%------------------------------------------------------------------------------ % File : Otter---3.3 % Problem : NUM925+6 : TPTP v8.1.0. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : otter-tptp-script %s % Computer : n011.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jul 27 13:10:17 EDT 2022 % Result : Unknown 8.10s 8.09s % Output : None % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : NUM925+6 : TPTP v8.1.0. Released v5.3.0. % 0.07/0.12 % Command : otter-tptp-script %s % 0.12/0.33 % Computer : n011.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Wed Jul 27 09:50:55 EDT 2022 % 0.12/0.33 % CPUTime : % 8.03/8.02 ----- Otter 3.3f, August 2004 ----- % 8.03/8.02 The process was started by sandbox on n011.cluster.edu, % 8.03/8.02 Wed Jul 27 09:50:55 2022 % 8.03/8.02 The command was "./otter". The process ID is 22232. % 8.03/8.02 % 8.03/8.02 set(prolog_style_variables). % 8.03/8.02 set(auto). % 8.03/8.02 dependent: set(auto1). % 8.03/8.02 dependent: set(process_input). % 8.03/8.02 dependent: clear(print_kept). % 8.03/8.02 dependent: clear(print_new_demod). % 8.03/8.02 dependent: clear(print_back_demod). % 8.03/8.02 dependent: clear(print_back_sub). % 8.03/8.02 dependent: set(control_memory). % 8.03/8.02 dependent: assign(max_mem, 12000). % 8.03/8.02 dependent: assign(pick_given_ratio, 4). % 8.03/8.02 dependent: assign(stats_level, 1). % 8.03/8.02 dependent: assign(max_seconds, 10800). % 8.03/8.02 clear(print_given). % 8.03/8.02 % 8.03/8.02 formula_list(usable). % 8.03/8.02 all A (A=A). % 8.03/8.02 all X_a (one(X_a)->ti(X_a,one_one(X_a))=one_one(X_a)). % 8.03/8.02 all B_1_1 X_a (monoid_add(X_a)->plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1)). % 8.03/8.02 all B_1_1 X_a (monoid_add(X_a)->ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1)). % 8.03/8.02 all B_1_1 X_a (ab_semigroup_add(X_a)->plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1)). % 8.03/8.02 all B_1_1 X_a (ab_semigroup_add(X_a)->ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1)). % 8.03/8.02 all B_1_1 X_a (cancel_semigroup_add(X_a)->plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1)). % 8.03/8.02 all B_1_1 X_a (cancel_semigroup_add(X_a)->ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1)). % 8.03/8.02 all X_a (linordered_semiring(X_a)->ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a)). % 8.03/8.02 all X_a (zero(X_a)->ti(X_a,zero_zero(X_a))=zero_zero(X_a)). % 8.03/8.02 all X_a (ti(X_a,undefined(X_a))=undefined(X_a)). % 8.03/8.02 all X_a (ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a))=if(X_a)). % 8.03/8.02 ti(fun(int,int),bit0)=bit0. % 8.03/8.02 ti(fun(int,int),bit1)=bit1. % 8.03/8.02 ti(int,pls)=pls. % 8.03/8.02 all B_1_1 X_a (number(X_a)->number_number_of(X_a,ti(int,B_1_1))=number_number_of(X_a,B_1_1)). % 8.03/8.02 all B_1_1 X_a (number(X_a)->ti(X_a,number_number_of(X_a,B_1_1))=number_number_of(X_a,B_1_1)). % 8.03/8.02 ti(fun(int,int),succ)=succ. % 8.03/8.02 all X_a (semiring_1(X_a)->ti(fun(nat,X_a),semiring_1_of_nat(X_a))=semiring_1_of_nat(X_a)). % 8.03/8.02 ti(fun(real,real),sqrt)=sqrt. % 8.03/8.02 all X_a (ord(X_a)->ti(fun(X_a,fun(X_a,bool)),ord_less(X_a))=ord_less(X_a)). % 8.03/8.02 all X_b (ord(X_b)->ti(fun(X_b,fun(X_b,bool)),ord_less_e_q(X_b))=ord_less_e_q(X_b)). % 8.03/8.02 all B_1_1 X_a (power(X_a)->power_power(X_a,ti(X_a,B_1_1))=power_power(X_a,B_1_1)). % 8.03/8.02 all B_1_1 X_a (power(X_a)->ti(fun(nat,X_a),power_power(X_a,B_1_1))=power_power(X_a,B_1_1)). % 8.03/8.02 ti(bool,fFalse)=fFalse. % 8.03/8.02 ti(bool,fTrue)=fTrue. % 8.03/8.02 all X_a B_1_1 B_2 X_b (ord(X_b)->hAPP(X_a,X_b,ti(fun(X_a,X_b),B_1_1),B_2)=hAPP(X_a,X_b,B_1_1,B_2)). % 8.03/8.02 all X_a B_1_1 B_2 X_b (ord(X_b)->hAPP(X_a,X_b,B_1_1,ti(X_a,B_2))=hAPP(X_a,X_b,B_1_1,B_2)). % 8.03/8.02 all X_a B_1_1 B_2 X_b (ord(X_b)->ti(X_b,hAPP(X_a,X_b,B_1_1,B_2))=hAPP(X_a,X_b,B_1_1,B_2)). % 8.03/8.02 all B_1_1 B_2 X_a (power(X_a)->hAPP(nat,X_a,ti(fun(nat,X_a),B_1_1),B_2)=hAPP(nat,X_a,B_1_1,B_2)). % 8.03/8.02 all B_1_1 B_2 X_a (power(X_a)->hAPP(nat,X_a,B_1_1,ti(nat,B_2))=hAPP(nat,X_a,B_1_1,B_2)). % 8.03/8.02 all B_1_1 B_2 X_a (power(X_a)->ti(X_a,hAPP(nat,X_a,B_1_1,B_2))=hAPP(nat,X_a,B_1_1,B_2)). % 8.03/8.02 all X_a B_1_1 B_2 (hAPP(bool,fun(X_a,fun(X_a,X_a)),ti(fun(bool,fun(X_a,fun(X_a,X_a))),B_1_1),B_2)=hAPP(bool,fun(X_a,fun(X_a,X_a)),B_1_1,B_2)). % 8.03/8.02 all X_a B_1_1 B_2 (hAPP(bool,fun(X_a,fun(X_a,X_a)),B_1_1,ti(bool,B_2))=hAPP(bool,fun(X_a,fun(X_a,X_a)),B_1_1,B_2)). % 8.03/8.02 all X_a B_1_1 B_2 (ti(fun(X_a,fun(X_a,X_a)),hAPP(bool,fun(X_a,fun(X_a,X_a)),B_1_1,B_2))=hAPP(bool,fun(X_a,fun(X_a,X_a)),B_1_1,B_2)). % 8.03/8.02 all X_a B_1_1 B_2 (hAPP(X_a,fun(X_a,X_a),ti(fun(X_a,fun(X_a,X_a)),B_1_1),B_2)=hAPP(X_a,fun(X_a,X_a),B_1_1,B_2)). % 8.03/8.02 all X_a B_1_1 B_2 (hAPP(X_a,fun(X_a,X_a),B_1_1,ti(X_a,B_2))=hAPP(X_a,fun(X_a,X_a),B_1_1,B_2)). % 8.03/8.02 all X_a B_1_1 B_2 (ti(fun(X_a,X_a),hAPP(X_a,fun(X_a,X_a),B_1_1,B_2))=hAPP(X_a,fun(X_a,X_a),B_1_1,B_2)). % 8.03/8.02 all X_a B_1_1 B_2 (hAPP(X_a,X_a,ti(fun(X_a,X_a),B_1_1),B_2)=hAPP(X_a,X_a,B_1_1,B_2)). % 8.03/8.02 all X_a B_1_1 B_2 (hAPP(X_a,X_a,B_1_1,ti(X_a,B_2))=hAPP(X_a,X_a,B_1_1,B_2)). % 8.03/8.02 all X_a B_1_1 B_2 (ti(X_a,hAPP(X_a,X_a,B_1_1,B_2))=hAPP(X_a,X_a,B_1_1,B_2)). % 8.03/8.02 all B_1_1 (hBOOL(ti(bool,B_1_1))<->hBOOL(B_1_1)). % 8.03/8.02 ti(int,m1)=m1. % 8.03/8.02 ti(nat,n)=n. % 8.03/8.02 ti(int,t)=t. % 8.03/8.02 ti(nat,tn)=tn. % 8.03/8.02 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))). % 8.03/8.02 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)). % 8.03/8.02 all X_a (linordered_idom(X_a)-> (all Xa Ya (hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))=zero_zero(X_a)<->ti(X_a,Xa)=zero_zero(X_a)&ti(X_a,Ya)=zero_zero(X_a)))). % 8.03/8.02 all X_a (semiring_1(X_a)->hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=one_one(X_a)). % 8.03/8.02 all X_a (semiring_1(X_a)->hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=zero_zero(X_a)). % 8.03/8.02 all X_a (ring_11004092258visors(X_a)-> (all A_2 (hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=zero_zero(X_a)<->ti(X_a,A_2)=zero_zero(X_a)))). % 8.03/8.02 all X_a (number_ring(X_a)-> (all W_1 (hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,W_1))=number_number_of(X_a,hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,pls)),W_1))))). % 8.03/8.02 all X_a (number_ring(X_a)-> (all V_1 (hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V_1)),one_one(X_a))=number_number_of(X_a,hAPP(int,int,plus_plus(int,V_1),hAPP(int,int,bit1,pls)))))). % 8.03/8.02 all X_a (number_ring(X_a)->hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))=number_number_of(X_a,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). % 8.03/8.02 all X_a (number_semiring(X_a)->hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))=number_number_of(X_a,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). % 8.03/8.02 all X (hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). % 8.03/8.02 all X_a (power(X_a)&semiring_0(X_a)-> (all W_1 ((number_number_of(nat,W_1)=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,W_1))=one_one(X_a))& (number_number_of(nat,W_1)!=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,W_1))=zero_zero(X_a))))). % 8.03/8.02 all X_a (number_ring(X_a)->one_one(X_a)=number_number_of(X_a,hAPP(int,int,bit1,pls))). % 8.03/8.02 all X_a (number_ring(X_a)->number_number_of(X_a,hAPP(int,int,bit1,pls))=one_one(X_a)). % 8.03/8.02 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),n)). % 8.03/8.02 all X 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))). % 8.03/8.02 all K_2 L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,K_2)),number_number_of(int,L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1))). % 8.03/8.02 all V_1 W_1 (hAPP(int,int,plus_plus(int,number_number_of(int,V_1)),number_number_of(int,W_1))=number_number_of(int,hAPP(int,int,plus_plus(int,V_1),W_1))). % 8.03/8.02 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Xa Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Xa)),number_number_of(X_a,Ya)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),Ya))))). % 8.03/8.02 zero_zero(int)=number_number_of(int,pls). % 8.03/8.02 all M_1 N (hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),M_1)),N)=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,M_1),N))). % 8.03/8.02 all M_1 N (hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,M_1),N))=hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),M_1)),N)). % 8.03/8.02 all M_1 N Z_1 (hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),N)),Z_1))=hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,M_1),N))),Z_1)). % 8.03/8.02 all M_1 N (hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,M_1),N))). % 8.03/8.02 hAPP(nat,int,semiring_1_of_nat(int),one_one(nat))=one_one(int). % 8.03/8.02 number_number_of(nat,pls)=zero_zero(nat). % 8.03/8.02 zero_zero(nat)=number_number_of(nat,pls). % 8.03/8.02 all Na (hAPP(nat,int,semiring_1_of_nat(int),Na)=zero_zero(int)<->Na=zero_zero(nat)). % 8.03/8.02 hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat))=zero_zero(int). % 8.03/8.02 hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))=number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))). % 8.03/8.02 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2))). % 8.03/8.02 all K_2 L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K_2)),hAPP(int,int,bit1,L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1))). % 8.03/8.02 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)). % 8.03/8.02 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit0,K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2))). % 8.03/8.02 all K_2 L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K_2)),hAPP(int,int,bit0,L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1))). % 8.03/8.02 all K I_2 J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J_2))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,I_2),K)),hAPP(int,int,plus_plus(int,J_2),K)))). % 8.03/8.02 all V_2 V_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))->hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V_1)),number_number_of(nat,V_2))=number_number_of(nat,V_2))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls))->hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V_1)),number_number_of(nat,V_2))=number_number_of(nat,V_1))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls))->hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V_1)),number_number_of(nat,V_2))=number_number_of(nat,hAPP(int,int,plus_plus(int,V_1),V_2))))). % 8.03/8.02 one_one(int)=number_number_of(int,hAPP(int,int,bit1,pls)). % 8.03/8.02 number_number_of(nat,hAPP(int,int,bit1,pls))=one_one(nat). % 8.03/8.02 one_one(nat)=number_number_of(nat,hAPP(int,int,bit1,pls)). % 8.03/8.02 all X_a (number_ring(X_a)&ring_char_0(X_a)-> (all Xa Ya (number_number_of(X_a,Xa)=number_number_of(X_a,Ya)<->Xa=Ya))). % 8.03/8.02 all X_a (number(X_a)-> (all Wa Xa (number_number_of(X_a,Wa)=ti(X_a,Xa)<->ti(X_a,Xa)=number_number_of(X_a,Wa)))). % 8.03/8.02 all K_2 L_1 (hAPP(int,int,bit1,K_2)=hAPP(int,int,bit1,L_1)<->K_2=L_1). % 8.03/8.02 all K_2 L_1 (hAPP(int,int,bit0,K_2)=hAPP(int,int,bit0,L_1)<->K_2=L_1). % 8.03/8.02 all X_a (linordered_idom(X_a)-> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a)))))). % 8.03/8.02 all Z1 Z2 Z3 (hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,Z1),Z2)),Z3)=hAPP(int,int,plus_plus(int,Z1),hAPP(int,int,plus_plus(int,Z2),Z3))). % 8.03/8.02 all X Y Z_1 (hAPP(int,int,plus_plus(int,X),hAPP(int,int,plus_plus(int,Y),Z_1))=hAPP(int,int,plus_plus(int,Y),hAPP(int,int,plus_plus(int,X),Z_1))). % 8.03/8.02 all Z_1 W_1 (hAPP(int,int,plus_plus(int,Z_1),W_1)=hAPP(int,int,plus_plus(int,W_1),Z_1)). % 8.03/8.02 all Ma Na (hAPP(nat,int,semiring_1_of_nat(int),Ma)=hAPP(nat,int,semiring_1_of_nat(int),Na)<->Ma=Na). % 8.03/8.02 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Xa)),zero_zero(X_a)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),pls))))). % 8.03/8.02 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),number_number_of(X_a,Ya)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Ya))))). % 