TSTP Solution File: NUM923+7 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM923+7 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 13:33:12 EDT 2022
% Result : Timeout 300.09s 300.28s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM923+7 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jul 5 18:40:12 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.65/2.01 ============================== Prover9 ===============================
% 1.65/2.01 Prover9 (32) version 2009-11A, November 2009.
% 1.65/2.01 Process 24450 was started by sandbox on n029.cluster.edu,
% 1.65/2.01 Tue Jul 5 18:40:14 2022
% 1.65/2.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_24297_n029.cluster.edu".
% 1.65/2.01 ============================== end of head ===========================
% 1.65/2.01
% 1.65/2.01 ============================== INPUT =================================
% 1.65/2.01
% 1.65/2.01 % Reading from file /tmp/Prover9_24297_n029.cluster.edu
% 1.65/2.01
% 1.65/2.01 set(prolog_style_variables).
% 1.65/2.01 set(auto2).
% 1.65/2.01 % set(auto2) -> set(auto).
% 1.65/2.01 % set(auto) -> set(auto_inference).
% 1.65/2.01 % set(auto) -> set(auto_setup).
% 1.65/2.01 % set(auto_setup) -> set(predicate_elim).
% 1.65/2.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.65/2.01 % set(auto) -> set(auto_limits).
% 1.65/2.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.65/2.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.65/2.01 % set(auto) -> set(auto_denials).
% 1.65/2.01 % set(auto) -> set(auto_process).
% 1.65/2.01 % set(auto2) -> assign(new_constants, 1).
% 1.65/2.01 % set(auto2) -> assign(fold_denial_max, 3).
% 1.65/2.01 % set(auto2) -> assign(max_weight, "200.000").
% 1.65/2.01 % set(auto2) -> assign(max_hours, 1).
% 1.65/2.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.65/2.01 % set(auto2) -> assign(max_seconds, 0).
% 1.65/2.01 % set(auto2) -> assign(max_minutes, 5).
% 1.65/2.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.65/2.01 % set(auto2) -> set(sort_initial_sos).
% 1.65/2.01 % set(auto2) -> assign(sos_limit, -1).
% 1.65/2.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.65/2.01 % set(auto2) -> assign(max_megs, 400).
% 1.65/2.01 % set(auto2) -> assign(stats, some).
% 1.65/2.01 % set(auto2) -> clear(echo_input).
% 1.65/2.01 % set(auto2) -> set(quiet).
% 1.65/2.01 % set(auto2) -> clear(print_initial_clauses).
% 1.65/2.01 % set(auto2) -> clear(print_given).
% 1.65/2.01 assign(lrs_ticks,-1).
% 1.65/2.01 assign(sos_limit,10000).
% 1.65/2.01 assign(order,kbo).
% 1.65/2.01 set(lex_order_vars).
% 1.65/2.01 clear(print_given).
% 1.65/2.01
% 1.65/2.01 % formulas(sos). % not echoed (1214 formulas)
% 1.65/2.01
% 1.65/2.01 ============================== end of input ==========================
% 1.65/2.01
% 1.65/2.01 % From the command line: assign(max_seconds, 300).
% 1.65/2.01
% 1.65/2.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.65/2.01
% 1.65/2.01 % Formulas that are not ordinary clauses:
% 1.65/2.01 1 (all X_a (archim1727834104eiling(X_a) -> ti(fun(X_a,int),archimedean_ceiling(X_a)) = archimedean_ceiling(X_a))) # label(tsy_c_Archimedean__Field_Oceiling_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 2 (all X_a (archim1727834104eiling(X_a) -> ti(fun(X_a,int),archim2085082626_floor(X_a)) = archim2085082626_floor(X_a))) # label(tsy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 3 (all X_a all X_b ti(fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),in_rel(X_a,X_b)) = in_rel(X_a,X_b)) # label(tsy_c_FunDef_Oin__rel_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 4 (all X_a (ordere142940540dd_abs(X_a) -> ti(fun(X_a,X_a),abs_abs(X_a)) = abs_abs(X_a))) # label(tsy_c_Groups_Oabs__class_Oabs_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 5 (all X_a (minus(X_a) -> ti(fun(X_a,fun(X_a,X_a)),minus_minus(X_a)) = minus_minus(X_a))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 6 (all X_a (one(X_a) -> ti(X_a,one_one(X_a)) = one_one(X_a))) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 7 (all X_a (monoid_add(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 8 (all X_a (ab_semigroup_add(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 9 (all X_a (cancel_semigroup_add(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_2_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 10 (all X_a (no_zero_divisors(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_0_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 11 (all X_a (mult_zero(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_1_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 12 (all X_a (monoid_mult(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_2_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 13 (all X_a (semiring(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_3_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 14 (all X_a (ab_semigroup_mult(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_4_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 15 (all X_a (zero(X_a) -> ti(X_a,zero_zero(X_a)) = zero_zero(X_a))) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 16 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 17 (all X_a ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a)) = if(X_a)) # label(tsy_c_If_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 18 (all X_a (number(X_a) -> ti(fun(int,X_a),number_number_of(X_a)) = number_number_of(X_a))) # label(tsy_c_Int_Onumber__class_Onumber__of_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 19 (all X_a (ring_1(X_a) -> ti(fun(X_a,bool),ring_1_Ints(X_a)) = ring_1_Ints(X_a))) # label(tsy_c_Int_Oring__1__class_OInts_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 20 (all X_a (semiring_1(X_a) -> ti(fun(nat,X_a),semiring_1_of_nat(X_a)) = semiring_1_of_nat(X_a))) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 21 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,bool)),ord_less(X_a)) = ord_less(X_a))) # label(tsy_c_Orderings_Oord__class_Oless_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 22 (all X_b (ord(X_b) -> ti(fun(X_b,fun(X_b,bool)),ord_less_eq(X_b)) = ord_less_eq(X_b))) # label(tsy_c_Orderings_Oord__class_Oless__eq_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 23 (all X_a all X_b ti(fun(X_a,fun(X_b,product_prod(X_a,X_b))),product_Pair(X_a,X_b)) = product_Pair(X_a,X_b)) # label(tsy_c_Product__Type_OPair_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 24 (all X_b all X_c all X_a ti(fun(fun(product_prod(X_b,X_c),X_a),fun(X_b,fun(X_c,X_a))),product_curry(X_b,X_c,X_a)) = product_curry(X_b,X_c,X_a)) # label(tsy_c_Product__Type_Ocurry_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 25 (all X_b all X_c all X_a ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),produc1605651328_split(X_b,X_c,X_a)) = produc1605651328_split(X_b,X_c,X_a)) # label(tsy_c_Product__Type_Ointernal__split_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 26 (all X_b all X_c all X_a ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),product_prod_rec(X_b,X_c,X_a)) = product_prod_rec(X_b,X_c,X_a)) # label(tsy_c_Product__Type_Oprod_Oprod__rec_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 27 (all X_c all X_a all B_1_1 all B_2_1 hAPP(X_c,X_a,ti(fun(X_c,X_a),B_1_1),B_2_1) = hAPP(X_c,X_a,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 28 (all X_c all X_a all B_1_1 all B_2_1 hAPP(X_c,X_a,B_1_1,ti(X_c,B_2_1)) = hAPP(X_c,X_a,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 29 (all X_a all X_c all B_1_1 all B_2_1 ti(X_a,hAPP(X_c,X_a,B_1_1,B_2_1)) = hAPP(X_c,X_a,B_1_1,B_2_1)) # label(tsy_c_hAPP_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 30 (all B_1_1 (hBOOL(ti(bool,B_1_1)) <-> hBOOL(B_1_1))) # label(tsy_c_hBOOL_arg1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 31 (all X_a ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a)) = member(X_a)) # label(tsy_c_member_res) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 32 (all A_1 all R all B all M all C all D_1 all N_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R),B))),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R),D_1))),N_1)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),N_1))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_1),N_1))))) # label(fact_0_xzgcda__linear__aux1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 33 (all X_a (ring(X_a) -> (all X all Y all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),B))))) # label(fact_1_mult__diff__mult) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 34 (all X_a (real_normed_algebra(X_a) -> (all X all Y all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B)))))) # label(fact_2_mult_Oprod__diff__prod) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 35 (all X_a (ring(X_a) -> (all Aa all E_1 all C_1 all Ba all D_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2) <-> ti(X_a,C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Ba),Aa)),E_1)),D_2))))) # label(fact_3_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 36 (all X_a (ring(X_a) -> (all Aa all E_1 all C_1 all Ba all D_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),E_1)),C_1) = ti(X_a,D_2))))) # label(fact_4_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 37 (all X_1 (hBOOL(hAPP(int,bool,twoSqu658283162sum2sq,X_1)) <-> (exists A_2 exists B_2 hAPP(product_prod(int,int),int,twoSqu1929807760sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_2),B_2)) = X_1))) # label(fact_5_is__sum2sq__def) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 38 (all A_1 all B all C (hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B) = C -> A_1 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) # label(fact_6_Int2_Oaux1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 39 (all W_1 all Z1 all Z2 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z1),Z2)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),Z2))) # label(fact_7_zdiff__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 40 (all Z1 all Z2 all W_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z1),Z2)),W_1) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W_1))) # label(fact_8_zdiff__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 41 (all W_1 all Z1 all Z2 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),Z2))) # label(fact_9_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 42 (all Z1 all Z2 all W_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)),W_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W_1))) # label(fact_10_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 43 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),B) = ti(X_a,A_1)))) # label(fact_11_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 44 (all X_a (ab_semigroup_mult(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))) # label(fact_12_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 45 (all X_a (cancel_semigroup_add(X_a) -> (all B all A_1 all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_13_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 46 (all X_a (cancel146912293up_add(X_a) -> (all A_1 all B all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_14_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 47 (all X_a (cancel_semigroup_add(X_a) -> (all A_1 all B all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_15_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 48 (all X_a (cancel_semigroup_add(X_a) -> (all Ba all Aa all C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa) <-> ti(X_a,Ba) = ti(X_a,C_1))))) # label(fact_16_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 49 (all X_a (cancel_semigroup_add(X_a) -> (all Aa all Ba all C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1) <-> ti(X_a,Ba) = ti(X_a,C_1))))) # label(fact_17_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 50 (all X_a (ab_semigroup_add(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))) # label(fact_18_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 51 (all X_a (ab_group_add(X_a) -> (all Aa all Ba all C_1 all D_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_2) -> (ti(X_a,Aa) = ti(X_a,Ba) <-> ti(X_a,C_1) = ti(X_a,D_2)))))) # label(fact_19_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 52 (all Z1 all Z2 all Z3 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),Z2)),Z3) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),Z3))) # label(fact_20_zmult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 53 (all Z_1 all W_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_1),Z_1)) # label(fact_21_zmult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 54 (all Z1 all Z2 all Z3 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)),Z3) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z2),Z3))) # label(fact_22_zadd__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 55 (all X all Y all Z_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y),Z_1)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Z_1))) # label(fact_23_zadd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 56 (all Z_1 all W_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),W_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),Z_1)) # label(fact_24_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 57 (all X_a (semiring(X_a) -> (all A_1 all E_2 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),E_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),E_2)),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),E_2)),C)))) # label(fact_25_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 58 (all X_a (real_normed_algebra(X_a) -> (all X all Y all Ya hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)),Ya) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Ya))))) # label(fact_26_mult__left_Oadd) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 59 (all X_a (real_normed_algebra(X_a) -> (all A_1 all A_5 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),A_5)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_5),B))))) # label(fact_27_mult_Oadd__left) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 60 (all X_a (comm_semiring(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))) # label(fact_28_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 61 (all X_a (real_normed_algebra(X_a) -> (all Xa all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),Y))))) # label(fact_29_mult__right_Oadd) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 62 (all X_a (real_normed_algebra(X_a) -> (all A_1 all B all B_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B_1))))) # label(fact_30_mult_Oadd__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 63 (all X_a (real_normed_algebra(X_a) -> (all X all Y all Ya hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)),Ya) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Ya))))) # label(fact_31_mult__left_Odiff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 64 (all X_a (real_normed_algebra(X_a) -> (all A_1 all A_5 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_5)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_5),B))))) # label(fact_32_mult_Odiff__left) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 65 (all X_a (real_normed_algebra(X_a) -> (all Xa all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),Y))))) # label(fact_33_mult__right_Odiff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 66 (all X_a (real_normed_algebra(X_a) -> (all A_1 all B all B_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),B_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B_1))))) # label(fact_34_mult_Odiff__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 67 (all X_a (ab_group_add(X_a) -> (all A_1 all C all B all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C),D_1))))) # label(fact_35_add__diff__add) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 68 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),B) = ti(X_a,A_1)))) # label(fact_36_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 69 (all X_a (semiri456707255roduct(X_a) -> (all W all Y_1 all X_1 all Z (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Y_1)) <-> ti(X_a,W) = ti(X_a,X_1) | ti(X_a,Y_1) = ti(X_a,Z))))) # label(fact_37_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 70 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),M)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),M)))) # label(fact_38_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 71 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))) # label(fact_39_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 72 (all X_a (semiri456707255roduct(X_a) -> (all C_1 all D_2 all Aa all Ba (ti(X_a,Aa) != ti(X_a,Ba) & ti(X_a,C_1) != ti(X_a,D_2) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),D_2)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),D_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),C_1)))))) # label(fact_40_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 73 (all X_a (comm_semiring_1(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z_1))))) # label(fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 74 (all X_b all X_a (minus(X_a) -> (all A_3 all B_4 all X_1 hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),minus_minus(fun(X_b,X_a)),A_3),B_4),X_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_b,X_a,A_3,X_1)),hAPP(X_b,X_a,B_4,X_1))))) # label(fact_42_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 75 (all X_a all X_b (minus(X_b) -> (all A_3 all B_4 all X_2 hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),minus_minus(fun(X_a,X_b)),A_3),B_4),X_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,A_3,X_2)),hAPP(X_a,X_b,B_4,X_2))))) # label(fact_43_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 76 (all X_b all X_a all A_1 all B all A_5 all B_1 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_1),B) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_5),B_1) -> -(ti(X_a,A_1) = ti(X_a,A_5) -> ti(X_b,B) != ti(X_b,B_1)))) # label(fact_44_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 77 (all X_b all X_a all Aa all Ba all A_4 all B_3 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_3) <-> ti(X_a,Aa) = ti(X_a,A_4) & ti(X_b,Ba) = ti(X_b,B_3))) # label(fact_45_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 78 (all X_a all X_b all P_1 ((all X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,X1))) <-> (all A_2 all B_2 hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_2)))))) # label(fact_46_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 79 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1))))) # label(fact_47_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 80 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),B)))) # label(fact_48_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 81 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1) = ti(X_a,A_1)))) # label(fact_49_times_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 82 (all X_a (ab_sem1668676832m_mult(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X) = ti(X_a,X)))) # label(fact_50_mult__idem) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 83 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)))) # label(fact_51_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 84 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))) # label(fact_52_mult__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 85 (all X_a (comm_semiring_1(X_a) -> (all Lx all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ry))))) # label(fact_53_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 86 (all X_a (comm_semiring_1(X_a) -> (all Lx all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ry)))) # label(fact_54_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 87 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Rx))))) # label(fact_55_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 88 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ly)))) # label(fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 89 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)))))) # label(fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 90 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Ry))))) # label(fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 91 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Ry))))) # label(fact_59_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 92 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)))) # label(fact_60_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 93 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),D_1))))) # label(fact_61_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 94 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),D_1)))) # label(fact_62_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 95 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))) # label(fact_63_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 96 (all X_b all X_c all X_a all F1 all Aa all Ba hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_rec(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,Aa),Ba)) # label(fact_64_prod_Orecs) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 97 (all X_a all X_b all P_1 ((exists X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,X1))) <-> (exists A_2 exists B_2 hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_2)))))) # label(fact_65_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 98 (all X_a all X_b all X_c all X_d all X_e all X_f all X_1 all P_1 ((all A_2 all B_2 all C_2 all D all E all F_1 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_2),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B_2),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C_2),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_1)))))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,P_1,X_1)))) # label(fact_66_prod__induct6) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 99 (all X_a all X_b all X_c all X_d all X_e all X_f all Y -(all A_2 all B_2 all C_2 all D all E all F_1 ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),Y) != hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_2),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B_2),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C_2),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_1))))))) # label(fact_67_prod__cases6) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 100 (all X_a all X_b all X_c all X_d all X_e all X_1 all P_1 ((all A_2 all B_2 all C_2 all D all E hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),A_2),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),B_2),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),C_2),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),D),E))))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,P_1,X_1)))) # label(fact_68_prod__induct5) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 101 (all X_a all X_b all X_c all X_d all X_e all Y -(all A_2 all B_2 all C_2 all D all E ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),Y) != hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),A_2),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),B_2),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),C_2),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),D),E)))))) # label(fact_69_prod__cases5) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 102 (all X_a all X_b all X_c all X_d all X_1 all P_1 ((all A_2 all B_2 all C_2 all D hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_2),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B_2),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C_2),D)))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,P_1,X_1)))) # label(fact_70_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 103 (all X_a all X_b all X_c all X_d all Y -(all A_2 all B_2 all C_2 all D ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),Y) != hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_2),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B_2),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C_2),D))))) # label(fact_71_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 104 (all X_a all X_b all X_c all X_1 all P_1 ((all A_2 all B_2 all C_2 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,P_1,hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_2),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B_2),C_2))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,P_1,X_1)))) # label(fact_72_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 105 (all X_a all X_b all X_c all Y -(all A_2 all B_2 all C_2 ti(product_prod(X_a,product_prod(X_b,X_c)),Y) != hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_2),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B_2),C_2)))) # label(fact_73_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 106 (all X_a all X_b all P_3 -(all X_2 all Y_2 ti(product_prod(X_a,X_b),P_3) != hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2))) # label(fact_74_PairE) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 107 (all X_a all X_b all F all G ((all X_2 hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2)) -> ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G))) # label(fact_75_ext) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 108 (all X_a all X_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) <-> hBOOL(hAPP(X_a,bool,A_3,X_1)))) # label(fact_76_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 109 (all X_a all X_b all Y -(all A_2 all B_2 ti(product_prod(X_a,X_b),Y) != hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_2))) # label(fact_77_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 110 (all X_b all X_c all X_a all C_1 all Aa all Ba hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),produc1605651328_split(X_b,X_c,X_a),C_1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),C_1,Aa),Ba)) # label(fact_78_internal__split__conv) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 111 (all X_a all X_b all F all Aa all Ba (hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba)))) # label(fact_79_curryI) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 112 (all X_a (ordered_ring(X_a) -> (all Aa all E_1 all C_1 all Ba all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),E_1)),C_1)),D_2)))))) # label(fact_80_le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 113 (all X_a (ordered_ring(X_a) -> (all Aa all E_1 all C_1 all Ba all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Ba),Aa)),E_1)),D_2))))))) # label(fact_81_le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 114 (all X_a (ring_1(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),one_one(X_a)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a)))))) # label(fact_82_real__squared__diff__one__factored) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 115 (all X_a (ordered_ring(X_a) -> (all Aa all E_1 all C_1 all Ba all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),E_1)),C_1)),D_2)))))) # label(fact_83_less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.01 116 (all X_a (ordered_ring(X_a) -> (all Aa all E_1 all C_1 all Ba all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),E_1)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),E_1)),D_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Ba),Aa)),E_1)),D_2))))))) # label(fact_84_less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 117 (all X_a (number_ring(X_a) -> (all V all W_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W_1))),C)))) # label(fact_85_add__number__of__diff1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 118 (all X_c all X_a all X_b all F all Aa all Ba hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),hAPP(fun(product_prod(X_b,X_c),X_a),fun(X_b,fun(X_c,X_a)),product_curry(X_b,X_c,X_a),F),Aa),Ba) = hAPP(product_prod(X_b,X_c),X_a,F,hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba))) # label(fact_86_curry__conv) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 119 (all X_a (linordered_semidom(X_a) -> (all N_1 all M (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M),N_1)))))))) # label(fact_87_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 120 (all X_a (linordered_semidom(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))))))) # label(fact_88_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 121 (all X_a (ordere223160158up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_89_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 122 (all X_a (ordere223160158up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_90_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 123 (all X_a (one(X_a) -> (all X_1 (one_one(X_a) = ti(X_a,X_1) <-> ti(X_a,X_1) = one_one(X_a))))) # label(fact_91_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 124 (all W all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),one_one(int)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),Z)))) # label(fact_92_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 125 (all X_a (number(X_a) -> (all W all X_1 (hAPP(int,X_a,number_number_of(X_a),W) = ti(X_a,X_1) <-> ti(X_a,X_1) = hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_93_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 126 (all X_a (number(X_a) & linorder(X_a) -> (all V_1 all W (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),hAPP(int,X_a,number_number_of(X_a),W))) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W)),hAPP(int,X_a,number_number_of(X_a),V_1))))))) # label(fact_94_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 127 (all X_a (number_ring(X_a) & ring_char_0(X_a) -> (all X_1 all Y_1 (hAPP(int,X_a,number_number_of(X_a),X_1) = hAPP(int,X_a,number_number_of(X_a),Y_1) <-> X_1 = Y_1)))) # label(fact_95_eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 128 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)))))) # label(fact_96_less__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 129 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),Y_1)))))) # label(fact_97_le__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 130 (all W all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),one_one(int))),Z)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z)))) # label(fact_98_add1__zle__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 131 (all X_a (linordered_idom(X_a) -> (all X all Y (ti(X_a,X) != ti(X_a,Y) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_99_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 132 (all W_1 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),one_one(int))),Z_1)))) # label(fact_100_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 133 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (ti(X_a,X) != ti(X_a,Y) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))))))) # label(fact_101_order__le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 134 (all W all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),one_one(int)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z)))) # label(fact_102_zle__diff1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 135 (all Z_4 all Z_1 all W_3 all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_3),W_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_4),Z_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_3),Z_4)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),Z_1)))))) # label(fact_103_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 136 (all W all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),one_one(int)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z)) | W = Z)) # label(fact_104_zless__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 137 (all X_a (ordere236663937imp_le(X_a) -> (all Aa all C_1 all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)))))) # label(fact_105_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 138 (all X_a (ordere236663937imp_le(X_a) -> (all C_1 all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)))))) # label(fact_106_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 139 (all X_a (ordere223160158up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))))) # label(fact_107_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 140 (all X_a (ordere223160158up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))))))) # label(fact_108_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 141 (all X_a (ordere223160158up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_109_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 142 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_110_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 143 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_111_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 144 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 145 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)))) # label(fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 146 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_114_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 147 (all X_a (comm_monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_115_mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 148 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)))) # label(fact_116_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 149 (all X_a (comm_monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)))) # label(fact_117_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 150 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba all C_1 all D_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_2) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_2))))))) # label(fact_118_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 151 (all X_a (ordere236663937imp_le(X_a) -> (all Aa all C_1 all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)))))) # label(fact_119_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 152 (all X_a (ordere236663937imp_le(X_a) -> (all C_1 all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)))))) # label(fact_120_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 153 (all X_a (ordere779506340up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))))) # label(fact_121_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 154 (all X_a (ordere779506340up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))))))) # label(fact_122_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 155 (all X_a (ordere779506340up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_123_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 156 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_124_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 157 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_125_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 158 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba all C_1 all D_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_2) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D_2))))))) # label(fact_126_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 159 (all V all W_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W_1)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W_1))) # label(fact_127_times__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 160 (all V all W_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W_1)) = hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W_1))) # label(fact_128_plus__numeral__code_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 161 (all K all I all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),J)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I),K)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),J),K))))) # label(fact_129_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 162 (all K all I all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),J)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),I)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),J))))) # label(fact_130_zadd__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 163 (all Z_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),Z_1) = Z_1) # label(fact_131_zmult__1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 164 (all Z_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),one_one(int)) = Z_1) # label(fact_132_zmult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 165 (all X_b (number(X_b) & semiring(X_b) -> (all V all B all C hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),C)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),B)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),C))))) # label(fact_133_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 166 (all X_b (number(X_b) & semiring(X_b) -> (all A_1 all B all V hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_1),B)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_1),hAPP(int,X_b,number_number_of(X_b),V))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B),hAPP(int,X_b,number_number_of(X_b),V)))))) # label(fact_134_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 167 (all X_b (number(X_b) & ring(X_b) -> (all V all B all C hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B),C)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),B)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),C))))) # label(fact_135_right__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 168 (all X_b (number(X_b) & ring(X_b) -> (all A_1 all B all V hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_1),B)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_1),hAPP(int,X_b,number_number_of(X_b),V))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),B),hAPP(int,X_b,number_number_of(X_b),V)))))) # label(fact_136_left__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 169 (all X_a (number_ring(X_a) -> (all V all W_1 hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W_1))))) # label(fact_137_number__of__mult) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 170 (all X_a (number_ring(X_a) -> (all V all W_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W_1)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W_1))))) # label(fact_138_arith__simps_I32_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 171 (all X_a (number_ring(X_a) -> (all V all W_1 all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W_1))),Z_1)))) # label(fact_139_mult__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 172 (all X_a (number_ring(X_a) -> (all V all W_1 hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W_1))))) # label(fact_140_number__of__add) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 173 (all X_a (number_ring(X_a) -> (all V all W_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W_1)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W_1))))) # label(fact_141_add__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 174 (all X_a (number_ring(X_a) -> (all V all W_1 all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W_1))),Z_1)))) # label(fact_142_add__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 175 (all X_a (number_ring(X_a) -> (all V all W_1 hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),V),W_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W_1))))) # label(fact_143_number__of__diff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 176 (all X_a (comm_semiring_1(X_a) -> (all M hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),M) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),M)))) # label(fact_144_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 177 (all X_a (comm_semiring_1(X_a) -> (all M all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M)))) # label(fact_145_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 178 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),M) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M)))) # label(fact_146_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 179 (all X_b all X_a all F all Aa all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))))) # label(fact_147_curryD) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 180 (all X_b all X_a all F all Aa all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))))) # label(fact_148_curryE) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 181 (all X_a (preorder(X_a) -> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),X))))) # label(fact_149_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 182 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))))))) # label(fact_150_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 183 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))))))) # label(fact_151_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 184 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))))))) # label(fact_152_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 185 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))))))) # label(fact_153_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 186 (all X_a (order(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (ti(X_a,A_1) != ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_154_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 187 (all X_a (order(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (ti(X_a,A_1) != ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_155_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 188 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) | ti(X_a,X) = ti(X_a,Y))))) # label(fact_156_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 189 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_157_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 190 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_158_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 191 (all W_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),W_1))) # label(fact_159_zle__refl) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 192 (all K hAPP(int,int,number_number_of(int),K) = K) # label(fact_160_number__of__is__id) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 193 (all Z_1 all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),W_1)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_1)))) # label(fact_161_zle__linear) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 194 (all Z all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),W)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),W)) & Z != W)) # label(fact_162_zless__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 195 (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),Y)) | X = Y | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X)))) # label(fact_163_zless__linear) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 196 (all K_1 all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),K_1)),hAPP(int,int,number_number_of(int),L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),L)))) # label(fact_164_less__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 197 (all K_1 all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),K_1)),hAPP(int,int,number_number_of(int),L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_1),L)))) # label(fact_165_less__eq__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 198 (all K all I all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),J)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J),K)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),K))))) # label(fact_166_zle__trans) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 199 (all Z_1 all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),W_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_1)) -> Z_1 = W_1))) # label(fact_167_zle__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 200 (all X_a all X_b (ord(X_b) -> (all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) <-> (all X_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2)))))))) # label(fact_168_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 201 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_169_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 202 (all X_a (order(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) = ti(X_a,Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)))))) # label(fact_170_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 203 (all X_a (preorder(X_a) -> (all X all Y (X = Y -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_171_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 204 (all X_a all X_b (ord(X_b) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))))) # label(fact_172_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 205 (all X_a (order(X_a) -> (all Y_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_173_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 206 (all X_a (ord(X_a) -> (all C all A_1 all B (A_1 = B -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_174_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 207 (all X_a (order(X_a) -> (all C all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))))))) # label(fact_175_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 208 (all X_a (ord(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (B = C -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_176_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 209 (all X_a (order(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))))))) # label(fact_177_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 210 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> ti(X_a,X) = ti(X_a,Y)))))) # label(fact_178_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 211 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z_1))))))) # label(fact_179_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 212 (all X_a (order(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> ti(X_a,X) = ti(X_a,Y)))))) # label(fact_180_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 213 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),X))))))) # label(fact_181_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 214 (all X_a all X_b (ord(X_b) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))))) # label(fact_182_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 215 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_183_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 216 (all X_a (preorder(X_a) -> (all X -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X))))) # label(fact_184_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 217 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) != ti(X_a,Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)))))) # label(fact_185_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 218 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) | ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_186_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 219 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) | ti(X_a,X) = ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_187_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 220 (all X_a (linorder(X_a) -> (all Y_1 all X_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_188_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 221 (all X_a (linorder(X_a) -> (all X all Y (ti(X_a,X) != ti(X_a,Y) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_189_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 222 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ti(X_a,X) != ti(X_a,Y))))) # label(fact_190_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 223 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_191_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 224 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_192_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 225 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ti(X_a,X) != ti(X_a,Y))))) # label(fact_193_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 226 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ti(X_a,Y) != ti(X_a,X))))) # label(fact_194_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 227 (all X_a (preorder(X_a) -> (all P_1 all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) -> hBOOL(P_1)))))) # label(fact_195_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 228 (all X_a (preorder(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)))))) # label(fact_196_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 229 (all X_a (order(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_197_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 230 (all X_a (ord(X_a) -> (all C all A_1 all B (A_1 = B -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_198_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 231 (all X_a (order(X_a) -> (all C all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))))))) # label(fact_199_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 232 (all X_a (ord(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (B = C -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_200_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 233 (all X_a (order(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))))))) # label(fact_201_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 234 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))))))) # label(fact_202_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 235 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))))))) # label(fact_203_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 236 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_204_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 237 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (ti(X_a,X) != ti(X_a,Y) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_205_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 238 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)))))) # label(fact_206_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 239 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)))))) # label(fact_207_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 240 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_208_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 241 (all X_a (order(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & ti(X_a,X_1) != ti(X_a,Y_1))))) # label(fact_209_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 242 (all X_a (preorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)))))) # label(fact_210_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 243 (all X_a (order(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) | ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_211_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 244 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_212_leI) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 245 (all X_a (linorder(X_a) -> (all Y all X (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_213_not__leE) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 246 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_214_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 247 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,A_1) != ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_215_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 248 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,A_1) != ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_216_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 249 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_217_leD) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 250 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),one_one(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)))) # label(fact_218_norR__mem__unique__aux) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 251 (all P_1 all I_1 all K_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_1),K_1)) -> (hBOOL(hAPP(int,bool,P_1,K_1)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),K_1)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I_1)))))) # label(fact_219_int__le__induct) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 252 (all P_1 all I_1 all K_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),K_1)) -> (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),one_one(int)))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),K_1)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I_1)))))) # label(fact_220_int__less__induct) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 253 (all P_1 all K_1 all I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_1),I_1)) -> (hBOOL(hAPP(int,bool,P_1,K_1)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_1),I_2)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I_1)))))) # label(fact_221_int__ge__induct) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 254 (all P_1 all K_1 all I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),I_1)) -> (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),one_one(int)))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),I_2)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I_1)))))) # label(fact_222_int__gr__induct) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 255 (all X_a (dense_linorder(X_a) -> (all Z_1 all Y ((all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_1)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)))))) # label(fact_223_dense__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 256 (all X_a (dense_linorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ((all W_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W_2),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W_2),Z_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1))))))) # label(fact_224_dense__le__bounded) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 257 (all X_b all X_a (order(X_a) & order(X_b) -> (all C_1 all F all Ba all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),hAPP(X_a,X_b,F,Ba))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Aa))))))))) # label(fact_225_xt5) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 258 (all X_a all X_b (ord(X_b) -> (all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G)) <-> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) & -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),G),F)))))) # label(fact_226_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 259 (all X_a all X_b (ord(X_b) -> (all F all G ((all X_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2)))) -> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)))))) # label(fact_227_le__funI) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 260 (all X_b all X_a (order(X_a) & ord(X_b) -> (all C_1 all F all Ba all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Ba)),Aa)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),Ba)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C_1)),Aa)))))))) # label(fact_228_xt6) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 261 (all X_b all X_a (order(X_a) & order(X_b) -> (all C_1 all F all Ba all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Ba)),Aa)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),Ba)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C_1)),Aa)))))))) # label(fact_229_xt4) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 262 (all X_a all X_b (order(X_b) & order(X_a) -> (all C_1 all Aa all F all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),hAPP(X_b,X_a,F,Ba))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,C_1))))))))) # label(fact_230_order__le__less__subst1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 263 (all X_a all X_b (order(X_b) & order(X_a) -> (all C_1 all Aa all F all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,Ba))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),hAPP(X_b,X_a,F,C_1))))))))) # label(fact_231_order__less__le__subst1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 264 (all X_a all X_b (order(X_b) & order(X_a) -> (all F all C_1 all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Ba)),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),C_1)))))))) # label(fact_232_order__le__less__subst2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 265 (all X_a all X_b (order(X_b) & order(X_a) -> (all F all C_1 all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Ba)),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Aa)),C_1)))))))) # label(fact_233_order__less__le__subst2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 266 (all X_b all X_a (order(X_a) & order(X_b) -> (all C_1 all F all Ba all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Ba))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,Aa))))))))) # label(fact_234_xt7) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 267 (all I_1 all P_1 all K_1 (hBOOL(hAPP(int,bool,P_1,K_1)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_1),I_2)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),K_1)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I_1)))))) # label(fact_235_int__induct) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 