)].
2.30/2.59	253 plus_plus(int,A,B) = plus_plus(int,B,A) # label(fact_47_zadd__commute) # label(axiom).  [clausify(40)].
2.30/2.59	262 -ord_less(int,bit1(A),bit1(B)) | ord_less(int,A,B) # label(fact_30_less__int__code_I16_J) # label(axiom).  [clausify(45)].
2.30/2.59	263 -ord_less(int,plus_plus(int,A,plus_plus(int,A,one_one(int))),plus_plus(int,B,plus_plus(int,B,one_one(int)))) | ord_less(int,A,B).  [copy(262),rewrite([204(2),253(6),253(7),204(8),253(12),253(13)])].
2.30/2.59	273 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].
2.30/2.59	297 -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(63)].
2.30/2.59	304 number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)) # label(fact_29_nat__1__add__1) # label(axiom).  [assumption].
2.30/2.59	305 number_number_of(nat,plus_plus(int,pls,plus_plus(int,pls,plus_plus(int,one_one(int),plus_plus(int,pls,plus_plus(int,pls,one_one(int))))))) = plus_plus(nat,one_one(nat),one_one(nat)).  [copy(304),rewrite([204(3),253(7),253(9),214(10),225(19),225(18)])].
2.30/2.59	328 no_zero_divisors(int) # label(arity_Int_Oint___Rings_Ono__zero__divisors) # label(axiom).  [assumption].
2.30/2.59	339 plus_plus(int,A,zero_zero(int)) = A # label(fact_79_zadd__0__right) # label(axiom).  [clausify(90)].
2.30/2.59	340 -ord_less(int,pls,pls) # label(fact_32_rel__simps_I2_J) # label(axiom).  [assumption].
2.30/2.59	357 zero_zero(int) = pls # label(fact_73_Pls__def) # label(axiom).  [assumption].
2.30/2.59	358 pls = zero_zero(int).  [copy(357),flip(a)].
2.30/2.59	365 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).  [clausify(111)].
2.30/2.59	366 power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,plus_plus(int,zero_zero(int),plus_plus(int,zero_zero(int),plus_plus(int,one_one(int),plus_plus(int,zero_zero(int),plus_plus(int,zero_zero(int),one_one(int)))))))) = zero_zero(int).  [copy(365),rewrite([358(10),204(12),253(16),253(19),214(20),225(31),225(30)])].
2.30/2.59	439 -mult_zero(int) | -zero_neq_one(int) | -no_zero_divisors(int) | power_power(int,A,number_number_of(nat,B)) != zero_zero(int) | ti(int,A) = zero_zero(int).  [resolve(149,a,138,a)].
2.30/2.59	440 power_power(int,A,number_number_of(nat,B)) != zero_zero(int) | ti(int,A) = zero_zero(int).  [copy(439),unit_del(a,213),unit_del(b,206),unit_del(c,328)].
2.30/2.59	476 ti(int,plus_plus(int,A,B)) = plus_plus(int,A,B).  [resolve(167,a,165,a)].
2.30/2.59	495 one_one(int) = c_0.  [new_symbol(201)].
2.30/2.59	503 plus_plus(int,A,plus_plus(int,B,C)) = plus_plus(int,C,plus_plus(int,A,B)).  [back_rewrite(225),rewrite([253(4)]),flip(a)].
2.30/2.59	508 -ord_less(int,zero_zero(int),zero_zero(int)).  [back_rewrite(340),rewrite([358(2),358(4)])].
2.30/2.59	513 number_number_of(nat,plus_plus(int,zero_zero(int),plus_plus(int,zero_zero(int),plus_plus(int,c_0,c_0)))) = plus_plus(nat,one_one(nat),one_one(nat)).  [back_rewrite(305),rewrite([358(3),358(6),495(10),358(11),358(14),495(17),253(17),339(17),253(14),339(14)])].
2.30/2.59	546 power_power(int,plus_plus(int,c_0,semiring_1_of_nat(int,n)),plus_plus(nat,one_one(nat),one_one(nat))) = zero_zero(int).  [back_rewrite(366),rewrite([495(4),495(17),495(24),253(24),339(24),253(21),339(21),513(21)])].
2.30/2.59	558 ord_less(int,zero_zero(int),plus_plus(int,c_0,semiring_1_of_nat(int,n))).  [back_rewrite(273),rewrite([495(6)])].
2.30/2.59	561 -ord_less(int,plus_plus(int,A,plus_plus(int,A,c_0)),plus_plus(int,B,plus_plus(int,B,c_0))) | ord_less(int,A,B).  [back_rewrite(263),rewrite([495(5),495(10)])].
2.30/2.59	659 ti(int,A) = A.  [para(339(a,1),476(a,1,2)),rewrite([339(6)])].
2.30/2.59	675 power_power(int,A,number_number_of(nat,B)) != zero_zero(int) | zero_zero(int) = A.  [back_rewrite(440),rewrite([659(9)]),flip(b)].
2.30/2.59	717 plus_plus(int,zero_zero(int),plus_plus(int,A,B)) = plus_plus(int,A,B).  [para(339(a,1),503(a,1,3)),flip(a)].
2.30/2.59	732 plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,c_0,c_0)).  [back_rewrite(513),rewrite([717(12),717(9)]),flip(a)].
2.30/2.59	749 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(546),rewrite([732(13)])].
2.30/2.59	883 ord_less(int,A,plus_plus(int,A,plus_plus(int,c_0,semiring_1_of_nat(int,n)))).  [resolve(558,a,297,a),rewrite([253(5),339(5),253(9)])].
2.30/2.59	1939 -ord_less(int,c_0,plus_plus(int,A,plus_plus(int,A,c_0))) | ord_less(int,zero_zero(int),A).  [para(717(a,1),561(a,2)),rewrite([253(6),339(6)])].
2.30/2.59	4050 -ord_less(int,c_0,c_0).  [para(717(a,1),1939(a,3)),rewrite([253(7),339(7)]),unit_del(b,508)].
2.30/2.59	8754 plus_plus(int,c_0,semiring_1_of_nat(int,n)) = zero_zero(int).  [resolve(749,a,675,a),flip(a)].
2.30/2.59	8763 ord_less(int,A,A).  [back_rewrite(883),rewrite([8754(8),339(5)])].
2.30/2.59	8764 $F.  [resolve(8763,a,4050,a)].
2.30/2.59	
2.30/2.59	% SZS output end Refutation
2.30/2.59	============================== end of proof ==========================
2.30/2.59	
2.30/2.59	============================== STATISTICS ============================
2.30/2.59	
2.30/2.59	Given=912. Generated=32020. Kept=8445. proofs=1.
2.30/2.59	Usable=847. Sos=7138. Demods=190. Limbo=9, Disabled=726. Hints=0.
2.30/2.59	Megabytes=13.25.
2.30/2.59	User_CPU=2.02, System_CPU=0.03, Wall_clock=2.
2.30/2.59	
2.30/2.59	============================== end of statistics =====================
2.30/2.59	
2.30/2.59	============================== end of search =========================
2.30/2.59	
2.30/2.59	THEOREM PROVED
2.30/2.59	% SZS status Theorem
2.30/2.59	
2.30/2.59	Exiting with 1 proof.
2.30/2.59	
2.30/2.59	Process 7756 exit (max_proofs) Sat Jul 14 04:19:12 2018
2.30/2.59	Prover9 interrupted
2.30/2.59	EOF