8.03/8.02 all K_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K_2)),pls))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),pls))). % 8.03/8.02 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit0,K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2))). % 8.03/8.02 all K_2 L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K_2)),hAPP(int,int,bit0,L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1))). % 8.03/8.02 all K_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K_2)),pls))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),pls))). % 8.03/8.02 all K_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,K_2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K_2))). % 8.03/8.02 all Wa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,Wa)),zero_zero(int)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),zero_zero(int)))). % 8.03/8.02 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))). % 8.03/8.02 all Wa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,Wa)),zero_zero(int)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),zero_zero(int)))). % 8.03/8.02 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))). % 8.03/8.02 all Wa Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_2))|Wa=Z_2). % 8.03/8.02 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)))). % 8.03/8.02 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Xa)),one_one(X_a)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),hAPP(int,int,bit1,pls)))))). % 8.03/8.02 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),number_number_of(X_a,Ya)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),Ya))))). % 8.03/8.02 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),Z_2)),Z_2)),zero_zero(int)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int)))). % 8.03/8.02 all X_a (linord219039673up_add(X_a)-> (all A_2 (hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2)=zero_zero(X_a)<->ti(X_a,A_2)=zero_zero(X_a)))). % 8.03/8.02 all K (hAPP(int,int,bit1,K)!=pls). % 8.03/8.02 all L (pls!=hAPP(int,int,bit1,L)). % 8.03/8.02 all K L (hAPP(int,int,bit1,K)!=hAPP(int,int,bit0,L)). % 8.03/8.02 all K L (hAPP(int,int,bit0,K)!=hAPP(int,int,bit1,L)). % 8.03/8.02 all K_2 (hAPP(int,int,bit0,K_2)=pls<->K_2=pls). % 8.03/8.02 all L_1 (pls=hAPP(int,int,bit0,L_1)<->pls=L_1). % 8.03/8.02 hAPP(int,int,bit0,pls)=pls. % 8.03/8.02 pls=zero_zero(int). % 8.03/8.02 zero_zero(int)!=one_one(int). % 8.03/8.02 all K (hAPP(int,int,plus_plus(int,K),pls)=K). % 8.03/8.02 all K (hAPP(int,int,plus_plus(int,pls),K)=K). % 8.03/8.02 all K L (hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,K)),hAPP(int,int,bit0,L))=hAPP(int,int,bit0,hAPP(int,int,plus_plus(int,K),L))). % 8.03/8.02 all K (hAPP(int,int,bit0,K)=hAPP(int,int,plus_plus(int,K),K)). % 8.03/8.02 all Z_1 (hAPP(int,int,plus_plus(int,Z_1),zero_zero(int))=Z_1). % 8.03/8.02 all Z_1 (hAPP(int,int,plus_plus(int,zero_zero(int)),Z_1)=Z_1). % 8.03/8.02 all X_a (number_semiring(X_a)->number_number_of(X_a,pls)=zero_zero(X_a)). % 8.03/8.02 all X_a (number_ring(X_a)->number_number_of(X_a,pls)=zero_zero(X_a)). % 8.03/8.02 all X_a (number_ring(X_a)->zero_zero(X_a)=number_number_of(X_a,pls)). % 8.03/8.02 all X_a (number_ring(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,pls)),A_1)=ti(X_a,A_1)))). % 8.03/8.02 all X_a (number_ring(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,A_1),number_number_of(X_a,pls))=ti(X_a,A_1)))). % 8.03/8.02 all X_a (power(X_a)&mult_zero(X_a)&no_zero_divisors(X_a)&zero_ne_q_one(X_a)-> (all A_2 Wa (hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,Wa))=zero_zero(X_a)<->ti(X_a,A_2)=zero_zero(X_a)&number_number_of(nat,Wa)!=zero_zero(nat)))). % 8.03/8.02 all X_a (number_ring(X_a)-> (all V_1 W_1 Z_1 (hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V_1)),hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,W_1)),Z_1))=hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,hAPP(int,int,plus_plus(int,V_1),W_1))),Z_1)))). % 8.03/8.02 all X_a (number_ring(X_a)-> (all V_1 W_1 (hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V_1)),number_number_of(X_a,W_1))=number_number_of(X_a,hAPP(int,int,plus_plus(int,V_1),W_1))))). % 8.03/8.02 all X_a (number_ring(X_a)-> (all V_1 W_1 (number_number_of(X_a,hAPP(int,int,plus_plus(int,V_1),W_1))=hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V_1)),number_number_of(X_a,W_1))))). % 8.03/8.02 all K L (hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,K)),hAPP(int,int,bit0,L))=hAPP(int,int,bit1,hAPP(int,int,plus_plus(int,K),L))). % 8.03/8.02 all K L (hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,K)),hAPP(int,int,bit1,L))=hAPP(int,int,bit1,hAPP(int,int,plus_plus(int,K),L))). % 8.03/8.02 all K (hAPP(int,int,bit1,K)=hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),K)),K)). % 8.03/8.02 all Z_1 (hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),Z_1)),Z_1)!=zero_zero(int)). % 8.03/8.02 all X_a (number_semiring(X_a)-> (all N (number_number_of(X_a,hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))). % 8.03/8.02 all X_a (linordered_idom(X_a)-> (all A_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,power_power(X_a,A_2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))<->ti(X_a,A_2)!=zero_zero(X_a)))). % 8.03/8.02 all X_a (linordered_idom(X_a)-> (all A_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(X_a)))))). % 8.03/8.02 all X_a (linordered_idom(X_a)-> (all Xa Ya (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,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))<->ti(X_a,Xa)!=zero_zero(X_a)|ti(X_a,Ya)!=zero_zero(X_a)))). % 8.03/8.02 all X_a (linordered_idom(X_a)-> (all X Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X_a)))))). % 8.03/8.02 all X_a (number_ring(X_a)-> (all W_1 (number_number_of(X_a,hAPP(int,int,bit0,W_1))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),number_number_of(X_a,W_1))),number_number_of(X_a,W_1))))). % 8.03/8.02 all X_a (number_ring(X_a)-> (all W_1 (number_number_of(X_a,hAPP(int,int,bit1,W_1))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,W_1))),number_number_of(X_a,W_1))))). % 8.03/8.02 all X_a (number_semiring(X_a)->number_number_of(X_a,hAPP(int,int,bit1,pls))=one_one(X_a)). % 8.03/8.02 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),m1),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))). % 8.03/8.02 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all N 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),N)),hAPP(nat,X_a,power_power(X_a,number_number_of(X_a,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))))). % 8.03/8.02 number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))=hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). % 8.03/8.02 number_number_of(int,hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))=hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))). % 8.03/8.02 all Xa Ya (hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))=zero_zero(real)<->Xa=zero_zero(real)&Ya=zero_zero(real)). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all Na (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),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all N A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N))))))). % 8.03/8.02 all X_a (power(X_a)&semiring_0(X_a)-> (all N ((N=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),N)=one_one(X_a))& (N!=zero_zero(nat)->hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),N)=zero_zero(X_a))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all A_1 N N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_2))-> (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),A_1),one_one(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_2)),hAPP(nat,X_a,power_power(X_a,A_1),N)))))))). % 8.03/8.02 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,plus_plus(X_a,one_one(X_a)),one_one(X_a))))). % 8.03/8.02 all P_1 K_2 I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),I))-> (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,K_2),one_one(int))))-> ((all I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),I_1))-> (hBOOL(hAPP(int,bool,P_1,I_1))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,I_1),one_one(int)))))))->hBOOL(hAPP(int,bool,P_1,I))))). % 8.03/8.02 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),tn)). % 8.03/8.02 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))). % 8.03/8.02 zero_zero(real)!=one_one(real). % 8.03/8.02 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))). % 8.03/8.02 all I_2 J_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_2),J_2)),I_2))). % 8.03/8.02 all J_2 I_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,J_2),I_2)),I_2))). % 8.03/8.02 all K (number_number_of(int,K)=K). % 8.03/8.02 all Ma Na (Ma!=Na<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma))). % 8.03/8.02 all M_1 N (hAPP(nat,nat,plus_plus(nat,M_1),N)=hAPP(nat,nat,plus_plus(nat,N),M_1)). % 8.03/8.02 all X Y Z_1 (hAPP(nat,nat,plus_plus(nat,X),hAPP(nat,nat,plus_plus(nat,Y),Z_1))=hAPP(nat,nat,plus_plus(nat,Y),hAPP(nat,nat,plus_plus(nat,X),Z_1))). % 8.03/8.02 all M_1 N K (hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,plus_plus(nat,M_1),N)),K)=hAPP(nat,nat,plus_plus(nat,M_1),hAPP(nat,nat,plus_plus(nat,N),K))). % 8.03/8.02 all K_2 Ma Na (hAPP(nat,nat,plus_plus(nat,K_2),Ma)=hAPP(nat,nat,plus_plus(nat,K_2),Na)<->Ma=Na). % 8.03/8.02 all Ma K_2 Na (hAPP(nat,nat,plus_plus(nat,Ma),K_2)=hAPP(nat,nat,plus_plus(nat,Na),K_2)<->Ma=Na). % 8.03/8.02 all K_2 Ma Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,K_2),Ma)),hAPP(nat,nat,plus_plus(nat,K_2),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))). % 8.03/8.02 all X 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)))). % 8.03/8.02 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))). % 8.03/8.02 all N M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_1))->M_1!=N). % 8.03/8.02 all S T_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3))->S!=T_3). % 8.03/8.02 all M_1 I_2 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,plus_plus(nat,J_2),M_1)))). % 8.03/8.02 all M_1 I_2 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,plus_plus(nat,M_1),J_2)))). % 8.03/8.02 all K I_2 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),hAPP(nat,nat,plus_plus(nat,J_2),K)))). % 8.03/8.02 all K L I_2 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),hAPP(nat,nat,plus_plus(nat,J_2),L))))). % 8.03/8.02 all M_1 N K L (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L))-> (hAPP(nat,nat,plus_plus(nat,M_1),L)=hAPP(nat,nat,plus_plus(nat,K),N)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))). % 8.03/8.02 all I_2 J_2 K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_2),J_2)),K))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K))). % 8.03/8.02 all P_1 Ma Na ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Na),Ma)))-> ((Ma=Na->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Na),Ma)))-> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Na),Ma)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Na),Ma))))). % 8.03/8.02 all N (N!=zero_zero(nat)->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))). % 8.03/8.02 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))->N!=zero_zero(nat)). % 8.03/8.02 all M_1 N I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),I_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,I_2),M_1)),hAPP(nat,nat,power_power(nat,I_2),N)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))). % 8.03/8.02 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))). % 8.03/8.02 all Xa Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa))|Na=zero_zero(nat)). % 8.03/8.02 all Ma Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,Ma),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))). % 8.03/8.02 all Na (Na!