268 (all B all A_1 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A_1))))) # label(fact_236_Euler_Oaux2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 269 (all X_1 all P_1 ((all A_2 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_2),one_one(int))))) -> hBOOL(hAPP(int,bool,P_1,A_2)))) -> hBOOL(hAPP(int,bool,P_1,X_1)))) # label(fact_237_d22set__induct__old) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 270 (all X_a (linord626643107strict(X_a) -> (all V all U_1 all Y all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U_1),V) = one_one(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)))))))))) # label(fact_238_convex__bound__lt) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 271 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a))),X_1)))))) # label(fact_239_number__of__le__ceiling) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 272 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a)))))))) # label(fact_240_ceiling__less__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 273 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)))))) # label(fact_241_zero__less__ceiling) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 274 (all X_a (zero(X_a) -> (all X_1 (zero_zero(X_a) = ti(X_a,X_1) <-> ti(X_a,X_1) = zero_zero(X_a))))) # label(fact_242_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 275 (all X_a (archim1727834104eiling(X_a) -> hAPP(X_a,int,archimedean_ceiling(X_a),zero_zero(X_a)) = zero_zero(int))) # label(fact_243_ceiling__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.02 276 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),zero_zero(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))))))) # label(fact_244_ceiling__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 277 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),one_one(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))))))) # label(fact_245_ceiling__less__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 278 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)))))) # label(fact_246_one__le__ceiling) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 279 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_1) = zero_zero(X_a)))) # label(fact_247_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 280 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_248_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 281 (all X_a (mult_zero(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_1) = zero_zero(X_a)))) # label(fact_249_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 282 (all X_a (real_normed_algebra(X_a) -> (all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),B) = zero_zero(X_a)))) # label(fact_250_mult_Ozero__left) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 283 (all X_a (real_normed_algebra(X_a) -> (all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),Y) = zero_zero(X_a)))) # label(fact_251_mult__left_Ozero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 284 (all X_a (mult_zero(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_252_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 285 (all X_a (real_normed_algebra(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_253_mult_Ozero__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 286 (all X_a (real_normed_algebra(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_254_mult__right_Ozero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 287 (all X_a (ring_n68954251visors(X_a) -> (all Aa all Ba (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba) = zero_zero(X_a) <-> ti(X_a,Aa) = zero_zero(X_a) | ti(X_a,Ba) = zero_zero(X_a))))) # label(fact_255_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 288 (all X_a (no_zero_divisors(X_a) -> (all B all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) != zero_zero(X_a)))))) # label(fact_256_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 289 (all X_a (no_zero_divisors(X_a) -> (all A_1 all B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = zero_zero(X_a) -> ti(X_a,A_1) = zero_zero(X_a) | ti(X_a,B) = zero_zero(X_a))))) # label(fact_257_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 290 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_258_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 291 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_259_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 292 (all X_a (semiri456707255roduct(X_a) -> (all Ba all Aa (ti(X_a,Ba) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Ba),Aa) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_260_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 293 (all X_a (monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_261_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 294 (all X_a (comm_monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_262_add__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 295 (all X_a (linord219039673up_add(X_a) -> (all Aa (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_263_double__zero__sym) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 296 (all X_a (monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_264_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 297 (all X_a (comm_monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_265_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 298 (all X_a (linord219039673up_add(X_a) -> (all Aa (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa) = zero_zero(X_a) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_266_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 299 (all X_a (zero_neq_one(X_a) -> one_one(X_a) != zero_zero(X_a))) # label(fact_267_one__neq__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 300 (all X_a (zero_neq_one(X_a) -> zero_zero(X_a) != one_one(X_a))) # label(fact_268_zero__neq__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 301 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_269_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 302 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_1) = zero_zero(X_a)))) # label(fact_270_diff__self) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 303 (all X_a (ab_group_add(X_a) -> (all Aa all Ba (ti(X_a,Aa) = ti(X_a,Ba) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = zero_zero(X_a))))) # label(fact_271_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 304 (all X_a (group_add(X_a) -> (all Aa all Ba (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba) = zero_zero(X_a) <-> ti(X_a,Aa) = ti(X_a,Ba))))) # label(fact_272_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 305 (all Z_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),Z_1) = Z_1) # label(fact_274_zadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 306 (all Z_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),zero_zero(int)) = Z_1) # label(fact_275_zadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 307 (all X_a (archim1727834104eiling(X_a) -> (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(X_a,int,archimedean_ceiling(X_a),Y))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_276_ceiling__less__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 308 (all X_a (archim1727834104eiling(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),Y)),hAPP(X_a,int,archimedean_ceiling(X_a),X))))))) # label(fact_277_ceiling__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 309 (all X_a (archim1727834104eiling(X_a) -> hAPP(X_a,int,archimedean_ceiling(X_a),one_one(X_a)) = one_one(int))) # label(fact_278_ceiling__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 310 (all X_a (archim1727834104eiling(X_a) -> (all V hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(int,X_a,number_number_of(X_a),V)) = hAPP(int,int,number_number_of(int),V)))) # label(fact_279_ceiling__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 311 (all X_a (linordered_ring(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)))))) # label(fact_280_zero__le__square) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 312 (all X_a (linord581940658strict(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Ba)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),zero_zero(X_a))))))) # label(fact_281_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 313 (all X_a (linord581940658strict(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Ba)))))) # label(fact_282_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 314 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_283_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 315 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_284_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 316 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),zero_zero(X_a)))))))) # label(fact_285_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 317 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_286_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 318 (all X_a (ordered_ring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_287_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 319 (all X_a (ordered_semiring(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_288_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 320 (all X_a (ordered_semiring(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_289_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 321 (all X_a (ordere1490568538miring(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_290_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 322 (all X_a (ordered_ring(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_291_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 323 (all X_a (ordered_ring(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_292_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 324 (all X_a (ordered_semiring(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1)))))))))) # label(fact_293_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 325 (all X_a (ordered_semiring(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1)))))))))) # label(fact_294_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 326 (all X_a (ordered_ring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))))) # label(fact_295_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 327 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a))))))) # label(fact_296_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 328 (all X_a (linordered_ring(X_a) -> (all A_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)),zero_zero(X_a)))))) # label(fact_297_not__square__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 329 (all X_a (linord581940658strict(X_a) -> (all Aa all C_1 all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ba),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa)))))) # label(fact_298_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 330 (all X_a (linord581940658strict(X_a) -> (all C_1 all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa)))))) # label(fact_299_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 331 (all X_a (linord581940658strict(X_a) -> (all Aa all Ba all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba))))))) # label(fact_300_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 332 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_301_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 333 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_302_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 334 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),zero_zero(X_a)))))))) # label(fact_303_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 335 (all X_a (linord20386208strict(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))))))) # label(fact_304_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 336 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))))))) # label(fact_305_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 337 (all X_a (linord581940658strict(X_a) -> (all Aa all Ba all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ba),Aa))))))) # label(fact_306_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 338 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_307_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 339 (all X_a (linord581940658strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_308_mult__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 340 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_309_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 341 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_310_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 342 (all X_a (linord893533164strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_311_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 343 (all X_a (linord581940658strict(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_312_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 344 (all X_a (linord581940658strict(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_313_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 345 (all X_a (linord219039673up_add(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Aa)))))) # label(fact_314_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 346 (all X_a (linord219039673up_add(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),zero_zero(X_a))))))) # label(fact_315_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 347 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_316_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 348 (all X_a (ordere216010020id_add(X_a) -> (all Y_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y_1)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_1) = zero_zero(X_a) <-> ti(X_a,X_1) = zero_zero(X_a) & ti(X_a,Y_1) = zero_zero(X_a))))))) # label(fact_317_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 349 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_318_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 350 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_319_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 351 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_320_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 352 (all X_a (linord219039673up_add(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Aa)))))) # label(fact_321_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 353 (all X_a (linordered_idom(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))))))) # label(fact_322_even__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 354 (all X_a (linord219039673up_add(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a))))))) # label(fact_323_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 355 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_324_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 356 (all X_a (linordered_semidom(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_325_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 357 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_326_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 358 (all X_a (linordered_semidom(X_a) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),zero_zero(X_a))))) # label(fact_327_not__one__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 359 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),one_one(X_a))))) # label(fact_328_zero__le__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 360 (all X_a (linordered_semidom(X_a) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a))))) # label(fact_329_not__one__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 361 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a))))) # label(fact_330_zero__less__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 362 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),zero_zero(X_a))))))) # label(fact_331_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 363 (all X_a (semiri456707255roduct(X_a) -> (all C all D_1 all A_1 all B all R (ti(X_a,R) != zero_zero(X_a) -> (ti(X_a,A_1) = ti(X_a,B) & ti(X_a,C) != ti(X_a,D_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R),C)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R),D_1))))))) # label(fact_332_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 364 (all X_a (ordered_ab_group_add(X_a) -> (all Aa all Ba (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),Ba)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),zero_zero(X_a))))))) # label(fact_333_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 365 (all A_1 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),A_1)) -> (X != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),one_one(int)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),one_one(int)))))))) # label(fact_334_Euler_Oaux1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 366 (all K all I all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),J)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),J)))))) # label(fact_336_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 367 (all Z_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_1)),Z_1) != zero_zero(int)) # label(fact_337_odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 368 (all K_1 all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),L)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),L)),zero_zero(int))))) # label(fact_338_less__bin__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 369 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),X_1)))))) # label(fact_339_one__less__ceiling) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 370 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),one_one(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),one_one(X_a))))))) # label(fact_340_ceiling__le__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 371 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),X_1)))))) # label(fact_341_number__of__less__ceiling) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 372 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),V_1))))))) # label(fact_342_ceiling__le__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 373 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),one_one(int))))) # label(fact_343_ceiling__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 374 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(int,int,number_number_of(int),V))))) # label(fact_344_ceiling__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 375 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),one_one(int))))) # label(fact_345_ceiling__diff__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 376 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(int,int,number_number_of(int),V))))) # label(fact_346_ceiling__diff__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 377 (all X_a (linord581940658strict(X_a) -> (all Aa all Ba all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Aa),Ba))))))) # label(fact_347_mult__le__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 378 (all X_a (linord581940658strict(X_a) -> (all Aa all Ba all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Aa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),Ba))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Ba),Aa))))))) # label(fact_348_mult__le__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 379 (all X_a (linord20386208strict(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1)))))))))) # label(fact_349_mult__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 380 (all X_a (linord20386208strict(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1)))))))))) # label(fact_350_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 381 (all X_a (linord20386208strict(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1)))))))))) # label(fact_351_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 382 (all X_a (linord20386208strict(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D_1)))))))))) # label(fact_352_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 383 (all X_a (linordered_semiring(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_353_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 384 (all X_a (linord20386208strict(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_354_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 385 (all X_a (linordered_semiring(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_355_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 386 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_356_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 387 (all X_a (linord20386208strict(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))))))) # label(fact_357_mult__right__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 388 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))))))) # label(fact_358_mult__left__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 389 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_359_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 390 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_360_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 391 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_361_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 392 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_362_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 393 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_363_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 394 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_364_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 395 (all X_a (linordered_idom(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),X)))))))) # label(fact_365_mult__right__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 396 (all X_a (linordered_idom(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),X)),X)))))))) # label(fact_366_mult__left__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 397 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))))) # label(fact_367_zero__less__two) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 398 (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)))) # label(fact_368_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 399 (all N_2 all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M_1)) -> (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M_1),N_2) = one_one(int) <-> M_1 = one_one(int) & N_2 = one_one(int)))) # label(fact_369_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 400 (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z)),Z)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),zero_zero(int))))) # label(fact_370_odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 401 (all X_a (linord1278240602ring_1(X_a) -> (all V all U_1 all Y all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U_1),V) = one_one(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)))))))))) # label(fact_371_convex__bound__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 402 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_1))))) # label(fact_372_le__imp__0__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 403 (all R all Q all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (A_1 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),R),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q),one_one(int))))))) # label(fact_373_self__quotient__aux2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 404 (all R all Q all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (A_1 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),R),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R),A_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Q)))))) # label(fact_374_self__quotient__aux1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 405 (all B all Q all R all B_1 all Q_1 all R_3 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q)),R) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),Q_1)),R_3) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),Q_1)),R_3)),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_1),Q))))))))) # label(fact_375_zdiv__mono2__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 406 (all B all Q_1 all R_3 all Q all R (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_1)),R_3)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q)),R))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_3)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q),Q_1))))))) # label(fact_376_unique__quotient__lemma__neg) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 407 (all B all Q all R all B_1 all Q_1 all R_3 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q)),R) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),Q_1)),R_3) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),Q_1)),R_3))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q),Q_1))))))))) # label(fact_377_zdiv__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 408 (all B all Q_1 all R_3 all Q all R (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_1)),R_3)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q)),R))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_1),Q))))))) # label(fact_378_unique__quotient__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 409 (all B_1 all Q_1 all R_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),Q_1)),R_3)),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_1),zero_zero(int))))))) # label(fact_379_q__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 410 (all B_1 all Q_1 all R_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),Q_1)),R_3))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_3),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Q_1)))))) # label(fact_380_q__pos__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 411 (all M all R all S all T_3 all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)) -> (hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,M),N_1) = hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),R),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),S),T_3)) -> R = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_3),N_1))))) # label(fact_381_xzgcd__linear) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 412 (all X_a (linord581940658strict(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1)))) <-> ti(X_a,X_1) != zero_zero(X_a) | ti(X_a,Y_1) != zero_zero(X_a))))) # label(fact_382_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 413 (all X_a (linordered_ring(X_a) -> (all X all Y -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y))),zero_zero(X_a)))))) # label(fact_383_not__sum__squares__lt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 414 (all X_a (linord581940658strict(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))),zero_zero(X_a))) <-> ti(X_a,X_1) = zero_zero(X_a) & ti(X_a,Y_1) = zero_zero(X_a))))) # label(fact_384_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 415 (all X_a (linordered_ring(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y))))))) # label(fact_385_sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 416 (all X_a (linord581940658strict(X_a) -> (all X_1 all Y_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1)) = zero_zero(X_a) <-> ti(X_a,X_1) = zero_zero(X_a) & ti(X_a,Y_1) = zero_zero(X_a))))) # label(fact_386_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 417 (all M all N_1 all R_3 all S_1 all S all T_4 all T_3 all Rn all Sn all Tn all R (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R)) -> (hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N_1),R_3),R),S_1),S),T_4),T_3) = hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),Rn),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Sn),Tn)) -> (R_3 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_1),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_4),N_1)) -> (R = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_3),N_1)) -> Rn = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Sn),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Tn),N_1))))))) # label(fact_387_xzgcda__linear) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 418 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_388_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.03 419 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)))))) # label(fact_389_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 420 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))))) # label(fact_390_pos__zmult__pos) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 421 (all M all N_1 hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,M),N_1) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N_1),M),N_1),one_one(int)),zero_zero(int)),zero_zero(int)),one_one(int))) # label(fact_393_xzgcd__def) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 422 (all K_1 all P_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> ((all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_1)) -> (all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_2)))))))))) # label(fact_394_decr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 423 (all K_1 all P_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> ((all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_1)) -> (all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_2)))))))))) # label(fact_395_incr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 424 (all X_a (linord1117847801e_zero(X_a) -> (all X all Y ((all Z_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Z_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_3),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_3),X)),Y))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_396_field__le__mult__one__interval) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 425 (all A_1 all B all Q all R (A_1 = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q)),R) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R),B))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R),zero_zero(int)))) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q),R)))))) # label(fact_397_divmod__int__relI) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 426 (all Y all X ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),X)) -> hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),X)) -> hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y) = zero_zero(int)))) # label(fact_398_tsub__def) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 427 (all B (B != zero_zero(int) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,zero_zero(int)),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int)))))) # label(fact_399_divmod__int__rel__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 428 (all A_1 all Q all R (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),A_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q),R))) -> (A_1 != zero_zero(int) -> R = zero_zero(int)))) # label(fact_400_self__remainder) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 429 (all Q_1 all R_3 all A_1 all B all Q all R (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q),R))) -> (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_1),R_3))) -> (B != zero_zero(int) -> Q = Q_1)))) # label(fact_401_unique__quotient) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 430 (all Q_1 all R_3 all A_1 all B all Q all R (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q),R))) -> (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_1),R_3))) -> (B != zero_zero(int) -> R = R_3)))) # label(fact_402_unique__remainder) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 431 (all A_1 all Q all R (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),A_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q),R))) -> (A_1 != zero_zero(int) -> Q = one_one(int)))) # label(fact_403_self__quotient) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 432 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y)))))) # label(fact_404_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 433 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),X)) -> hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y))) # label(fact_405_tsub__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 434 (all P_2 all P_1 all X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(P_1) <-> hBOOL(P_2))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) & hBOOL(P_1) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) & hBOOL(P_2)))) # label(fact_406_conj__le__cong) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 435 (all P_2 all P_1 all X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(P_1) <-> hBOOL(P_2))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hBOOL(P_1)) <-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hBOOL(P_2))))) # label(fact_407_imp__le__cong) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 436 (all X_a (linordered_field(X_a) -> (all X all Y ((all E (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),E)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),E))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_408_field__le__epsilon) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 437 (all X_a (linorder(X_a) -> (all T_3 exists Z_3 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_3),X_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_3)))))) # label(fact_409_pinf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 438 (all X_a (linorder(X_a) -> (all T_3 exists Z_3 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_3)))))) # label(fact_410_minf_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 439 (all X_a (linorder(X_a) -> (all T_3 exists Z_3 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_3),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_3),X_2)))))) # label(fact_411_pinf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 440 (all X_a (linorder(X_a) -> (all T_3 exists Z_3 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_3)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_3),X_2)))))) # label(fact_412_minf_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 441 (all P_1 all P1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> ((all X_2 all K_2 (hBOOL(hAPP(int,bool,P1,X_2)) <-> hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_2),D_2)))))) -> ((exists Z_3 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Z_3)) -> (hBOOL(hAPP(int,bool,P_1,X_2)) <-> hBOOL(hAPP(int,bool,P1,X_2))))) -> ((exists X1 hBOOL(hAPP(int,bool,P1,X1))) -> (exists X1 hBOOL(hAPP(int,bool,P_1,X1)))))))) # label(fact_413_minusinfinity) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 442 (all P_1 all P_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> ((all X_2 all K_2 (hBOOL(hAPP(int,bool,P_2,X_2)) <-> hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_2),D_2)))))) -> ((exists Z_3 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_3),X_2)) -> (hBOOL(hAPP(int,bool,P_1,X_2)) <-> hBOOL(hAPP(int,bool,P_2,X_2))))) -> ((exists X1 hBOOL(hAPP(int,bool,P_2,X1))) -> (exists X1 hBOOL(hAPP(int,bool,P_1,X1)))))))) # label(fact_414_plusinfinity) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 443 (all N_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N_1),zero_zero(int))) -> hAPP(int,int,zfact,N_1) = one_one(int)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N_1),zero_zero(int))) -> hAPP(int,int,zfact,N_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N_1),hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N_1),one_one(int))))))) # label(fact_415_zfact_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 444 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a)))))))) # label(fact_416_floor__le__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 445 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a))),X_1)))))) # label(fact_417_number__of__less__floor) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 446 (all X_a (archim1727834104eiling(X_a) -> hAPP(X_a,int,archim2085082626_floor(X_a),zero_zero(X_a)) = zero_zero(int))) # label(fact_418_floor__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 447 (all X_a (archim1727834104eiling(X_a) -> (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(X_a,int,archim2085082626_floor(X_a),Y))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_419_floor__less__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 448 (all X_a (archim1727834104eiling(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(X_a,int,archim2085082626_floor(X_a),Y))))))) # label(fact_420_floor__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 449 (all X_a (archim1727834104eiling(X_a) -> hAPP(X_a,int,archim2085082626_floor(X_a),one_one(X_a)) = one_one(int))) # label(fact_421_floor__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 450 (all X_a (archim1727834104eiling(X_a) -> (all V hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(int,X_a,number_number_of(X_a),V)) = hAPP(int,int,number_number_of(int),V)))) # label(fact_422_floor__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 451 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),zero_zero(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),zero_zero(X_a))))))) # label(fact_423_floor__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 452 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)))))) # label(fact_424_zero__le__floor) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 453 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),X_1)))))) # label(fact_425_zero__less__floor) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 454 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),zero_zero(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a))))))) # label(fact_426_floor__le__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 455 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),one_one(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a))))))) # label(fact_427_floor__less__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 456 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),X_1)))))) # label(fact_428_one__le__floor) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 457 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),V_1))))))) # label(fact_429_floor__less__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 458 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),X_1)))))) # label(fact_430_number__of__le__floor) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 459 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int))))) # label(fact_431_floor__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 460 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(int,int,number_number_of(int),V))))) # label(fact_432_floor__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 461 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int))))) # label(fact_433_floor__diff__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 462 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(int,int,number_number_of(int),V))))) # label(fact_434_floor__diff__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 463 (all B all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(real,int,archim2085082626_floor(real),A_1)),hAPP(real,int,archim2085082626_floor(real),B))),hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B))))))) # label(fact_435_le__mult__floor) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 464 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)))))) # label(fact_436_posDivAlg__correct) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 465 (all Z_1 all X all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Z_1))),one_one(int))),D_1)))))) # label(fact_437_incr__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 466 (all X all Z_1 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Z_1))),one_one(int))),D_1))),Z_1)))) # label(fact_438_decr__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 467 (all X_a (linordered_idom(X_a) -> (all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),Aa)),Aa)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),zero_zero(X_a)))))))) # label(fact_439_Ints__odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 468 (all W_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),W_1),W_1))) # label(fact_440_real__le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 469 (all Z_1 all W_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Z_1),W_1)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),W_1),Z_1)))) # label(fact_441_real__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 470 (all Z_1 all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z_1),X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z_1),Y))))) # label(fact_442_real__add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 471 (all K all I all J (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),I),J)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),J),K)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),I),K))))) # label(fact_443_real__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 472 (all Z_1 all W_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Z_1),W_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),W_1),Z_1)) -> Z_1 = W_1))) # label(fact_444_real__le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 473 (all Z1 all Z2 all W_1 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z1),Z2)),W_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),W_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z2),W_1))) # label(fact_445_real__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 474 (all Z1 all Z2 all Z3 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),Z2)),Z3) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z2),Z3))) # label(fact_446_real__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 475 (all Z_1 all W_1 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),W_1) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),W_1),Z_1)) # label(fact_447_real__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 476 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)) = hAPP(X_a,X_a,abs_abs(X_a),A_1)))) # label(fact_448_abs__idempotent) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 477 (all Z_1 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),one_one(real)),Z_1) = Z_1) # label(fact_449_real__mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 478 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) | X_1 = Y_1)) # label(fact_450_less__eq__real__def) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 479 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) & X_1 != Y_1)) # label(fact_451_real__less__def) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 480 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1))))) # label(fact_452_abs__minus__commute) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 481 (all X_a (linordered_idom(X_a) -> hAPP(X_a,X_a,abs_abs(X_a),one_one(X_a)) = one_one(X_a))) # label(fact_453_abs__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 482 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))) # label(fact_454_abs__add__abs) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 483 (all X_a (linordered_idom(X_a) -> (all A_1 all B hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))) # label(fact_455_abs__mult) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 484 (all X_a (linordered_idom(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),A_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)))) # label(fact_456_abs__mult__self) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 485 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),hAPP(X_a,X_a,abs_abs(X_a),A_1)))))) # label(fact_457_abs__ge__self) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 486 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_458_abs__le__D1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 487 (all X_a (ordere142940540dd_abs(X_a) -> hAPP(X_a,X_a,abs_abs(X_a),zero_zero(X_a)) = zero_zero(X_a))) # label(fact_459_abs__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 488 (all X_a (ordere142940540dd_abs(X_a) -> (all Aa (hAPP(X_a,X_a,abs_abs(X_a),Aa) = zero_zero(X_a) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_460_abs__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 489 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_1)),zero_zero(real))))) # label(fact_461_real__le__eq__diff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 490 (all Aa all Ba all C_1 (C_1 != zero_zero(real) -> (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),Aa) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),Ba) <-> Aa = Ba))) # label(fact_462_real__mult__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 491 (all Aa all Ba all C_1 (C_1 != zero_zero(real) -> (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Aa),C_1) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Ba),C_1) <-> Aa = Ba))) # label(fact_463_real__mult__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 492 (all X_1 all Y_1 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),X_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Y_1)) = zero_zero(real) <-> X_1 = zero_zero(real) & Y_1 = zero_zero(real))) # label(fact_464_real__two__squares__add__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 493 (all X_1 all Y_1 all Z (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),Z)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Z))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1))))) # label(fact_466_real__mult__less__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 494 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)))))) # label(fact_467_real__mult__order) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 495 (all X all Y all Z_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),Y)))))) # label(fact_468_real__mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 496 (all X_1 all Y_1 all Z (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z),X_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1))))) # label(fact_469_real__mult__le__cancel__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 497 (all X_1 all Y_1 all Z (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),Z)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Z))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1))))) # label(fact_470_real__mult__le__cancel__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 498 (all X_a (ring_1(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),zero_zero(X_a)),ring_1_Ints(X_a))))) # label(fact_471_Ints__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 499 (all X_a (ring_1(X_a) -> (all Ba all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Aa),Ba)),ring_1_Ints(X_a)))))))) # label(fact_472_Ints__mult) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 500 (all X_a (ring_1(X_a) -> (all Ba all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Ba)),ring_1_Ints(X_a)))))))) # label(fact_473_Ints__add) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 501 (all X_a (number_ring(X_a) -> (all W hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(int,X_a,number_number_of(X_a),W)),ring_1_Ints(X_a)))))) # label(fact_474_Ints__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 502 (all X_a (ring_1(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),one_one(X_a)),ring_1_Ints(X_a))))) # label(fact_475_Ints__1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 503 (all X_a (ring_1(X_a) -> (all Ba all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ba),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),Ba)),ring_1_Ints(X_a)))))))) # label(fact_476_Ints__diff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 504 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,abs_abs(X_a),A_1)))))) # label(fact_477_abs__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 505 (all X_a (ordere142940540dd_abs(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),Aa)),zero_zero(X_a))) <-> ti(X_a,Aa) = zero_zero(X_a))))) # label(fact_478_abs__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 506 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> hAPP(X_a,X_a,abs_abs(X_a),A_1) = ti(X_a,A_1))))) # label(fact_479_abs__of__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 507 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),zero_zero(X_a)))))) # label(fact_480_abs__not__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 508 (all X_a (ordere142940540dd_abs(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,abs_abs(X_a),Aa))) <-> ti(X_a,Aa) != zero_zero(X_a))))) # label(fact_481_zero__less__abs__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 509 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hAPP(X_a,X_a,abs_abs(X_a),A_1) = ti(X_a,A_1))))) # label(fact_482_abs__of__pos) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 510 (all X_a (linordered_idom(X_a) -> (all B all D_1 all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),B)),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),D_1)))))))) # label(fact_483_abs__mult__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 511 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))))) # label(fact_484_abs__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 512 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1))))))) # label(fact_485_abs__triangle__ineq2__sym) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 513 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))))) # label(fact_486_abs__triangle__ineq2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 514 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))))) # label(fact_487_abs__triangle__ineq3) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 515 (all X_a (linordered_idom(X_a) -> (all X_1 all Aa all R_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_1),Aa))),R_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Aa),R_2)),X_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),R_2))))))) # label(fact_488_abs__diff__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 516 (all M all N_1 (hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N_1)) = one_one(int) -> hAPP(int,int,abs_abs(int),M) = one_one(int))) # label(fact_489_abs__zmult__eq__1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 517 (all X_a (ordered_ring_abs(X_a) -> (all B all A_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a)))) -> hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))))) # label(fact_490_abs__eq__mult) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 518 (all X_a (linordered_idom(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),Y)),X) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),X)))))) # label(fact_491_abs__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 519 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B all C all D_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1)))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),C))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),D_1)))))))) # label(fact_492_abs__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 520 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))))) # label(fact_493_abs__triangle__ineq4) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 521 (all X_a (ring_char_0(X_a) -> (all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Aa),Aa) = zero_zero(X_a) <-> ti(X_a,Aa) = zero_zero(X_a)))))) # label(fact_494_Ints__double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 522 (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),Z)),one_one(int))) <-> Z = zero_zero(int))) # label(fact_495_zabs__less__one__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 523 (all B hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,zero_zero(int)),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int))) # label(fact_496_posDivAlg__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 524 (all X_a (ring_char_0(X_a) -> (all Aa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Aa),ring_1_Ints(X_a))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),Aa)),Aa) != zero_zero(X_a))))) # label(fact_497_Ints__odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 525 (all K all L_1 ((L_1 = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L_1) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),hAPP(int,int,abs_abs(int),K))) & (L_1 != zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L_1) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,abs_abs(int),K)),hAPP(int,int,abs_abs(int),L_1))))) # label(fact_498_pdivmod__posDivAlg) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 526 (all K_1 all F all N_2 all M_1 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),I_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),one_one(nat)))),hAPP(nat,int,F,I_2)))),one_one(int))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,M_1)),K_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_1),hAPP(nat,int,F,N_2))) -> (exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),I_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),N_2)) & hAPP(nat,int,F,I_2) = K_1))))))) # label(fact_499_nat__intermed__int__val) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 527 (all K_1 all F all N_2 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),one_one(nat)))),hAPP(nat,int,F,I_2)))),one_one(int))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,zero_zero(nat))),K_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_1),hAPP(nat,int,F,N_2))) -> (exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),N_2)) & hAPP(nat,int,F,I_2) = K_1)))))) # label(fact_500_nat0__intermed__int__val) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 528 (all K_1 all F all N_2 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),one_one(nat)))),hAPP(nat,int,F,I_2)))),one_one(int))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,zero_zero(nat))),K_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_1),hAPP(nat,int,F,N_2))) -> (exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),N_2)) & hAPP(nat,int,F,I_2) = K_1)))))) # label(fact_501_int__val__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 529 (all N_1 all M ((M = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1) = zero_zero(nat)) & (M != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N_1))))) # label(fact_502_mult__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 530 (all X -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),X)),one_one(real))),X))) # label(fact_503_abs__add__one__not__less__self) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 531 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(real,real,abs_abs(real),X))))) # label(fact_504_abs__add__one__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 532 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N_1))) # label(fact_505_le0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 533 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))) # label(fact_506_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 534 (all U_1 all V all X all Y (X = Y -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),U_1)),V)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),U_1)),Y))),V))))) # label(fact_507_sin__bound__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 535 (all U all M_1 all N_2 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_2)))))) # label(fact_508_nat__less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 536 (all K all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))) # label(fact_509_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 537 (all M all N_1 all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))) # label(fact_510_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 538 (all I all J all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),K)),J)) # label(fact_511_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 539 (all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),M)) # label(fact_512_nat__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 540 (all M all N_1 all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))) # label(fact_513_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 541 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N_1) = zero_zero(nat)) # label(fact_514_mult__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 542 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),zero_zero(nat)) = zero_zero(nat)) # label(fact_515_mult__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 543 (all M_1 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2) = zero_zero(nat) <-> M_1 = zero_zero(nat) | N_2 = zero_zero(nat))) # label(fact_516_mult__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 544 (all K_1 all M_1 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2) <-> K_1 = zero_zero(nat) | M_1 = N_2)) # label(fact_517_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 545 (all K_1 all M_1 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2) <-> M_1 = N_2 | K_1 = zero_zero(nat))) # label(fact_518_mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 546 (all M_1 all K_1 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_1) <-> M_1 = N_2 | K_1 = zero_zero(nat))) # label(fact_519_mult__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 547 (all M all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1) = zero_zero(nat) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M) = zero_zero(nat) -> M = N_1))) # label(fact_520_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 548 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M) = zero_zero(nat)) # label(fact_521_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 549 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat)) = M) # label(fact_522_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 550 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N_1) = zero_zero(nat)) # label(fact_523_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 551 (all P_1 all M_1 all N_2 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),M_1))) -> ((M_1 = N_2 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),M_1))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),M_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),M_1)))))) # label(fact_524_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 552 (all S all T_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3)) -> S != T_3)) # label(fact_525_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 553 (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M)) -> M != N_1)) # label(fact_526_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 554 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))) # label(fact_527_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 555 (all X all Y (X != Y -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X))))) # label(fact_528_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 556 (all M_1 all N_2 (M_1 != N_2 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1)))) # label(fact_529_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 557 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))) # label(fact_530_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 558 (all L_1 all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M)))))) # label(fact_531_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 559 (all N_1 all J all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),N_1)),K)))) # label(fact_532_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 560 (all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)),N_1) = M) # label(fact_533_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 561 (all N_1 all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)),N_1) = M) # label(fact_534_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 562 (all I all J all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))) # label(fact_535_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 563 (all K all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) # label(fact_536_Nat_Odiff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 564 (all M all K all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) # label(fact_537_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 565 (all M_1 all K_1 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K_1) <-> M_1 = N_2)) # label(fact_538_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 566 (all K_1 all M_1 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2) <-> M_1 = N_2)) # label(fact_539_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 567 (all M all N_1 all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K))) # label(fact_540_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 568 (all X all Y all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Z_1))) # label(fact_541_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 569 (all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)) # label(fact_542_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 570 (all K all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))) # label(fact_543_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 571 (all M all N_1 all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))) # label(fact_544_add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 572 (all I all U_1 all J all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),U_1)),K)) # label(fact_545_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 573 (all M all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),M))) # label(fact_546_Nat_Odiff__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 574 (all L_1 all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M))))) # label(fact_547_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 575 (all L_1 all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),L_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),L_1))))) # label(fact_548_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 576 (all I all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),I)) = I)) # label(fact_549_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 577 (all N_2 all K_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_2)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),K_1) <-> M_1 = N_2)))) # label(fact_550_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 578 (all N_1 all K all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)))) # label(fact_551_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 579 (all N_2 all K_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2)))))) # label(fact_552_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 580 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_1))) # label(fact_553_le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 581 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)))) # label(fact_554_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.04 582 (all M all N_1 (M = N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)))) # label(fact_555_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 583 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),K))))) # label(fact_556_le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 584 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> M = N_1))) # label(fact_557_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 585 (all K all L_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),L_1)))))) # label(fact_558_mult__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 586 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),I)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),J))))) # label(fact_559_mult__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 587 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),K))))) # label(fact_560_mult__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 588 (all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M))))) # label(fact_561_le__cube) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 589 (all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M)))) # label(fact_562_le__square) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 590 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N_1) = N_1) # label(fact_563_nat__mult__1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 591 (all M_1 all N_2 (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2) <-> M_1 = one_one(nat) & N_2 = one_one(nat))) # label(fact_564_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 592 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),one_one(nat)) = N_1) # label(fact_565_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 593 (all M_1 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2) = one_one(nat) <-> M_1 = one_one(nat) & N_2 = one_one(nat))) # label(fact_566_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 594 (all N_2 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),M_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)))) # label(fact_567_zero__less__diff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 595 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),M))))) # label(fact_568_diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 596 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))) # label(fact_569_not__less0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 597 (all N_2 (N_2 != zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)))) # label(fact_570_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 598 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))) # label(fact_571_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 599 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> N_1 != zero_zero(nat))) # label(fact_572_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 600 (all N_1 (N_1 != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)))) # label(fact_573_gr0I) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 601 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),I)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),J)))))) # label(fact_574_mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 602 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),K)))))) # label(fact_575_mult__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 603 (all M_1 all N_2 all K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2))))) # label(fact_576_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 604 (all M_1 all N_2 all K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2) <-> M_1 = N_2))) # label(fact_577_nat__mult__eq__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 605 (all M_1 all K_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)))) # label(fact_578_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 606 (all K_1 all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)))) # label(fact_579_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 607 (all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)))) # label(fact_580_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 608 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N_1) = N_1) # label(fact_581_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 609 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),zero_zero(nat)) = M) # label(fact_582_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 610 (all M_1 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2) = zero_zero(nat) <-> M_1 = zero_zero(nat) & N_2 = zero_zero(nat))) # label(fact_583_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 611 (all M all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1) = M -> N_1 = zero_zero(nat))) # label(fact_584_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 612 (all N_1 all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)) = zero_zero(nat)) # label(fact_585_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 613 (all M_1 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),N_2) = zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2)))) # label(fact_586_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 614 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1) = zero_zero(nat))) # label(fact_587_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 615 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N_1))) # label(fact_588_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 616 (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),zero_zero(nat))) <-> N_2 = zero_zero(nat))) # label(fact_589_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 617 (all I all J -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),I))) # label(fact_590_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 618 (all J all I -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I)),I))) # label(fact_591_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 619 (all K_1 all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)))) # label(fact_592_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 620 (all M all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M))))) # label(fact_593_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 621 (all M all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J))))) # label(fact_594_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 622 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))))) # label(fact_595_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 623 (all K all L_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1)))))) # label(fact_596_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 624 (all M all N_1 all K all L_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))))) # label(fact_597_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 625 (all I all J all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K)))) # label(fact_598_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 626 (all M all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) = M)) # label(fact_599_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 627 (all I_1 all J_2 all K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_2)))) # label(fact_600_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 628 (all M all N_1 (M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1) -> N_1 = one_one(nat) | M = zero_zero(nat))) # label(fact_601_mult__eq__self__implies__10) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 629 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) | M = N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)))) # label(fact_602_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 630 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> (M != N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))))) # label(fact_603_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 631 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)))) # label(fact_604_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 632 (all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)) | M_1 = N_2)) # label(fact_605_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 633 (all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2)) & M_1 != N_2)) # label(fact_606_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 634 (all N_2 all K_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)))))) # label(fact_607_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 635 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),C)))))) # label(fact_608_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 636 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),J))) # label(fact_609_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 637 (all J_2 all K_1 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1)),I_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1))))) # label(fact_610_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 638 (all M all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)),K))))) # label(fact_611_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 639 (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) = M)) # label(fact_612_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 640 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),K))) # label(fact_613_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 641 (all I_1 all K_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_2))))) # label(fact_614_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 642 (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),N_1) = M)) # label(fact_615_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 643 (all K_1 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1) = K_1 <-> J_2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),I_1)))) # label(fact_616_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 644 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)))) # label(fact_617_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 645 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I)),K))) # label(fact_618_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 646 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I))) # label(fact_619_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 647 (all U all M_1 all N_2 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2) <-> M_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_2)))) # label(fact_620_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 648 (all U_1 all M all N_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I)),U_1)),N_1)))) # label(fact_621_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 649 (all U all M_1 all N_2 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N_2)))))) # label(fact_622_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 650 (all U all M_1 all N_2 all J_2 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),I_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M_1) = N_2))) # label(fact_623_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 651 (all U_1 all M all N_1 all J all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),U_1)),M)),N_1))) # label(fact_624_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 652 (all U all M_1 all N_2 all J_2 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),I_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M_1)),N_2))))) # label(fact_625_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 653 (all M all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N_1)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1))))) # label(fact_626_add__leE) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 654 (all M all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)))) # label(fact_627_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 655 (all M all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)))) # label(fact_628_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 656 (all K all L_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1)))))) # label(fact_629_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 657 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))))) # label(fact_630_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 658 (all M all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J))))) # label(fact_631_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 659 (all M all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M))))) # label(fact_632_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 660 (all K_1 all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2)))) # label(fact_633_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 661 (all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2)) <-> (exists K_2 N_2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2)))) # label(fact_634_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 662 (all N_1 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)))) # label(fact_635_le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 663 (all N_1 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)))) # label(fact_636_le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 664 (all X_1 all Y_1 all Z (X_1 = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y_1),Z) <-> Y_1 = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Z))) # label(fact_637_eq__diff__eq_H) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 665 (all P_1 all Aa all Ba (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba))) <-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba)) & -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) | (exists D (Aa = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),D) & -hBOOL(hAPP(nat,bool,P_1,D))))))) # label(fact_638_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 666 (all P_1 all Aa all Ba (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Aa),Ba))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Aa),Ba)) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))) & (all D (Aa = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ba),D) -> hBOOL(hAPP(nat,bool,P_1,D)))))) # label(fact_639_nat__diff__split) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 667 (all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)))) # label(fact_640_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 668 (all K_1 all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2))))) # label(fact_641_mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 669 (all M_1 all K_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),K_1))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2))))) # label(fact_642_mult__le__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 670 (all M_1 all N_2 all K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2))))) # label(fact_643_nat__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 671 (all U all M_1 all N_2 all J_2 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),I_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M_1)),N_2))))) # label(fact_644_nat__less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 672 (all N_2 all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> (hBOOL(hAPP(nat,bool,P_1,N_2)) -> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_2),N_2)) & (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),K_2)) -> -hBOOL(hAPP(nat,bool,P_1,I_2)))) & hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),one_one(nat))))))))) # label(fact_645_ex__least__nat__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 673 (all X all Y all C (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,abs_abs(real),Y)))) -> X = zero_zero(real)))) # label(fact_646_rabs__ratiotest__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 674 (all M_1 all K_1 all F ((all M_2 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M_2)),hAPP(nat,nat,F,N))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,M_1)),K_1)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)))))) # label(fact_647_mono__nat__linear__lb) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 675 (all N_2 all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> (hBOOL(hAPP(nat,bool,P_1,N_2)) -> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),N_2)) & (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K_2)) -> -hBOOL(hAPP(nat,bool,P_1,I_2)))) & hBOOL(hAPP(nat,bool,P_1,K_2))))))) # label(fact_648_ex__least__nat__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 676 (all K_1 all L (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),L)) <-> (exists N L = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N)))) # label(fact_649_le__Suc__ex__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 677 (all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> (exists K_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_2)) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K_2) = J)))) # label(fact_650_less__imp__add__positive) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 678 (all X_1 (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),X_1))) <-> X_1 = zero_zero(real))) # label(fact_651_not__real__square__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 679 (all N_1 all M all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M) -> N_1 = M))) # label(fact_652_mult__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 680 (all B all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),B)) -> (exists D (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D)) & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y_2))),D)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_1),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),B))))))))) # label(fact_653_lemma__interval) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 681 (all K all L_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),L_1)) -> (exists N L_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N)))) # label(fact_654_le__Suc__ex) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 682 (all I_1 all J_2 all F ((all I_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_2)),hAPP(nat,nat,F,J_1))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_2)))))) # label(fact_655_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 683 (all B all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),B)) -> (exists D (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D)) & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y_2))),D)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),B))))))))) # label(fact_656_lemma__interval__lt) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 684 (all D2 all D1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D2)) -> (exists E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),E),D1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),E),D2))))))) # label(fact_657_real__lbound__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 685 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),one_one(real))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),one_one(nat)))) # label(fact_658_natceiling__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 686 (all N_1 hAPP(real,nat,natceiling,hAPP(int,real,number_number_of(real),N_1)) = hAPP(int,nat,number_number_of(nat),N_1)) # label(fact_659_natceiling__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 687 (all X hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(real,nat,natceiling,X)))) # label(fact_661_zero__le__natceiling) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 688 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X)),hAPP(real,nat,natceiling,Y))))) # label(fact_662_natceiling__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 689 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hAPP(real,nat,natceiling,X) = zero_zero(nat))) # label(fact_664_natceiling__neg) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 690 (all X_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X_1)),one_one(nat))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real))))) # label(fact_665_natceiling__le__eq__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 691 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),one_one(real))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),one_one(nat)))) # label(fact_666_natfloor__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 692 (all N_2 all M_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_2),M_1) = one_one(nat) <-> N_2 = one_one(nat) & M_1 = one_one(nat))) # label(fact_667_nat__mult__eq__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 693 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N_1)),one_one(real)))) -> hAPP(real,nat,natceiling,X) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat))))) # label(fact_668_natceiling__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 694 (all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,real_1(nat),N_1)))) # label(fact_669_real__of__nat__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 695 (all N_1 hAPP(real,nat,natceiling,hAPP(nat,real,real_1(nat),N_1)) = N_1) # label(fact_670_natceiling__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 696 (all N_2 all M_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(nat,real,real_1(nat),M_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1)))) # label(fact_671_real__of__nat__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 697 (all N_2 (hAPP(nat,real,real_1(nat),N_2) = zero_zero(real) <-> N_2 = zero_zero(nat))) # label(fact_673_real__of__nat__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 698 (all X hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X)) = hAPP(nat,real,real_1(nat),X)) # label(fact_674_abs__real__of__nat__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 699 (all N_1 hAPP(real,nat,natfloor,hAPP(nat,real,real_1(nat),N_1)) = N_1) # label(fact_675_natfloor__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 700 (all N_2 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,real_1(nat),N_2)),ring_1_Ints(real)))) # label(fact_676_Ints__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 701 (all N_1 hAPP(real,nat,natfloor,hAPP(int,real,number_number_of(real),N_1)) = hAPP(int,nat,number_number_of(nat),N_1)) # label(fact_677_natfloor__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 702 (all N_2 all M_1 (hAPP(nat,real,real_1(nat),N_2) = hAPP(nat,real,real_1(nat),M_1) <-> N_2 = M_1)) # label(fact_678_real__of__nat__inject) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 703 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X))),X)))) # label(fact_679_real__natfloor__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 704 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),X)),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(real,nat,natfloor,A_1))))) # label(fact_680_le__natfloor) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 705 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),one_one(real))),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X))))) # label(fact_681_real__natfloor__gt__diff__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 706 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),A_1)),X)) -> hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,real_1(nat),A_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(real,nat,natfloor,X)),A_1))) # label(fact_682_natfloor__subtract) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 707 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X))),one_one(real))))) # label(fact_683_real__natfloor__add__one__gt) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 708 (all Aa all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Aa),hAPP(real,nat,natfloor,X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),Aa)),X_1))))) # label(fact_684_le__natfloor__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 709 (all N_1 -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_1)),zero_zero(real)))) # label(fact_685_not__real__of__nat__less__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 710 (all N_2 all M_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(nat,real,real_1(nat),M_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),M_1)))) # label(fact_686_real__of__nat__le__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 711 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(real,nat,natfloor,X)),N_1))))) # label(fact_687_less__natfloor) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 712 (all M all N_1 hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),M)),hAPP(nat,real,real_1(nat),N_1))) # label(fact_688_real__of__nat__mult) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 713 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(nat,real,real_1(nat),A_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),A_1))) # label(fact_689_natfloor__add) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 714 (all M all N_1 hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),M)),hAPP(nat,real,real_1(nat),N_1))) # label(fact_690_real__of__nat__add) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 715 (all Z_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,Z_1)),one_one(nat))),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Z_1),hAPP(nat,real,real_1(nat),N_1))))) # label(fact_691_ge__natfloor__plus__one__imp__gt) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 716 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N_1)),one_one(real)))) -> hAPP(real,nat,natfloor,X) = N_1))) # label(fact_692_natfloor__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 717 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(nat,real,real_1(nat),hAPP(real,nat,natceiling,X))))) # label(fact_694_real__natceiling__ge) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 718 (all X hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(real,nat,natfloor,X)))) # label(fact_696_zero__le__natfloor) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 719 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natfloor,X)),hAPP(real,nat,natfloor,Y))))) # label(fact_697_natfloor__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 720 (all N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N_2)),zero_zero(real))) <-> N_2 = zero_zero(nat))) # label(fact_699_real__of__nat__le__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 721 (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,real_1(nat),M)),hAPP(nat,real,real_1(nat),N_1)))) # label(fact_700_real__of__nat__diff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 722 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(nat,real,real_1(nat),A_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X)),A_1)))) # label(fact_701_natceiling__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 723 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hAPP(real,nat,natfloor,X) = zero_zero(nat))) # label(fact_702_natfloor__neg) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 724 (all N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)))) # label(fact_703_real__of__nat__gt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 725 (all N_2 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N_2)),one_one(real))),hAPP(nat,real,real_1(nat),M_1))))) # label(fact_704_nat__less__real__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 726 (all N_2 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),M_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),M_1)),one_one(real)))))) # label(fact_705_nat__le__real__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 727 (all Aa all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X_1)),Aa)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(nat,real,real_1(nat),Aa)))))) # label(fact_706_natceiling__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 728 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),A_1)),X)) -> hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,real_1(nat),A_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(real,nat,natceiling,X)),A_1))) # label(fact_707_natceiling__subtract) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 729 (all X_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),hAPP(real,nat,natfloor,X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X_1)))) # label(fact_708_le__natfloor__eq__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 730 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(nat,real,real_1(nat),A_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),A_1))) # label(fact_709_natceiling__add) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 731 (all B all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(real,nat,natfloor,A_1)),hAPP(real,nat,natfloor,B))),hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B))))))) # label(fact_710_le__mult__natfloor) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 732 (all R (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),R)) -> (exists N (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))),R)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(nat,real,real_1(nat),N))))))) # label(fact_711_reals__Archimedean6) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 733 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (all Y_2 exists N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),X)))))) # label(fact_712_reals__Archimedean3) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 734 (all X all N_1 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,number_number_of(real),N_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),hAPP(int,nat,number_number_of(nat),N_1))))) # label(fact_713_natceiling__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 735 (all Z_2 (hBOOL(hAPP(int,bool,nat_neg,Z_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int))))) # label(fact_716_neg__def) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 736 (all X_1 (-hBOOL(hAPP(int,bool,nat_neg,X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)))) # label(fact_717_not__neg__eq__ge__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 737 (all V (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(int,nat,number_number_of(nat),V) = zero_zero(nat))) # label(fact_718_neg__imp__number__of__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 738 (all V_1 all V_3 (hAPP(int,nat,number_number_of(nat),V_1) = hAPP(int,nat,number_number_of(nat),V_3) <-> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),V_3)),zero_zero(int)))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1))) -> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(int,int,number_number_of(int),V_1) = zero_zero(int)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> V_1 = V_3)))) # label(fact_719_eq__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 739 (all V_2 all K all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_2)),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_2)),K)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_2)),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),K)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_2)),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_2))),K))))) # label(fact_720_nat__number__of__add__left) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 740 (all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,real,real_1(nat),hAPP(int,nat,number_number_of(nat),V)) = zero_zero(real)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,real,real_1(nat),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,real,number_number_of(real),V)))) # label(fact_721_real__of__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 741 (all X_1 all N_2 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_2))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),N_2)),hAPP(real,nat,natfloor,X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),N_2)),X_1)))))) # label(fact_722_le__natfloor__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 742 (all X_1 all N_2 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_2))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X_1)),hAPP(int,nat,number_number_of(nat),N_2))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(int,real,number_number_of(real),N_2))))))) # label(fact_723_natceiling__le__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 743 (all X all N_1 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,number_number_of(real),N_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),hAPP(int,nat,number_number_of(nat),N_1))))) # label(fact_724_natfloor__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 744 (all X exists N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),N)))) # label(fact_725_reals__Archimedean2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 745 (all Y all X all Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_726_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.05 746 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_727_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 747 (all Y all X all Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_728_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 748 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_729_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 749 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)))) # label(fact_730_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 750 (all X_b all X_a all R_1 all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),in_rel(X_a,X_b),R_1),X_1),Y_1)) <-> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y_1)),R_1)))) # label(fact_731_in__rel__def) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 751 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real)))) -> hAPP(real,int,archimedean_ceiling(real),X) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_1),one_one(int))))) # label(fact_732_ceiling__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 752 (all X all Y hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y))) # label(fact_733_real__of__int__add) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 753 (all X all A_1 hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,real_1(int),A_1))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1)) # label(fact_734_ceiling__add) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 754 (all X_1 (hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),X_1)) = X_1 <-> (exists N X_1 = hAPP(int,real,real_1(int),N)))) # label(fact_735_real__of__int__floor__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 755 (all N_1 hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),N_1)) = N_1) # label(fact_736_floor__real__of__int) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 756 (all X_a (archim1727834104eiling(X_a) -> (all R hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(X_a,int,archim2085082626_floor(X_a),R))) = hAPP(X_a,int,archim2085082626_floor(X_a),R)))) # label(fact_737_ceiling__floor) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 757 (all X_1 (hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),X_1)) = X_1 <-> (exists N X_1 = hAPP(int,real,real_1(int),N)))) # label(fact_738_real__of__int__ceiling__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 758 (all N_1 hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N_1)) = N_1) # label(fact_739_ceiling__real__of__int) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 759 (all V hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)) = hAPP(int,real,number_number_of(real),V)) # label(fact_740_real__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 760 (all X_1 all Y_1 (hAPP(int,real,real_1(int),X_1) = hAPP(int,real,real_1(int),Y_1) <-> X_1 = Y_1)) # label(fact_741_real__of__int__inject) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 761 (all R hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),R),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R))))) # label(fact_742_real__of__int__ceiling__ge) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 762 (all X all Y hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y))) # label(fact_744_real__of__int__mult) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 763 (all X_1 all Aa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),X_1)),Aa)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(int,real,real_1(int),Aa))))) # label(fact_745_ceiling__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 764 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(int,real,real_1(int),A_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1)))) # label(fact_746_ceiling__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 765 (all X all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(int,real,real_1(int),A_1))))) # label(fact_747_ceiling__le__real) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 766 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),X_1)),hAPP(int,real,real_1(int),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),Y_1)))) # label(fact_748_real__of__int__le__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 767 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),X_1)),hAPP(int,real,real_1(int),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)))) # label(fact_749_real__of__int__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 768 (all Aa all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),hAPP(real,int,archimedean_ceiling(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),Aa)),X_1)))) # label(fact_750_less__ceiling__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 769 (all X_1 (hAPP(int,real,real_1(int),X_1) = zero_zero(real) <-> X_1 = zero_zero(int))) # label(fact_751_real__of__int__zero__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 770 (all X all A_1 hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(int,real,real_1(int),A_1))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1)) # label(fact_753_ceiling__subtract) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 771 (all X all Y hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y))) # label(fact_754_real__of__int__diff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 772 (all X_a (archim1727834104eiling(X_a) -> (all R hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(X_a,int,archimedean_ceiling(X_a),R))) = hAPP(X_a,int,archimedean_ceiling(X_a),R)))) # label(fact_755_floor__ceiling) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 773 (all R hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R))),R))) # label(fact_756_real__of__int__floor__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 774 (all X hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X)) = hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X))) # label(fact_757_real__of__int__abs) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 775 (all X_1 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(int,real,real_1(int),X_1)),ring_1_Ints(real)))) # label(fact_758_Ints__real__of__int) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 776 (all R hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R),one_one(real))))) # label(fact_759_real__of__int__ceiling__le__add__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 777 (all R hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R))),one_one(real))),R))) # label(fact_760_real__of__int__ceiling__diff__one__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 778 (all X_1 all Aa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),X_1)),Aa)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(int,real,real_1(int),Aa))))) # label(fact_761_floor__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 779 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),A_1)),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),hAPP(real,int,archim2085082626_floor(real),X))))) # label(fact_762_le__floor) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 780 (all Aa all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Aa),hAPP(real,int,archim2085082626_floor(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),Aa)),X_1)))) # label(fact_763_le__floor__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 781 (all A_1 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),hAPP(real,int,archim2085082626_floor(real),X))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),A_1)),X)))) # label(fact_764_real__le__floor) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 782 (all X all A_1 hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,real_1(int),A_1))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),X)),A_1)) # label(fact_765_floor__add) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 783 (all X all A_1 hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(int,real,real_1(int),A_1))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),X)),A_1)) # label(fact_766_floor__subtract) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 784 (all N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,real_1(int),N_2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_2)))) # label(fact_767_real__of__int__gt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 785 (all N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_2)),zero_zero(real))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),N_2),zero_zero(int))))) # label(fact_768_real__of__int__lt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 786 (all N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,real_1(int),N_2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_2)))) # label(fact_769_real__of__int__ge__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 787 (all N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_2)),zero_zero(real))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N_2),zero_zero(int))))) # label(fact_770_real__of__int__le__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 788 (all N_2 all M_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),N_2)),hAPP(int,real,real_1(int),M_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),N_2)),M_1)))) # label(fact_771_number__of__less__real__of__int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 789 (all M_1 all N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),M_1)),hAPP(int,real,number_number_of(real),N_2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M_1),hAPP(int,int,number_number_of(int),N_2))))) # label(fact_772_number__of__less__real__of__int__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 790 (all N_2 all M_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),N_2)),hAPP(int,real,real_1(int),M_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),N_2)),M_1)))) # label(fact_773_number__of__le__real__of__int__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 791 (all M_1 all N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),M_1)),hAPP(int,real,number_number_of(real),N_2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M_1),hAPP(int,int,number_number_of(int),N_2))))) # label(fact_774_number__of__le__real__of__int__iff2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 792 (all N_2 all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),N_2),M_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_2)),one_one(real))),hAPP(int,real,real_1(int),M_1))))) # label(fact_775_int__less__real__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 793 (all N_2 all M_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N_2),M_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_2)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),M_1)),one_one(real)))))) # label(fact_776_int__le__real__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 794 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),X)),one_one(real)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N_1),X)))) # label(fact_777_lemma__floor2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 795 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),N_1)),one_one(real))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(int,real,real_1(int),N_1))) -> hAPP(real,int,archimedean_ceiling(real),X) = N_1))) # label(fact_778_ceiling__eq3) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 796 (all X_1 all Aa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),X_1)),Aa)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),Aa)),one_one(real)))))) # label(fact_779_ceiling__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 797 (all Aa all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Aa),hAPP(real,int,archimedean_ceiling(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),Aa)),one_one(real))),X_1)))) # label(fact_780_le__ceiling__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 798 (all R hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),R),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R))),one_one(real))))) # label(fact_781_real__of__int__floor__add__one__ge) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 799 (all R hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R))),one_one(real))))) # label(fact_782_real__of__int__floor__add__one__gt) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 800 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real)))) -> hAPP(real,int,archim2085082626_floor(real),X) = N_1))) # label(fact_783_floor__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 801 (all R hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R),one_one(real))),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R))))) # label(fact_784_real__of__int__floor__ge__diff__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 802 (all R hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R),one_one(real))),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R))))) # label(fact_785_real__of__int__floor__gt__diff__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 803 (all N_1 all M all R (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),M)),R)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M),N_1))))) # label(fact_786_lemma__floor) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 804 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real)))) -> hAPP(real,int,archimedean_ceiling(real),X) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_1),one_one(int))))) # label(fact_787_ceiling__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 805 (all N_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real)))) -> hAPP(real,int,archim2085082626_floor(real),X) = N_1))) # label(fact_788_floor__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 806 (all Aa all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Aa),hAPP(real,int,archim2085082626_floor(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),Aa)),one_one(real))),X_1)))) # label(fact_789_less__floor__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 807 (all X_1 all Aa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),X_1)),Aa)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),Aa)),one_one(real)))))) # label(fact_790_floor__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 808 (all R (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),R)) -> (exists N (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N)),R)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int))))))))) # label(fact_791_reals__Archimedean__6b__int) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 809 (all R (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),zero_zero(real))) -> (exists N (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N)),R)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int))))))))) # label(fact_792_reals__Archimedean__6c__int) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 810 (all R exists N (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N)),R)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int))))))) # label(fact_793_real__lb__ub__int) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 811 (all X_a (number_ring(X_a) -> (all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,X_a,number_number_of(X_a),V)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = zero_zero(X_a)))))) # label(fact_794_of__nat__number__of__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 812 (all N_1 hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,real_1(nat),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),N_1)) # label(fact_795_ceiling__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 813 (all X_a (number_semiring(X_a) -> (all N_1 hAPP(int,X_a,number_number_of(X_a),hAPP(nat,int,semiring_1_of_nat(int),N_1)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))) # label(fact_796_number__of__int) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 814 (all K -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K)),zero_zero(int)))) # label(fact_797_int__less__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 815 (all N_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N_1)))) # label(fact_798_zero__zle__int) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 816 (all P_1 ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hBOOL(hAPP(int,bool,P_1,X_2)))) <-> (all X_2 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_2)))))) # label(fact_799_transfer__int__nat__quantifiers_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 817 (all P_1 ((exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) & hBOOL(hAPP(int,bool,P_1,X_2)))) <-> (exists X_2 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_2)))))) # label(fact_800_transfer__int__nat__quantifiers_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 818 (all Z_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Z_1)))) # label(fact_801_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 819 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)))) # label(fact_802_Nat__Transfer_Otransfer__int__nat__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 820 (all M_1 all N_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)))) # label(fact_803_zless__int) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 821 (all X_a (linordered_semidom(X_a) -> (all N_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))))) # label(fact_804_of__nat__0__le__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 822 (all X_a (linordered_semidom(X_a) -> (all M hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)))))) # label(fact_805_zero__le__imp__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 823 (all X_a (linordered_semidom(X_a) -> (all M -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),zero_zero(X_a)))))) # label(fact_806_of__nat__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 824 (all X_a (semiring_1(X_a) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),zero_zero(nat)) = zero_zero(X_a))) # label(fact_807_of__nat__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 825 (all X_a (linordered_semidom(X_a) -> (all M all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)))))) # label(fact_808_of__nat__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 826 (all X_a (linordered_semidom(X_a) -> (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))))) # label(fact_809_less__imp__of__nat__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 827 (all X_a (linordered_semidom(X_a) -> (all M_1 all N_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)))))) # label(fact_810_of__nat__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 828 (all X_a (linordered_semidom(X_a) -> (all M_1 all N_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2)))))) # label(fact_811_of__nat__le__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 829 (all X_a (semiring_1(X_a) -> (all M all N_1 hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))) # label(fact_812_of__nat__add) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 830 (all X_a (semiring_1(X_a) -> (all M all N_1 hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))) # label(fact_813_of__nat__mult) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 831 (all X_a (semiring_1(X_a) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),one_one(nat)) = one_one(X_a))) # label(fact_814_of__nat__1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 832 (all X_a (archim1727834104eiling(X_a) -> (all N_1 hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),N_1)))) # label(fact_815_floor__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 833 (all X_a (semiring_char_0(X_a) -> (all M_1 all N_2 (hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2) <-> M_1 = N_2)))) # label(fact_816_of__nat__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 834 (all M hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),M)) = hAPP(nat,int,semiring_1_of_nat(int),M)) # label(fact_817_abs__int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 835 (all X_a (linordered_idom(X_a) -> (all N_1 hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))) # label(fact_818_abs__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 836 (all N_2 (hAPP(nat,int,semiring_1_of_nat(int),N_2) = zero_zero(int) <-> N_2 = zero_zero(nat))) # label(fact_819_int__eq__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 837 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Y))) # label(fact_824_Nat__Transfer_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 838 (all M all N_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))) # label(fact_825_zadd__int) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 839 (all M all N_1 all Z_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)),Z_1)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))),Z_1)) # label(fact_826_zadd__int__left) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 840 (all W all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),Z)) <-> (exists N Z = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),hAPP(nat,int,semiring_1_of_nat(int),N))))) # label(fact_827_zle__iff__zadd) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 841 (all M all N_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))) # label(fact_828_zmult__int) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 842 (all M all N_1 hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1))) # label(fact_829_int__mult) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 843 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y))) # label(fact_830_Nat__Transfer_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 844 (all M_1 all N_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2)))) # label(fact_831_zle__int) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 845 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_1)))) # label(fact_832_Nat__Transfer_Otransfer__int__nat__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 846 (all X_a (ring_1(X_a) -> (all N_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)),ring_1_Ints(X_a)))))) # label(fact_833_Ints__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 847 (all N_1 -hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),N_1)))) # label(fact_834_not__neg__int) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 848 (all X_a (archim1727834104eiling(X_a) -> (all N_1 hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),N_1)))) # label(fact_835_ceiling__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 849 (all N_1 hAPP(int,real,real_1(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)) = hAPP(nat,real,real_1(nat),N_1)) # label(fact_837_real__of__int__of__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 850 (all N_1 hAPP(real,int,archim2085082626_floor(real),hAPP(nat,real,real_1(nat),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),N_1)) # label(fact_839_floor__real__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 851 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X),Y))) # label(fact_840_Nat__Transfer_Otransfer__int__nat__functions_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 852 (all X_a (ring_1(X_a) -> (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))))) # label(fact_841_of__nat__diff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 853 (all N_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),N_2)),zero_zero(int))) <-> N_2 = zero_zero(nat))) # label(fact_842_int__le__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 854 (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)))) # label(fact_843_zdiff__int) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 855 (all X_a (linordered_semidom(X_a) -> (all N_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)))))) # label(fact_844_of__nat__0__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 856 (all N_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)))) # label(fact_845_zero__less__int__conv) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 857 (all K all I all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K)),I)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K)),J)))))) # label(fact_846_zmult__zless__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 858 (all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V)) = zero_zero(int)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,int,number_number_of(int),V)))) # label(fact_847_int__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 859 (all X_a (number_ring(X_a) -> (all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = zero_zero(X_a)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,X_a,number_number_of(X_a),V)))))) # label(fact_848_of__nat__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 860 (all P_1 all X_1 all Y_1 (hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_1)))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Y_1),X_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)) -> hBOOL(hAPP(int,bool,P_1,zero_zero(int)))))) # label(fact_849_zdiff__int__split) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 861 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> (exists N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) & K = hAPP(nat,int,semiring_1_of_nat(int),N))))) # label(fact_850_zero__less__imp__eq__int) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 862 (all X_a (archim1804426504_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (exists N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)),X)))))))) # label(fact_851_ex__less__of__nat__mult) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 863 (all M_1 all N_2 (hAPP(nat,int,semiring_1_of_nat(int),M_1) = hAPP(nat,int,semiring_1_of_nat(int),N_2) <-> M_1 = N_2)) # label(fact_852_int__int__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 864 (all X_1 all Y_1 all P_1 ((hBOOL(P_1) -> hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),P_1),X_1),Y_1))) & (-hBOOL(P_1) -> hAPP(nat,int,semiring_1_of_nat(int),Y_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),P_1),X_1),Y_1))))) # label(fact_853_int__if__cong) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 865 (all X_1 all Y_1 (hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),Y_1) <-> X_1 = Y_1)) # label(fact_854_Nat__Transfer_Otransfer__int__nat__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 866 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K)) -> (exists N K = hAPP(nat,int,semiring_1_of_nat(int),N)))) # label(fact_855_zero__le__imp__eq__int) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 867 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> -(all M_2 Z_1 != hAPP(nat,int,semiring_1_of_nat(int),M_2)))) # label(fact_856_nonneg__eq__int) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 868 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K)) -> -(all N K != hAPP(nat,int,semiring_1_of_nat(int),N)))) # label(fact_857_nonneg__int__cases) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 869 (all Z_1 -(all M_2 all N Z_1 != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M_2)),hAPP(nat,int,semiring_1_of_nat(int),N)))) # label(fact_858_int__diff__cases) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 870 (all X_a (archim1804426504_field(X_a) -> (all X exists N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))))) # label(fact_859_ex__less__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 871 (all X_a (archim1804426504_field(X_a) -> (all X exists N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))))) # label(fact_860_ex__le__of__nat) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 872 (all V_2 all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_2)) = zero_zero(nat)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_2)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_2))))) # label(fact_861_mult__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 873 (all V_2 all K all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V_2)),K)) = zero_zero(nat)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V_2)),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_2))),K)))) # label(fact_862_nat__number__of__mult__left) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 874 (all X_a (number_ring(X_a) -> hAPP(int,X_a,number_number_of(X_a),pls) = zero_zero(X_a))) # label(fact_863_number__of__Pls) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 875 (all X_a (number_semiring(X_a) -> hAPP(int,X_a,number_number_of(X_a),pls) = zero_zero(X_a))) # label(fact_864_semiring__numeral__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 876 (all X_a (number_ring(X_a) -> zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),pls))) # label(fact_865_semiring__norm_I112_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 877 (all X_a (number_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),pls)),A_1) = ti(X_a,A_1)))) # label(fact_866_add__numeral__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 878 (all X_a (number_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),pls)) = ti(X_a,A_1)))) # label(fact_867_add__numeral__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 879 (all K hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),pls) = K) # label(fact_868_diff__bin__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 880 (all W_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),W_1) = pls) # label(fact_869_mult__Pls) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 881 (all K hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),K) = K) # label(fact_871_add__Pls) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 882 (all K hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),pls) = K) # label(fact_872_add__Pls__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 883 (all V_1 (zero_zero(nat) = hAPP(int,nat,number_number_of(nat),V_1) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),pls)))) # label(fact_880_eq__0__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 884 (all V_1 (hAPP(int,nat,number_number_of(nat),V_1) = zero_zero(nat) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),pls)))) # label(fact_881_eq__number__of__0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 885 (all V_1 all V_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_3))) <-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),V_3)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_3))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),V_3)))) # label(fact_882_less__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 886 (all V_1 all V_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_3))) <-> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),V_3)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),pls))))) # label(fact_884_le__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 887 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Y_1)))))) # label(fact_885_less__special_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 888 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),pls)))))) # label(fact_886_less__special_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 889 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),Y_1)))))) # label(fact_887_le__special_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 890 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),pls)))))) # label(fact_888_le__special_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 891 (all X_a (number_semiring(X_a) -> (all V_2 all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V_2)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),V_2)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_2))))))) # label(fact_889_semiring__mult__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 892 (all X_a (number_semiring(X_a) -> (all V_2 all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V_2)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),V_2)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_2))))))) # label(fact_890_semiring__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 893 (all V_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),V_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_1)))) # label(fact_891_less__0__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 894 (all V_2 all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_2)) = hAPP(int,nat,number_number_of(nat),V_2)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_2)) = hAPP(int,nat,number_number_of(nat),V)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_2)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_2)))))) # label(fact_892_add__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 895 (all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V)) = one_one(nat)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))))) # label(fact_893_nat__1__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 896 (all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)) = one_one(nat)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))))) # label(fact_894_nat__number__of__add__1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 897 (all K hAPP(int,int,succ,K) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),one_one(int))) # label(fact_895_succ__def) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 898 (all X_a (number_ring(X_a) -> (all K hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,K)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),K))))) # label(fact_896_number__of__succ) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 899 (all X_a (number_semiring(X_a) -> (all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),V)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,V)))))) # label(fact_897_semiring__1__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 900 (all X_a (number_semiring(X_a) -> (all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),one_one(X_a)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,V)))))) # label(fact_898_semiring__number__of__add__1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 901 (all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)) = zero_zero(nat)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,pred,V))))) # label(fact_899_nat__number__of__diff__1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 902 (all N_1 all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N_1)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))),N_1)))) # label(fact_900_Suc__nat__number__of__add) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 903 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,N_1)))) # label(fact_901_lessI) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 904 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N_1))))) # label(fact_902_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 905 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1)))) # label(fact_903_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 906 (all X hAPP(int,int,succ,hAPP(int,int,pred,X)) = X) # label(fact_904_succ__pred) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 907 (all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2))) <-> M_1 = zero_zero(nat) | (exists J_1 (M_1 = hAPP(nat,nat,suc,J_1) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),N_2)))))) # label(fact_905_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 908 (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,zero_zero(nat)))) <-> N_2 = zero_zero(nat))) # label(fact_906_less__Suc0) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 909 (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)) <-> (exists M_2 N_2 = hAPP(nat,nat,suc,M_2)))) # label(fact_907_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 910 (all M_1 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2) = hAPP(nat,nat,suc,zero_zero(nat)) <-> M_1 = hAPP(nat,nat,suc,zero_zero(nat)) & N_2 = zero_zero(nat) | M_1 = zero_zero(nat) & N_2 = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_908_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 911 (all M_1 all N_2 (hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),N_2) <-> M_1 = hAPP(nat,nat,suc,zero_zero(nat)) & N_2 = zero_zero(nat) | M_1 = zero_zero(nat) & N_2 = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_909_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 912 (all M_1 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2) = hAPP(nat,nat,suc,zero_zero(nat)) <-> M_1 = hAPP(nat,nat,suc,zero_zero(nat)) & N_2 = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_910_mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 913 (all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)) <-> (exists K_2 N_2 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2))))) # label(fact_911_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 914 (all I all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),I))))) # label(fact_912_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 915 (all I all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),M))))) # label(fact_913_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 916 (all N_2 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_2)),M_1)))) # label(fact_915_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 917 (all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2)))) # label(fact_916_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 918 (all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N_2)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)))) # label(fact_917_Suc__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 919 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N_1))))) # label(fact_918_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 920 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N_1)))) # label(fact_919_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 921 (all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1))) <-> N_2 = M_1))) # label(fact_920_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 922 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)))) # label(fact_921_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 923 (all K_1 all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)))) # label(fact_922_Suc__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 924 (all M all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),hAPP(nat,nat,suc,M)))) # label(fact_923_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 925 (all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,M)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))) # label(fact_924_mult__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 926 (all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))) # label(fact_925_mult__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 927 (all K_1 all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2)))) # label(fact_926_Suc__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 928 (all N_1 hAPP(nat,nat,suc,N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N_1)) # label(fact_927_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 929 (all N_1 hAPP(nat,nat,suc,N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat))) # label(fact_928_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 930 (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N_1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)))) # label(fact_929_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 931 (all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N_1)),one_one(nat)) = N_1) # label(fact_930_diff__Suc__1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 932 (all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N_1)) # label(fact_931_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 933 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)))) # label(fact_932_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 934 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N_1))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> M = hAPP(nat,nat,suc,N_1)))) # label(fact_933_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 935 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N_1))))) # label(fact_934_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 936 (all N_2 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_2)),hAPP(nat,nat,suc,M_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),M_1)))) # label(fact_935_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 937 (all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,suc,N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2)) | M_1 = hAPP(nat,nat,suc,N_2))) # label(fact_936_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 938 (all M_1 all N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_2)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_2)),M_1)))) # label(fact_937_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 939 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),N_1))) # label(fact_938_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 940 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_939_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 941 (all Nat_3 zero_zero(nat) != hAPP(nat,nat,suc,Nat_3)) # label(fact_940_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 942 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_941_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 943 (all Nat_2 hAPP(nat,nat,suc,Nat_2) != zero_zero(nat)) # label(fact_942_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 944 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_943_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 945 (all M hAPP(nat,nat,suc,M) != zero_zero(nat)) # label(fact_944_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 946 (all M_1 all N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1))))) # label(fact_945_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 947 (all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)) | M_1 = N_2)) # label(fact_946_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 948 (all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_2)))) # label(fact_947_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 949 (all N_2 all M_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_2),hAPP(nat,nat,suc,M_1))) <-> N_2 = M_1))) # label(fact_948_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.06 950 (all N_1 all M (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M))) -> M = N_1))) # label(fact_949_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 951 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N_1))))) # label(fact_950_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 952 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> (hAPP(nat,nat,suc,M) != N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N_1))))) # label(fact_951_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 953 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I)),K))))) # label(fact_952_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 954 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N_1))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> M = N_1))) # label(fact_953_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 955 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)))) # label(fact_954_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 956 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)))) # label(fact_955_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 957 (all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))) # label(fact_956_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 958 (all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N_1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))) # label(fact_957_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 959 (all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N_1))) # label(fact_958_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 960 (all M all N_1 all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N_1)),hAPP(nat,nat,suc,K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),K)) # label(fact_959_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 961 (all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) # label(fact_960_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 962 (all N_1 N_1 != hAPP(nat,nat,suc,N_1)) # label(fact_961_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 963 (all N_1 hAPP(nat,nat,suc,N_1) != N_1) # label(fact_962_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 964 (all Nat_1 all Nat (hAPP(nat,nat,suc,Nat_1) = hAPP(nat,nat,suc,Nat) <-> Nat_1 = Nat)) # label(fact_963_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 965 (all X all Y (hAPP(nat,nat,suc,X) = hAPP(nat,nat,suc,Y) -> X = Y)) # label(fact_964_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 966 (all K_1 all M_1 all N_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K_1)),N_2) <-> M_1 = N_2)) # label(fact_965_Suc__mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 967 (all K hAPP(int,int,pred,K) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),one_one(int))) # label(fact_966_pred__def) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 968 (all K_1 all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_1),L)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,pred,K_1)),L)))) # label(fact_967_le__iff__pred__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 969 (all M all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(int,nat,number_number_of(nat),V)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,pred,V))))) # label(fact_968_Suc__diff__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 970 (all X_a (semiring_1(X_a) -> (all M hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,M)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M))))) # label(fact_969_of__nat__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 971 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)))))) # label(fact_970_one__less__mult) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 972 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),M)))))) # label(fact_971_n__less__n__mult__m) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 973 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)))))) # label(fact_972_n__less__m__mult__n) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 974 (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1) = M -> N_1 = hAPP(nat,nat,suc,zero_zero(nat))))) # label(fact_973_mn__eq__m__one) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 975 (all M all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1) = K -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),K))))))) # label(fact_974_prod__mn__less__k) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 976 (all M all K (M != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),K))))) # label(fact_975_one__less__k) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 977 (all M all K (M != hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K) -> (M != hAPP(nat,nat,suc,zero_zero(nat)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M))))) # label(fact_976_one__less__m) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 978 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))) = N_1)) # label(fact_977_Suc__pred) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 979 (all I all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,I))),N_1)))) # label(fact_978_diff__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 980 (all M_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_2)))) # label(fact_979_one__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 981 (all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_1))))) # label(fact_980_real__of__nat__Suc__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 982 (all M all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,suc,J)))) # label(fact_983_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 983 (all M all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K))),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,J)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)))) # label(fact_984_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 984 (all W all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z)) <-> (exists N Z = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N)))))) # label(fact_985_zless__iff__Suc__zadd) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 985 (all M hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M))) # label(fact_986_int__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 986 (all N_1 hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_1)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N_1)),one_one(real))) # label(fact_987_real__of__nat__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 987 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> N_1 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat))))) # label(fact_988_Suc__pred_H) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 988 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat))) = N_1)) # label(fact_989_Suc__diff__1) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 989 (all N_1 all M ((M = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1) = N_1) & (M != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N_1))))) # label(fact_990_add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 1.65/2.07 990 (all V (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),V))) -> hAPP(int,nat,number_number_of(nat),V) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))))) # label(fact_991_expand__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.18 991 (all V_1 (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) <-> hAPP(int,nat,number_number_of(nat),V_1) = zero_zero(nat))) # label(fact_992_neg__number__of__pred__iff__0) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.18 992 (all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V)) = one_one(nat)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))))) # label(fact_993_Suc__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.18 993 (all R (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),R)) -> (exists N (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N)),R)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N)))))))) # label(fact_994_reals__Archimedean6a) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.18 994 (all T_2 all T_1 (preorder(T_1) -> preorder(fun(T_2,T_1)))) # label(arity_fun___Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.18 995 (all T_2 all T_1 (order(T_1) -> order(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oorder) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.18 996 (all T_2 all T_1 (ord(T_1) -> ord(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oord) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.18 997 (all T_2 all T_1 (minus(T_1) -> minus(fun(T_2,T_1)))) # label(arity_fun___Groups_Ominus) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.18 998 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.18 999 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y) = ti(X_a,X)) # label(help_If_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.18 1000 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y) = ti(X_a,Y)) # label(help_If_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.18 1001 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_If_3_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.96/2.18
% 1.96/2.18 ============================== end of process non-clausal formulas ===
% 1.96/2.18
% 1.96/2.18 ============================== PROCESS INITIAL CLAUSES ===============
% 1.96/2.18
% 1.96/2.18 ============================== PREDICATE ELIMINATION =================
% 1.96/2.18 1002 archim1727834104eiling(real) # label(arity_RealDef_Oreal___Archimedean__Field_Ofloor__ceiling) # label(axiom). [assumption].
% 1.96/2.18 1003 -archim1727834104eiling(A) | ti(fun(A,int),archimedean_ceiling(A)) = archimedean_ceiling(A) # label(tsy_c_Archimedean__Field_Oceiling_res) # label(axiom). [clausify(1)].
% 1.96/2.18 1004 -archim1727834104eiling(A) | archim2085082626_floor(A) = ti(fun(A,int),archim2085082626_floor(A)) # label(tsy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_res) # label(axiom). [clausify(2)].
% 1.96/2.18 1005 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),B)),one_one(A))),C)) # label(fact_239_number__of__le__ceiling) # label(axiom). [clausify(271)].
% 1.96/2.18 1006 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),B)),one_one(A))),C)) # label(fact_239_number__of__le__ceiling) # label(axiom). [clausify(271)].
% 1.96/2.18 1007 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) # label(fact_240_ceiling__less__number__of) # label(axiom). [clausify(272)].
% 1.96/2.18 1008 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) # label(fact_240_ceiling__less__number__of) # label(axiom). [clausify(272)].
% 1.96/2.18 1009 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,archimedean_ceiling(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_241_zero__less__ceiling) # label(axiom). [clausify(273)].
% 1.96/2.18 1010 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,archimedean_ceiling(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_241_zero__less__ceiling) # label(axiom). [clausify(273)].
% 1.96/2.18 1011 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),zero_zero(A)) = zero_zero(int) # label(fact_243_ceiling__zero) # label(axiom). [clausify(275)].
% 1.96/2.18 1012 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),zero_zero(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_244_ceiling__le__zero) # label(axiom). [clausify(276)].
% 1.96/2.18 1013 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),zero_zero(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_244_ceiling__le__zero) # label(axiom). [clausify(276)].
% 1.96/2.18 1014 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_245_ceiling__less__one) # label(axiom). [clausify(277)].
% 1.96/2.18 1015 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_245_ceiling__less__one) # label(axiom). [clausify(277)].
% 1.96/2.18 1016 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_246_one__le__ceiling) # label(axiom). [clausify(278)].
% 1.96/2.18 1017 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_246_one__le__ceiling) # label(axiom). [clausify(278)].
% 1.96/2.18 1018 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(A,int,archimedean_ceiling(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_276_ceiling__less__cancel) # label(axiom). [clausify(307)].
% 1.96/2.18 1019 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_277_ceiling__mono) # label(axiom). [clausify(308)].
% 1.96/2.18 1020 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),one_one(A)) = one_one(int) # label(fact_278_ceiling__one) # label(axiom). [clausify(309)].
% 1.96/2.18 1021 -archim1727834104eiling(A) | hAPP(int,int,number_number_of(int),B) = hAPP(A,int,archimedean_ceiling(A),hAPP(int,A,number_number_of(A),B)) # label(fact_279_ceiling__number__of) # label(axiom). [clausify(310)].
% 1.96/2.18 1022 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) # label(fact_339_one__less__ceiling) # label(axiom). [clausify(369)].
% 1.96/2.18 1023 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) # label(fact_339_one__less__ceiling) # label(axiom). [clausify(369)].
% 1.96/2.18 1024 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),one_one(A))) # label(fact_340_ceiling__le__one) # label(axiom). [clausify(370)].
% 1.96/2.18 1025 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),one_one(A))) # label(fact_340_ceiling__le__one) # label(axiom). [clausify(370)].
% 1.96/2.18 1026 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),C)) # label(fact_341_number__of__less__ceiling) # label(axiom). [clausify(371)].
% 1.96/2.18 1027 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),C)) # label(fact_341_number__of__less__ceiling) # label(axiom). [clausify(371)].
% 1.96/2.18 1028 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_342_ceiling__le__number__of) # label(axiom). [clausify(372)].
% 1.96/2.18 1029 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_342_ceiling__le__number__of) # label(axiom). [clausify(372)].
% 1.96/2.18 1030 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int)) = hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))) # label(fact_343_ceiling__add__one) # label(axiom). [clausify(373)].
% 1.96/2.18 1031 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C)) = hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_344_ceiling__add__number__of) # label(axiom). [clausify(374)].
% 1.96/2.18 1032 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int)) = hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),one_one(A))) # label(fact_345_ceiling__diff__one) # label(axiom). [clausify(375)].
% 1.96/2.18 1033 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C)) = hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_346_ceiling__diff__number__of) # label(axiom). [clausify(376)].
% 1.96/2.18 1034 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) # label(fact_416_floor__le__number__of) # label(axiom). [clausify(444)].
% 1.96/2.18 1035 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) # label(fact_416_floor__le__number__of) # label(axiom). [clausify(444)].
% 1.96/2.18 1036 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),one_one(A))),C)) # label(fact_417_number__of__less__floor) # label(axiom). [clausify(445)].
% 1.96/2.18 1037 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),one_one(A))),C)) # label(fact_417_number__of__less__floor) # label(axiom). [clausify(445)].
% 1.96/2.18 1038 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),zero_zero(A)) = zero_zero(int) # label(fact_418_floor__zero) # label(axiom). [clausify(446)].
% 1.96/2.18 1039 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(A,int,archim2085082626_floor(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_419_floor__less__cancel) # label(axiom). [clausify(447)].
% 1.96/2.18 1040 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(A,int,archim2085082626_floor(A),C))) # label(fact_420_floor__mono) # label(axiom). [clausify(448)].
% 1.96/2.18 1041 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),one_one(A)) = one_one(int) # label(fact_421_floor__one) # label(axiom). [clausify(449)].
% 1.96/2.18 1042 -archim1727834104eiling(A) | hAPP(int,int,number_number_of(int),B) = hAPP(A,int,archim2085082626_floor(A),hAPP(int,A,number_number_of(A),B)) # label(fact_422_floor__number__of) # label(axiom). [clausify(450)].
% 1.96/2.18 1043 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_423_floor__less__zero) # label(axiom). [clausify(451)].
% 1.96/2.18 1044 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_423_floor__less__zero) # label(axiom). [clausify(451)].
% 1.96/2.18 1045 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_424_zero__le__floor) # label(axiom). [clausify(452)].
% 1.96/2.18 1046 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_424_zero__le__floor) # label(axiom). [clausify(452)].
% 1.96/2.18 1047 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) # label(fact_425_zero__less__floor) # label(axiom). [clausify(453)].
% 1.96/2.18 1048 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) # label(fact_425_zero__less__floor) # label(axiom). [clausify(453)].
% 1.96/2.18 1049 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) # label(fact_426_floor__le__zero) # label(axiom). [clausify(454)].
% 1.96/2.18 1050 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) # label(fact_426_floor__le__zero) # label(axiom). [clausify(454)].
% 1.96/2.18 1051 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) # label(fact_427_floor__less__one) # label(axiom). [clausify(455)].
% 1.96/2.18 1052 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) # label(fact_427_floor__less__one) # label(axiom). [clausify(455)].
% 1.96/2.18 1053 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(A,int,archim2085082626_floor(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) # label(fact_428_one__le__floor) # label(axiom). [clausify(456)].
% 1.96/2.18 1054 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(A,int,archim2085082626_floor(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) # label(fact_428_one__le__floor) # label(axiom). [clausify(456)].
% 1.96/2.18 1055 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_429_floor__less__number__of) # label(axiom). [clausify(457)].
% 1.96/2.18 1056 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_429_floor__less__number__of) # label(axiom). [clausify(457)].
% 1.96/2.18 1057 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),C)) # label(fact_430_number__of__le__floor) # label(axiom). [clausify(458)].
% 1.96/2.18 1058 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),C)) # label(fact_430_number__of__le__floor) # label(axiom). [clausify(458)].
% 1.96/2.18 1059 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int)) = hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))) # label(fact_431_floor__add__one) # label(axiom). [clausify(459)].
% 1.96/2.18 1060 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C)) = hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_432_floor__add__number__of) # label(axiom). [clausify(460)].
% 1.96/2.18 1061 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int)) = hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),one_one(A))) # label(fact_433_floor__diff__one) # label(axiom). [clausify(461)].
% 1.96/2.18 1062 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C)) = hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_434_floor__diff__number__of) # label(axiom). [clausify(462)].
% 1.96/2.18 1063 -archim1727834104eiling(A) | hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(A,int,archim2085082626_floor(A),B))) = hAPP(A,int,archim2085082626_floor(A),B) # label(fact_737_ceiling__floor) # label(axiom). [clausify(756)].
% 1.96/2.18 1064 -archim1727834104eiling(A) | hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(A,int,archimedean_ceiling(A),B))) = hAPP(A,int,archimedean_ceiling(A),B) # label(fact_755_floor__ceiling) # label(axiom). [clausify(772)].
% 1.96/2.18 1065 -archim1727834104eiling(A) | hAPP(nat,int,semiring_1_of_nat(int),B) = hAPP(A,int,archim2085082626_floor(A),hAPP(nat,A,semiring_1_of_nat(A),B)) # label(fact_815_floor__of__nat) # label(axiom). [clausify(832)].
% 1.96/2.18 1066 -archim1727834104eiling(A) | hAPP(nat,int,semiring_1_of_nat(int),B) = hAPP(A,int,archimedean_ceiling(A),hAPP(nat,A,semiring_1_of_nat(A),B)) # label(fact_835_ceiling__of__nat) # label(axiom). [clausify(848)].
% 1.96/2.18 Derived: ti(fun(real,int),archimedean_ceiling(real)) = archimedean_ceiling(real). [resolve(1002,a,1003,a)].
% 1.96/2.18 Derived: archim2085082626_floor(real) = ti(fun(real,int),archim2085082626_floor(real)). [resolve(1002,a,1004,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archimedean_ceiling(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),A)),one_one(real))),B)). [resolve(1002,a,1005,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archimedean_ceiling(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),A)),one_one(real))),B)). [resolve(1002,a,1006,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))). [resolve(1002,a,1007,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))). [resolve(1002,a,1008,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(real,int,archimedean_ceiling(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(1002,a,1009,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(real,int,archimedean_ceiling(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(1002,a,1010,a)].
% 1.96/2.18 Derived: hAPP(real,int,archimedean_ceiling(real),zero_zero(real)) = zero_zero(int). [resolve(1002,a,1011,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),zero_zero(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(1002,a,1012,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),zero_zero(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(1002,a,1013,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(1002,a,1014,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(1002,a,1015,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(1002,a,1016,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(1002,a,1017,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(real,int,archimedean_ceiling(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(1002,a,1018,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(real,int,archimedean_ceiling(real),B))). [resolve(1002,a,1019,a)].
% 1.96/2.18 Derived: hAPP(real,int,archimedean_ceiling(real),one_one(real)) = one_one(int). [resolve(1002,a,1020,a)].
% 1.96/2.18 Derived: hAPP(int,int,number_number_of(int),A) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),A)). [resolve(1002,a,1021,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)). [resolve(1002,a,1022,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)). [resolve(1002,a,1023,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),one_one(real))). [resolve(1002,a,1024,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),one_one(real))). [resolve(1002,a,1025,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archimedean_ceiling(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),B)). [resolve(1002,a,1026,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archimedean_ceiling(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),B)). [resolve(1002,a,1027,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(1002,a,1028,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(1002,a,1029,a)].
% 1.96/2.18 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int)) = hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real))). [resolve(1002,a,1030,a)].
% 1.96/2.18 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(1002,a,1031,a)].
% 1.96/2.18 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int)) = hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),one_one(real))). [resolve(1002,a,1032,a)].
% 1.96/2.18 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(1002,a,1033,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))). [resolve(1002,a,1034,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))). [resolve(1002,a,1035,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),one_one(real))),B)). [resolve(1002,a,1036,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),one_one(real))),B)). [resolve(1002,a,1037,a)].
% 1.96/2.18 Derived: hAPP(real,int,archim2085082626_floor(real),zero_zero(real)) = zero_zero(int). [resolve(1002,a,1038,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(real,int,archim2085082626_floor(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(1002,a,1039,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(real,int,archim2085082626_floor(real),B))). [resolve(1002,a,1040,a)].
% 1.96/2.18 Derived: hAPP(real,int,archim2085082626_floor(real),one_one(real)) = one_one(int). [resolve(1002,a,1041,a)].
% 1.96/2.18 Derived: hAPP(int,int,number_number_of(int),A) = hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,number_number_of(real),A)). [resolve(1002,a,1042,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(1002,a,1043,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(1002,a,1044,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(1002,a,1045,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(1002,a,1046,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)). [resolve(1002,a,1047,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)). [resolve(1002,a,1048,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))). [resolve(1002,a,1049,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))). [resolve(1002,a,1050,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))). [resolve(1002,a,1051,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))). [resolve(1002,a,1052,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(real,int,archim2085082626_floor(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)). [resolve(1002,a,1053,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(real,int,archim2085082626_floor(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)). [resolve(1002,a,1054,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(1002,a,1055,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(1002,a,1056,a)].
% 1.96/2.18 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),B)). [resolve(1002,a,1057,a)].
% 1.96/2.18 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),B)). [resolve(1002,a,1058,a)].
% 1.96/2.18 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int)) = hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real))). [resolve(1002,a,1059,a)].
% 1.96/2.18 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(1002,a,1060,a)].
% 1.96/2.18 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int)) = hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),one_one(real))). [resolve(1002,a,1061,a)].
% 2.10/2.30 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B)) = hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(1002,a,1062,a)].
% 2.10/2.30 Derived: hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),A))) = hAPP(real,int,archim2085082626_floor(real),A). [resolve(1002,a,1063,a)].
% 2.10/2.30 Derived: hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),A))) = hAPP(real,int,archimedean_ceiling(real),A). [resolve(1002,a,1064,a)].
% 2.10/2.30 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(real,int,archim2085082626_floor(real),hAPP(nat,real,semiring_1_of_nat(real),A)). [resolve(1002,a,1065,a)].
% 2.10/2.30 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,semiring_1_of_nat(real),A)). [resolve(1002,a,1066,a)].
% 2.10/2.30 1067 ordere142940540dd_abs(int) # label(arity_Int_Oint___Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption].
% 2.10/2.30 1068 -ordere142940540dd_abs(A) | abs_abs(A) = ti(fun(A,A),abs_abs(A)) # label(tsy_c_Groups_Oabs__class_Oabs_res) # label(axiom). [clausify(4)].
% 2.10/2.30 1069 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,abs_abs(A),B)) = hAPP(A,A,abs_abs(A),B) # label(fact_448_abs__idempotent) # label(axiom). [clausify(476)].
% 2.10/2.30 1070 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)) = hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B)) # label(fact_452_abs__minus__commute) # label(axiom). [clausify(480)].
% 2.10/2.30 1071 -ordere142940540dd_abs(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)) = hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C))) # label(fact_454_abs__add__abs) # label(axiom). [clausify(482)].
% 2.10/2.30 1072 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,abs_abs(A),B))) # label(fact_457_abs__ge__self) # label(axiom). [clausify(485)].
% 2.10/2.30 1073 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_458_abs__le__D1) # label(axiom). [clausify(486)].
% 2.10/2.30 1074 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),zero_zero(A)) = zero_zero(A) # label(fact_459_abs__zero) # label(axiom). [clausify(487)].
% 2.10/2.30 1075 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),B) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_460_abs__eq__0) # label(axiom). [clausify(488)].
% 2.10/2.30 1076 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),B) = zero_zero(A) | zero_zero(A) != ti(A,B) # label(fact_460_abs__eq__0) # label(axiom). [clausify(488)].
% 2.10/2.30 1077 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,abs_abs(A),B))) # label(fact_477_abs__ge__zero) # label(axiom). [clausify(504)].
% 2.10/2.30 1078 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),zero_zero(A))) | zero_zero(A) = ti(A,B) # label(fact_478_abs__le__zero__iff) # label(axiom). [clausify(505)].
% 2.10/2.30 1079 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),zero_zero(A))) | zero_zero(A) != ti(A,B) # label(fact_478_abs__le__zero__iff) # label(axiom). [clausify(505)].
% 2.10/2.30 1080 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hAPP(A,A,abs_abs(A),B) = ti(A,B) # label(fact_479_abs__of__nonneg) # label(axiom). [clausify(506)].
% 2.10/2.30 1081 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),B)),zero_zero(A))) # label(fact_480_abs__not__less__zero) # label(axiom). [clausify(507)].
% 2.10/2.30 1082 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,abs_abs(A),B))) | zero_zero(A) != ti(A,B) # label(fact_481_zero__less__abs__iff) # label(axiom). [clausify(508)].
% 2.10/2.30 1083 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,abs_abs(A),B))) | zero_zero(A) = ti(A,B) # label(fact_481_zero__less__abs__iff) # label(axiom). [clausify(508)].
% 2.10/2.30 1084 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hAPP(A,A,abs_abs(A),B) = ti(A,B) # label(fact_482_abs__of__pos) # label(axiom). [clausify(509)].
% 2.10/2.30 1085 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)))) # label(fact_484_abs__triangle__ineq) # label(axiom). [clausify(511)].
% 2.10/2.30 1086 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C))),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B)))) # label(fact_485_abs__triangle__ineq2__sym) # label(axiom). [clausify(512)].
% 2.10/2.30 1087 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C))),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)))) # label(fact_486_abs__triangle__ineq2) # label(axiom). [clausify(513)].
% 2.10/2.30 1088 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)))),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)))) # label(fact_487_abs__triangle__ineq3) # label(axiom). [clausify(514)].
% 2.10/2.30 1089 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),E)))),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D))),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E))))) # label(fact_492_abs__diff__triangle__ineq) # label(axiom). [clausify(519)].
% 2.10/2.30 1090 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C))),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)))) # label(fact_493_abs__triangle__ineq4) # label(axiom). [clausify(520)].
% 2.10/2.30 Derived: abs_abs(int) = ti(fun(int,int),abs_abs(int)). [resolve(1067,a,1068,a)].
% 2.10/2.30 Derived: hAPP(int,int,abs_abs(int),hAPP(int,int,abs_abs(int),A)) = hAPP(int,int,abs_abs(int),A). [resolve(1067,a,1069,a)].
% 2.10/2.30 Derived: hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)) = hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),A)). [resolve(1067,a,1070,a)].
% 2.10/2.30 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B)) = hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B))). [resolve(1067,a,1071,a)].
% 2.10/2.30 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,abs_abs(int),A))). [resolve(1067,a,1072,a)].
% 2.10/2.30 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1067,a,1073,a)].
% 2.10/2.30 Derived: hAPP(int,int,abs_abs(int),zero_zero(int)) = zero_zero(int). [resolve(1067,a,1074,a)].
% 2.10/2.30 Derived: hAPP(int,int,abs_abs(int),A) != zero_zero(int) | zero_zero(int) = ti(int,A). [resolve(1067,a,1075,a)].
% 2.10/2.30 Derived: hAPP(int,int,abs_abs(int),A) = zero_zero(int) | zero_zero(int) != ti(int,A). [resolve(1067,a,1076,a)].
% 2.10/2.30 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,abs_abs(int),A))). [resolve(1067,a,1077,a)].