=zero_zero(nat)<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))). % 8.03/8.02 all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))). % 8.03/8.02 all Xa Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na)))<->Na=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa))). % 8.03/8.02 all Xa Ya (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya))). % 8.03/8.02 all Xa Wa (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),number_number_of(nat,Wa))))<->number_number_of(nat,Wa)=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa))). % 8.03/8.02 all Ma Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))). % 8.03/8.02 all Va V (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,Va)),number_number_of(nat,V)))<-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Va),V))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V)))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Va),V))). % 8.03/8.02 all X_a (linordered_idom(X_a)-> (all 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))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))). % 8.03/8.02 all M_1 N (hAPP(nat,nat,plus_plus(nat,M_1),N)=M_1->N=zero_zero(nat)). % 8.03/8.02 all Ma Na (hAPP(nat,nat,plus_plus(nat,Ma),Na)=zero_zero(nat)<->Ma=zero_zero(nat)&Na=zero_zero(nat)). % 8.03/8.02 all M_1 (hAPP(nat,nat,plus_plus(nat,M_1),zero_zero(nat))=M_1). % 8.03/8.02 all N (hAPP(nat,nat,plus_plus(nat,zero_zero(nat)),N)=N). % 8.03/8.02 all X_a (monoid_mult(X_a)-> (all A_1 (hAPP(nat,X_a,power_power(X_a,A_1),one_one(nat))=ti(X_a,A_1)))). % 8.03/8.02 all X_a (semiring_char_0(X_a)-> (all Ma Na (hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma)=hAPP(nat,X_a,semiring_1_of_nat(X_a),Na)<->Ma=Na))). % 8.03/8.02 all Xa Ya (hAPP(nat,int,semiring_1_of_nat(int),Xa)=hAPP(nat,int,semiring_1_of_nat(int),Ya)<->Xa=Ya). % 8.03/8.02 all Xa Ya P_1 ((hBOOL(P_1)->hAPP(nat,int,semiring_1_of_nat(int),Xa)=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),Xa),Ya)))& (-hBOOL(P_1)->hAPP(nat,int,semiring_1_of_nat(int),Ya)=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),Xa),Ya)))). % 8.03/8.02 all Va (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,Va)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Va))). % 8.03/8.02 all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na))). % 8.03/8.02 all X_a (zero_ne_q_one(X_a)->one_one(X_a)!=zero_zero(X_a)). % 8.03/8.02 all X_a (zero_ne_q_one(X_a)->zero_zero(X_a)!=one_one(X_a)). % 8.03/8.02 all X_a (ring_11004092258visors(X_a)-> (all N A_1 (ti(X_a,A_1)!=zero_zero(X_a)->hAPP(nat,X_a,power_power(X_a,A_1),N)!=zero_zero(X_a)))). % 8.03/8.02 all X_a (monoid_mult(X_a)-> (all N (hAPP(nat,X_a,power_power(X_a,one_one(X_a)),N)=one_one(X_a)))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all Ma Na (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),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))->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)))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all M_1 N (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)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))))). % 8.03/8.02 all X_a (semiring_1(X_a)-> (all M_1 N (hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,plus_plus(nat,M_1),N))=hAPP(X_a,X_a,plus_plus(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))))). % 8.03/8.02 all X_a (semiring_1(X_a)->hAPP(nat,X_a,semiring_1_of_nat(X_a),one_one(nat))=one_one(X_a)). % 8.03/8.02 all X_a (semiring_1(X_a)-> (all M_1 N (hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,power_power(nat,M_1),N))=hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),N)))). % 8.03/8.02 one_one(int)=hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)). % 8.03/8.02 all X Y (hAPP(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,plus_plus(nat,X),Y))). % 8.03/8.02 all X N (hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X)),N)=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X),N))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all B C_1 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_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1))))))). % 8.03/8.02 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)))). % 8.03/8.02 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)))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all N 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)),hAPP(nat,X_a,power_power(X_a,A_1),N)))))). % 8.03/8.02 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,plus_plus(X_a,A_1),one_one(X_a)))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all Ma Na A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_2))-> (hAPP(nat,X_a,power_power(X_a,A_2),Ma)=hAPP(nat,X_a,power_power(X_a,A_2),Na)<->Ma=Na)))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all Xa Ya B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,B_1),Xa)),hAPP(nat,X_a,power_power(X_a,B_1),Ya)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya)))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all M_1 N A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M_1)),hAPP(nat,X_a,power_power(X_a,A_1),N)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all A_1 N N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N)),hAPP(nat,X_a,power_power(X_a,A_1),N_2))))))). % 8.03/8.02 all X_a (power(X_a)&mult_zero(X_a)&no_zero_divisors(X_a)&zero_ne_q_one(X_a)-> (all A_2 Na (hAPP(nat,X_a,power_power(X_a,A_2),Na)=zero_zero(X_a)<->ti(X_a,A_2)=zero_zero(X_a)&Na!=zero_zero(nat)))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all M_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_1)),zero_zero(X_a)))))). % 8.03/8.02 all X_a (power(X_a)-> (all A_1 (hAPP(nat,X_a,power_power(X_a,A_1),zero_zero(nat))=one_one(X_a)))). % 8.03/8.02 all X_a (semiring_1(X_a)->hAPP(nat,X_a,semiring_1_of_nat(X_a),zero_zero(nat))=zero_zero(X_a)). % 8.03/8.02 zero_zero(int)=hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)). % 8.03/8.02 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). % 8.03/8.02 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))-> (exists N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))&K=hAPP(nat,int,semiring_1_of_nat(int),N_1)))). % 8.03/8.02 all I_2 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2))-> (exists K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1))&hAPP(nat,nat,plus_plus(nat,I_2),K_1)=J_2))). % 8.03/8.02 all Xa Na (hAPP(nat,nat,power_power(nat,Xa),Na)=one_one(nat)<->Xa=one_one(nat)|Na=zero_zero(nat)). % 8.03/8.02 all X_a (comm_semiring_1(X_a)-> (all X (hAPP(nat,X_a,power_power(X_a,X),zero_zero(nat))=one_one(X_a)))). % 8.03/8.02 all X_a (linord219039673up_add(X_a)-> (all A_2 (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,plus_plus(X_a,A_2),A_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))))). % 8.03/8.02 all X_a (linord219039673up_add(X_a)-> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a)))))). % 8.03/8.02 all X_a (zero(X_a)-> (all Xa (zero_zero(X_a)=ti(X_a,Xa)<->ti(X_a,Xa)=zero_zero(X_a)))). % 8.03/8.02 all X_a (cancel_semigroup_add(X_a)-> (all B A_1 C_1 (hAPP(X_a,X_a,plus_plus(X_a,B),A_1)=hAPP(X_a,X_a,plus_plus(X_a,C_1),A_1)->ti(X_a,B)=ti(X_a,C_1)))). % 8.03/8.02 all X_a (cancel146912293up_add(X_a)-> (all A_1 B C_1 (hAPP(X_a,X_a,plus_plus(X_a,A_1),B)=hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)->ti(X_a,B)=ti(X_a,C_1)))). % 8.03/8.02 all X_a (cancel_semigroup_add(X_a)-> (all A_1 B C_1 (hAPP(X_a,X_a,plus_plus(X_a,A_1),B)=hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)->ti(X_a,B)=ti(X_a,C_1)))). % 8.03/8.02 all X_a (comm_semiring_1(X_a)-> (all A_1 B C_1 D (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),hAPP(X_a,X_a,plus_plus(X_a,C_1),D))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),D))))). % 8.03/8.02 all X_a (cancel_semigroup_add(X_a)-> (all B_1 A_2 C (hAPP(X_a,X_a,plus_plus(X_a,B_1),A_2)=hAPP(X_a,X_a,plus_plus(X_a,C),A_2)<->ti(X_a,B_1)=ti(X_a,C)))). % 8.03/8.02 all X_a (cancel_semigroup_add(X_a)-> (all A_2 B_1 C (hAPP(X_a,X_a,plus_plus(X_a,A_2),B_1)=hAPP(X_a,X_a,plus_plus(X_a,A_2),C)<->ti(X_a,B_1)=ti(X_a,C)))). % 8.03/8.02 all X_a (comm_semiring_1(X_a)-> (all A_1 B C_1 (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C_1)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),B)))). % 8.03/8.02 all X_a (ab_semigroup_add(X_a)-> (all A_1 B C_1 (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C_1)=hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,B),C_1))))). % 8.03/8.02 all X_a (comm_semiring_1(X_a)-> (all A_1 B C_1 (hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C_1)=hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,B),C_1))))). % 8.03/8.02 all X_a (comm_semiring_1(X_a)-> (all A_1 C_1 D (hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,C_1),D))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),D)))). % 8.03/8.02 all X_a (comm_semiring_1(X_a)-> (all A_1 C_1 D (hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,C_1),D))=hAPP(X_a,X_a,plus_plus(X_a,C_1),hAPP(X_a,X_a,plus_plus(X_a,A_1),D))))). % 8.03/8.02 all X_a (comm_semiring_1(X_a)-> (all A_1 C_1 (hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)=hAPP(X_a,X_a,plus_plus(X_a,C_1),A_1)))). % 8.03/8.02 all X_a (one(X_a)-> (all Xa (one_one(X_a)=ti(X_a,Xa)<->ti(X_a,Xa)=one_one(X_a)))). % 8.03/8.02 all X_a (semiri456707255roduct(X_a)-> (all B_1 A_2 (ti(X_a,B_1)=hAPP(X_a,X_a,plus_plus(X_a,B_1),A_2)<->ti(X_a,A_2)=zero_zero(X_a)))). % 8.03/8.02 all X_a (comm_monoid_add(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1)))). % 8.03/8.02 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1)))). % 8.03/8.02 all X_a (monoid_add(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1)))). % 8.03/8.02 all X_a (linord219039673up_add(X_a)-> (all A_2 (zero_zero(X_a)=hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2)<->ti(X_a,A_2)=zero_zero(X_a)))). % 8.03/8.02 all X_a (comm_monoid_add(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)=ti(X_a,A_1)))). % 8.03/8.02 all X_a (comm_semiring_1(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)=ti(X_a,A_1)))). % 8.03/8.02 all X_a (monoid_add(X_a)-> (all A_1 (hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)=ti(X_a,A_1)))). % 8.03/8.02 all X_a (ordere236663937imp_le(X_a)-> (all C_1 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))). % 8.03/8.02 all X_a (ordere236663937imp_le(X_a)-> (all A_1 C_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),C_1)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))). % 8.03/8.02 all X_a (ordere223160158up_add(X_a)-> (all C_1 D A_1 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_1),D))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),D))))))). % 8.03/8.02 all X_a (ordere223160158up_add(X_a)-> (all C_1 A_1 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,plus_plus(X_a,C_1),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B)))))). % 8.03/8.02 all X_a (ordere223160158up_add(X_a)-> (all C_1 A_1 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,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),C_1)))))). % 8.03/8.02 all X_a (ordere236663937imp_le(X_a)-> (all C A_2 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_2)),hAPP(X_a,X_a,plus_plus(X_a,C),B_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))))). % 8.03/8.02 all X_a (ordere236663937imp_le(X_a)-> (all A_2 C B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_2),C)),hAPP(X_a,X_a,plus_plus(X_a,B_1),C)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))))). % 8.03/8.02 all X_a (comm_semiring_1(X_a)-> (all X (hAPP(nat,X_a,power_power(X_a,X),one_one(nat))=ti(X_a,X)))). % 8.03/8.02 all Ma Na (hAPP(nat,nat,power_power(nat,Ma),Na)=zero_zero(nat)<->Na!