% 2.10/2.31 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),A)),zero_zero(int))) | zero_zero(int) = ti(int,A). [resolve(1067,a,1078,a)].
% 2.10/2.31 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),A)),zero_zero(int))) | zero_zero(int) != ti(int,A). [resolve(1067,a,1079,a)].
% 2.10/2.31 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hAPP(int,int,abs_abs(int),A) = ti(int,A). [resolve(1067,a,1080,a)].
% 2.10/2.31 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),A)),zero_zero(int))). [resolve(1067,a,1081,a)].
% 2.10/2.31 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,abs_abs(int),A))) | zero_zero(int) != ti(int,A). [resolve(1067,a,1082,a)].
% 2.10/2.31 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,abs_abs(int),A))) | zero_zero(int) = ti(int,A). [resolve(1067,a,1083,a)].
% 2.10/2.31 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hAPP(int,int,abs_abs(int),A) = ti(int,A). [resolve(1067,a,1084,a)].
% 2.10/2.31 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B)))). [resolve(1067,a,1085,a)].
% 2.10/2.31 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),A)))). [resolve(1067,a,1086,a)].
% 2.10/2.31 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)))). [resolve(1067,a,1087,a)].
% 2.10/2.31 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B)))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)))). [resolve(1067,a,1088,a)].
% 2.10/2.31 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),D)))),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),C))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),D))))). [resolve(1067,a,1089,a)].
% 2.10/2.31 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B))),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B)))). [resolve(1067,a,1090,a)].
% 2.10/2.31 1091 ordere142940540dd_abs(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption].
% 2.10/2.31 Derived: abs_abs(real) = ti(fun(real,real),abs_abs(real)). [resolve(1091,a,1068,a)].
% 2.10/2.31 Derived: hAPP(real,real,abs_abs(real),hAPP(real,real,abs_abs(real),A)) = hAPP(real,real,abs_abs(real),A). [resolve(1091,a,1069,a)].
% 2.10/2.31 Derived: hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A)). [resolve(1091,a,1070,a)].
% 2.10/2.31 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B))). [resolve(1091,a,1071,a)].
% 2.10/2.31 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,abs_abs(real),A))). [resolve(1091,a,1072,a)].
% 2.10/2.31 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(1091,a,1073,a)].
% 2.10/2.31 Derived: hAPP(real,real,abs_abs(real),zero_zero(real)) = zero_zero(real). [resolve(1091,a,1074,a)].
% 2.10/2.31 Derived: hAPP(real,real,abs_abs(real),A) != zero_zero(real) | zero_zero(real) = ti(real,A). [resolve(1091,a,1075,a)].
% 2.10/2.31 Derived: hAPP(real,real,abs_abs(real),A) = zero_zero(real) | zero_zero(real) != ti(real,A). [resolve(1091,a,1076,a)].
% 2.10/2.31 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,abs_abs(real),A))). [resolve(1091,a,1077,a)].
% 2.10/2.31 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),A)),zero_zero(real))) | zero_zero(real) = ti(real,A). [resolve(1091,a,1078,a)].
% 2.10/2.31 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),A)),zero_zero(real))) | zero_zero(real) != ti(real,A). [resolve(1091,a,1079,a)].
% 2.10/2.31 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hAPP(real,real,abs_abs(real),A) = ti(real,A). [resolve(1091,a,1080,a)].
% 2.10/2.31 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),A)),zero_zero(real))). [resolve(1091,a,1081,a)].
% 2.10/2.31 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),A))) | zero_zero(real) != ti(real,A). [resolve(1091,a,1082,a)].
% 2.10/2.31 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),A))) | zero_zero(real) = ti(real,A). [resolve(1091,a,1083,a)].
% 2.10/2.31 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hAPP(real,real,abs_abs(real),A) = ti(real,A). [resolve(1091,a,1084,a)].
% 2.10/2.31 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)))). [resolve(1091,a,1085,a)].
% 2.10/2.31 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B))),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A)))). [resolve(1091,a,1086,a)].
% 2.10/2.31 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B))),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)))). [resolve(1091,a,1087,a)].
% 2.10/2.31 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)))),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)))). [resolve(1091,a,1088,a)].
% 2.10/2.31 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),D)))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C))),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D))))). [resolve(1091,a,1089,a)].
% 2.10/2.31 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)))). [resolve(1091,a,1090,a)].
% 2.41/2.61 1092 one(int) # label(arity_Int_Oint___Groups_Oone) # label(axiom). [assumption].
% 2.41/2.61 1093 -one(A) | one_one(A) = ti(A,one_one(A)) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom). [clausify(6)].
% 2.41/2.61 Derived: one_one(int) = ti(int,one_one(int)). [resolve(1092,a,1093,a)].
% 2.41/2.61 1094 one(nat) # label(arity_Nat_Onat___Groups_Oone) # label(axiom). [assumption].
% 2.41/2.61 Derived: one_one(nat) = ti(nat,one_one(nat)). [resolve(1094,a,1093,a)].
% 2.41/2.61 1095 one(real) # label(arity_RealDef_Oreal___Groups_Oone) # label(axiom). [assumption].
% 2.41/2.61 Derived: one_one(real) = ti(real,one_one(real)). [resolve(1095,a,1093,a)].
% 2.41/2.61 1096 monoid_add(int) # label(arity_Int_Oint___Groups_Omonoid__add) # label(axiom). [assumption].
% 2.41/2.61 1097 -monoid_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom). [clausify(7)].
% 2.41/2.61 1098 -monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_261_add__0__left) # label(axiom). [clausify(293)].
% 2.41/2.61 1099 -monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_264_add__0__right) # label(axiom). [clausify(296)].
% 2.41/2.61 Derived: plus_plus(int) = ti(fun(int,fun(int,int)),plus_plus(int)). [resolve(1096,a,1097,a)].
% 2.41/2.61 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),A) = ti(int,A). [resolve(1096,a,1098,a)].
% 2.41/2.61 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),zero_zero(int)) = ti(int,A). [resolve(1096,a,1099,a)].
% 2.41/2.61 1100 monoid_add(nat) # label(arity_Nat_Onat___Groups_Omonoid__add) # label(axiom). [assumption].
% 2.41/2.61 Derived: plus_plus(nat) = ti(fun(nat,fun(nat,nat)),plus_plus(nat)). [resolve(1100,a,1097,a)].
% 2.41/2.61 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),A) = ti(nat,A). [resolve(1100,a,1098,a)].
% 2.41/2.61 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),zero_zero(nat)) = ti(nat,A). [resolve(1100,a,1099,a)].
% 2.41/2.61 1101 monoid_add(real) # label(arity_RealDef_Oreal___Groups_Omonoid__add) # label(axiom). [assumption].
% 2.41/2.61 Derived: plus_plus(real) = ti(fun(real,fun(real,real)),plus_plus(real)). [resolve(1101,a,1097,a)].
% 2.41/2.61 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),zero_zero(real)),A) = ti(real,A). [resolve(1101,a,1098,a)].
% 2.41/2.61 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),zero_zero(real)) = ti(real,A). [resolve(1101,a,1099,a)].
% 2.41/2.61 1102 ab_semigroup_add(int) # label(arity_Int_Oint___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 2.41/2.61 1103 -ab_semigroup_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom). [clausify(8)].
% 2.41/2.61 1104 -ab_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_18_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom). [clausify(50)].
% 2.41/2.61 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)). [resolve(1102,a,1104,a)].
% 2.41/2.61 1105 ab_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 2.41/2.61 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)). [resolve(1105,a,1104,a)].
% 2.41/2.61 1106 ab_semigroup_add(real) # label(arity_RealDef_Oreal___Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 2.41/2.61 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)). [resolve(1106,a,1104,a)].
% 2.57/2.81 1107 cancel_semigroup_add(int) # label(arity_Int_Oint___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.57/2.81 1108 -cancel_semigroup_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_2_res) # label(axiom). [clausify(9)].
% 2.57/2.81 1109 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) | ti(A,B) = ti(A,D) # label(fact_13_add__right__imp__eq) # label(axiom). [clausify(45)].
% 2.57/2.81 1110 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) = ti(A,D) # label(fact_15_add__left__imp__eq) # label(axiom). [clausify(47)].
% 2.57/2.81 1111 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) | ti(A,B) = ti(A,D) # label(fact_16_add__right__cancel) # label(axiom). [clausify(48)].
% 2.57/2.81 1112 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) | ti(A,B) != ti(A,D) # label(fact_16_add__right__cancel) # label(axiom). [clausify(48)].
% 2.57/2.81 1113 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) = ti(A,D) # label(fact_17_add__left__cancel) # label(axiom). [clausify(49)].
% 2.57/2.81 1114 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) != ti(A,D) # label(fact_17_add__left__cancel) # label(axiom). [clausify(49)].
% 2.57/2.81 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B) | ti(int,A) = ti(int,C). [resolve(1107,a,1109,a)].
% 2.57/2.81 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C) | ti(int,B) = ti(int,C). [resolve(1107,a,1110,a)].
% 2.57/2.81 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B) | ti(int,A) != ti(int,C). [resolve(1107,a,1112,a)].
% 2.57/2.81 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C) | ti(int,B) != ti(int,C). [resolve(1107,a,1114,a)].
% 2.57/2.81 1115 cancel_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.57/2.81 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B) | ti(nat,A) = ti(nat,C). [resolve(1115,a,1109,a)].
% 2.57/2.81 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C) | ti(nat,B) = ti(nat,C). [resolve(1115,a,1110,a)].
% 2.57/2.81 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B) | ti(nat,A) != ti(nat,C). [resolve(1115,a,1112,a)].
% 2.57/2.81 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C) | ti(nat,B) != ti(nat,C). [resolve(1115,a,1114,a)].
% 2.57/2.81 1116 cancel_semigroup_add(real) # label(arity_RealDef_Oreal___Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.57/2.81 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B) | ti(real,A) = ti(real,C). [resolve(1116,a,1109,a)].
% 2.57/2.81 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C) | ti(real,B) = ti(real,C). [resolve(1116,a,1110,a)].
% 2.57/2.81 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B) | ti(real,A) != ti(real,C). [resolve(1116,a,1112,a)].
% 2.57/2.81 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C) | ti(real,B) != ti(real,C). [resolve(1116,a,1114,a)].
% 2.57/2.81 1117 no_zero_divisors(int) # label(arity_Int_Oint___Rings_Ono__zero__divisors) # label(axiom). [assumption].
% 2.57/2.81 1118 -no_zero_divisors(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_0_res) # label(axiom). [clausify(10)].
% 2.81/3.00 1119 -no_zero_divisors(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) != zero_zero(A) # label(fact_256_no__zero__divisors) # label(axiom). [clausify(288)].
% 2.81/3.00 1120 -no_zero_divisors(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) != zero_zero(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) # label(fact_257_divisors__zero) # label(axiom). [clausify(289)].
% 2.81/3.00 Derived: times_times(int) = ti(fun(int,fun(int,int)),times_times(int)). [resolve(1117,a,1118,a)].
% 2.81/3.00 Derived: zero_zero(int) = ti(int,A) | zero_zero(int) = ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B) != zero_zero(int). [resolve(1117,a,1119,a)].
% 2.81/3.00 1121 no_zero_divisors(nat) # label(arity_Nat_Onat___Rings_Ono__zero__divisors) # label(axiom). [assumption].
% 2.81/3.00 Derived: times_times(nat) = ti(fun(nat,fun(nat,nat)),times_times(nat)). [resolve(1121,a,1118,a)].
% 2.81/3.00 Derived: zero_zero(nat) = ti(nat,A) | zero_zero(nat) = ti(nat,B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B) != zero_zero(nat). [resolve(1121,a,1119,a)].
% 2.81/3.00 1122 no_zero_divisors(real) # label(arity_RealDef_Oreal___Rings_Ono__zero__divisors) # label(axiom). [assumption].
% 2.81/3.00 Derived: times_times(real) = ti(fun(real,fun(real,real)),times_times(real)). [resolve(1122,a,1118,a)].
% 2.81/3.00 Derived: zero_zero(real) = ti(real,A) | zero_zero(real) = ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B) != zero_zero(real). [resolve(1122,a,1119,a)].
% 2.81/3.00 1123 mult_zero(int) # label(arity_Int_Oint___Rings_Omult__zero) # label(axiom). [assumption].
% 2.81/3.00 1124 -mult_zero(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_1_res) # label(axiom). [clausify(11)].
% 2.81/3.00 1125 -mult_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) = zero_zero(A) # label(fact_249_mult__zero__left) # label(axiom). [clausify(281)].
% 2.81/3.00 1126 -mult_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) = zero_zero(A) # label(fact_252_mult__zero__right) # label(axiom). [clausify(284)].
% 2.81/3.00 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),A) = zero_zero(int). [resolve(1123,a,1125,a)].
% 2.81/3.00 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),zero_zero(int)) = zero_zero(int). [resolve(1123,a,1126,a)].
% 2.81/3.00 1127 mult_zero(nat) # label(arity_Nat_Onat___Rings_Omult__zero) # label(axiom). [assumption].
% 2.81/3.00 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),A) = zero_zero(nat). [resolve(1127,a,1125,a)].
% 2.81/3.00 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),zero_zero(nat)) = zero_zero(nat). [resolve(1127,a,1126,a)].
% 2.81/3.00 1128 mult_zero(real) # label(arity_RealDef_Oreal___Rings_Omult__zero) # label(axiom). [assumption].
% 2.81/3.00 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),zero_zero(real)),A) = zero_zero(real). [resolve(1128,a,1125,a)].
% 2.81/3.00 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),zero_zero(real)) = zero_zero(real). [resolve(1128,a,1126,a)].
% 2.81/3.00 1129 monoid_mult(int) # label(arity_Int_Oint___Groups_Omonoid__mult) # label(axiom). [assumption].
% 2.81/3.00 1130 -monoid_mult(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_2_res) # label(axiom). [clausify(12)].
% 2.81/3.00 1131 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) = ti(A,B) # label(fact_114_mult__1__left) # label(axiom). [clausify(146)].
% 2.81/3.00 1132 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) = ti(A,B) # label(fact_116_mult__1__right) # label(axiom). [clausify(148)].
% 2.81/3.00 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),A) = ti(int,A). [resolve(1129,a,1131,a)].
% 2.81/3.00 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),one_one(int)) = ti(int,A). [resolve(1129,a,1132,a)].
% 2.81/3.00 1133 monoid_mult(nat) # label(arity_Nat_Onat___Groups_Omonoid__mult) # label(axiom). [assumption].
% 2.81/3.00 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),A) = ti(nat,A). [resolve(1133,a,1131,a)].
% 2.87/3.09 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),one_one(nat)) = ti(nat,A). [resolve(1133,a,1132,a)].
% 2.87/3.09 1134 monoid_mult(real) # label(arity_RealDef_Oreal___Groups_Omonoid__mult) # label(axiom). [assumption].
% 2.87/3.09 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),one_one(real)),A) = ti(real,A). [resolve(1134,a,1131,a)].
% 2.87/3.09 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),one_one(real)) = ti(real,A). [resolve(1134,a,1132,a)].
% 2.87/3.09 1135 semiring(int) # label(arity_Int_Oint___Rings_Osemiring) # label(axiom). [assumption].
% 2.87/3.09 1136 -semiring(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_3_res) # label(axiom). [clausify(13)].
% 2.87/3.09 1137 -semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),E)) # label(fact_25_combine__common__factor) # label(axiom). [clausify(57)].
% 2.87/3.09 1138 -number(A) | -semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)) # label(fact_133_right__distrib__number__of) # label(axiom). [clausify(165)].
% 2.87/3.09 1139 -number(A) | -semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(int,A,number_number_of(A),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D))) # label(fact_134_left__distrib__number__of) # label(axiom). [clausify(166)].
% 2.87/3.09 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),D)). [resolve(1135,a,1137,a)].
% 2.87/3.09 Derived: -number(int) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),C)). [resolve(1135,a,1138,b)].
% 2.87/3.09 Derived: -number(int) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,number_number_of(int),C)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),C))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,number_number_of(int),C))). [resolve(1135,a,1139,b)].
% 2.87/3.09 1140 semiring(nat) # label(arity_Nat_Onat___Rings_Osemiring) # label(axiom). [assumption].
% 2.87/3.09 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)),D)). [resolve(1140,a,1137,a)].
% 2.87/3.09 Derived: -number(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),A)),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),A)),C)). [resolve(1140,a,1138,b)].
% 3.07/3.29 Derived: -number(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(int,nat,number_number_of(nat),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(int,nat,number_number_of(nat),C))). [resolve(1140,a,1139,b)].
% 3.07/3.29 1141 semiring(real) # label(arity_RealDef_Oreal___Rings_Osemiring) # label(axiom). [assumption].
% 3.07/3.29 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),D)). [resolve(1141,a,1137,a)].
% 3.07/3.29 Derived: -number(real) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),C)). [resolve(1141,a,1138,b)].
% 3.07/3.29 Derived: -number(real) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(int,real,number_number_of(real),C)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(int,real,number_number_of(real),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(int,real,number_number_of(real),C))). [resolve(1141,a,1139,b)].
% 3.07/3.29 1142 ab_semigroup_mult(int) # label(arity_Int_Oint___Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.07/3.29 1143 -ab_semigroup_mult(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_4_res) # label(axiom). [clausify(14)].
% 3.07/3.29 1144 -ab_semigroup_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_12_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom). [clausify(44)].
% 3.07/3.29 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)). [resolve(1142,a,1144,a)].
% 3.07/3.29 1145 ab_semigroup_mult(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.07/3.29 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(1145,a,1144,a)].
% 3.07/3.29 1146 ab_semigroup_mult(real) # label(arity_RealDef_Oreal___Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.07/3.29 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)). [resolve(1146,a,1144,a)].
% 3.07/3.29 1147 zero(int) # label(arity_Int_Oint___Groups_Ozero) # label(axiom). [assumption].
% 3.07/3.29 1148 -zero(A) | zero_zero(A) = ti(A,zero_zero(A)) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom). [clausify(15)].
% 3.07/3.29 Derived: zero_zero(int) = ti(int,zero_zero(int)). [resolve(1147,a,1148,a)].
% 3.19/3.39 1149 zero(nat) # label(arity_Nat_Onat___Groups_Ozero) # label(axiom). [assumption].
% 3.19/3.39 Derived: zero_zero(nat) = ti(nat,zero_zero(nat)). [resolve(1149,a,1148,a)].
% 3.19/3.39 1150 zero(real) # label(arity_RealDef_Oreal___Groups_Ozero) # label(axiom). [assumption].
% 3.19/3.39 Derived: zero_zero(real) = ti(real,zero_zero(real)). [resolve(1150,a,1148,a)].
% 3.19/3.39 1151 ring_1(int) # label(arity_Int_Oint___Rings_Oring__1) # label(axiom). [assumption].
% 3.19/3.39 1152 -ring_1(A) | ring_1_Ints(A) = ti(fun(A,bool),ring_1_Ints(A)) # label(tsy_c_Int_Oring__1__class_OInts_res) # label(axiom). [clausify(19)].
% 3.19/3.39 1153 -ring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),one_one(A))) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),one_one(A)) # label(fact_82_real__squared__diff__one__factored) # label(axiom). [clausify(114)].
% 3.19/3.39 1154 -ring_1(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),zero_zero(A)),ring_1_Ints(A))) # label(fact_471_Ints__0) # label(axiom). [clausify(498)].
% 3.19/3.39 1155 -ring_1(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),ring_1_Ints(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),ring_1_Ints(A))) # label(fact_472_Ints__mult) # label(axiom). [clausify(499)].
% 3.19/3.39 1156 -ring_1(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),ring_1_Ints(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),ring_1_Ints(A))) # label(fact_473_Ints__add) # label(axiom). [clausify(500)].
% 3.19/3.39 1157 -ring_1(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),one_one(A)),ring_1_Ints(A))) # label(fact_475_Ints__1) # label(axiom). [clausify(502)].
% 3.19/3.39 1158 -ring_1(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),ring_1_Ints(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),ring_1_Ints(A))) # label(fact_476_Ints__diff) # label(axiom). [clausify(503)].
% 3.19/3.39 1159 -ring_1(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(nat,A,semiring_1_of_nat(A),B)),ring_1_Ints(A))) # label(fact_833_Ints__of__nat) # label(axiom). [clausify(846)].
% 3.19/3.39 1160 -ring_1(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,semiring_1_of_nat(A),C)),hAPP(nat,A,semiring_1_of_nat(A),B)) # label(fact_841_of__nat__diff) # label(axiom). [clausify(852)].
% 3.19/3.39 Derived: ring_1_Ints(int) = ti(fun(int,bool),ring_1_Ints(int)). [resolve(1151,a,1152,a)].
% 3.19/3.39 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),one_one(int)). [resolve(1151,a,1153,a)].
% 3.19/3.39 Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),zero_zero(int)),ring_1_Ints(int))). [resolve(1151,a,1154,a)].
% 3.19/3.39 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),ring_1_Ints(int))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),ring_1_Ints(int))). [resolve(1151,a,1155,a)].
% 3.19/3.39 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),ring_1_Ints(int))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),ring_1_Ints(int))). [resolve(1151,a,1156,a)].
% 3.29/3.48 Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),one_one(int)),ring_1_Ints(int))). [resolve(1151,a,1157,a)].
% 3.29/3.48 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),ring_1_Ints(int))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),ring_1_Ints(int))). [resolve(1151,a,1158,a)].
% 3.29/3.48 Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),A)),ring_1_Ints(int))). [resolve(1151,a,1159,a)].
% 3.29/3.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),B)),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(1151,a,1160,a)].
% 3.29/3.48 1161 ring_1(real) # label(arity_RealDef_Oreal___Rings_Oring__1) # label(axiom). [assumption].
% 3.29/3.48 Derived: ring_1_Ints(real) = ti(fun(real,bool),ring_1_Ints(real)). [resolve(1161,a,1152,a)].
% 3.29/3.48 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),one_one(real))) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),one_one(real)). [resolve(1161,a,1153,a)].
% 3.29/3.48 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),zero_zero(real)),ring_1_Ints(real))). [resolve(1161,a,1154,a)].
% 3.29/3.48 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),ring_1_Ints(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),ring_1_Ints(real))). [resolve(1161,a,1155,a)].
% 3.29/3.48 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),ring_1_Ints(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),ring_1_Ints(real))). [resolve(1161,a,1156,a)].
% 3.29/3.48 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),one_one(real)),ring_1_Ints(real))). [resolve(1161,a,1157,a)].
% 3.29/3.48 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),ring_1_Ints(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),ring_1_Ints(real))). [resolve(1161,a,1158,a)].
% 3.29/3.48 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,semiring_1_of_nat(real),A)),ring_1_Ints(real))). [resolve(1161,a,1159,a)].
% 3.29/3.48 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,semiring_1_of_nat(real),B)),hAPP(nat,real,semiring_1_of_nat(real),A)). [resolve(1161,a,1160,a)].
% 3.29/3.48 1162 semiring_1(int) # label(arity_Int_Oint___Rings_Osemiring__1) # label(axiom). [assumption].
% 3.29/3.49 1163 -semiring_1(A) | semiring_1_of_nat(A) = ti(fun(nat,A),semiring_1_of_nat(A)) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat_res) # label(axiom). [clausify(20)].
% 3.29/3.49 1164 -semiring_1(A) | hAPP(nat,A,semiring_1_of_nat(A),zero_zero(nat)) = zero_zero(A) # label(fact_807_of__nat__0) # label(axiom). [clausify(824)].
% 3.29/3.49 1165 -semiring_1(A) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C)) # label(fact_812_of__nat__add) # label(axiom). [clausify(829)].
% 3.29/3.49 1166 -semiring_1(A) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C)) # label(fact_813_of__nat__mult) # label(axiom). [clausify(830)].
% 3.29/3.49 1167 -semiring_1(A) | hAPP(nat,A,semiring_1_of_nat(A),one_one(nat)) = one_one(A) # label(fact_814_of__nat__1) # label(axiom). [clausify(831)].
% 3.29/3.49 1168 -semiring_1(A) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,suc,B)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),hAPP(nat,A,semiring_1_of_nat(A),B)) # label(fact_969_of__nat__Suc) # label(axiom). [clausify(970)].
% 3.29/3.49 Derived: semiring_1_of_nat(int) = ti(fun(nat,int),semiring_1_of_nat(int)). [resolve(1162,a,1163,a)].
% 3.29/3.49 Derived: hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) = zero_zero(int). [resolve(1162,a,1164,a)].
% 3.29/3.49 Derived: hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B)). [resolve(1162,a,1165,a)].
% 3.29/3.49 Derived: hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B)). [resolve(1162,a,1166,a)].
% 3.29/3.49 Derived: hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)) = one_one(int). [resolve(1162,a,1167,a)].
% 3.29/3.49 Derived: hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,A)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(1162,a,1168,a)].
% 3.29/3.49 1169 semiring_1(nat) # label(arity_Nat_Onat___Rings_Osemiring__1) # label(axiom). [assumption].
% 3.29/3.49 Derived: semiring_1_of_nat(nat) = ti(fun(nat,nat),semiring_1_of_nat(nat)). [resolve(1169,a,1163,a)].
% 3.29/3.49 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),zero_zero(nat)) = zero_zero(nat). [resolve(1169,a,1164,a)].
% 3.29/3.49 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B)). [resolve(1169,a,1165,a)].
% 3.29/3.49 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B)). [resolve(1169,a,1166,a)].
% 3.29/3.49 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),one_one(nat)) = one_one(nat). [resolve(1169,a,1167,a)].
% 3.29/3.49 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(nat,nat,suc,A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(nat,nat,semiring_1_of_nat(nat),A)). [resolve(1169,a,1168,a)].
% 3.29/3.49 1170 semiring_1(real) # label(arity_RealDef_Oreal___Rings_Osemiring__1) # label(axiom). [assumption].
% 3.29/3.49 Derived: semiring_1_of_nat(real) = ti(fun(nat,real),semiring_1_of_nat(real)). [resolve(1170,a,1163,a)].
% 3.29/3.49 Derived: hAPP(nat,real,semiring_1_of_nat(real),zero_zero(nat)) = zero_zero(real). [resolve(1170,a,1164,a)].
% 3.29/3.49 Derived: hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B)). [resolve(1170,a,1165,a)].
% 3.29/3.49 Derived: hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B)). [resolve(1170,a,1166,a)].
% 3.35/3.59 Derived: hAPP(nat,real,semiring_1_of_nat(real),one_one(nat)) = one_one(real). [resolve(1170,a,1167,a)].
% 3.35/3.59 Derived: hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,suc,A)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(nat,real,semiring_1_of_nat(real),A)). [resolve(1170,a,1168,a)].
% 3.35/3.59 1171 ring(int) # label(arity_Int_Oint___Rings_Oring) # label(axiom). [assumption].
% 3.35/3.59 1172 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),D)) # label(fact_1_mult__diff__mult) # label(axiom). [clausify(33)].
% 3.35/3.59 1173 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C)),D) = ti(A,F) # label(fact_3_eq__add__iff2) # label(axiom). [clausify(35)].
% 3.35/3.59 1174 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C)),D) != ti(A,F) # label(fact_3_eq__add__iff2) # label(axiom). [clausify(35)].
% 3.35/3.59 1175 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F) = ti(A,D) # label(fact_4_eq__add__iff1) # label(axiom). [clausify(36)].
% 3.35/3.59 1176 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F) != ti(A,D) # label(fact_4_eq__add__iff1) # label(axiom). [clausify(36)].
% 3.35/3.59 1177 -number(A) | -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)) # label(fact_135_right__diff__distrib__number__of) # label(axiom). [clausify(167)].
% 3.35/3.59 1178 -number(A) | -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(int,A,number_number_of(A),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),D))) # label(fact_136_left__diff__distrib__number__of) # label(axiom). [clausify(168)].
% 3.35/3.59 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),C))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),C)). [resolve(1171,a,1172,a)].
% 3.35/3.59 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B)),C) = ti(int,E). [resolve(1171,a,1173,a)].
% 3.35/3.59 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B)),C) != ti(int,E). [resolve(1171,a,1174,a)].
% 3.35/3.59 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),D),A)),B)),E) = ti(int,C). [resolve(1171,a,1175,a)].
% 3.35/3.59 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),D),A)),B)),E) != ti(int,C). [resolve(1171,a,1176,a)].
% 3.35/3.59 Derived: -number(int) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),C)). [resolve(1171,a,1177,b)].
% 3.35/3.59 Derived: -number(int) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),hAPP(int,int,number_number_of(int),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),C))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,number_number_of(int),C))). [resolve(1171,a,1178,b)].
% 3.35/3.59 1179 ring(real) # label(arity_RealDef_Oreal___Rings_Oring) # label(axiom). [assumption].
% 3.35/3.59 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),D)),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),C)). [resolve(1179,a,1172,a)].
% 3.35/3.59 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),D)),B)),C) = ti(real,E). [resolve(1179,a,1173,a)].
% 3.35/3.59 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),D)),B)),C) != ti(real,E). [resolve(1179,a,1174,a)].
% 3.49/3.68 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),A)),B)),E) = ti(real,C). [resolve(1179,a,1175,a)].
% 3.49/3.68 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),A)),B)),E) != ti(real,C). [resolve(1179,a,1176,a)].
% 3.49/3.68 Derived: -number(real) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),C)). [resolve(1179,a,1177,b)].
% 3.49/3.68 Derived: -number(real) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),hAPP(int,real,number_number_of(real),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(int,real,number_number_of(real),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(int,real,number_number_of(real),C))). [resolve(1179,a,1178,b)].
% 3.49/3.68 1180 real_normed_algebra(real) # label(arity_RealDef_Oreal___RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 3.49/3.68 1181 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),E))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E))) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)) # label(fact_2_mult_Oprod__diff__prod) # label(axiom). [clausify(34)].
% 3.49/3.68 1182 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_26_mult__left_Oadd) # label(axiom). [clausify(58)].
% 3.49/3.68 1183 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_27_mult_Oadd__left) # label(axiom). [clausify(59)].
% 3.49/3.68 1184 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_29_mult__right_Oadd) # label(axiom). [clausify(61)].
% 3.49/3.68 1185 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_30_mult_Oadd__right) # label(axiom). [clausify(62)].
% 3.49/3.68 1186 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_31_mult__left_Odiff) # label(axiom). [clausify(63)].
% 3.49/3.69 1187 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_32_mult_Odiff__left) # label(axiom). [clausify(64)].
% 3.49/3.69 1188 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_33_mult__right_Odiff) # label(axiom). [clausify(65)].
% 3.49/3.69 1189 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_34_mult_Odiff__right) # label(axiom). [clausify(66)].
% 3.49/3.69 1190 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) = zero_zero(A) # label(fact_250_mult_Ozero__left) # label(axiom). [clausify(282)].
% 3.49/3.69 1191 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) = zero_zero(A) # label(fact_251_mult__left_Ozero) # label(axiom). [clausify(283)].
% 3.49/3.69 1192 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) = zero_zero(A) # label(fact_253_mult_Ozero__right) # label(axiom). [clausify(285)].
% 3.49/3.69 1193 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) = zero_zero(A) # label(fact_254_mult__right_Ozero) # label(axiom). [clausify(286)].
% 3.49/3.69 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D))) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D)). [resolve(1180,a,1181,a)].
% 3.49/3.69 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)). [resolve(1180,a,1182,a)].
% 3.49/3.69 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)). [resolve(1180,a,1184,a)].
% 3.49/3.69 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)). [resolve(1180,a,1186,a)].
% 3.49/3.69 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)). [resolve(1180,a,1188,a)].
% 3.79/3.97 1194 group_add(int) # label(arity_Int_Oint___Groups_Ogroup__add) # label(axiom). [assumption].
% 3.79/3.97 1195 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),C) = ti(A,B) # label(fact_11_diff__add__cancel) # label(axiom). [clausify(43)].
% 3.79/3.97 1196 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),C) = ti(A,B) # label(fact_36_add__diff__cancel) # label(axiom). [clausify(68)].
% 3.79/3.97 1197 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),zero_zero(A)) = ti(A,B) # label(fact_269_diff__0__right) # label(axiom). [clausify(301)].
% 3.79/3.97 1198 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),B) = zero_zero(A) # label(fact_270_diff__self) # label(axiom). [clausify(302)].
% 3.79/3.97 1199 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != zero_zero(A) | ti(A,C) = ti(A,B) # label(fact_272_right__minus__eq) # label(axiom). [clausify(304)].
% 3.79/3.97 1200 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) = zero_zero(A) | ti(A,C) != ti(A,B) # label(fact_272_right__minus__eq) # label(axiom). [clausify(304)].
% 3.79/3.97 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),B) = ti(int,A). [resolve(1194,a,1195,a)].
% 3.79/3.97 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),B) = ti(int,A). [resolve(1194,a,1196,a)].
% 3.79/3.97 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),zero_zero(int)) = ti(int,A). [resolve(1194,a,1197,a)].
% 3.79/3.97 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),A) = zero_zero(int). [resolve(1194,a,1198,a)].