=zero_zero(nat)&Ma=zero_zero(nat)). % 8.03/8.02 all X_a (ordere216010020id_add(X_a)-> (all B 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,plus_plus(X_a,A_1),B)),zero_zero(X_a))))))). % 8.03/8.02 all X_a (ordere216010020id_add(X_a)-> (all 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))->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,plus_plus(X_a,A_1),B))))))). % 8.03/8.02 all A_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))-> (exists X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1))&hAPP(nat,real,power_power(real,X_1),N)=A_1& (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1))&hAPP(nat,real,power_power(real,Y_1),N)=A_1->Y_1=X_1)))))). % 8.03/8.02 all A_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))-> (exists R (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R))&hAPP(nat,real,power_power(real,R),N)=A_1)))). % 8.03/8.02 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),t)). % 8.03/8.02 all V_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))->hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V_1)),one_one(nat))=one_one(nat))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))->hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V_1)),one_one(nat))=number_number_of(nat,hAPP(int,int,succ,V_1)))). % 8.03/8.02 all V_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))->hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,V_1))=one_one(nat))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))->hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,V_1))=number_number_of(nat,hAPP(int,int,succ,V_1)))). % 8.03/8.02 all X_a (ordere236663937imp_le(X_a)-> (all A_2 C B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_2),C)),hAPP(X_a,X_a,plus_plus(X_a,B_1),C)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B_1))))). % 8.03/8.02 all X_a (ordere236663937imp_le(X_a)-> (all C A_2 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_2)),hAPP(X_a,X_a,plus_plus(X_a,C),B_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B_1))))). % 8.03/8.02 all X_a (ordere779506340up_add(X_a)-> (all C_1 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),C_1)))))). % 8.03/8.02 all X_a (ordere779506340up_add(X_a)-> (all C_1 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B)))))). % 8.03/8.02 all X_a (ordere779506340up_add(X_a)-> (all C_1 D A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),D))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),D))))))). % 8.03/8.02 all X_a (ordere236663937imp_le(X_a)-> (all A_1 C_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),C_1)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))))). % 8.03/8.02 all X_a (ordere236663937imp_le(X_a)-> (all C_1 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all A_1 N N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),N_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N)),hAPP(nat,X_a,power_power(X_a,A_1),N_2))))))). % 8.03/8.02 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2))). % 8.03/8.02 all K_2 L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K_2)),hAPP(int,int,bit1,L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),L_1))). % 8.03/8.02 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),pls)). % 8.03/8.02 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit0,K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2))). % 8.03/8.02 all K_2 L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,K_2)),hAPP(int,int,bit0,L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),L_1))). % 8.03/8.02 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),zero_zero(int))). % 8.03/8.02 all W_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),W_1)). % 8.03/8.02 all Z_1 W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),W_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_1))). % 8.03/8.02 all K I_2 J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),J_2))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),J_2),K))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),K)))). % 8.03/8.02 all Z_1 W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),W_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_1))->Z_1=W_1)). % 8.03/8.02 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Xa Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,Xa)),number_number_of(X_a,Ya)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),Ya))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all Ma Na (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))))). % 8.03/8.02 all Z_2 Wa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),Wa))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_2),Wa))&Z_2!=Wa). % 8.03/8.02 all K I_2 J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),J_2))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,K),I_2)),hAPP(int,int,plus_plus(int,K),J_2)))). % 8.03/8.02 all K_2 L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,K_2)),number_number_of(int,L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),L_1))). % 8.03/8.02 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),number_number_of(X_a,Ya)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),Ya))))). % 8.03/8.02 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,Xa)),zero_zero(X_a)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),pls))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all A_1 N N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),N_2))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),one_one(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_2)),hAPP(nat,X_a,power_power(X_a,A_1),N)))))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all Xa Ya B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,B_1),Xa)),hAPP(nat,X_a,power_power(X_a,B_1),Ya)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Xa),Ya)))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all M_1 N A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M_1)),hAPP(nat,X_a,power_power(X_a,A_1),N)))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N)))))). % 8.03/8.02 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),number_number_of(X_a,Ya)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,pls)),Ya))))). % 8.03/8.02 all X_a (number_ring(X_a)&linordered_idom(X_a)-> (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,Xa)),one_one(X_a)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),hAPP(int,int,bit1,pls)))))). % 8.03/8.02 all X_a (linord219039673up_add(X_a)-> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_2))))). % 8.03/8.02 all X_a (linord219039673up_add(X_a)-> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2)),zero_zero(X_a)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),zero_zero(X_a)))))). % 8.03/8.02 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_1),B))))))). % 8.03/8.02 all X_a (ordere216010020id_add(X_a)-> (all Ya Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Xa))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Ya))-> (hAPP(X_a,X_a,plus_plus(X_a,Xa),Ya)=zero_zero(X_a)<->ti(X_a,Xa)=zero_zero(X_a)&ti(X_a,Ya)=zero_zero(X_a)))))). % 8.03/8.02 all X_a (ordere216010020id_add(X_a)-> (all B C_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),C_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1))))))). % 8.03/8.02 all X_a (ordere216010020id_add(X_a)-> (all B A_1 C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1))))))). % 8.03/8.02 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),zero_zero(X_a))))))). % 8.03/8.02 all X_a (ordere223160158up_add(X_a)-> (all C_1 D A_1 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_e_q(X_a),C_1),D))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),D))))))). % 8.03/8.02 all X_a (ordere223160158up_add(X_a)-> (all C_1 D A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),D))))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),zero_zero(X_a)))). % 8.03/8.02 all X_a (linordered_semidom(X_a)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),one_one(X_a)))). % 8.03/8.02 all X_a (number(X_a)&linorder(X_a)-> (all Va Wa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,Va)),number_number_of(X_a,Wa)))<-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Wa)),number_number_of(X_a,Va)))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all N A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N)))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all N A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N)),hAPP(nat,X_a,power_power(X_a,B),N))))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all N A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N)))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all M_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))). % 8.03/8.02 all K_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),hAPP(int,int,bit1,K_2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K_2))). % 8.03/8.02 all K_2 L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,K_2)),hAPP(int,int,bit1,L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),L_1))). % 8.03/8.02 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit1,K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2))). % 8.03/8.02 all K_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),hAPP(int,int,bit0,K_2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K_2))). % 8.03/8.02 all K_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,K_2)),pls))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),pls))). % 8.03/8.02 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),one_one(int))). % 8.03/8.02 all Y X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,X),Y))))). % 8.03/8.02 all Z_3 Z_1 W_2 W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),W_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_3),Z_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,W_2),Z_3)),hAPP(int,int,plus_plus(int,W_1),Z_1))))). % 8.03/8.02 all Z_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Z_1))). % 8.03/8.02 all P_1 ((exists X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))&hBOOL(hAPP(int,bool,P_1,X_1))))<-> (exists X_1 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_1))))). % 8.03/8.02 all P_1 ((all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))->hBOOL(hAPP(int,bool,P_1,X_1))))<-> (all X_1 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_1))))). % 8.03/8.02 all N hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N))). % 8.03/8.02 all N X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,power_power(int,X),N)))). % 8.03/8.02 all Wa Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),Z_2))<-> (exists N_1 (Z_2=hAPP(int,int,plus_plus(int,Wa),hAPP(nat,int,semiring_1_of_nat(int),N_1))))). % 8.03/8.02 all X_a (number_semiring(X_a)-> (all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))->hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,V_1))=number_number_of(X_a,hAPP(int,int,succ,V_1))))). % 8.03/8.02 all X_a (number_semiring(X_a)-> (all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))->hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V_1)),one_one(X_a))=number_number_of(X_a,hAPP(int,int,succ,V_1))))). % 8.03/8.02 all X_a (ordere216010020id_add(X_a)-> (all 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_e_q(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,plus_plus(X_a,A_1),B))))))). % 8.03/8.02 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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,plus_plus(X_a,A_1),B))))))). % 8.03/8.02 all X_a (ordere216010020id_add(X_a)-> (all B C_1 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_e_q(X_a),B),C_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1))))))). % 8.03/8.02 all X_a (ordere216010020id_add(X_a)-> (all B C_1 A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1))))))). % 8.03/8.02 all X_a (ordere216010020id_add(X_a)-> (all B 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_e_q(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,plus_plus(X_a,A_1),B)),zero_zero(X_a))))))). % 8.03/8.02 all X_a (ordere216010020id_add(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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,plus_plus(X_a,A_1),B)),zero_zero(X_a))))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all A_1 N B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N)),hAPP(nat,X_a,power_power(X_a,B),N)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))). % 8.03/8.02 all Va (zero_zero(nat)=number_number_of(nat,Va)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),pls))). % 8.03/8.02 all Va (number_number_of(nat,Va)=zero_zero(nat)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),pls))). % 