% 3.79/3.97 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != zero_zero(int) | ti(int,B) = ti(int,A). [resolve(1194,a,1199,a)].
% 3.79/3.97 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) = zero_zero(int) | ti(int,B) != ti(int,A). [resolve(1194,a,1200,a)].
% 3.79/3.97 1201 group_add(real) # label(arity_RealDef_Oreal___Groups_Ogroup__add) # label(axiom). [assumption].
% 3.79/3.97 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),B) = ti(real,A). [resolve(1201,a,1195,a)].
% 3.79/3.97 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),B) = ti(real,A). [resolve(1201,a,1196,a)].
% 3.79/3.97 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),zero_zero(real)) = ti(real,A). [resolve(1201,a,1197,a)].
% 3.79/3.97 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),A) = zero_zero(real). [resolve(1201,a,1198,a)].
% 3.79/3.97 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != zero_zero(real) | ti(real,B) = ti(real,A). [resolve(1201,a,1199,a)].
% 3.79/3.97 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) = zero_zero(real) | ti(real,B) != ti(real,A). [resolve(1201,a,1200,a)].
% 3.79/3.97 1202 cancel146912293up_add(int) # label(arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.79/3.97 1203 -cancel146912293up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) = ti(A,D) # label(fact_14_add__imp__eq) # label(axiom). [clausify(46)].
% 3.79/3.97 1204 cancel146912293up_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.79/3.97 1205 cancel146912293up_add(real) # label(arity_RealDef_Oreal___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.79/3.97 1206 ab_group_add(int) # label(arity_Int_Oint___Groups_Oab__group__add) # label(axiom). [assumption].
% 3.79/3.97 1207 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | ti(A,E) != ti(A,D) | ti(A,C) = ti(A,B) # label(fact_19_diff__eq__diff__eq) # label(axiom). [clausify(51)].
% 3.79/3.97 1208 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | ti(A,E) = ti(A,D) | ti(A,C) != ti(A,B) # label(fact_19_diff__eq__diff__eq) # label(axiom). [clausify(51)].
% 3.97/4.16 1209 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E)) # label(fact_35_add__diff__add) # label(axiom). [clausify(67)].
% 3.97/4.16 1210 -ab_group_add(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B) = zero_zero(A) # label(fact_271_eq__iff__diff__eq__0) # label(axiom). [clausify(303)].
% 3.97/4.16 1211 -ab_group_add(A) | ti(A,B) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B) != zero_zero(A) # label(fact_271_eq__iff__diff__eq__0) # label(axiom). [clausify(303)].
% 3.97/4.16 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | ti(int,D) != ti(int,C) | ti(int,B) = ti(int,A). [resolve(1206,a,1207,a)].
% 3.97/4.16 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | ti(int,D) = ti(int,C) | ti(int,B) != ti(int,A). [resolve(1206,a,1208,a)].
% 3.97/4.16 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D)). [resolve(1206,a,1209,a)].
% 3.97/4.16 1212 ab_group_add(real) # label(arity_RealDef_Oreal___Groups_Oab__group__add) # label(axiom). [assumption].
% 3.97/4.16 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | ti(real,D) != ti(real,C) | ti(real,B) = ti(real,A). [resolve(1212,a,1207,a)].
% 3.97/4.16 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | ti(real,D) = ti(real,C) | ti(real,B) != ti(real,A). [resolve(1212,a,1208,a)].
% 3.97/4.16 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D)). [resolve(1212,a,1209,a)].
% 3.97/4.16 1213 comm_semiring(int) # label(arity_Int_Oint___Rings_Ocomm__semiring) # label(axiom). [assumption].
% 3.97/4.16 1214 -comm_semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_28_comm__semiring__class_Odistrib) # label(axiom). [clausify(60)].
% 3.97/4.16 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)). [resolve(1213,a,1214,a)].
% 3.97/4.16 1215 comm_semiring(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring) # label(axiom). [assumption].
% 3.97/4.16 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(1215,a,1214,a)].
% 3.97/4.16 1216 comm_semiring(real) # label(arity_RealDef_Oreal___Rings_Ocomm__semiring) # label(axiom). [assumption].
% 3.97/4.16 1217 semiri456707255roduct(int) # label(arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption].
% 3.97/4.16 1218 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,B) = ti(A,D) | ti(A,C) = ti(A,E) # label(fact_37_crossproduct__eq) # label(axiom). [clausify(69)].
% 3.97/4.16 1219 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,B) != ti(A,D) # label(fact_37_crossproduct__eq) # label(axiom). [clausify(69)].
% 3.97/4.16 1220 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,C) != ti(A,E) # label(fact_37_crossproduct__eq) # label(axiom). [clausify(69)].
% 3.97/4.16 1221 -semiri456707255roduct(A) | ti(A,B) = ti(A,C) | ti(A,D) = ti(A,E) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_40_crossproduct__noteq) # label(axiom). [clausify(72)].
% 3.97/4.16 1222 -semiri456707255roduct(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_40_crossproduct__noteq) # label(axiom). [clausify(72)].
% 3.97/4.16 1223 -semiri456707255roduct(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),B)) # label(fact_40_crossproduct__noteq) # label(axiom). [clausify(72)].
% 3.97/4.16 1224 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != ti(A,B) | zero_zero(A) = ti(A,C) # label(fact_260_add__0__iff) # label(axiom). [clausify(292)].
% 3.97/4.16 1225 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_260_add__0__iff) # label(axiom). [clausify(292)].
% 3.97/4.16 1226 -semiri456707255roduct(A) | zero_zero(A) = ti(A,B) | ti(A,C) != ti(A,D) | ti(A,E) = ti(A,F) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),F)) # label(fact_332_add__scale__eq__noteq) # label(axiom). [clausify(363)].
% 3.97/4.16 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) | ti(int,A) = ti(int,C) | ti(int,B) = ti(int,D). [resolve(1217,a,1218,a)].
% 3.97/4.16 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) | ti(int,A) != ti(int,C). [resolve(1217,a,1219,a)].
% 3.97/4.16 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) | ti(int,B) != ti(int,D). [resolve(1217,a,1220,a)].
% 3.97/4.17 Derived: ti(int,A) = ti(int,B) | ti(int,C) = ti(int,D) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)). [resolve(1217,a,1221,a)].
% 3.97/4.17 Derived: ti(int,A) != ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)). [resolve(1217,a,1222,a)].
% 3.97/4.17 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != ti(int,A) | zero_zero(int) = ti(int,B). [resolve(1217,a,1224,a)].
% 3.97/4.17 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = ti(int,A) | zero_zero(int) != ti(int,B). [resolve(1217,a,1225,a)].
% 3.97/4.17 Derived: zero_zero(int) = ti(int,A) | ti(int,B) != ti(int,C) | ti(int,D) = ti(int,E) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),E)). [resolve(1217,a,1226,a)].
% 3.97/4.17 1227 semiri456707255roduct(nat) # label(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption].
% 3.97/4.17 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) | ti(nat,A) = ti(nat,C) | ti(nat,B) = ti(nat,D). [resolve(1227,a,1218,a)].
% 3.97/4.17 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) | ti(nat,A) != ti(nat,C). [resolve(1227,a,1219,a)].
% 3.97/4.17 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) | ti(nat,B) != ti(nat,D). [resolve(1227,a,1220,a)].
% 3.97/4.17 Derived: ti(nat,A) = ti(nat,B) | ti(nat,C) = ti(nat,D) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)). [resolve(1227,a,1221,a)].
% 3.97/4.17 Derived: ti(nat,A) != ti(nat,B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)). [resolve(1227,a,1222,a)].
% 3.97/4.17 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != ti(nat,A) | zero_zero(nat) = ti(nat,B). [resolve(1227,a,1224,a)].
% 3.97/4.17 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = ti(nat,A) | zero_zero(nat) != ti(nat,B). [resolve(1227,a,1225,a)].
% 3.97/4.17 Derived: zero_zero(nat) = ti(nat,A) | ti(nat,B) != ti(nat,C) | ti(nat,D) = ti(nat,E) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),E)). [resolve(1227,a,1226,a)].
% 4.04/4.26 1228 semiri456707255roduct(real) # label(arity_RealDef_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossp) # label(axiom). [assumption].
% 4.04/4.26 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)) | ti(real,A) = ti(real,C) | ti(real,B) = ti(real,D). [resolve(1228,a,1218,a)].
% 4.04/4.26 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)) | ti(real,A) != ti(real,C). [resolve(1228,a,1219,a)].
% 4.04/4.26 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)) | ti(real,B) != ti(real,D). [resolve(1228,a,1220,a)].
% 4.04/4.26 Derived: ti(real,A) = ti(real,B) | ti(real,C) = ti(real,D) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)). [resolve(1228,a,1221,a)].
% 4.04/4.26 Derived: ti(real,A) != ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)). [resolve(1228,a,1222,a)].
% 4.04/4.26 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != ti(real,A) | zero_zero(real) = ti(real,B). [resolve(1228,a,1224,a)].
% 4.04/4.26 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = ti(real,A) | zero_zero(real) != ti(real,B). [resolve(1228,a,1225,a)].
% 4.04/4.26 Derived: zero_zero(real) = ti(real,A) | ti(real,B) != ti(real,C) | ti(real,D) = ti(real,E) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),E)). [resolve(1228,a,1226,a)].
% 4.04/4.26 1229 comm_semiring_1(int) # label(arity_Int_Oint___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 4.04/4.26 1230 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_38_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom). [clausify(70)].
% 4.04/4.26 1231 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_39_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom). [clausify(71)].
% 4.04/4.26 1232 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom). [clausify(73)].
% 4.04/4.26 1233 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E)) # label(fact_47_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom). [clausify(79)].
% 4.04/4.26 1234 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_48_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom). [clausify(80)].
% 4.04/4.26 1235 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B) # label(fact_51_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom). [clausify(83)].
% 4.04/4.26 1236 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_53_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom). [clausify(85)].
% 4.04/4.26 1237 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_54_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom). [clausify(86)].
% 4.04/4.26 1238 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_55_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom). [clausify(87)].
% 4.04/4.26 1239 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom). [clausify(88)].
% 4.04/4.26 1240 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E))) # label(fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom). [clausify(89)].
% 4.04/4.26 1241 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),E)) # label(fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom). [clausify(90)].
% 4.04/4.26 1242 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)) # label(fact_59_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom). [clausify(91)].
% 4.04/4.26 1243 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B) # label(fact_60_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom). [clausify(92)].
% 4.04/4.26 1244 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)) # label(fact_61_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom). [clausify(93)].
% 4.04/4.26 1245 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_62_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom). [clausify(94)].
% 4.04/4.26 1246 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_63_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom). [clausify(95)].
% 4.04/4.26 1247 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) = ti(A,B) # label(fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom). [clausify(144)].
% 4.04/4.26 1248 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) = ti(A,B) # label(fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom). [clausify(145)].
% 4.04/4.26 1249 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) # label(fact_144_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom). [clausify(176)].
% 4.04/4.26 1250 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_145_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom). [clausify(177)].
% 4.04/4.26 1251 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),C) # label(fact_146_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom). [clausify(178)].
% 4.04/4.26 1252 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) = zero_zero(A) # label(fact_247_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom). [clausify(279)].
% 4.04/4.26 1253 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) = zero_zero(A) # label(fact_248_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom). [clausify(280)].
% 4.04/4.26 1254 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_258_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom). [clausify(290)].
% 4.04/4.26 1255 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_259_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom). [clausify(291)].
% 4.04/4.26 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)). [resolve(1229,a,1232,a)].
% 4.04/4.26 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D)). [resolve(1229,a,1233,a)].
% 4.04/4.26 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),B). [resolve(1229,a,1234,a)].
% 4.04/4.26 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A). [resolve(1229,a,1235,a)].
% 4.04/4.26 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)). [resolve(1229,a,1236,a)].
% 4.04/4.26 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),B). [resolve(1229,a,1239,a)].
% 4.04/4.26 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)). [resolve(1229,a,1242,a)].
% 4.04/4.26 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A). [resolve(1229,a,1243,a)].
% 4.04/4.26 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)). [resolve(1229,a,1244,a)].
% 4.04/4.26 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int))),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A). [resolve(1229,a,1249,a)].
% 4.04/4.26 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int))),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)). [resolve(1229,a,1250,a)].
% 4.04/4.26 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int))),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),B). [resolve(1229,a,1251,a)].
% 4.04/4.26 1256 comm_semiring_1(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 4.04/4.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)). [resolve(1256,a,1232,a)].
% 4.04/4.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D)). [resolve(1256,a,1233,a)].
% 4.04/4.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),B). [resolve(1256,a,1234,a)].
% 4.04/4.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A). [resolve(1256,a,1235,a)].
% 4.04/4.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)). [resolve(1256,a,1236,a)].
% 4.04/4.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),B). [resolve(1256,a,1239,a)].
% 4.04/4.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D)). [resolve(1256,a,1242,a)].
% 4.04/4.27 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),A). [resolve(1256,a,1243,a)].
% 4.04/4.27 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)). [resolve(1256,a,1244,a)].
% 4.04/4.27 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat))),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),A). [resolve(1256,a,1249,a)].
% 4.04/4.27 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)). [resolve(1256,a,1250,a)].
% 4.04/4.27 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),B). [resolve(1256,a,1251,a)].
% 4.04/4.27 1257 comm_semiring_1(real) # label(arity_RealDef_Oreal___Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 4.04/4.27 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D)). [resolve(1257,a,1233,a)].
% 4.04/4.27 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),B). [resolve(1257,a,1234,a)].
% 4.04/4.27 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A). [resolve(1257,a,1235,a)].
% 4.04/4.27 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)). [resolve(1257,a,1236,a)].
% 4.04/4.27 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),B). [resolve(1257,a,1239,a)].
% 4.04/4.27 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D)). [resolve(1257,a,1242,a)].
% 4.04/4.27 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A). [resolve(1257,a,1243,a)].
% 4.04/4.27 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)). [resolve(1257,a,1244,a)].
% 4.04/4.27 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real))),A) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A). [resolve(1257,a,1249,a)].
% 4.04/4.27 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real))),B) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)). [resolve(1257,a,1250,a)].
% 4.25/4.46 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real))),B) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),B). [resolve(1257,a,1251,a)].
% 4.25/4.46 1258 ordered_ring(int) # label(arity_Int_Oint___Rings_Oordered__ring) # label(axiom). [assumption].
% 4.25/4.46 1259 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C)),D)),F)) # label(fact_80_le__add__iff1) # label(axiom). [clausify(112)].
% 4.25/4.46 1260 -ordered_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C)),D)),F)) # label(fact_80_le__add__iff1) # label(axiom). [clausify(112)].
% 4.25/4.46 1261 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F))) # label(fact_81_le__add__iff2) # label(axiom). [clausify(113)].
% 4.25/4.46 1262 -ordered_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F))) # label(fact_81_le__add__iff2) # label(axiom). [clausify(113)].
% 4.25/4.46 1263 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C)),D)),F)) # label(fact_83_less__add__iff1) # label(axiom). [clausify(115)].
% 4.25/4.46 1264 -ordered_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C)),D)),F)) # label(fact_83_less__add__iff1) # label(axiom). [clausify(115)].
% 4.25/4.46 1265 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F))) # label(fact_84_less__add__iff2) # label(axiom). [clausify(116)].
% 4.25/4.46 1266 -ordered_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F))) # label(fact_84_less__add__iff2) # label(axiom). [clausify(116)].
% 4.25/4.46 1267 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_287_mult__nonpos__nonpos) # label(axiom). [clausify(318)].
% 4.25/4.46 1268 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_291_mult__right__mono__neg) # label(axiom). [clausify(322)].
% 4.25/4.46 1269 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_292_mult__left__mono__neg) # label(axiom). [clausify(323)].
% 4.25/4.46 1270 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_295_split__mult__pos__le) # label(axiom). [clausify(326)].
% 4.25/4.46 1271 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_295_split__mult__pos__le) # label(axiom). [clausify(326)].
% 4.25/4.46 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B)),C)),E)). [resolve(1258,a,1259,a)].
% 4.25/4.46 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B)),C)),E)). [resolve(1258,a,1260,a)].
% 4.25/4.46 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),D),A)),B)),E))). [resolve(1258,a,1261,a)].
% 4.25/4.46 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),D),A)),B)),E))). [resolve(1258,a,1262,a)].
% 4.25/4.46 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B)),C)),E)). [resolve(1258,a,1263,a)].
% 4.25/4.46 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B)),C)),E)). [resolve(1258,a,1264,a)].
% 4.25/4.46 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),D),A)),B)),E))). [resolve(1258,a,1265,a)].
% 4.25/4.46 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),D),A)),B)),E))). [resolve(1258,a,1266,a)].
% 4.25/4.46 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(1258,a,1267,a)].
% 4.25/4.46 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))). [resolve(1258,a,1268,a)].
% 4.25/4.46 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A))). [resolve(1258,a,1269,a)].
% 4.25/4.46 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(1258,a,1270,a)].
% 4.25/4.47 1272 ordered_ring(real) # label(arity_RealDef_Oreal___Rings_Oordered__ring) # label(axiom). [assumption].
% 4.25/4.47 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),D)),B)),C)),E)). [resolve(1272,a,1259,a)].
% 4.25/4.47 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),D)),B)),C)),E)). [resolve(1272,a,1260,a)].
% 4.25/4.47 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),A)),B)),E))). [resolve(1272,a,1261,a)].
% 4.25/4.47 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),A)),B)),E))). [resolve(1272,a,1262,a)].
% 4.25/4.47 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),D)),B)),C)),E)). [resolve(1272,a,1263,a)].
% 4.25/4.47 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),D)),B)),C)),E)). [resolve(1272,a,1264,a)].
% 4.25/4.47 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),A)),B)),E))). [resolve(1272,a,1265,a)].
% 4.37/4.56 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),A)),B)),E))). [resolve(1272,a,1266,a)].
% 4.37/4.56 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(1272,a,1267,a)].
% 4.37/4.56 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))). [resolve(1272,a,1268,a)].
% 4.37/4.56 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))). [resolve(1272,a,1269,a)].
% 4.37/4.56 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(1272,a,1270,a)].
% 4.37/4.56 1273 number_ring(int) # label(arity_Int_Oint___Int_Onumber__ring) # label(axiom). [assumption].
% 4.37/4.56 1274 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),C)),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C))),D) # label(fact_85_add__number__of__diff1) # label(axiom). [clausify(117)].
% 4.37/4.56 1275 -number_ring(A) | -ring_char_0(A) | hAPP(int,A,number_number_of(A),B) != hAPP(int,A,number_number_of(A),C) | B = C # label(fact_95_eq__number__of) # label(axiom). [clausify(127)].
% 4.37/4.56 1276 -number_ring(A) | -ring_char_0(A) | hAPP(int,A,number_number_of(A),B) = hAPP(int,A,number_number_of(A),C) | B != C # label(fact_95_eq__number__of) # label(axiom). [clausify(127)].
% 4.37/4.56 1277 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) # label(fact_96_less__number__of) # label(axiom). [clausify(128)].
% 4.37/4.56 1278 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) # label(fact_96_less__number__of) # label(axiom). [clausify(128)].
% 4.37/4.56 1279 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) # label(fact_97_le__number__of) # label(axiom). [clausify(129)].
% 4.37/4.56 1280 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) # label(fact_97_le__number__of) # label(axiom). [clausify(129)].
% 4.37/4.56 1281 -number_ring(A) | hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) # label(fact_137_number__of__mult) # label(axiom). [clausify(169)].
% 4.37/4.56 1282 -number_ring(A) | hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) # label(fact_138_arith__simps_I32_J) # label(axiom). [clausify(170)].
% 4.37/4.56 1283 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D)) # label(fact_139_mult__number__of__left) # label(axiom). [clausify(171)].
% 4.37/4.56 1284 -number_ring(A) | hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) # label(fact_140_number__of__add) # label(axiom). [clausify(172)].
% 4.37/4.56 1285 -number_ring(A) | hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) # label(fact_141_add__number__of__eq) # label(axiom). [clausify(173)].
% 4.37/4.56 1286 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C))),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),C)),D)) # label(fact_142_add__number__of__left) # label(axiom). [clausify(174)].
% 4.37/4.56 1287 -number_ring(A) | hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) # label(fact_143_number__of__diff) # label(axiom). [clausify(175)].
% 4.37/4.56 1288 -number_ring(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(int,A,number_number_of(A),B)),ring_1_Ints(A))) # label(fact_474_Ints__number__of) # label(axiom). [clausify(501)].
% 4.37/4.56 1289 -number_ring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(int,nat,number_number_of(nat),B)) = hAPP(int,A,number_number_of(A),B) # label(fact_794_of__nat__number__of__lemma) # label(axiom). [clausify(811)].
% 4.37/4.56 1290 -number_ring(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(A) # label(fact_794_of__nat__number__of__lemma) # label(axiom). [clausify(811)].
% 4.37/4.56 1291 -number_ring(A) | -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),B))) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(A) # label(fact_848_of__nat__number__of__eq) # label(axiom). [clausify(859)].
% 4.37/4.56 1292 -number_ring(A) | hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),B))) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(int,nat,number_number_of(nat),B)) = hAPP(int,A,number_number_of(A),B) # label(fact_848_of__nat__number__of__eq) # label(axiom). [clausify(859)].
% 4.37/4.56 1293 -number_ring(A) | hAPP(int,A,number_number_of(A),pls) = zero_zero(A) # label(fact_863_number__of__Pls) # label(axiom). [clausify(874)].
% 4.37/4.56 1294 -number_ring(A) | hAPP(int,A,number_number_of(A),pls) = zero_zero(A) # label(fact_865_semiring__norm_I112_J) # label(axiom). [clausify(876)].
% 4.37/4.56 1295 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),pls)),B) = ti(A,B) # label(fact_866_add__numeral__0) # label(axiom). [clausify(877)].
% 4.37/4.56 1296 -number_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(int,A,number_number_of(A),pls)) = ti(A,B) # label(fact_867_add__numeral__0__right) # label(axiom). [clausify(878)].
% 4.37/4.56 1297 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)) # label(fact_885_less__special_I1_J) # label(axiom). [clausify(887)].
% 4.37/4.56 1298 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)) # label(fact_885_less__special_I1_J) # label(axiom). [clausify(887)].
% 4.37/4.56 1299 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)) # label(fact_886_less__special_I3_J) # label(axiom). [clausify(888)].
% 4.37/4.56 1300 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)) # label(fact_886_less__special_I3_J) # label(axiom). [clausify(888)].
% 4.37/4.56 1301 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) # label(fact_887_le__special_I1_J) # label(axiom). [clausify(889)].
% 4.37/4.56 1302 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) # label(fact_887_le__special_I1_J) # label(axiom). [clausify(889)].
% 4.37/4.56 1303 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),pls)) # label(fact_888_le__special_I3_J) # label(axiom). [clausify(890)].
% 4.37/4.56 1304 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),pls)) # label(fact_888_le__special_I3_J) # label(axiom). [clausify(890)].
% 4.37/4.56 1305 -number_ring(A) | hAPP(int,A,number_number_of(A),hAPP(int,int,succ,B)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),hAPP(int,A,number_number_of(A),B)) # label(fact_896_number__of__succ) # label(axiom). [clausify(898)].
% 4.37/4.56 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,number_number_of(int),B)),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),C). [resolve(1273,a,1274,a)].
% 4.37/4.56 Derived: -ring_char_0(int) | hAPP(int,int,number_number_of(int),A) != hAPP(int,int,number_number_of(int),B) | A = B. [resolve(1273,a,1275,a)].
% 4.37/4.56 Derived: -ring_char_0(int) | hAPP(int,int,number_number_of(int),A) = hAPP(int,int,number_number_of(int),B) | A != B. [resolve(1273,a,1276,a)].
% 4.37/4.56 Derived: -linordered_idom(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(1273,a,1277,a)].
% 4.37/4.56 Derived: -linordered_idom(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(1273,a,1278,a)].
% 4.37/4.56 Derived: -linordered_idom(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1273,a,1279,a)].
% 4.37/4.56 Derived: -linordered_idom(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1273,a,1280,a)].
% 4.37/4.56 Derived: hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B)). [resolve(1273,a,1281,a)].
% 4.37/4.56 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))),C) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),B)),C)). [resolve(1273,a,1283,a)].
% 4.37/4.56 Derived: hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B)). [resolve(1273,a,1284,a)].
% 4.37/4.56 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),B)),C)). [resolve(1273,a,1286,a)].
% 4.37/4.56 Derived: hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B)). [resolve(1273,a,1287,a)].
% 4.37/4.56 Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,number_number_of(int),A)),ring_1_Ints(int))). [resolve(1273,a,1288,a)].
% 4.37/4.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),A)) = hAPP(int,int,number_number_of(int),A). [resolve(1273,a,1289,a)].
% 4.37/4.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(int). [resolve(1273,a,1290,a)].
% 4.37/4.56 Derived: -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),A))) | hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(int). [resolve(1273,a,1291,a)].
% 4.37/4.56 Derived: hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),A))) | hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),A)) = hAPP(int,int,number_number_of(int),A). [resolve(1273,a,1292,a)].
% 4.37/4.56 Derived: hAPP(int,int,number_number_of(int),pls) = zero_zero(int). [resolve(1273,a,1293,a)].
% 4.37/4.56 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),pls)),A) = ti(int,A). [resolve(1273,a,1295,a)].
% 4.37/4.56 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,number_number_of(int),pls)) = ti(int,A). [resolve(1273,a,1296,a)].
% 4.37/4.56 Derived: -linordered_idom(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(1273,a,1297,a)].
% 4.37/4.56 Derived: -linordered_idom(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(1273,a,1298,a)].
% 4.37/4.57 Derived: -linordered_idom(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). [resolve(1273,a,1299,a)].
% 4.37/4.57 Derived: -linordered_idom(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). [resolve(1273,a,1300,a)].
% 4.37/4.57 Derived: -linordered_idom(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)). [resolve(1273,a,1301,a)].
% 4.37/4.57 Derived: -linordered_idom(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)). [resolve(1273,a,1302,a)].
% 4.37/4.57 Derived: -linordered_idom(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)). [resolve(1273,a,1303,a)].
% 4.37/4.57 Derived: -linordered_idom(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)). [resolve(1273,a,1304,a)].
% 4.37/4.57 Derived: hAPP(int,int,number_number_of(int),hAPP(int,int,succ,A)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,number_number_of(int),A)). [resolve(1273,a,1305,a)].
% 4.37/4.57 1306 number_ring(real) # label(arity_RealDef_Oreal___Int_Onumber__ring) # label(axiom). [assumption].
% 4.37/4.57 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),B)),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),C). [resolve(1306,a,1274,a)].
% 4.37/4.57 Derived: -ring_char_0(real) | hAPP(int,real,number_number_of(real),A) != hAPP(int,real,number_number_of(real),B) | A = B. [resolve(1306,a,1275,a)].
% 4.37/4.57 Derived: -ring_char_0(real) | hAPP(int,real,number_number_of(real),A) = hAPP(int,real,number_number_of(real),B) | A != B. [resolve(1306,a,1276,a)].
% 4.37/4.57 Derived: -linordered_idom(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(1306,a,1277,a)].
% 4.37/4.57 Derived: -linordered_idom(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(1306,a,1278,a)].
% 4.37/4.57 Derived: -linordered_idom(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1306,a,1279,a)].
% 4.37/4.57 Derived: -linordered_idom(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1306,a,1280,a)].
% 4.37/4.57 Derived: hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B)). [resolve(1306,a,1281,a)].
% 4.37/4.57 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))),C) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),C)). [resolve(1306,a,1283,a)].
% 4.37/4.57 Derived: hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B)). [resolve(1306,a,1284,a)].
% 4.37/4.57 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),B)),C)). [resolve(1306,a,1286,a)].
% 4.37/4.57 Derived: hAPP(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B)). [resolve(1306,a,1287,a)].
% 4.37/4.57 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(int,real,number_number_of(real),A)),ring_1_Ints(real))). [resolve(1306,a,1288,a)].
% 4.37/4.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,real,semiring_1_of_nat(real),hAPP(int,nat,number_number_of(nat),A)) = hAPP(int,real,number_number_of(real),A). [resolve(1306,a,1289,a)].
% 4.37/4.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,real,semiring_1_of_nat(real),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(real). [resolve(1306,a,1290,a)].
% 4.37/4.57 Derived: -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),A))) | hAPP(nat,real,semiring_1_of_nat(real),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(real). [resolve(1306,a,1291,a)].
% 4.37/4.57 Derived: hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),A))) | hAPP(nat,real,semiring_1_of_nat(real),hAPP(int,nat,number_number_of(nat),A)) = hAPP(int,real,number_number_of(real),A). [resolve(1306,a,1292,a)].
% 4.37/4.57 Derived: hAPP(int,real,number_number_of(real),pls) = zero_zero(real). [resolve(1306,a,1293,a)].
% 4.37/4.57 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),pls)),A) = ti(real,A). [resolve(1306,a,1295,a)].
% 4.37/4.57 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(int,real,number_number_of(real),pls)) = ti(real,A). [resolve(1306,a,1296,a)].
% 4.37/4.57 Derived: -linordered_idom(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(1306,a,1297,a)].
% 4.37/4.57 Derived: -linordered_idom(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). [resolve(1306,a,1298,a)].
% 4.37/4.57 Derived: -linordered_idom(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). [resolve(1306,a,1299,a)].
% 4.37/4.57 Derived: -linordered_idom(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). [resolve(1306,a,1300,a)].
% 4.37/4.57 Derived: -linordered_idom(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)). [resolve(1306,a,1301,a)].
% 4.37/4.57 Derived: -linordered_idom(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)). [resolve(1306,a,1302,a)].
% 4.43/4.66 Derived: -linordered_idom(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)). [resolve(1306,a,1303,a)].
% 4.43/4.66 Derived: -linordered_idom(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),pls)). [resolve(1306,a,1304,a)].
% 4.43/4.66 Derived: hAPP(int,real,number_number_of(real),hAPP(int,int,succ,A)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(int,real,number_number_of(real),A)). [resolve(1306,a,1305,a)].
% 4.43/4.66 1307 linordered_semidom(int) # label(arity_Int_Oint___Rings_Olinordered__semidom) # label(axiom). [assumption].
% 4.43/4.66 1308 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_87_less__1__mult) # label(axiom). [clausify(119)].
% 4.43/4.66 1309 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A)))) # label(fact_88_less__add__one) # label(axiom). [clausify(120)].
% 4.43/4.66 1310 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_325_pos__add__strict) # label(axiom). [clausify(356)].
% 4.43/4.66 1311 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),zero_zero(A))) # label(fact_327_not__one__le__zero) # label(axiom). [clausify(358)].
% 4.43/4.66 1312 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),one_one(A))) # label(fact_328_zero__le__one) # label(axiom). [clausify(359)].
% 4.43/4.66 1313 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),zero_zero(A))) # label(fact_329_not__one__less__zero) # label(axiom). [clausify(360)].
% 4.43/4.66 1314 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),one_one(A))) # label(fact_330_zero__less__one) # label(axiom). [clausify(361)].
% 4.43/4.66 1315 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A)))) # label(fact_367_zero__less__two) # label(axiom). [clausify(397)].
% 4.43/4.66 1316 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) # label(fact_804_of__nat__0__le__iff) # label(axiom). [clausify(821)].
% 4.43/4.66 1317 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) # label(fact_805_zero__le__imp__of__nat) # label(axiom). [clausify(822)].
% 4.43/4.66 1318 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),zero_zero(A))) # label(fact_806_of__nat__less__0__iff) # label(axiom). [clausify(823)].
% 4.43/4.66 1319 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) # label(fact_808_of__nat__less__imp__less) # label(axiom). [clausify(825)].
% 4.43/4.66 1320 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_809_less__imp__of__nat__less) # label(axiom). [clausify(826)].
% 4.43/4.66 1321 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) # label(fact_810_of__nat__less__iff) # label(axiom). [clausify(827)].
% 4.48/4.66 1322 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) # label(fact_810_of__nat__less__iff) # label(axiom). [clausify(827)].
% 4.48/4.66 1323 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) # label(fact_811_of__nat__le__iff) # label(axiom). [clausify(828)].
% 4.48/4.66 1324 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) # label(fact_811_of__nat__le__iff) # label(axiom). [clausify(828)].
% 4.48/4.66 1325 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) # label(fact_844_of__nat__0__less__iff) # label(axiom). [clausify(855)].
% 4.48/4.66 1326 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) # label(fact_844_of__nat__0__less__iff) # label(axiom). [clausify(855)].
% 4.48/4.66 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(1307,a,1308,a)].
% 4.48/4.66 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int)))). [resolve(1307,a,1309,a)].
% 4.48/4.66 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))). [resolve(1307,a,1310,a)].
% 4.48/4.66 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),zero_zero(int))). [resolve(1307,a,1311,a)].
% 4.48/4.66 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))). [resolve(1307,a,1312,a)].
% 4.48/4.66 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),zero_zero(int))). [resolve(1307,a,1313,a)].