8.03/8.02 all K_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,K_2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K_2))). % 8.03/8.02 all K_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K_2)),pls))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),pls))). % 8.03/8.02 all K_2 L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K_2)),hAPP(int,int,bit1,L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),L_1))). % 8.03/8.02 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit1,K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2))). % 8.03/8.02 all K_2 L_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K_2)),hAPP(int,int,bit0,L_1)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1))). % 8.03/8.02 all K1 K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit0,K2)))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2))). % 8.03/8.02 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z_2))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2))). % 8.03/8.02 all Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)))<->Na=zero_zero(nat)). % 8.03/8.02 hAPP(int,int,succ,pls)=hAPP(int,int,bit1,pls). % 8.03/8.02 all K (hAPP(int,int,succ,hAPP(int,int,bit0,K))=hAPP(int,int,bit1,K)). % 8.03/8.02 all K (hAPP(int,int,succ,hAPP(int,int,bit1,K))=hAPP(int,int,bit0,hAPP(int,int,succ,K))). % 8.03/8.02 all Wa Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),Z_2))). % 8.03/8.02 all Wa Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,Wa),one_one(int))),Z_2))<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_2))). % 8.03/8.02 all W_1 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_e_q(int),hAPP(int,int,plus_plus(int,W_1),one_one(int))),Z_1))). % 8.03/8.02 all K (hAPP(int,int,succ,K)=hAPP(int,int,plus_plus(int,K),one_one(int))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all A_1 N B (hAPP(nat,X_a,power_power(X_a,A_1),N)=hAPP(nat,X_a,power_power(X_a,B),N)-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))->ti(X_a,A_1)=ti(X_a,B))))))). % 8.03/8.02 all X_a (number_semiring(X_a)-> (all V_2 V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_2))->hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V_1)),number_number_of(X_a,V_2))=number_number_of(X_a,hAPP(int,int,plus_plus(int,V_1),V_2)))))). % 8.03/8.02 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))). % 8.03/8.02 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),Z_1)))). % 8.03/8.02 all X_a (number_ring(X_a)-> (all K (number_number_of(X_a,hAPP(int,int,succ,K))=hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,K))))). % 8.03/8.02 all K L (hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L))=hAPP(int,int,bit0,hAPP(int,int,plus_plus(int,K),hAPP(int,int,succ,L)))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all N A_1 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_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N)),hAPP(nat,X_a,power_power(X_a,B),N)))))))). % 8.03/8.02 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). % 8.03/8.02 all X hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). % 8.03/8.02 all X_a (linordered_idom(X_a)-> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y)))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all X Y (hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))->ti(X_a,X)=ti(X_a,Y)))))). % 8.03/8.02 all X_a (number_ring(X_a)-> (all V_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,V_1)))->hAPP(nat,X_a,semiring_1_of_nat(X_a),number_number_of(nat,V_1))=number_number_of(X_a,V_1))& (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,V_1)))->hAPP(nat,X_a,semiring_1_of_nat(X_a),number_number_of(nat,V_1))=zero_zero(X_a))))). % 8.03/8.02 all X_a (linordered_semidom(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))). % 8.03/8.02 all X_a (linordered_idom(X_a)-> (all X Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))). % 8.03/8.02 all X_a (linordered_idom(X_a)-> (all Xa Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X_a)))<->ti(X_a,Xa)=zero_zero(X_a)&ti(X_a,Ya)=zero_zero(X_a)))). % 8.03/8.02 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))->X=zero_zero(int)|X=one_one(int))). % 8.03/8.02 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,N)))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit0,N))))&hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit1,N))))). % 8.03/8.02 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,pls))). % 8.03/8.02 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))-> (exists N_1 (K=hAPP(nat,int,semiring_1_of_nat(int),N_1)))). % 8.03/8.02 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))-> -(all N_1 (K!=hAPP(nat,int,semiring_1_of_nat(int),N_1)))). % 8.03/8.02 all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N)). % 8.03/8.02 all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N)). % 8.03/8.02 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Na),zero_zero(nat)))<->Na=zero_zero(nat)). % 8.03/8.02 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))|M_1=N->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))). % 8.03/8.02 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))-> (M_1!=N->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))). % 8.03/8.02 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))). % 8.03/8.02 all Ma Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))|Ma=Na). % 8.03/8.02 all Ma Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))&Ma!=Na). % 8.03/8.03 all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),N)). % 8.03/8.03 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M_1))). % 8.03/8.03 all M_1 N (M_1=N->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))). % 8.03/8.03 all K I_2 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),K))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),K)))). % 8.03/8.03 all M_1 N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M_1))->M_1=N)). % 8.03/8.03 all Xa Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya))|Xa=Ya). % 8.03/8.03 all Xa Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya))&Xa!=Ya). % 8.03/8.03 all N M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),hAPP(nat,nat,plus_plus(nat,M_1),N))). % 8.03/8.03 all N M_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),hAPP(nat,nat,plus_plus(nat,N),M_1))). % 8.03/8.03 all Ma Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))<-> (exists K_1 (Na=hAPP(nat,nat,plus_plus(nat,Ma),K_1)))). % 8.03/8.03 all K_2 Ma Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,K_2),Ma)),hAPP(nat,nat,plus_plus(nat,K_2),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))). % 8.03/8.03 all M_1 I_2 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),hAPP(nat,nat,plus_plus(nat,J_2),M_1)))). % 8.03/8.03 all M_1 I_2 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),hAPP(nat,nat,plus_plus(nat,M_1),J_2)))). % 8.03/8.03 all K I_2 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),hAPP(nat,nat,plus_plus(nat,J_2),K)))). % 8.03/8.03 all K L I_2 J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),L))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),hAPP(nat,nat,plus_plus(nat,J_2),L))))). % 8.03/8.03 all M_1 K N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M_1),K)),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N))). % 8.03/8.03 all M_1 K N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M_1),K)),N))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))). % 8.03/8.03 all M_1 K N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M_1),K)),N))-> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N)))). % 8.03/8.03 all Z_1 X Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,plus_plus(real,Z_1),X)),hAPP(real,real,plus_plus(real,Z_1),Y)))). % 8.03/8.03 all Xa Ya (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Xa),Ya))). % 8.03/8.03 all Ma Na (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),Na)))<->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))). % 8.03/8.03 all Va V (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,Va)),number_number_of(nat,V)))<-> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),V))->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),pls)))). % 8.03/8.03 all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),one_one(real)),hAPP(nat,real,power_power(real,number_number_of(real,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))). % 8.03/8.03 all P_2 P_1 Xa ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))-> (hBOOL(P_1)<->hBOOL(P_2)))-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))&hBOOL(P_1)<->hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))&hBOOL(P_2))). % 8.03/8.03 all P_2 P_1 Xa ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))-> (hBOOL(P_1)<->hBOOL(P_2)))-> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))->hBOOL(P_1))<-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Xa))->hBOOL(P_2)))). % 8.03/8.03 all Na P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))-> (hBOOL(hAPP(nat,bool,P_1,Na))-> (exists K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),Na))& (all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),K_1))-> -hBOOL(hAPP(nat,bool,P_1,I_1))))&hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,plus_plus(nat,K_1),one_one(nat)))))))). % 8.03/8.03 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1))-> -(all M (Z_1!=hAPP(nat,int,semiring_1_of_nat(int),M)))). % 8.03/8.03 all Ma K_2 F ((all M 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,F,M)),hAPP(nat,nat,F,N_1)))))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,F,Ma)),K_2)),hAPP(nat,nat,F,hAPP(nat,nat,plus_plus(nat,Ma),K_2))))). % 8.03/8.03 all W_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W_1),W_1)). % 8.03/8.03 all Z_1 W_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z_1),W_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W_1),Z_1))). % 8.03/8.03 all K I_2 J_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),I_2),J_2))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),J_2),K))->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),I_2),K)))). % 8.03/8.03 all Z_1 W_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z_1),W_1))-> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W_1),Z_1))->Z_1=W_1)). % 8.03/8.03 all P_1 K_2 I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),I))-> (hBOOL(hAPP(int,bool,P_1,K_2))-> ((all I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),I_1))-> (hBOOL(hAPP(int,bool,P_1,I_1))->hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,I_1),one_one(int)))))))->hBOOL(hAPP(int,bool,P_1,I))))). % 8.03/8.03 all Na P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))-> (hBOOL(hAPP(nat,bool,P_1,Na))-> (exists K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K_1),Na))& (all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K_1))-> -hBOOL(hAPP(nat,bool,P_1,I_1))))&hBOOL(hAPP(nat,bool,P_1,K_1)))))). % 8.03/8.03 all I J F ((all I_1 J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_1)))))-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))->hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,F,I)),hAPP(nat,nat,F,J))))). % 8.03/8.03 all X_a (preorder(X_a)-> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),X)))). % 8.03/8.03 all X_a (linorder(X_a)-> (all X Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))))). % 8.03/8.03 all X_a X_b (ord(X_b)-> (all Xa 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_e_q(fun(X_a,X_b)),F),G))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,Xa)),hAPP(X_a,X_b,G,Xa)))))). % 8.03/8.03 all X_a (order(X_a)-> (all Z_1 Y X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Z_1),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Z_1),X)))))). % 8.03/8.03 all X_a (order(X_a)-> (all Y X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))->ti(X_a,X)=ti(X_a,Y))))). % 8.03/8.03 all X_a (preorder(X_a)-> (all Z_1 X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Z_1)))))). % 8.03/8.03 all X_a (order(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))->ti(X_a,X)=ti(X_a,Y))))). % 