% 4.48/4.66 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))). [resolve(1307,a,1314,a)].
% 4.48/4.66 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int)))). [resolve(1307,a,1315,a)].
% 4.48/4.66 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),A))). [resolve(1307,a,1316,a)].
% 4.48/4.66 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),zero_zero(int))). [resolve(1307,a,1318,a)].
% 4.48/4.66 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1307,a,1319,a)].
% 4.48/4.66 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B))). [resolve(1307,a,1320,a)].
% 4.48/4.66 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1307,a,1323,a)].
% 4.48/4.67 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1307,a,1324,a)].
% 4.48/4.67 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(1307,a,1325,a)].
% 4.48/4.67 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(1307,a,1326,a)].
% 4.48/4.67 1327 linordered_semidom(nat) # label(arity_Nat_Onat___Rings_Olinordered__semidom) # label(axiom). [assumption].
% 4.48/4.67 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))). [resolve(1327,a,1308,a)].
% 4.48/4.67 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat)))). [resolve(1327,a,1309,a)].
% 4.48/4.67 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(1327,a,1310,a)].
% 4.48/4.67 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),zero_zero(nat))). [resolve(1327,a,1311,a)].
% 4.48/4.67 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),one_one(nat))). [resolve(1327,a,1312,a)].
% 4.48/4.67 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),zero_zero(nat))). [resolve(1327,a,1313,a)].
% 4.48/4.67 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),one_one(nat))). [resolve(1327,a,1314,a)].
% 4.48/4.67 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat)))). [resolve(1327,a,1315,a)].
% 4.48/4.67 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(nat,nat,semiring_1_of_nat(nat),A))). [resolve(1327,a,1316,a)].
% 4.48/4.67 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),zero_zero(nat))). [resolve(1327,a,1318,a)].
% 4.48/4.67 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1327,a,1319,a)].
% 4.48/4.67 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))). [resolve(1327,a,1320,a)].
% 4.48/4.67 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1327,a,1323,a)].
% 4.48/4.67 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1327,a,1324,a)].
% 4.48/4.67 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,semiring_1_of_nat(nat),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(1327,a,1325,a)].
% 4.48/4.67 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,semiring_1_of_nat(nat),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(1327,a,1326,a)].
% 4.55/4.77 1328 linordered_semidom(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semidom) # label(axiom). [assumption].
% 4.55/4.77 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(1328,a,1308,a)].
% 4.55/4.77 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real)))). [resolve(1328,a,1309,a)].
% 4.55/4.77 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))). [resolve(1328,a,1310,a)].
% 4.55/4.77 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),zero_zero(real))). [resolve(1328,a,1311,a)].
% 4.55/4.77 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),one_one(real))). [resolve(1328,a,1312,a)].
% 4.55/4.77 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),zero_zero(real))). [resolve(1328,a,1313,a)].
% 4.55/4.77 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),one_one(real))). [resolve(1328,a,1314,a)].
% 4.55/4.77 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real)))). [resolve(1328,a,1315,a)].
% 4.55/4.77 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,semiring_1_of_nat(real),A))). [resolve(1328,a,1316,a)].
% 4.55/4.77 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,semiring_1_of_nat(real),A)),zero_zero(real))). [resolve(1328,a,1318,a)].
% 4.55/4.77 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1328,a,1319,a)].
% 4.55/4.77 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))). [resolve(1328,a,1320,a)].
% 4.55/4.77 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1328,a,1323,a)].
% 4.55/4.77 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1328,a,1324,a)].
% 4.55/4.77 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,semiring_1_of_nat(real),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(1328,a,1325,a)].
% 4.55/4.77 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,semiring_1_of_nat(real),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(1328,a,1326,a)].
% 4.55/4.77 1329 ordere223160158up_add(int) # label(arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 4.55/4.77 1330 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_89_add__less__le__mono) # label(axiom). [clausify(121)].
% 4.58/4.77 1331 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_90_add__le__less__mono) # label(axiom). [clausify(122)].
% 4.58/4.77 1332 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_107_add__strict__right__mono) # label(axiom). [clausify(139)].
% 4.58/4.77 1333 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_108_add__strict__left__mono) # label(axiom). [clausify(140)].
% 4.58/4.77 1334 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_109_add__strict__mono) # label(axiom). [clausify(141)].
% 4.58/4.77 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D))). [resolve(1329,a,1330,a)].
% 4.58/4.77 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D))). [resolve(1329,a,1331,a)].
% 4.58/4.77 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C))). [resolve(1329,a,1332,a)].
% 4.58/4.77 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))). [resolve(1329,a,1333,a)].
% 4.58/4.77 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D))). [resolve(1329,a,1334,a)].
% 4.58/4.77 1335 ordere223160158up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 4.58/4.77 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))). [resolve(1335,a,1330,a)].
% 4.58/4.77 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))). [resolve(1335,a,1331,a)].
% 4.58/4.77 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C))). [resolve(1335,a,1332,a)].
% 4.58/4.77 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))). [resolve(1335,a,1333,a)].
% 4.67/4.87 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))). [resolve(1335,a,1334,a)].
% 4.67/4.87 1336 ordere223160158up_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 4.67/4.87 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D))). [resolve(1336,a,1330,a)].
% 4.67/4.87 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D))). [resolve(1336,a,1331,a)].
% 4.67/4.87 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C))). [resolve(1336,a,1332,a)].
% 4.67/4.87 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B))). [resolve(1336,a,1333,a)].
% 4.67/4.87 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D))). [resolve(1336,a,1334,a)].
% 4.67/4.87 1337 linorder(int) # label(arity_Int_Oint___Orderings_Olinorder) # label(axiom). [assumption].
% 4.67/4.87 1338 -number(A) | -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,A,number_number_of(A),B))) # label(fact_94_le__number__of__eq__not__less) # label(axiom). [clausify(126)].
% 4.67/4.87 1339 -number(A) | -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,A,number_number_of(A),B))) # label(fact_94_le__number__of__eq__not__less) # label(axiom). [clausify(126)].
% 4.67/4.87 1340 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) # label(fact_157_linorder__antisym__conv2) # label(axiom). [clausify(189)].
% 4.67/4.87 1341 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_157_linorder__antisym__conv2) # label(axiom). [clausify(189)].
% 4.67/4.87 1342 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_169_linorder__linear) # label(axiom). [clausify(201)].
% 4.67/4.87 1343 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_183_linorder__le__cases) # label(axiom). [clausify(215)].
% 4.67/4.87 1344 -linorder(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_185_linorder__neq__iff) # label(axiom). [clausify(217)].
% 4.67/4.87 1345 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_185_linorder__neq__iff) # label(axiom). [clausify(217)].
% 4.67/4.87 1346 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_185_linorder__neq__iff) # label(axiom). [clausify(217)].
% 4.67/4.87 1347 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,C) = ti(A,B) # label(fact_186_not__less__iff__gr__or__eq) # label(axiom). [clausify(218)].
% 4.67/4.87 1348 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_186_not__less__iff__gr__or__eq) # label(axiom). [clausify(218)].
% 4.67/4.87 1349 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_186_not__less__iff__gr__or__eq) # label(axiom). [clausify(218)].
% 4.67/4.87 1350 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_187_linorder__less__linear) # label(axiom). [clausify(219)].
% 4.67/4.87 1351 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,B) = ti(A,C) # label(fact_188_linorder__antisym__conv3) # label(axiom). [clausify(220)].
% 4.67/4.87 1352 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,B) != ti(A,C) # label(fact_188_linorder__antisym__conv3) # label(axiom). [clausify(220)].
% 4.67/4.87 1353 -linorder(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_189_linorder__neqE) # label(axiom). [clausify(221)].
% 4.67/4.87 1354 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_205_linorder__cases) # label(axiom). [clausify(237)].
% 4.67/4.87 1355 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_206_linorder__not__less) # label(axiom). [clausify(238)].
% 4.67/4.87 1356 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_206_linorder__not__less) # label(axiom). [clausify(238)].
% 4.67/4.87 1357 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_207_linorder__not__le) # label(axiom). [clausify(239)].
% 4.67/4.87 1358 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_207_linorder__not__le) # label(axiom). [clausify(239)].
% 4.67/4.87 1359 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_208_linorder__le__less__linear) # label(axiom). [clausify(240)].
% 4.67/4.87 1360 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_212_leI) # label(axiom). [clausify(244)].
% 4.67/4.87 1361 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_213_not__leE) # label(axiom). [clausify(245)].
% 4.67/4.87 1362 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = ti(A,B) # label(fact_214_linorder__antisym__conv1) # label(axiom). [clausify(246)].
% 4.67/4.87 1363 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_214_linorder__antisym__conv1) # label(axiom). [clausify(246)].
% 4.67/4.88 1364 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_217_leD) # label(axiom). [clausify(249)].
% 4.67/4.88 1365 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f81(A,B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_409_pinf_I6_J) # label(axiom). [clausify(437)].
% 4.67/4.88 1366 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f82(A,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_410_minf_I6_J) # label(axiom). [clausify(438)].
% 4.67/4.88 1367 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f83(A,B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_411_pinf_I8_J) # label(axiom). [clausify(439)].
% 4.67/4.88 1368 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f84(A,C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_412_minf_I8_J) # label(axiom). [clausify(440)].
% 4.67/4.88 Derived: -number(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(int,int,number_number_of(int),A))). [resolve(1337,a,1338,b)].
% 4.67/4.88 Derived: -number(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(int,int,number_number_of(int),A))). [resolve(1337,a,1339,b)].
% 4.67/4.88 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,B) = ti(int,A). [resolve(1337,a,1340,a)].
% 4.67/4.88 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,B) != ti(int,A). [resolve(1337,a,1341,a)].
% 4.67/4.88 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1337,a,1342,a)].
% 4.67/4.88 Derived: ti(int,A) = ti(int,B) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(1337,a,1344,a)].
% 4.67/4.88 Derived: ti(int,A) != ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)). [resolve(1337,a,1345,a)].
% 4.67/4.88 Derived: ti(int,A) != ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(1337,a,1346,a)].
% 4.67/4.88 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)). [resolve(1337,a,1348,a)].
% 4.67/4.88 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1337,a,1355,a)].
% 4.67/4.88 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1337,a,1356,a)].
% 4.67/4.88 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,B) != ti(int,A). [resolve(1337,a,1363,a)].
% 4.67/4.88 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f81(int,A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1337,a,1365,a)].
% 4.67/4.88 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f82(int,B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1337,a,1366,a)].
% 4.67/4.88 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f83(int,A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1337,a,1367,a)].
% 4.67/4.88 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f84(int,B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1337,a,1368,a)].
% 4.67/4.88 1369 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom). [assumption].
% 4.67/4.88 Derived: -number(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),B)),hAPP(int,nat,number_number_of(nat),A))). [resolve(1369,a,1338,b)].
% 4.67/4.88 Derived: -number(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),B)),hAPP(int,nat,number_number_of(nat),A))). [resolve(1369,a,1339,b)].
% 4.67/4.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) = ti(nat,A). [resolve(1369,a,1340,a)].
% 4.67/4.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) != ti(nat,A). [resolve(1369,a,1341,a)].
% 4.67/4.88 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1369,a,1342,a)].
% 4.67/4.88 Derived: ti(nat,A) = ti(nat,B) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1369,a,1344,a)].
% 4.67/4.88 Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(1369,a,1345,a)].
% 4.67/4.88 Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1369,a,1346,a)].
% 4.67/4.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(1369,a,1348,a)].
% 4.67/4.88 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1369,a,1355,a)].
% 4.67/4.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1369,a,1356,a)].
% 4.67/4.88 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,B) != ti(nat,A). [resolve(1369,a,1363,a)].
% 4.67/4.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f81(nat,A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1369,a,1365,a)].
% 4.67/4.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f82(nat,B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1369,a,1366,a)].
% 4.67/4.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f83(nat,A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1369,a,1367,a)].
% 4.67/4.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f84(nat,B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1369,a,1368,a)].
% 4.67/4.88 1370 linorder(real) # label(arity_RealDef_Oreal___Orderings_Olinorder) # label(axiom). [assumption].
% 4.67/4.88 Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),hAPP(int,real,number_number_of(real),A))). [resolve(1370,a,1338,b)].
% 4.67/4.88 Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),hAPP(int,real,number_number_of(real),A))). [resolve(1370,a,1339,b)].
% 4.79/4.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | ti(real,B) = ti(real,A). [resolve(1370,a,1340,a)].
% 4.79/4.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | ti(real,B) != ti(real,A). [resolve(1370,a,1341,a)].
% 4.79/4.98 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(1370,a,1342,a)].
% 4.79/4.98 Derived: ti(real,A) = ti(real,B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(1370,a,1344,a)].
% 4.79/4.98 Derived: ti(real,A) != ti(real,B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)). [resolve(1370,a,1345,a)].
% 4.79/4.98 Derived: ti(real,A) != ti(real,B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(1370,a,1346,a)].
% 4.79/4.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)). [resolve(1370,a,1348,a)].
% 4.79/4.98 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(1370,a,1355,a)].
% 4.79/4.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(1370,a,1356,a)].
% 4.79/4.98 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | ti(real,B) != ti(real,A). [resolve(1370,a,1363,a)].
% 4.79/4.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f81(real,A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(1370,a,1365,a)].
% 4.79/4.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),f82(real,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(1370,a,1366,a)].
% 4.79/4.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f83(real,A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(1370,a,1367,a)].
% 4.79/4.98 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),f84(real,B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(1370,a,1368,a)].
% 4.79/4.98 1371 ordere236663937imp_le(int) # label(arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 4.79/4.98 1372 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_105_add__less__cancel__right) # label(axiom). [clausify(137)].
% 4.79/4.98 1373 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_105_add__less__cancel__right) # label(axiom). [clausify(137)].
% 4.79/4.98 1374 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_106_add__less__cancel__left) # label(axiom). [clausify(138)].
% 4.79/4.98 1375 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_106_add__less__cancel__left) # label(axiom). [clausify(138)].
% 4.79/4.98 1376 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_110_add__less__imp__less__right) # label(axiom). [clausify(142)].
% 4.79/4.98 1377 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_111_add__less__imp__less__left) # label(axiom). [clausify(143)].
% 4.79/4.98 1378 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_119_add__le__cancel__right) # label(axiom). [clausify(151)].
% 4.79/4.98 1379 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_119_add__le__cancel__right) # label(axiom). [clausify(151)].
% 4.79/4.98 1380 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_120_add__le__cancel__left) # label(axiom). [clausify(152)].
% 4.79/4.98 1381 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_120_add__le__cancel__left) # label(axiom). [clausify(152)].
% 4.79/4.98 1382 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_124_add__le__imp__le__right) # label(axiom). [clausify(156)].
% 4.79/4.98 1383 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_125_add__le__imp__le__left) # label(axiom). [clausify(157)].
% 4.79/4.98 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(1371,a,1372,a)].
% 4.79/4.98 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(1371,a,1374,a)].
% 4.79/4.98 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(1371,a,1378,a)].
% 4.79/4.98 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(1371,a,1379,a)].
% 4.79/4.98 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(1371,a,1380,a)].
% 4.79/4.98 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(1371,a,1381,a)].
% 4.88/5.09 1384 ordere236663937imp_le(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 4.88/5.09 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1384,a,1372,a)].
% 4.88/5.09 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(1384,a,1374,a)].
% 4.88/5.09 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1384,a,1378,a)].
% 4.88/5.09 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1384,a,1379,a)].
% 4.88/5.09 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1384,a,1380,a)].
% 4.88/5.09 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1384,a,1381,a)].
% 4.88/5.09 1385 ordere236663937imp_le(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 4.88/5.09 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)). [resolve(1385,a,1372,a)].
% 4.88/5.09 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)). [resolve(1385,a,1374,a)].
% 4.88/5.09 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)). [resolve(1385,a,1378,a)].
% 4.88/5.09 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)). [resolve(1385,a,1379,a)].
% 4.88/5.09 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(1385,a,1380,a)].
% 4.88/5.09 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(1385,a,1381,a)].
% 4.88/5.09 1386 comm_monoid_mult(int) # label(arity_Int_Oint___Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 4.88/5.09 1387 -comm_monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) = ti(A,B) # label(fact_115_mult__1) # label(axiom). [clausify(147)].
% 4.88/5.09 1388 -comm_monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) = ti(A,B) # label(fact_117_mult_Ocomm__neutral) # label(axiom). [clausify(149)].
% 4.95/5.20 1389 comm_monoid_mult(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 4.95/5.20 1390 comm_monoid_mult(real) # label(arity_RealDef_Oreal___Groups_Ocomm__monoid__mult) # label(axiom). [assumption].
% 4.95/5.20 1391 ordered_ab_group_add(int) # label(arity_Int_Oint___Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 4.95/5.20 1392 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_118_diff__eq__diff__less) # label(axiom). [clausify(150)].
% 4.95/5.20 1393 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_118_diff__eq__diff__less) # label(axiom). [clausify(150)].
% 4.95/5.20 1394 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_126_diff__eq__diff__less__eq) # label(axiom). [clausify(158)].
% 4.95/5.20 1395 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_126_diff__eq__diff__less__eq) # label(axiom). [clausify(158)].
% 4.95/5.20 1396 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),zero_zero(A))) # label(fact_331_le__iff__diff__le__0) # label(axiom). [clausify(362)].
% 4.95/5.20 1397 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),zero_zero(A))) # label(fact_331_le__iff__diff__le__0) # label(axiom). [clausify(362)].
% 4.95/5.20 1398 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),zero_zero(A))) # label(fact_333_less__iff__diff__less__0) # label(axiom). [clausify(364)].
% 4.95/5.20 1399 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),zero_zero(A))) # label(fact_333_less__iff__diff__less__0) # label(axiom). [clausify(364)].
% 4.95/5.20 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(1391,a,1392,a)].
% 4.95/5.20 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(1391,a,1393,a)].
% 4.95/5.20 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1391,a,1394,a)].
% 4.95/5.20 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1391,a,1395,a)].
% 4.95/5.20 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),zero_zero(int))). [resolve(1391,a,1396,a)].
% 5.09/5.30 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),zero_zero(int))). [resolve(1391,a,1397,a)].
% 5.09/5.30 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),zero_zero(int))). [resolve(1391,a,1398,a)].
% 5.09/5.30 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),zero_zero(int))). [resolve(1391,a,1399,a)].
% 5.09/5.30 1400 ordered_ab_group_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 5.09/5.30 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(1400,a,1392,a)].
% 5.09/5.30 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(1400,a,1393,a)].
% 5.09/5.30 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(1400,a,1394,a)].
% 5.09/5.30 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(1400,a,1395,a)].
% 5.09/5.30 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),zero_zero(real))). [resolve(1400,a,1396,a)].
% 5.09/5.30 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),zero_zero(real))). [resolve(1400,a,1397,a)].
% 5.09/5.30 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),zero_zero(real))). [resolve(1400,a,1398,a)].
% 5.09/5.30 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),zero_zero(real))). [resolve(1400,a,1399,a)].
% 5.09/5.30 1401 ordere779506340up_add(int) # label(arity_Int_Oint___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 5.09/5.30 1402 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_121_add__right__mono) # label(axiom). [clausify(153)].
% 5.09/5.30 1403 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_122_add__left__mono) # label(axiom). [clausify(154)].
% 5.09/5.30 1404 -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_123_add__mono) # label(axiom). [clausify(155)].
% 5.18/5.40 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D))). [resolve(1401,a,1404,a)].
% 5.18/5.40 1405 ordere779506340up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 5.18/5.40 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))). [resolve(1405,a,1404,a)].
% 5.18/5.40 1406 ordere779506340up_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption].
% 5.18/5.40 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D))). [resolve(1406,a,1404,a)].
% 5.18/5.40 1407 dense_linorder(real) # label(arity_RealDef_Oreal___Orderings_Odense__linorder) # label(axiom). [assumption].
% 5.18/5.40 1408 -dense_linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f55(A,B,C)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_223_dense__le) # label(axiom). [clausify(255)].
% 5.18/5.40 1409 -dense_linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f55(A,B,C)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_223_dense__le) # label(axiom). [clausify(255)].
% 5.18/5.40 1410 -dense_linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f56(A,D,B,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_224_dense__le__bounded) # label(axiom). [clausify(256)].
% 5.18/5.40 1411 -dense_linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f56(A,D,B,C)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_224_dense__le__bounded) # label(axiom). [clausify(256)].
% 5.18/5.40 1412 -dense_linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f56(A,D,B,C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_224_dense__le__bounded) # label(axiom). [clausify(256)].
% 5.18/5.40 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f55(real,A,B)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(1407,a,1408,a)].
% 5.18/5.40 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),f55(real,A,B)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(1407,a,1409,a)].
% 5.18/5.40 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),f56(real,C,A,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(1407,a,1410,a)].
% 5.18/5.40 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f56(real,C,A,B)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(1407,a,1411,a)].
% 5.18/5.40 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),f56(real,C,A,B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(1407,a,1412,a)].
% 5.47/5.71 1413 linord626643107strict(int) # label(arity_Int_Oint___Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption].
% 5.47/5.71 1414 -linord626643107strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),F)) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),E),F) != one_one(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),D))),C)) # label(fact_238_convex__bound__lt) # label(axiom). [clausify(270)].
% 5.47/5.71 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),E)) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),D),E) != one_one(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),E),C))),B)). [resolve(1413,a,1414,a)].
% 5.47/5.71 1415 linord626643107strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption].
% 5.47/5.71 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),E)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),D),E) != one_one(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),C))),B)). [resolve(1415,a,1414,a)].
% 5.47/5.71 1416 ring_n68954251visors(int) # label(arity_Int_Oint___Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 5.47/5.71 1417 -ring_n68954251visors(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) != zero_zero(A) | zero_zero(A) = ti(A,B) | zero_zero(A) = ti(A,C) # label(fact_255_mult__eq__0__iff) # label(axiom). [clausify(287)].
% 5.47/5.71 1418 -ring_n68954251visors(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) = zero_zero(A) | zero_zero(A) != ti(A,B) # label(fact_255_mult__eq__0__iff) # label(axiom). [clausify(287)].
% 5.47/5.71 1419 -ring_n68954251visors(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) = zero_zero(A) | zero_zero(A) != ti(A,C) # label(fact_255_mult__eq__0__iff) # label(axiom). [clausify(287)].
% 5.47/5.71 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B) = zero_zero(int) | zero_zero(int) != ti(int,A). [resolve(1416,a,1418,a)].
% 5.47/5.71 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B) = zero_zero(int) | zero_zero(int) != ti(int,B). [resolve(1416,a,1419,a)].
% 5.47/5.71 1420 ring_n68954251visors(real) # label(arity_RealDef_Oreal___Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 5.47/5.71 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B) = zero_zero(real) | zero_zero(real) != ti(real,A). [resolve(1420,a,1418,a)].
% 5.47/5.71 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B) = zero_zero(real) | zero_zero(real) != ti(real,B). [resolve(1420,a,1419,a)].
% 5.47/5.71 1421 comm_monoid_add(int) # label(arity_Int_Oint___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 5.47/5.71 1422 -comm_monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) = ti(A,B) # label(fact_262_add__0) # label(axiom). [clausify(294)].
% 5.47/5.71 1423 -comm_monoid_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) = ti(A,B) # label(fact_265_add_Ocomm__neutral) # label(axiom). [clausify(297)].
% 5.61/5.81 1424 comm_monoid_add(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 5.61/5.81 1425 comm_monoid_add(real) # label(arity_RealDef_Oreal___Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 5.61/5.81 1426 linord219039673up_add(int) # label(arity_Int_Oint___Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 5.61/5.81 1427 -linord219039673up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_263_double__zero__sym) # label(axiom). [clausify(295)].
% 5.61/5.81 1428 -linord219039673up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) = zero_zero(A) | zero_zero(A) != ti(A,B) # label(fact_263_double__zero__sym) # label(axiom). [clausify(295)].
% 5.61/5.81 1429 -linord219039673up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_266_double__eq__0__iff) # label(axiom). [clausify(298)].
% 5.61/5.81 1430 -linord219039673up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) = zero_zero(A) | zero_zero(A) != ti(A,B) # label(fact_266_double__eq__0__iff) # label(axiom). [clausify(298)].
% 5.61/5.81 1431 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_314_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(345)].
% 5.61/5.81 1432 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_314_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(345)].
% 5.61/5.81 1433 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_315_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(346)].
% 5.61/5.81 1434 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_315_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(346)].
% 5.61/5.81 1435 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_321_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(352)].
% 5.61/5.81 1436 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_321_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(352)].
% 5.61/5.81 1437 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_323_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(354)].
% 5.61/5.81 1438 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_323_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(354)].
% 5.61/5.81 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) != zero_zero(int) | zero_zero(int) = ti(int,A). [resolve(1426,a,1427,a)].
% 5.61/5.81 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) = zero_zero(int) | zero_zero(int) != ti(int,A). [resolve(1426,a,1428,a)].
% 5.61/5.81 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(1426,a,1431,a)].
% 5.71/5.91 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(1426,a,1432,a)].
% 5.71/5.91 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(1426,a,1433,a)].
% 5.71/5.91 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(1426,a,1434,a)].
% 5.71/5.91 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(1426,a,1435,a)].
% 5.71/5.91 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(1426,a,1437,a)].
% 5.71/5.91 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(1426,a,1438,a)].
% 5.71/5.91 1439 linord219039673up_add(real) # label(arity_RealDef_Oreal___Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 5.71/5.91 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A) != zero_zero(real) | zero_zero(real) = ti(real,A). [resolve(1439,a,1427,a)].
% 5.71/5.91 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A) = zero_zero(real) | zero_zero(real) != ti(real,A). [resolve(1439,a,1428,a)].
% 5.71/5.91 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(1439,a,1431,a)].
% 5.71/5.91 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(1439,a,1432,a)].
% 5.71/5.91 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(1439,a,1433,a)].
% 5.71/5.91 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(1439,a,1434,a)].
% 5.71/5.91 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(1439,a,1435,a)].
% 5.71/5.91 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(1439,a,1437,a)].
% 5.71/5.91 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(1439,a,1438,a)].
% 5.71/5.91 1440 zero_neq_one(int) # label(arity_Int_Oint___Rings_Ozero__neq__one) # label(axiom). [assumption].
% 5.71/5.91 1441 -zero_neq_one(A) | zero_zero(A) != one_one(A) # label(fact_267_one__neq__zero) # label(axiom). [clausify(299)].
% 5.92/6.11 1442 -zero_neq_one(A) | zero_zero(A) != one_one(A) # label(fact_268_zero__neq__one) # label(axiom). [clausify(300)].
% 5.92/6.11 Derived: zero_zero(int) != one_one(int). [resolve(1440,a,1441,a)].
% 5.92/6.11 1443 zero_neq_one(nat) # label(arity_Nat_Onat___Rings_Ozero__neq__one) # label(axiom). [assumption].
% 5.92/6.11 Derived: zero_zero(nat) != one_one(nat). [resolve(1443,a,1441,a)].
% 5.92/6.11 1444 zero_neq_one(real) # label(arity_RealDef_Oreal___Rings_Ozero__neq__one) # label(axiom). [assumption].
% 5.92/6.11 Derived: zero_zero(real) != one_one(real). [resolve(1444,a,1441,a)].
% 5.92/6.11 1445 linordered_ring(int) # label(arity_Int_Oint___Rings_Olinordered__ring) # label(axiom). [assumption].
% 5.92/6.11 1446 -linordered_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B))) # label(fact_280_zero__le__square) # label(axiom). [clausify(311)].
% 5.92/6.11 1447 -linordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),zero_zero(A))) # label(fact_297_not__square__less__zero) # label(axiom). [clausify(328)].
% 5.92/6.11 1448 -linordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C))),zero_zero(A))) # label(fact_383_not__sum__squares__lt__zero) # label(axiom). [clausify(413)].
% 5.92/6.11 1449 -linordered_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C)))) # label(fact_385_sum__squares__ge__zero) # label(axiom). [clausify(415)].
% 5.92/6.11 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A))). [resolve(1445,a,1446,a)].
% 5.92/6.11 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),zero_zero(int))). [resolve(1445,a,1447,a)].
% 5.92/6.11 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B))),zero_zero(int))). [resolve(1445,a,1448,a)].
% 5.92/6.11 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B)))). [resolve(1445,a,1449,a)].
% 5.92/6.11 1450 linordered_ring(real) # label(arity_RealDef_Oreal___Rings_Olinordered__ring) # label(axiom). [assumption].
% 5.92/6.11 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A))). [resolve(1450,a,1446,a)].
% 5.92/6.11 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),zero_zero(real))). [resolve(1450,a,1447,a)].
% 5.92/6.11 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B))),zero_zero(real))). [resolve(1450,a,1448,a)].
% 5.92/6.11 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)))). [resolve(1450,a,1449,a)].
% 5.92/6.11 1451 linord581940658strict(int) # label(arity_Int_Oint___Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 5.92/6.11 1452 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_281_zero__le__mult__iff) # label(axiom). [clausify(312)].
% 5.92/6.11 1453 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) # label(fact_281_zero__le__mult__iff) # label(axiom). [clausify(312)].
% 5.92/6.11 1454 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_281_zero__le__mult__iff) # label(axiom). [clausify(312)].
% 5.92/6.11 1455 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) # label(fact_281_zero__le__mult__iff) # label(axiom). [clausify(312)].
% 5.92/6.11 1456 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) # label(fact_281_zero__le__mult__iff) # label(axiom). [clausify(312)].
% 5.92/6.11 1457 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) # label(fact_281_zero__le__mult__iff) # label(axiom). [clausify(312)].
% 5.92/6.11 1458 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_282_mult__le__0__iff) # label(axiom). [clausify(313)].
% 5.92/6.11 1459 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) # label(fact_282_mult__le__0__iff) # label(axiom). [clausify(313)].
% 5.92/6.11 1460 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_282_mult__le__0__iff) # label(axiom). [clausify(313)].
% 5.92/6.11 1461 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) # label(fact_282_mult__le__0__iff) # label(axiom). [clausify(313)].
% 5.92/6.11 1462 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) # label(fact_282_mult__le__0__iff) # label(axiom). [clausify(313)].
% 5.92/6.11 1463 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) # label(fact_282_mult__le__0__iff) # label(axiom). [clausify(313)].
% 5.92/6.11 1464 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_298_mult__less__cancel__right__disj) # label(axiom). [clausify(329)].
% 5.92/6.11 1465 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B)) # label(fact_298_mult__less__cancel__right__disj) # label(axiom). [clausify(329)].
% 5.92/6.11 1466 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_298_mult__less__cancel__right__disj) # label(axiom). [clausify(329)].
% 5.92/6.11 1467 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B)) # label(fact_298_mult__less__cancel__right__disj) # label(axiom). [clausify(329)].
% 5.92/6.11 1468 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_298_mult__less__cancel__right__disj) # label(axiom). [clausify(329)].
% 5.92/6.11 1469 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B)) # label(fact_298_mult__less__cancel__right__disj) # label(axiom). [clausify(329)].
% 5.92/6.11 1470 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_299_mult__less__cancel__left__disj) # label(axiom). [clausify(330)].
% 5.92/6.11 1471 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) # label(fact_299_mult__less__cancel__left__disj) # label(axiom). [clausify(330)].
% 5.92/6.11 1472 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_299_mult__less__cancel__left__disj) # label(axiom). [clausify(330)].
% 5.92/6.11 1473 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) # label(fact_299_mult__less__cancel__left__disj) # label(axiom). [clausify(330)].
% 5.92/6.11 1474 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_299_mult__less__cancel__left__disj) # label(axiom). [clausify(330)].
% 5.92/6.11 1475 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) # label(fact_299_mult__less__cancel__left__disj) # label(axiom). [clausify(330)].
% 5.92/6.11 1476 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_300_mult__less__cancel__left__pos) # label(axiom). [clausify(331)].
% 5.92/6.11 1477 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_300_mult__less__cancel__left__pos) # label(axiom). [clausify(331)].
% 5.92/6.11 1478 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) # label(fact_306_mult__less__cancel__left__neg) # label(axiom). [clausify(337)].
% 5.92/6.11 1479 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) # label(fact_306_mult__less__cancel__left__neg) # label(axiom). [clausify(337)].
% 5.92/6.11 1480 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_308_mult__neg__neg) # label(axiom). [clausify(339)].
% 5.92/6.11 1481 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_312_mult__strict__right__mono__neg) # label(axiom). [clausify(343)].
% 5.92/6.11 1482 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_313_mult__strict__left__mono__neg) # label(axiom). [clausify(344)].
% 5.92/6.11 1483 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_347_mult__le__cancel__left__pos) # label(axiom). [clausify(377)].
% 5.92/6.11 1484 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_347_mult__le__cancel__left__pos) # label(axiom). [clausify(377)].
% 5.92/6.11 1485 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) # label(fact_348_mult__le__cancel__left__neg) # label(axiom). [clausify(378)].
% 5.92/6.11 1486 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) # label(fact_348_mult__le__cancel__left__neg) # label(axiom). [clausify(378)].