8.03/8.03 all X_a (order(X_a)-> (all C_1 B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))-> (ti(X_a,B)=ti(X_a,C_1)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),A_1)))))). % 8.03/8.03 all X_a (ord(X_a)-> (all C_1 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (B=C_1->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),C_1)))))). % 8.03/8.03 all X_a (order(X_a)-> (all C_1 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_e_q(X_a),C_1),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),A_1)))))). % 8.03/8.03 all X_a (ord(X_a)-> (all C_1 A_1 B (A_1=B-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),C_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),C_1)))))). % 8.03/8.03 all X_a (order(X_a)-> (all Ya Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ya),Xa))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))<->ti(X_a,Xa)=ti(X_a,Ya))))). % 8.03/8.03 all X_a X_b (ord(X_b)-> (all Xa 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_e_q(fun(X_a,X_b)),F),G))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,Xa)),hAPP(X_a,X_b,G,Xa)))))). % 8.03/8.03 all X_a (preorder(X_a)-> (all X Y (X=Y->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))))). % 8.03/8.03 all X_a (order(X_a)-> (all Xa Ya (ti(X_a,Xa)=ti(X_a,Ya)<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))&hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ya),Xa))))). % 8.03/8.03 all X_a (linorder(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))))). % 8.03/8.03 all X_a X_b (ord(X_b)-> (all 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_e_q(fun(X_a,X_b)),F),G))<-> (all X_1 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))))). % 8.03/8.03 all X_a (linorder(X_a)-> (all 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)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))). % 8.03/8.03 all X_a (preorder(X_a)-> (all X 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))))). % 8.03/8.03 all X_a (order(X_a)-> (all Z_1 Y 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)))))). % 8.03/8.03 all X_a (preorder(X_a)-> (all Z_1 X 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)))))). % 8.03/8.03 all X_a (order(X_a)-> (all C_1 B 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_1)->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_1)))))). % 8.03/8.03 all X_a (ord(X_a)-> (all C_1 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))-> (B=C_1->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C_1)))))). % 8.03/8.03 all X_a (order(X_a)-> (all C_1 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),C_1),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_1)))))). % 8.03/8.03 all X_a (ord(X_a)-> (all C_1 A_1 B (A_1=B-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C_1)))))). % 8.03/8.03 all X_a (order(X_a)-> (all B 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))))). % 8.03/8.03 all X_a (preorder(X_a)-> (all A_1 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))))). % 8.03/8.03 all X_a (preorder(X_a)-> (all P_1 Xa Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa))->hBOOL(P_1))))). % 8.03/8.03 all X_a (order(X_a)-> (all X 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)))). % 8.03/8.03 all X_a (order(X_a)-> (all 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)))). % 8.03/8.03 all X_a (preorder(X_a)-> (all X 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))))). % 8.03/8.03 all X_a (preorder(X_a)-> (all X 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))))). % 8.03/8.03 all X_a (order(X_a)-> (all 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)))). % 8.03/8.03 all X_a (linorder(X_a)-> (all 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))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))). % 8.03/8.03 all X_a (linorder(X_a)-> (all Ya Xa (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa))-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))<->ti(X_a,Xa)=ti(X_a,Ya))))). % 8.03/8.03 all X_a (linorder(X_a)-> (all 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)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))). % 8.03/8.03 all X_a (linorder(X_a)-> (all Xa Ya (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa))|ti(X_a,Xa)=ti(X_a,Ya)))). % 8.03/8.03 all X_a (linorder(X_a)-> (all Xa Ya (ti(X_a,Xa)!=ti(X_a,Ya)<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa))))). % 8.03/8.03 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))))). % 8.03/8.03 all X_a (linorder(X_a)-> (all Xa Ya (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ya),Xa))))). % 8.03/8.03 all X_a (linorder(X_a)-> (all Xa Ya (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa))))). % 8.03/8.03 all X_a (linorder(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))). % 8.03/8.03 all X_a (order(X_a)-> (all Xa Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))&ti(X_a,Xa)!=ti(X_a,Ya)))). % 8.03/8.03 all X_a (preorder(X_a)-> (all Xa Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))& -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ya),Xa))))). % 8.03/8.03 all X_a (order(X_a)-> (all Xa Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))|ti(X_a,Xa)=ti(X_a,Ya)))). % 8.03/8.03 all X_a (linorder(X_a)-> (all X 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_e_q(X_a),Y),X))))). % 8.03/8.03 all X_a (linorder(X_a)-> (all Y X (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))))). % 8.03/8.03 all X_a (linorder(X_a)-> (all Xa Ya (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))<->ti(X_a,Xa)=ti(X_a,Ya))))). % 8.03/8.03 all X_a (order(X_a)-> (all 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_e_q(X_a),A_1),B))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))). % 8.03/8.03 all X_a (order(X_a)-> (all 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_e_q(X_a),B),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)))))). % 8.03/8.03 all X_a (linorder(X_a)-> (all Y X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))))). % 8.03/8.03 all X_a (preorder(X_a)-> (all X 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_e_q(X_a),X),Y))))). % 8.03/8.03 all X_a (linorder(X_a)-> (all Xa Ya (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))<->ti(X_a,Xa)=ti(X_a,Ya))))). % 8.03/8.03 all X_a (order(X_a)-> (all X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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)))). % 8.03/8.03 all X_a (order(X_a)-> (all A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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)))))). % 8.03/8.03 all X_a (order(X_a)-> (all B A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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)))))). % 8.03/8.03 all X_a (preorder(X_a)-> (all Z_1 X 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_e_q(X_a),Y),Z_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1)))))). % 8.03/8.03 all X_a (order(X_a)-> (all Z_1 Y 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_e_q(X_a),Z_1),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X)))))). % 8.03/8.03 all X_a (preorder(X_a)-> (all Z_1 X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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)))))). % 8.03/8.03 all X_a (order(X_a)-> (all Z_1 Y X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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)))))). % 8.03/8.03 all D2 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)))))). % 8.03/8.03 all X_a (dense_linorder(X_a)-> (all Z_1 Y ((all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Z_1))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1))))). % 8.03/8.03 all X_a X_b (ord(X_b)-> (all 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(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_e_q(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_e_q(fun(X_a,X_b)),G),F))))). % 8.03/8.03 all X_a X_b (ord(X_b)-> (all F G ((all X_1 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))->hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G))))). % 8.03/8.03 all X_a (linorder(X_a)-> (all T_3 exists Z all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X_1))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),T_3))))). % 8.03/8.03 all X_a (dense_linorder(X_a)-> (all Z_1 X Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))-> ((all W (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W),Y))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),W),Z_1)))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1)))))). % 8.03/8.03 all X_b X_a (order(X_a)&order(X_b)-> (all C F B_1 A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C),hAPP(X_a,X_b,F,B_1)))-> ((all 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(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Y_1)),hAPP(X_a,X_b,F,X_1)))))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C),hAPP(X_a,X_b,F,A_2)))))))). % 8.03/8.03 all X_a (linorder(X_a)-> (all T_3 exists Z all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),T_3))))). % 8.03/8.03 all X_a (linorder(X_a)-> (all T_3 exists Z all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),T_3),X_1))))). % 8.03/8.03 all X_b X_a (order(X_a)&order(X_b)-> (all C F B_1 A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_1),A_2))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C),hAPP(X_a,X_b,F,B_1)))-> ((all X_1 Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y_1),X_1))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,Y_1)),hAPP(X_a,X_b,F,X_1)))))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C),hAPP(X_a,X_b,F,A_2)))))))). % 8.03/8.03 all X_a X_b (order(X_b)&order(X_a)-> (all F C A_2 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,B_1)),C))-> ((all X_1 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_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,F,Y_1)))))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,A_2)),C))))))). % 8.03/8.03 all X_a (linorder(X_a)-> (all T_3 exists Z all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z))-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),T_3),X_1))))). % 8.03/8.03 all X_b X_a (order(X_a)&ord(X_b)-> (all C F B_1 A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_b,X_a,F,B_1)),A_2))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C),B_1))-> ((all X_1 Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Y_1)),hAPP(X_b,X_a,F,X_1)))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C)),A_2))))))). % 8.03/8.03 all X_a X_b (order(X_b)&order(X_a)-> (all F C A_2 B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B_1))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,B_1)),C))-> ((all X_1 Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),Y_1))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,F,Y_1)))))->hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,A_2)),C))))))). % 8.03/8.03 all X_a X_b (order(X_b)&order(X_a)-> (all C A_2 F B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,B_1)))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_1),C))-> ((all X_1 Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),X_1),Y_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(X_b,X_a,F,Y_1)))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,C)))))))). % 8.03/8.03 all X_b X_a (order(X_a)&order(X_b)-> (all C F B_1 A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,B_1)),A_2))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C),B_1))-> ((all X_1 Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),Y_1),X_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_b,X_a,F,Y_1)),hAPP(X_b,X_a,F,X_1)))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C)),A_2))))))). % 8.03/8.03 all X_a X_b (order(X_b)&order(X_a)-> (all C A_2 F B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),hAPP(X_b,X_a,F,B_1)))-> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_1),C))-> ((all X_1 Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,X_1)),hAPP(X_b,X_a,F,Y_1)))))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,C)))))))). % 8.03/8.03 all X Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,Y),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))). % 8.03/8.03 all A_1 B (hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,A_1),B)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)),B))),hAPP(nat,int,power_power(int,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). % 8.03/8.03 all K L (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit1,K)),L)=hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),L))),L)). % 8.03/8.03 all X_a (linord20386208strict(X_a)-> (all C_1 A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B)))-> (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_e_q(X_a),A_1),B)))))). % 8.03/8.03 all X_a (linord20386208strict(X_a)-> (all A_1 C_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),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_e_q(X_a),A_1),B)))))). % 8.03/8.03 all X_a (linord20386208strict(X_a)-> (all C_1 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),times_times(X_a),C_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))). % 8.03/8.03 all X_a (linordered_semiring(X_a)-> (all C_1 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),times_times(X_a),C_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))). % 8.03/8.03 all X_a (linord20386208strict(X_a)-> (all A_1 C_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),times_times(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))). % 8.03/8.03 all X_a (linordered_semiring(X_a)-> (all A_1 C_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),times_times(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1)))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))). % 8.03/8.03 all X_a (linord20386208strict(X_a)-> (all C_1 D A_1 B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D))-> (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_e_q(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),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D))))))))). % 8.03/8.03 all X_a (linord20386208strict(X_a)-> (all C_1 D A_1 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_e_q(X_a),C_1),D))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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_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),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D))))))))). % 8.03/8.03 all X_a (linord20386208strict(X_a)-> (all C_1 D A_1 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_1),D))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D))))))))). % 8.03/8.03 all X_a (linord20386208strict(X_a)-> (all C_1 D A_1 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_1),D))-> (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_e_q(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),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D))))))))). % 8.03/8.03 all X_a (linord581940658strict(X_a)-> (all A_2 B_1 C (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_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_1),A_2)))))). % 8.03/8.03 all X_a (linord581940658strict(X_a)-> (all A_2 B_1 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_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B_1)))))). % 8.03/8.03 all X_a (linord581940658strict(X_a)-> (all Xa Ya (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,plus_plus(X_a,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),Xa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ya),Ya))))<->ti(X_a,Xa)!=zero_zero(X_a)|ti(X_a,Ya)!=zero_zero(X_a)))). % 8.03/8.03 all X_a (linordered_ring(X_a)-> (all X Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(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)))))). % 8.03/8.03 all X_a (linordered_semidom(X_a)-> (all N A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,power_power(X_a,A_1),N))))))). % 8.03/8.03 all X_a (linordered_semidom(X_a)-> (all N A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_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),A_1),hAPP(nat,X_a,power_power(X_a,A_1),N))))))). % 8.03/8.03 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)),hAPP(real,real,sqrt,X)))). % 8.03/8.03 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X))->hAPP(real,real,sqrt,X)!=zero_zero(real)). % 8.03/8.03 all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,Xa)),zero_zero(real)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),zero_zero(real)))). % 8.03/8.03 all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,Ya)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Ya))). % 8.03/8.03 all Xa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,Xa)),one_one(real)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),one_one(real)))). % 8.03/8.03 all Ya (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,Ya)))<->hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Ya))). % 8.03/8.03 all X_a (linord581940658strict(X_a)-> (all C_1 B 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_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),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B))))))). % 8.03/8.03 all X_a (linord581940658strict(X_a)-> (all C_1 B 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_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),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1))))))). % 8.03/8.03 all X_a (linord893533164strict(X_a)-> (all C_1 A_1 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_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),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B))))))). % 8.03/8.03 all X_a (linord20386208strict(X_a)-> (all C_1 A_1 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_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),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B))))))). % 8.03/8.03 all X_a (linord20386208strict(X_a)-> (all C_1 A_1 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_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),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1))))))). % 8.03/8.03 all X_a (linord581940658strict(X_a)-> (all B 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))))))). % 8.03/8.03 all X_a (linord20386208strict(X_a)-> (all B 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))))))). % 8.03/8.04 all X_a (linord581940658strict(X_a)-> (all A_2 B_1 C (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_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B_1)))<->hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)))))). % 8.03/8.04 all X_a (linord20386208strict(X_a)-> (all B 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)))))). % 8.03/8.04 all T_2 T_1 (preorder(T_1)->preorder(fun(T_2,T_1))). % 8.03/8.04 all T_2 T_1 (order(T_1)->order(fun(T_2,T_1))). % 8.03/8.04 all T_2 T_1 (ord(T_1)->ord(fun(T_2,T_1))). % 8.03/8.04 semiri456707255roduct(int). % 8.03/8.04 ordere223160158up_add(int). % 8.03/8.04 ordere236663937imp_le(int). % 8.03/8.04 linord893533164strict(int). % 8.03/8.04 linord20386208strict(int). % 8.03/8.04 ordere779506340up_add(int). % 8.03/8.04 ordere216010020id_add(int). % 8.03/8.04 linord219039673up_add(int). % 8.03/8.04 cancel146912293up_add(int). % 8.03/8.04 ring_11004092258visors(int). % 8.03/8.04 linord581940658strict(int). % 8.03/8.04 cancel_semigroup_add(int). % 8.03/8.04 linordered_semiring(int). % 8.03/8.04 linordered_semidom(int). % 8.03/8.04 ab_semigroup_add(int). % 8.03/8.04 no_zero_divisors(int). % 8.03/8.04 comm_monoid_add(int). % 8.03/8.04 linordered_ring(int). % 8.03/8.04 linordered_idom(int). % 8.03/8.04 comm_semiring_1(int). % 8.03/8.04 semiring_char_0(int). % 8.03/8.04 number_semiring(int). % 8.03/8.04 zero_ne_q_one(int). % 8.03/8.04 preorder(int). % 8.03/8.04 linorder(int). % 8.03/8.04 monoid_mult(int). % 8.03/8.04 monoid_add(int). % 8.03/8.04 semiring_1(int). % 8.03/8.04 semiring_0(int). % 8.03/8.04 mult_zero(int). % 8.03/8.04 order(int). % 8.03/8.04 ring_char_0(int). % 8.03/8.04 number_ring(int). % 8.03/8.04 ord(int). % 8.03/8.04 power(int). % 8.03/8.04 zero(int). % 8.03/8.04 number(int). % 8.03/8.04 one(int). % 8.03/8.04 semiri456707255roduct(nat). % 8.03/8.04 ordere223160158up_add(nat). % 8.03/8.04 ordere236663937imp_le(nat). % 8.03/8.04 linord893533164strict(nat). % 8.03/8.04 linord20386208strict(nat). % 8.03/8.04 ordere779506340up_add(nat). % 8.03/8.04 ordere216010020id_add(nat). % 8.03/8.04 cancel146912293up_add(nat). % 8.03/8.04 cancel_semigroup_add(nat). % 8.03/8.04 linordered_semiring(nat). % 8.03/8.04 linordered_semidom(nat). % 8.03/8.04 ab_semigroup_add(nat). % 8.03/8.04 no_zero_divisors(nat). % 8.03/8.04 comm_monoid_add(nat). % 8.03/8.04 comm_semiring_1(nat). % 8.03/8.04 semiring_char_0(nat). % 8.03/8.04 number_semiring(nat). % 8.03/8.04 zero_ne_q_one(nat). % 8.03/8.04 preorder(nat). % 8.03/8.04 linorder(nat). % 8.03/8.04 monoid_mult(nat). % 8.03/8.04 monoid_add(nat). % 8.03/8.04 semiring_1(nat). % 8.03/8.04 semiring_0(nat). % 8.03/8.04 mult_zero(nat). % 8.03/8.04 order(nat). % 8.03/8.04 ord(nat). % 8.03/8.04 power(nat). % 8.03/8.04 zero(nat). % 8.03/8.04 number(nat). % 8.03/8.04 one(nat). % 8.03/8.04 preorder(bool). % 8.03/8.04 order(bool). % 8.03/8.04 ord(bool). % 8.03/8.04 semiri456707255roduct(real). % 8.03/8.04 ordere223160158up_add(real). % 8.03/8.04 ordere236663937imp_le(real). % 8.03/8.04 linord893533164strict(real). % 8.03/8.04 linord20386208strict(real). % 8.03/8.04 ordere779506340up_add(real). % 8.03/8.04 ordere216010020id_add(real). % 8.03/8.04 linord219039673up_add(real). % 8.03/8.04 cancel146912293up_add(real). % 8.03/8.04 ring_11004092258visors(real). % 8.03/8.04 linord581940658strict(real). % 8.03/8.04 cancel_semigroup_add(real). % 8.03/8.04 linordered_semiring(real). % 8.03/8.04 linordered_semidom(real). % 8.03/8.04 dense_linorder(real). % 8.03/8.04 ab_semigroup_add(real). % 8.03/8.04 no_zero_divisors(real). % 8.03/8.04 comm_monoid_add(real). % 8.03/8.04 linordered_ring(real). % 8.03/8.04 linordered_idom(real). % 8.03/8.04 comm_semiring_1(real). % 8.03/8.04 semiring_char_0(real). % 8.03/8.04 number_semiring(real). % 8.03/8.04 zero_ne_q_one(real). % 8.03/8.04 preorder(real). % 8.03/8.04 linorder(real). % 8.03/8.04 monoid_mult(real). % 8.03/8.04 monoid_add(real). % 8.03/8.04 semiring_1(real). % 8.03/8.04 semiring_0(real). % 8.03/8.04 mult_zero(real). % 8.03/8.04 order(real). % 8.03/8.04 ring_char_0(real). % 8.03/8.04 number_ring(real). % 8.03/8.04 ord(real). % 8.03/8.04 power(real). % 8.03/8.04 zero(real). % 8.03/8.04 number(real). % 8.03/8.04 one(real). % 8.03/8.04 all T A (ti(T,ti(T,A))=ti(T,A)). % 8.03/8.04 all X_a X 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)). % 8.03/8.04 all X_a X 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)). % 8.03/8.04 all P (ti(bool,P)=fTrue|ti(bool,P)=fFalse). % 8.03/8.04 -(hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))!