% 5.92/6.11 1487 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C)))) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_382_sum__squares__gt__zero__iff) # label(axiom). [clausify(412)].
% 5.92/6.11 1488 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C)))) | zero_zero(A) = ti(A,B) # label(fact_382_sum__squares__gt__zero__iff) # label(axiom). [clausify(412)].
% 5.92/6.11 1489 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C)))) | zero_zero(A) = ti(A,C) # label(fact_382_sum__squares__gt__zero__iff) # label(axiom). [clausify(412)].
% 5.92/6.11 1490 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C))),zero_zero(A))) | zero_zero(A) = ti(A,B) # label(fact_384_sum__squares__le__zero__iff) # label(axiom). [clausify(414)].
% 5.92/6.11 1491 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C))),zero_zero(A))) | zero_zero(A) = ti(A,C) # label(fact_384_sum__squares__le__zero__iff) # label(axiom). [clausify(414)].
% 5.92/6.11 1492 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C))),zero_zero(A))) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_384_sum__squares__le__zero__iff) # label(axiom). [clausify(414)].
% 5.92/6.11 1493 -linord581940658strict(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C)) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_386_sum__squares__eq__zero__iff) # label(axiom). [clausify(416)].
% 5.92/6.11 1494 -linord581940658strict(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C)) != zero_zero(A) | zero_zero(A) = ti(A,C) # label(fact_386_sum__squares__eq__zero__iff) # label(axiom). [clausify(416)].
% 5.92/6.11 1495 -linord581940658strict(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C)) = zero_zero(A) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_386_sum__squares__eq__zero__iff) # label(axiom). [clausify(416)].
% 5.92/6.11 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))). [resolve(1451,a,1453,a)].
% 5.92/6.11 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(1451,a,1454,a)].
% 5.92/6.11 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)). [resolve(1451,a,1459,a)].
% 5.92/6.11 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(1451,a,1460,a)].
% 5.92/6.11 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))). [resolve(1451,a,1462,a)].
% 5.92/6.11 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)). [resolve(1451,a,1463,a)].
% 5.92/6.11 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))). [resolve(1451,a,1464,a)].
% 5.92/6.11 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),A)). [resolve(1451,a,1465,a)].
% 5.92/6.11 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))). [resolve(1451,a,1466,a)].
% 5.92/6.11 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),A)). [resolve(1451,a,1467,a)].
% 5.92/6.11 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(1451,a,1468,a)].
% 5.92/6.11 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),A)). [resolve(1451,a,1469,a)].
% 5.92/6.11 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(1451,a,1470,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B)). [resolve(1451,a,1471,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(1451,a,1472,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B)). [resolve(1451,a,1473,a)].
% 5.92/6.12 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(1451,a,1474,a)].
% 5.92/6.12 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B)). [resolve(1451,a,1475,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(1451,a,1476,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B)). [resolve(1451,a,1478,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(1451,a,1480,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(1451,a,1483,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(1451,a,1484,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),B)). [resolve(1451,a,1485,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),B)). [resolve(1451,a,1486,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B)))) | zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B). [resolve(1451,a,1487,a)].
% 5.92/6.12 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B)))) | zero_zero(int) = ti(int,A). [resolve(1451,a,1488,a)].
% 5.92/6.12 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B)))) | zero_zero(int) = ti(int,B). [resolve(1451,a,1489,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B))),zero_zero(int))) | zero_zero(int) = ti(int,A). [resolve(1451,a,1490,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B))),zero_zero(int))) | zero_zero(int) = ti(int,B). [resolve(1451,a,1491,a)].
% 5.92/6.12 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B))),zero_zero(int))) | zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B). [resolve(1451,a,1492,a)].
% 5.92/6.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B)) != zero_zero(int) | zero_zero(int) = ti(int,A). [resolve(1451,a,1493,a)].
% 5.92/6.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B)) != zero_zero(int) | zero_zero(int) = ti(int,B). [resolve(1451,a,1494,a)].
% 5.92/6.12 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B)) = zero_zero(int) | zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B). [resolve(1451,a,1495,a)].
% 5.92/6.12 1496 linord581940658strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 5.92/6.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))). [resolve(1496,a,1453,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(1496,a,1454,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)). [resolve(1496,a,1459,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(1496,a,1460,a)].
% 5.92/6.12 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))). [resolve(1496,a,1462,a)].
% 5.92/6.12 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)). [resolve(1496,a,1463,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))). [resolve(1496,a,1464,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),A)). [resolve(1496,a,1465,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))). [resolve(1496,a,1466,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),A)). [resolve(1496,a,1467,a)].
% 5.92/6.12 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)). [resolve(1496,a,1468,a)].
% 5.92/6.12 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),A)). [resolve(1496,a,1469,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(1496,a,1470,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),B)). [resolve(1496,a,1471,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(1496,a,1472,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),B)). [resolve(1496,a,1473,a)].
% 5.92/6.12 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)). [resolve(1496,a,1474,a)].
% 5.92/6.12 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),B)). [resolve(1496,a,1475,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)). [resolve(1496,a,1476,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),B)). [resolve(1496,a,1478,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(1496,a,1480,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(1496,a,1483,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(1496,a,1484,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),B)). [resolve(1496,a,1485,a)].
% 5.92/6.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),B)). [resolve(1496,a,1486,a)].
% 6.02/6.23 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)))) | zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B). [resolve(1496,a,1487,a)].
% 6.02/6.23 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)))) | zero_zero(real) = ti(real,A). [resolve(1496,a,1488,a)].
% 6.02/6.23 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)))) | zero_zero(real) = ti(real,B). [resolve(1496,a,1489,a)].
% 6.02/6.23 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B))),zero_zero(real))) | zero_zero(real) = ti(real,A). [resolve(1496,a,1490,a)].
% 6.02/6.23 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B))),zero_zero(real))) | zero_zero(real) = ti(real,B). [resolve(1496,a,1491,a)].
% 6.02/6.23 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B))),zero_zero(real))) | zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B). [resolve(1496,a,1492,a)].
% 6.02/6.23 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)) != zero_zero(real) | zero_zero(real) = ti(real,A). [resolve(1496,a,1493,a)].
% 6.02/6.23 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)) != zero_zero(real) | zero_zero(real) = ti(real,B). [resolve(1496,a,1494,a)].
% 6.02/6.23 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)) = zero_zero(real) | zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B). [resolve(1496,a,1495,a)].
% 6.02/6.23 1497 ordere453448008miring(int) # label(arity_Int_Oint___Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 6.02/6.23 1498 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_283_mult__nonneg__nonneg) # label(axiom). [clausify(314)].
% 6.02/6.23 1499 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_284_mult__nonneg__nonpos) # label(axiom). [clausify(315)].
% 6.02/6.23 1500 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),zero_zero(A))) # label(fact_285_mult__nonneg__nonpos2) # label(axiom). [clausify(316)].
% 6.06/6.33 1501 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_286_mult__nonpos__nonneg) # label(axiom). [clausify(317)].
% 6.06/6.33 1502 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_296_split__mult__neg__le) # label(axiom). [clausify(327)].
% 6.06/6.33 1503 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_296_split__mult__neg__le) # label(axiom). [clausify(327)].
% 6.06/6.33 1504 ordere453448008miring(nat) # label(arity_Nat_Onat___Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 6.06/6.33 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))). [resolve(1504,a,1498,a)].
% 6.06/6.33 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),zero_zero(nat))). [resolve(1504,a,1499,a)].
% 6.06/6.33 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A)),zero_zero(nat))). [resolve(1504,a,1500,a)].
% 6.06/6.33 1505 ordere453448008miring(real) # label(arity_RealDef_Oreal___Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 6.06/6.33 1506 ordered_semiring(int) # label(arity_Int_Oint___Rings_Oordered__semiring) # label(axiom). [assumption].
% 6.06/6.33 1507 -ordered_semiring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_288_mult__right__mono) # label(axiom). [clausify(319)].
% 6.06/6.33 1508 -ordered_semiring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_289_mult__left__mono) # label(axiom). [clausify(320)].
% 6.06/6.33 1509 -ordered_semiring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_293_mult__mono_H) # label(axiom). [clausify(324)].
% 6.06/6.33 1510 -ordered_semiring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_294_mult__mono) # label(axiom). [clausify(325)].
% 6.06/6.33 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))). [resolve(1506,a,1507,a)].
% 6.06/6.33 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))). [resolve(1506,a,1508,a)].
% 6.06/6.33 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))). [resolve(1506,a,1509,a)].
% 6.06/6.33 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))). [resolve(1506,a,1510,a)].
% 6.06/6.33 1511 ordered_semiring(nat) # label(arity_Nat_Onat___Rings_Oordered__semiring) # label(axiom). [assumption].
% 6.06/6.33 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))). [resolve(1511,a,1507,a)].
% 6.06/6.33 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))). [resolve(1511,a,1508,a)].
% 6.06/6.33 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D))). [resolve(1511,a,1509,a)].
% 6.06/6.33 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D))). [resolve(1511,a,1510,a)].
% 6.32/6.54 1512 ordered_semiring(real) # label(arity_RealDef_Oreal___Rings_Oordered__semiring) # label(axiom). [assumption].
% 6.32/6.54 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))). [resolve(1512,a,1507,a)].
% 6.32/6.54 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))). [resolve(1512,a,1508,a)].
% 6.32/6.54 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(1512,a,1509,a)].
% 6.32/6.54 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(1512,a,1510,a)].
% 6.32/6.54 1513 ordere1490568538miring(int) # label(arity_Int_Oint___Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 6.32/6.54 1514 -ordere1490568538miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_290_comm__mult__left__mono) # label(axiom). [clausify(321)].
% 6.32/6.54 1515 ordere1490568538miring(nat) # label(arity_Nat_Onat___Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 6.32/6.54 1516 ordere1490568538miring(real) # label(arity_RealDef_Oreal___Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 6.32/6.54 1517 linord20386208strict(int) # label(arity_Int_Oint___Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 6.32/6.54 1518 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_301_mult__pos__pos) # label(axiom). [clausify(332)].
% 6.32/6.54 1519 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_302_mult__pos__neg) # label(axiom). [clausify(333)].
% 6.32/6.54 1520 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),zero_zero(A))) # label(fact_303_mult__pos__neg2) # label(axiom). [clausify(334)].
% 6.32/6.54 1521 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_304_zero__less__mult__pos) # label(axiom). [clausify(335)].
% 6.32/6.54 1522 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_305_zero__less__mult__pos2) # label(axiom). [clausify(336)].
% 6.32/6.54 1523 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_307_mult__neg__pos) # label(axiom). [clausify(338)].
% 6.32/6.54 1524 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_309_mult__strict__right__mono) # label(axiom). [clausify(340)].
% 6.32/6.54 1525 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_310_mult__strict__left__mono) # label(axiom). [clausify(341)].
% 6.32/6.54 1526 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_349_mult__strict__mono) # label(axiom). [clausify(379)].
% 6.32/6.54 1527 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_350_mult__strict__mono_H) # label(axiom). [clausify(380)].
% 6.32/6.54 1528 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_351_mult__less__le__imp__less) # label(axiom). [clausify(381)].
% 6.32/6.54 1529 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_352_mult__le__less__imp__less) # label(axiom). [clausify(382)].
% 6.32/6.54 1530 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_354_mult__less__imp__less__right) # label(axiom). [clausify(384)].
% 6.32/6.54 1531 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_356_mult__less__imp__less__left) # label(axiom). [clausify(386)].
% 6.32/6.54 1532 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_357_mult__right__le__imp__le) # label(axiom). [clausify(387)].
% 6.32/6.54 1533 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_358_mult__left__le__imp__le) # label(axiom). [clausify(388)].
% 6.32/6.54 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(1517,a,1518,a)].
% 6.32/6.54 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),zero_zero(int))). [resolve(1517,a,1519,a)].
% 6.32/6.54 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),zero_zero(int))). [resolve(1517,a,1520,a)].
% 6.32/6.54 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)). [resolve(1517,a,1521,a)].
% 6.32/6.54 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(1517,a,1522,a)].
% 6.32/6.54 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))). [resolve(1517,a,1526,a)].
% 6.32/6.54 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))). [resolve(1517,a,1527,a)].
% 6.32/6.54 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))). [resolve(1517,a,1528,a)].
% 6.36/6.54 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))). [resolve(1517,a,1529,a)].
% 6.36/6.54 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(1517,a,1530,a)].
% 6.36/6.54 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(1517,a,1531,a)].
% 6.36/6.54 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(1517,a,1532,a)].
% 6.36/6.54 1534 linord20386208strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 6.36/6.54 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))). [resolve(1534,a,1518,a)].
% 6.36/6.54 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),zero_zero(nat))). [resolve(1534,a,1519,a)].
% 6.36/6.54 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A)),zero_zero(nat))). [resolve(1534,a,1520,a)].
% 6.36/6.54 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)). [resolve(1534,a,1521,a)].
% 6.36/6.54 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(1534,a,1522,a)].
% 6.36/6.54 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))). [resolve(1534,a,1524,a)].
% 6.36/6.54 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))). [resolve(1534,a,1525,a)].
% 6.36/6.54 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D))). [resolve(1534,a,1526,a)].
% 6.36/6.54 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D))). [resolve(1534,a,1527,a)].
% 6.36/6.54 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D))). [resolve(1534,a,1528,a)].
% 6.36/6.54 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D))). [resolve(1534,a,1529,a)].
% 6.36/6.54 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1534,a,1530,a)].
% 6.36/6.54 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(1534,a,1531,a)].
% 6.36/6.54 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1534,a,1532,a)].
% 6.36/6.54 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1534,a,1533,a)].
% 6.36/6.54 1535 linord20386208strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 6.36/6.54 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(1535,a,1518,a)].
% 6.36/6.55 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))). [resolve(1535,a,1519,a)].
% 6.36/6.55 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),zero_zero(real))). [resolve(1535,a,1520,a)].
% 6.36/6.55 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(1535,a,1521,a)].
% 6.36/6.55 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(1535,a,1522,a)].
% 6.36/6.55 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(1535,a,1526,a)].
% 6.36/6.55 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(1535,a,1527,a)].
% 6.36/6.55 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(1535,a,1528,a)].
% 6.36/6.55 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(1535,a,1529,a)].
% 6.36/6.55 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)). [resolve(1535,a,1530,a)].
% 6.53/6.75 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)). [resolve(1535,a,1531,a)].
% 6.53/6.75 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)). [resolve(1535,a,1532,a)].
% 6.53/6.75 1536 linord893533164strict(int) # label(arity_Int_Oint___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 6.53/6.75 1537 -linord893533164strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_311_comm__mult__strict__left__mono) # label(axiom). [clausify(342)].
% 6.53/6.75 1538 linord893533164strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 6.53/6.75 1539 linord893533164strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 6.53/6.75 1540 ordere216010020id_add(int) # label(arity_Int_Oint___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 6.53/6.75 1541 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_316_add__nonneg__nonneg) # label(axiom). [clausify(347)].
% 6.53/6.75 1542 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != zero_zero(A) | zero_zero(A) = ti(A,B) # label(fact_317_add__nonneg__eq__0__iff) # label(axiom). [clausify(348)].
% 6.53/6.75 1543 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != zero_zero(A) | zero_zero(A) = ti(A,C) # label(fact_317_add__nonneg__eq__0__iff) # label(axiom). [clausify(348)].
% 6.53/6.75 1544 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = zero_zero(A) | zero_zero(A) != ti(A,B) | zero_zero(A) != ti(A,C) # label(fact_317_add__nonneg__eq__0__iff) # label(axiom). [clausify(348)].
% 6.53/6.75 1545 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_318_add__increasing) # label(axiom). [clausify(349)].
% 6.53/6.75 1546 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B))) # label(fact_319_add__increasing2) # label(axiom). [clausify(350)].
% 6.53/6.75 1547 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_320_add__nonpos__nonpos) # label(axiom). [clausify(351)].
% 6.53/6.76 1548 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_324_add__pos__pos) # label(axiom). [clausify(355)].
% 6.53/6.76 1549 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_326_add__neg__neg) # label(axiom). [clausify(357)].
% 6.53/6.76 1550 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_359_add__pos__nonneg) # label(axiom). [clausify(389)].
% 6.53/6.76 1551 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_360_add__nonneg__pos) # label(axiom). [clausify(390)].
% 6.53/6.76 1552 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_361_add__strict__increasing) # label(axiom). [clausify(391)].
% 6.53/6.76 1553 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_362_add__strict__increasing2) # label(axiom). [clausify(392)].
% 6.53/6.76 1554 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_363_add__neg__nonpos) # label(axiom). [clausify(393)].
% 6.53/6.76 1555 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_364_add__nonpos__neg) # label(axiom). [clausify(394)].
% 6.53/6.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))). [resolve(1540,a,1541,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != zero_zero(int) | zero_zero(int) = ti(int,A). [resolve(1540,a,1542,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != zero_zero(int) | zero_zero(int) = ti(int,B). [resolve(1540,a,1543,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = zero_zero(int) | zero_zero(int) != ti(int,A) | zero_zero(int) != ti(int,B). [resolve(1540,a,1544,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))). [resolve(1540,a,1545,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),A))). [resolve(1540,a,1546,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),zero_zero(int))). [resolve(1540,a,1547,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),zero_zero(int))). [resolve(1540,a,1549,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))). [resolve(1540,a,1550,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))). [resolve(1540,a,1551,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))). [resolve(1540,a,1552,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))). [resolve(1540,a,1553,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),zero_zero(int))). [resolve(1540,a,1554,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),zero_zero(int))). [resolve(1540,a,1555,a)].
% 6.53/6.76 1556 ordere216010020id_add(nat) # label(arity_Nat_Onat___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 6.53/6.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))). [resolve(1556,a,1541,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != zero_zero(nat) | zero_zero(nat) = ti(nat,A). [resolve(1556,a,1542,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != zero_zero(nat) | zero_zero(nat) = ti(nat,B). [resolve(1556,a,1543,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = zero_zero(nat) | zero_zero(nat) != ti(nat,A) | zero_zero(nat) != ti(nat,B). [resolve(1556,a,1544,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(1556,a,1545,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),A))). [resolve(1556,a,1546,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(1556,a,1547,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(1556,a,1549,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))). [resolve(1556,a,1550,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))). [resolve(1556,a,1551,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(1556,a,1552,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(1556,a,1553,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(1556,a,1554,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(1556,a,1555,a)].
% 6.53/6.76 1557 ordere216010020id_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 6.53/6.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))). [resolve(1557,a,1541,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != zero_zero(real) | zero_zero(real) = ti(real,A). [resolve(1557,a,1542,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != zero_zero(real) | zero_zero(real) = ti(real,B). [resolve(1557,a,1543,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = zero_zero(real) | zero_zero(real) != ti(real,A) | zero_zero(real) != ti(real,B). [resolve(1557,a,1544,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))). [resolve(1557,a,1545,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),A))). [resolve(1557,a,1546,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),zero_zero(real))). [resolve(1557,a,1547,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),zero_zero(real))). [resolve(1557,a,1549,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))). [resolve(1557,a,1550,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))). [resolve(1557,a,1551,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))). [resolve(1557,a,1552,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))). [resolve(1557,a,1553,a)].
% 6.53/6.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),zero_zero(real))). [resolve(1557,a,1554,a)].
% 6.89/7.08 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),zero_zero(real))). [resolve(1557,a,1555,a)].
% 6.89/7.08 1558 linordered_semiring(int) # label(arity_Int_Oint___Rings_Olinordered__semiring) # label(axiom). [assumption].
% 6.89/7.08 1559 -linordered_semiring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_353_mult__right__less__imp__less) # label(axiom). [clausify(383)].
% 6.89/7.08 1560 -linordered_semiring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_355_mult__left__less__imp__less) # label(axiom). [clausify(385)].
% 6.89/7.08 1561 linordered_semiring(nat) # label(arity_Nat_Onat___Rings_Olinordered__semiring) # label(axiom). [assumption].
% 6.89/7.08 1562 linordered_semiring(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semiring) # label(axiom). [assumption].
% 6.89/7.08 1563 linord1278240602ring_1(int) # label(arity_Int_Oint___Rings_Olinordered__semiring__1) # label(axiom). [assumption].
% 6.89/7.08 1564 -linord1278240602ring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),F)) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),E),F) != one_one(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),D))),C)) # label(fact_371_convex__bound__le) # label(axiom). [clausify(401)].
% 6.89/7.08 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),E)) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),D),E) != one_one(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),E),C))),B)). [resolve(1563,a,1564,a)].
% 6.89/7.08 1565 linord1278240602ring_1(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semiring__1) # label(axiom). [assumption].
% 6.89/7.08 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),E)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),D),E) != one_one(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),C))),B)). [resolve(1565,a,1564,a)].
% 6.89/7.08 1566 linord1117847801e_zero(real) # label(arity_RealDef_Oreal___Fields_Olinordered__field__inverse__zero) # label(axiom). [assumption].
% 7.08/7.29 1567 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),f79(A,B,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_396_field__le__mult__one__interval) # label(axiom). [clausify(424)].
% 7.08/7.29 1568 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f79(A,B,C)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_396_field__le__mult__one__interval) # label(axiom). [clausify(424)].
% 7.08/7.29 1569 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f79(A,B,C)),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_396_field__le__mult__one__interval) # label(axiom). [clausify(424)].
% 7.08/7.29 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f79(real,A,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(1566,a,1567,a)].
% 7.08/7.29 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f79(real,A,B)),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(1566,a,1568,a)].
% 7.08/7.29 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),f79(real,A,B)),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(1566,a,1569,a)].
% 7.08/7.29 1570 linordered_field(real) # label(arity_RealDef_Oreal___Fields_Olinordered__field) # label(axiom). [assumption].
% 7.08/7.29 1571 -linordered_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),f80(A,B,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_408_field__le__epsilon) # label(axiom). [clausify(436)].
% 7.08/7.29 1572 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),f80(A,B,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_408_field__le__epsilon) # label(axiom). [clausify(436)].
% 7.08/7.29 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f80(real,A,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(1570,a,1571,a)].
% 7.08/7.29 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),f80(real,A,B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(1570,a,1572,a)].
% 7.08/7.29 1573 ordered_ring_abs(int) # label(arity_Int_Oint___Rings_Oordered__ring__abs) # label(axiom). [assumption].
% 7.08/7.29 1574 -ordered_ring_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)) = hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_490_abs__eq__mult) # label(axiom). [clausify(517)].
% 7.08/7.29 1575 -ordered_ring_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)) = hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_490_abs__eq__mult) # label(axiom). [clausify(517)].
% 7.08/7.29 1576 -ordered_ring_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)) = hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_490_abs__eq__mult) # label(axiom). [clausify(517)].
% 7.08/7.29 1577 -ordered_ring_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)) = hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_490_abs__eq__mult) # label(axiom). [clausify(517)].
% 7.19/7.39 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B)) = hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)). [resolve(1573,a,1574,a)].
% 7.19/7.39 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B)) = hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)). [resolve(1573,a,1575,a)].
% 7.19/7.39 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B)) = hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)). [resolve(1573,a,1576,a)].
% 7.19/7.39 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),A)),hAPP(int,int,abs_abs(int),B)) = hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)). [resolve(1573,a,1577,a)].
% 7.19/7.39 1578 ordered_ring_abs(real) # label(arity_RealDef_Oreal___Rings_Oordered__ring__abs) # label(axiom). [assumption].
% 7.19/7.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)). [resolve(1578,a,1574,a)].
% 7.19/7.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)). [resolve(1578,a,1575,a)].
% 7.19/7.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)). [resolve(1578,a,1576,a)].
% 7.19/7.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)). [resolve(1578,a,1577,a)].
% 7.19/7.39 1579 number_semiring(int) # label(arity_Int_Oint___Int_Onumber__semiring) # label(axiom). [assumption].
% 7.19/7.39 1580 -number_semiring(A) | hAPP(nat,A,semiring_1_of_nat(A),B) = hAPP(int,A,number_number_of(A),hAPP(nat,int,semiring_1_of_nat(int),B)) # label(fact_796_number__of__int) # label(axiom). [clausify(813)].
% 7.19/7.39 1581 -number_semiring(A) | hAPP(int,A,number_number_of(A),pls) = zero_zero(A) # label(fact_864_semiring__numeral__0__eq__0) # label(axiom). [clausify(875)].
% 7.19/7.39 1582 -number_semiring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),C)) | hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) # label(fact_889_semiring__mult__number__of) # label(axiom). [clausify(891)].
% 7.19/7.40 1583 -number_semiring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),C)) | hAPP(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C)) # label(fact_890_semiring__add__number__of) # label(axiom). [clausify(892)].
% 7.19/7.40 1584 -number_semiring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(int,A,number_number_of(A),hAPP(int,int,succ,B)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),hAPP(int,A,number_number_of(A),B)) # label(fact_897_semiring__1__add__number__of) # label(axiom). [clausify(899)].
% 7.19/7.40 1585 -number_semiring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(int,A,number_number_of(A),hAPP(int,int,succ,B)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),one_one(A)) # label(fact_898_semiring__number__of__add__1) # label(axiom). [clausify(900)].
% 7.19/7.40 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(int,int,number_number_of(int),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(1579,a,1580,a)].
% 7.19/7.40 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,int,number_number_of(int),hAPP(int,int,succ,A)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),A)),one_one(int)). [resolve(1579,a,1585,a)].
% 7.19/7.40 1586 number_semiring(nat) # label(arity_Nat_Onat___Int_Onumber__semiring) # label(axiom). [assumption].
% 7.19/7.40 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) = hAPP(int,nat,number_number_of(nat),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(1586,a,1580,a)].
% 7.19/7.40 Derived: hAPP(int,nat,number_number_of(nat),pls) = zero_zero(nat). [resolve(1586,a,1581,a)].
% 7.19/7.40 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B)). [resolve(1586,a,1582,a)].
% 7.19/7.40 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B)). [resolve(1586,a,1583,a)].
% 7.19/7.40 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),A)). [resolve(1586,a,1584,a)].
% 7.19/7.40 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),A)),one_one(nat)). [resolve(1586,a,1585,a)].
% 7.19/7.40 1587 number_semiring(real) # label(arity_RealDef_Oreal___Int_Onumber__semiring) # label(axiom). [assumption].
% 7.19/7.40 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) = hAPP(int,real,number_number_of(real),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(1587,a,1580,a)].
% 7.19/7.40 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,real,number_number_of(real),hAPP(int,int,succ,A)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),one_one(real)). [resolve(1587,a,1585,a)].
% 7.88/8.12 1588 semiring_char_0(int) # label(arity_Int_Oint___Nat_Osemiring__char__0) # label(axiom). [assumption].
% 7.88/8.12 1589 -semiring_char_0(A) | hAPP(nat,A,semiring_1_of_nat(A),B) != hAPP(nat,A,semiring_1_of_nat(A),C) | B = C # label(fact_816_of__nat__eq__iff) # label(axiom). [clausify(833)].
% 7.88/8.12 1590 -semiring_char_0(A) | hAPP(nat,A,semiring_1_of_nat(A),B) = hAPP(nat,A,semiring_1_of_nat(A),C) | B != C # label(fact_816_of__nat__eq__iff) # label(axiom). [clausify(833)].
% 7.88/8.12 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) != hAPP(nat,int,semiring_1_of_nat(int),B) | A = B. [resolve(1588,a,1589,a)].
% 7.88/8.12 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(nat,int,semiring_1_of_nat(int),B) | A != B. [resolve(1588,a,1590,a)].
% 7.88/8.12 1591 semiring_char_0(nat) # label(arity_Nat_Onat___Nat_Osemiring__char__0) # label(axiom). [assumption].
% 7.88/8.12 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) != hAPP(nat,nat,semiring_1_of_nat(nat),B) | A = B. [resolve(1591,a,1589,a)].
% 7.88/8.12 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) = hAPP(nat,nat,semiring_1_of_nat(nat),B) | A != B. [resolve(1591,a,1590,a)].
% 7.88/8.12 1592 semiring_char_0(real) # label(arity_RealDef_Oreal___Nat_Osemiring__char__0) # label(axiom). [assumption].
% 7.88/8.12 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) != hAPP(nat,real,semiring_1_of_nat(real),B) | A = B. [resolve(1592,a,1589,a)].
% 7.88/8.12 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) = hAPP(nat,real,semiring_1_of_nat(real),B) | A != B. [resolve(1592,a,1590,a)].
% 7.88/8.12 1593 archim1804426504_field(real) # label(arity_RealDef_Oreal___Archimedean__Field_Oarchimedean__field) # label(axiom). [assumption].
% 7.88/8.12 1594 -archim1804426504_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),f128(A,C,B))),B))) # label(fact_851_ex__less__of__nat__mult) # label(axiom). [clausify(862)].
% 7.88/8.12 1595 -archim1804426504_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(nat,A,semiring_1_of_nat(A),f134(A,B)))) # label(fact_859_ex__less__of__nat) # label(axiom). [clausify(870)].
% 7.88/8.12 1596 -archim1804426504_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(nat,A,semiring_1_of_nat(A),f135(A,B)))) # label(fact_860_ex__le__of__nat) # label(axiom). [clausify(871)].
% 7.88/8.12 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),f128(real,B,A))),A))). [resolve(1593,a,1594,a)].
% 7.88/8.12 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(nat,real,semiring_1_of_nat(real),f134(real,A)))). [resolve(1593,a,1595,a)].
% 7.88/8.12 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(nat,real,semiring_1_of_nat(real),f135(real,A)))). [resolve(1593,a,1596,a)].
% 7.88/8.12
% 7.88/8.12 ============================== end predicate elimination =============
% 7.88/8.12
% 7.88/8.12 Auto_denials: (non-Horn, no changes).
% 7.88/8.12
% 7.88/8.12 Term ordering decisions:
% 7.88/8.12 Function symbol KB weights: int=1. nat=1. real=1. bool=1. suc=1. pls=1. nat_neg=1. natfloor=1. natceiling=1. succ=1. divmod_int_rel=1. pred=1. nat_tsub=1. posDivAlg=1. zfact=1. fFalse=1. fTrue=1. pdivmod=1. twoSqu1929807760sum2sq=1. twoSqu658283162sum2sq=1. xzgcd=1. xzgcda=1. a=1. b=1. p=1. q=1. fun=1. product_prod=1. ti=1. product_Pair=1. in_rel=1. f76=1. f81=1. f82=1. f83=1. f84=1. f99=1. f102=1. f105=1. f106=1. f107=1. f109=1. f113=1. f115=1. f126=1. f134=1. f135=1. f136=1. f138=1. f139=1. ord_less_eq=1. ord_less=1. zero_zero=1. times_times=1. plus_plus=1. number_number_of=1. minus_minus=1. one_one=1. semiring_1_of_nat=1. real_1=1. abs_abs=1. archim2085082626_floor=1. archimedean_ceiling=1. member=1. ring_1_Ints=1. if=1. undefined=1. f1=1. f2=1. f114=1. f116=1. f117=1. f118=1. f119=1. f120=1. f121=1. f122=1. f123=1. f124=1. f125=1. f127=1. f129=1. f130=1. f131=1. f132=1. f133=1. f137=1. f140=1. product_curry=1. produc1605651328_split=1. product_prod_rec=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1. f45=1. f46=1. f48=1. f49=1. f51=1. f52=1. f53=1. f54=1. f55=1. f74=1. f75=1. f77=1. f78=1. f79=1. f80=1. f85=1. f86=1. f88=1. f89=1. f90=1. f92=1. f95=1. f96=1. f97=1. f98=1. f100=1. f101=1. f103=1. f104=1. f108=1. f110=1. f111=1. f112=1. f128=1. hAPP=1. f42=1. f43=1. f44=1. f47=1. f50=1. f56=1. f59=1. f87=1. f91=1. f93=1. f94=1. f35=1. f36=1. f37=1. f38=1. f39=1. f40=1. f41=1. f26=1. f27=1. f28=1. f29=1. f30=1. f31=1. f32=1. f33=1. f34=1. f57=1. f58=1. f60=1. f61=1. f62=1. f63=1. f64=1. f65=1. f66=1. f67=1. f68=1. f69=1. f70=1. f71=1. f72=1. f73=1. f15=1. f16=1. f17=1. f18=1. f19=1. f20=1. f21=1. f22=1. f23=1. f24=1. f25=1. f9=1. f10=1. f11=1. f12=1. f13=1. f14=1.
% 64.49/64.72
% 64.49/64.72 ============================== end of process initial clauses ========
% 64.49/64.72
% 64.49/64.72 ============================== CLAUSES FOR SEARCH ====================
% 64.49/64.72
% 64.49/64.72 ============================== end of clauses for search =============
% 64.49/64.72
% 64.49/64.72 ============================== SEARCH ================================
% 64.49/64.72
% 64.49/64.72 % Starting search at 6.26 seconds.
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% 64.49/64.72 Low Water (keep): wt=164.000, iters=3648
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% 64.49/64.72 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 39 (0.00 of 7.31 sec).
% 64.49/64.72
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% 64.49/64.73 Low Water (keeCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------