=zero_zero(int)). % 8.03/8.04 end_of_list. % 8.03/8.04 % 8.03/8.04 -------> usable clausifies to: % 8.03/8.04 % 8.03/8.04 list(usable). % 8.03/8.04 0 [] A=A. % 8.03/8.04 0 [] -one(X_a)|ti(X_a,one_one(X_a))=one_one(X_a). % 8.03/8.04 0 [] -monoid_add(X_a)|plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1). % 8.03/8.04 0 [] -monoid_add(X_a)|ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1). % 8.03/8.04 0 [] -ab_semigroup_add(X_a)|plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1). % 8.03/8.04 0 [] -ab_semigroup_add(X_a)|ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1). % 8.03/8.04 0 [] -cancel_semigroup_add(X_a)|plus_plus(X_a,ti(X_a,B_1_1))=plus_plus(X_a,B_1_1). % 8.03/8.04 0 [] -cancel_semigroup_add(X_a)|ti(fun(X_a,X_a),plus_plus(X_a,B_1_1))=plus_plus(X_a,B_1_1). % 8.03/8.04 0 [] -linordered_semiring(X_a)|ti(fun(X_a,fun(X_a,X_a)),times_times(X_a))=times_times(X_a). % 8.03/8.04 0 [] -zero(X_a)|ti(X_a,zero_zero(X_a))=zero_zero(X_a). % 8.03/8.04 0 [] ti(X_a,undefined(X_a))=undefined(X_a). % 8.03/8.04 0 [] ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a))=if(X_a). % 8.03/8.04 0 [] ti(fun(int,int),bit0)=bit0. % 8.03/8.04 0 [] ti(fun(int,int),bit1)=bit1. % 8.03/8.04 0 [] ti(int,pls)=pls. % 8.03/8.04 0 [] -number(X_a)|number_number_of(X_a,ti(int,B_1_1))=number_number_of(X_a,B_1_1). % 8.03/8.04 0 [] -number(X_a)|ti(X_a,number_number_of(X_a,B_1_1))=number_number_of(X_a,B_1_1). % 8.03/8.04 0 [] ti(fun(int,int),succ)=succ. % 8.03/8.04 0 [] -semiring_1(X_a)|ti(fun(nat,X_a),semiring_1_of_nat(X_a))=semiring_1_of_nat(X_a). % 8.03/8.04 0 [] ti(fun(real,real),sqrt)=sqrt. % 8.03/8.04 0 [] -ord(X_a)|ti(fun(X_a,fun(X_a,bool)),ord_less(X_a))=ord_less(X_a). % 8.03/8.04 0 [] -ord(X_b)|ti(fun(X_b,fun(X_b,bool)),ord_less_e_q(X_b))=ord_less_e_q(X_b). % 8.03/8.04 0 [] -power(X_a)|power_power(X_a,ti(X_a,B_1_1))=power_power(X_a,B_1_1). % 8.03/8.04 0 [] -power(X_a)|ti(fun(nat,X_a),power_power(X_a,B_1_1))=power_power(X_a,B_1_1). % 8.03/8.04 0 [] ti(bool,fFalse)=fFalse. % 8.03/8.04 0 [] ti(bool,fTrue)=fTrue. % 8.03/8.04 0 [] -ord(X_b)|hAPP(X_a,X_b,ti(fun(X_a,X_b),B_1_1),B_2)=hAPP(X_a,X_b,B_1_1,B_2). % 8.03/8.04 0 [] -ord(X_b)|hAPP(X_a,X_b,B_1_1,ti(X_a,B_2))=hAPP(X_a,X_b,B_1_1,B_2). % 8.03/8.04 0 [] -ord(X_b)|ti(X_b,hAPP(X_a,X_b,B_1_1,B_2))=hAPP(X_a,X_b,B_1_1,B_2). % 8.03/8.04 0 [] -power(X_a)|hAPP(nat,X_a,ti(fun(nat,X_a),B_1_1),B_2)=hAPP(nat,X_a,B_1_1,B_2). % 8.03/8.04 0 [] -power(X_a)|hAPP(nat,X_a,B_1_1,ti(nat,B_2))=hAPP(nat,X_a,B_1_1,B_2). % 8.03/8.04 0 [] -power(X_a)|ti(X_a,hAPP(nat,X_a,B_1_1,B_2))=hAPP(nat,X_a,B_1_1,B_2). % 8.03/8.04 0 [] hAPP(bool,fun(X_a,fun(X_a,X_a)),ti(fun(bool,fun(X_a,fun(X_a,X_a))),B_1_1),B_2)=hAPP(bool,fun(X_a,fun(X_a,X_a)),B_1_1,B_2). % 8.03/8.04 0 [] hAPP(bool,fun(X_a,fun(X_a,X_a)),B_1_1,ti(bool,B_2))=hAPP(bool,fun(X_a,fun(X_a,X_a)),B_1_1,B_2). % 8.03/8.04 0 [] ti(fun(X_a,fun(X_a,X_a)),hAPP(bool,fun(X_a,fun(X_a,X_a)),B_1_1,B_2))=hAPP(bool,fun(X_a,fun(X_a,X_a)),B_1_1,B_2). % 8.03/8.04 0 [] hAPP(X_a,fun(X_a,X_a),ti(fun(X_a,fun(X_a,X_a)),B_1_1),B_2)=hAPP(X_a,fun(X_a,X_a),B_1_1,B_2). % 8.03/8.04 0 [] hAPP(X_a,fun(X_a,X_a),B_1_1,ti(X_a,B_2))=hAPP(X_a,fun(X_a,X_a),B_1_1,B_2). % 8.03/8.04 0 [] ti(fun(X_a,X_a),hAPP(X_a,fun(X_a,X_a),B_1_1,B_2))=hAPP(X_a,fun(X_a,X_a),B_1_1,B_2). % 8.03/8.04 0 [] hAPP(X_a,X_a,ti(fun(X_a,X_a),B_1_1),B_2)=hAPP(X_a,X_a,B_1_1,B_2). % 8.03/8.04 0 [] hAPP(X_a,X_a,B_1_1,ti(X_a,B_2))=hAPP(X_a,X_a,B_1_1,B_2). % 8.03/8.04 0 [] ti(X_a,hAPP(X_a,X_a,B_1_1,B_2))=hAPP(X_a,X_a,B_1_1,B_2). % 8.03/8.04 0 [] -hBOOL(ti(bool,B_1_1))|hBOOL(B_1_1). % 8.03/8.04 0 [] hBOOL(ti(bool,B_1_1))| -hBOOL(B_1_1). % 8.03/8.04 0 [] ti(int,m1)=m1. % 8.03/8.04 0 [] ti(nat,n)=n. % 8.03/8.04 0 [] ti(int,t)=t. % 8.03/8.04 0 [] ti(nat,tn)=tn. % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)). % 8.03/8.04 0 [] -linordered_idom(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))!=zero_zero(X_a)|ti(X_a,Xa)=zero_zero(X_a). % 8.03/8.04 0 [] -linordered_idom(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))!=zero_zero(X_a)|ti(X_a,Ya)=zero_zero(X_a). % 8.03/8.04 0 [] -linordered_idom(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))=zero_zero(X_a)|ti(X_a,Xa)!=zero_zero(X_a)|ti(X_a,Ya)!=zero_zero(X_a). % 8.03/8.04 0 [] -semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,one_one(X_a)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=one_one(X_a). % 8.03/8.04 0 [] -semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=zero_zero(X_a). % 8.03/8.04 0 [] -ring_11004092258visors(X_a)|hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))!=zero_zero(X_a)|ti(X_a,A_2)=zero_zero(X_a). % 8.03/8.04 0 [] -ring_11004092258visors(X_a)|hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=zero_zero(X_a)|ti(X_a,A_2)!=zero_zero(X_a). % 8.03/8.04 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,W_1))=number_number_of(X_a,hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,pls)),W_1)). % 8.03/8.04 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V_1)),one_one(X_a))=number_number_of(X_a,hAPP(int,int,plus_plus(int,V_1),hAPP(int,int,bit1,pls))). % 8.03/8.04 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))=number_number_of(X_a,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))). % 8.03/8.04 0 [] -number_semiring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),one_one(X_a))=number_number_of(X_a,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))). % 8.03/8.04 0 [] hAPP(nat,int,power_power(int,hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). % 8.03/8.04 0 [] -power(X_a)| -semiring_0(X_a)|number_number_of(nat,W_1)!=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,W_1))=one_one(X_a). % 8.03/8.04 0 [] -power(X_a)| -semiring_0(X_a)|number_number_of(nat,W_1)=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),number_number_of(nat,W_1))=zero_zero(X_a). % 8.03/8.04 0 [] -number_ring(X_a)|one_one(X_a)=number_number_of(X_a,hAPP(int,int,bit1,pls)). % 8.03/8.04 0 [] -number_ring(X_a)|number_number_of(X_a,hAPP(int,int,bit1,pls))=one_one(X_a). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),n)). % 8.03/8.04 0 [] 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)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,K_2)),number_number_of(int,L_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,K_2)),number_number_of(int,L_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1)). % 8.03/8.04 0 [] hAPP(int,int,plus_plus(int,number_number_of(int,V_1)),number_number_of(int,W_1))=number_number_of(int,hAPP(int,int,plus_plus(int,V_1),W_1)). % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Xa)),number_number_of(X_a,Ya)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),Ya)). % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Xa)),number_number_of(X_a,Ya)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),Ya)). % 8.03/8.04 0 [] zero_zero(int)=number_number_of(int,pls). % 8.03/8.04 0 [] hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),M_1)),N)=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,M_1),N)). % 8.03/8.04 0 [] hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,M_1),N))=hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),M_1)),N). % 8.03/8.04 0 [] hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),N)),Z_1))=hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,M_1),N))),Z_1). % 8.03/8.04 0 [] hAPP(int,int,plus_plus(int,hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,plus_plus(nat,M_1),N)). % 8.03/8.04 0 [] hAPP(nat,int,semiring_1_of_nat(int),one_one(nat))=one_one(int). % 8.03/8.04 0 [] number_number_of(nat,pls)=zero_zero(nat). % 8.03/8.04 0 [] zero_zero(nat)=number_number_of(nat,pls). % 8.03/8.04 0 [] hAPP(nat,int,semiring_1_of_nat(int),Na)!=zero_zero(int)|Na=zero_zero(nat). % 8.03/8.04 0 [] hAPP(nat,int,semiring_1_of_nat(int),Na)=zero_zero(int)|Na!=zero_zero(nat). % 8.03/8.04 0 [] hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat))=zero_zero(int). % 8.03/8.04 0 [] hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))=number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K_2)),hAPP(int,int,bit1,L_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K_2)),hAPP(int,int,bit1,L_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit0,K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit0,K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K_2)),hAPP(int,int,bit0,L_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K_2)),hAPP(int,int,bit0,L_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),J_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,I_2),K)),hAPP(int,int,plus_plus(int,J_2),K))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V_1)),number_number_of(nat,V_2))=number_number_of(nat,V_2). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls))|hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V_1)),number_number_of(nat,V_2))=number_number_of(nat,V_1). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls))|hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V_1)),number_number_of(nat,V_2))=number_number_of(nat,hAPP(int,int,plus_plus(int,V_1),V_2)). % 8.03/8.04 0 [] one_one(int)=number_number_of(int,hAPP(int,int,bit1,pls)). % 8.03/8.04 0 [] number_number_of(nat,hAPP(int,int,bit1,pls))=one_one(nat). % 8.03/8.04 0 [] one_one(nat)=number_number_of(nat,hAPP(int,int,bit1,pls)). % 8.03/8.04 0 [] -number_ring(X_a)| -ring_char_0(X_a)|number_number_of(X_a,Xa)!=number_number_of(X_a,Ya)|Xa=Ya. % 8.03/8.04 0 [] -number_ring(X_a)| -ring_char_0(X_a)|number_number_of(X_a,Xa)=number_number_of(X_a,Ya)|Xa!=Ya. % 8.03/8.04 0 [] -number(X_a)|number_number_of(X_a,Wa)!=ti(X_a,Xa)|ti(X_a,Xa)=number_number_of(X_a,Wa). % 8.03/8.04 0 [] -number(X_a)|number_number_of(X_a,Wa)=ti(X_a,Xa)|ti(X_a,Xa)!=number_number_of(X_a,Wa). % 8.03/8.04 0 [] hAPP(int,int,bit1,K_2)!=hAPP(int,int,bit1,L_1)|K_2=L_1. % 8.03/8.04 0 [] hAPP(int,int,bit1,K_2)=hAPP(int,int,bit1,L_1)|K_2!=L_1. % 8.03/8.04 0 [] hAPP(int,int,bit0,K_2)!=hAPP(int,int,bit0,L_1)|K_2=L_1. % 8.03/8.04 0 [] hAPP(int,int,bit0,K_2)=hAPP(int,int,bit0,L_1)|K_2!=L_1. % 8.03/8.04 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))). % 8.03/8.04 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))). % 8.03/8.04 0 [] hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,Z1),Z2)),Z3)=hAPP(int,int,plus_plus(int,Z1),hAPP(int,int,plus_plus(int,Z2),Z3)). % 8.03/8.04 0 [] hAPP(int,int,plus_plus(int,X),hAPP(int,int,plus_plus(int,Y),Z_1))=hAPP(int,int,plus_plus(int,Y),hAPP(int,int,plus_plus(int,X),Z_1)). % 8.03/8.04 0 [] hAPP(int,int,plus_plus(int,Z_1),W_1)=hAPP(int,int,plus_plus(int,W_1),Z_1). % 8.03/8.04 0 [] hAPP(nat,int,semiring_1_of_nat(int),Ma)!=hAPP(nat,int,semiring_1_of_nat(int),Na)|Ma=Na. % 8.03/8.04 0 [] hAPP(nat,int,semiring_1_of_nat(int),Ma)=hAPP(nat,int,semiring_1_of_nat(int),Na)|Ma!=Na. % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Xa)),zero_zero(X_a)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),pls)). % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Xa)),zero_zero(X_a)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),pls)). % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),number_number_of(X_a,Ya)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Ya)). % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),number_number_of(X_a,Ya)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Ya)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K_2)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),pls)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K_2)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),pls)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit0,K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit0,K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K_2)),hAPP(int,int,bit0,L_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K_2)),hAPP(int,int,bit0,L_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K_2)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),pls)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K_2)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),pls)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,K_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K_2)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,K_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K_2)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,Wa)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),zero_zero(int))). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,Wa)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),zero_zero(int))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,Wa)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),zero_zero(int))). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,Wa)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),zero_zero(int))). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_2))|Wa=Z_2. % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_2)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))|Wa!=Z_2. % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K)),zero_zero(int))). % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Xa)),one_one(X_a)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),hAPP(int,int,bit1,pls))). % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Xa)),one_one(X_a)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Xa),hAPP(int,int,bit1,pls))). % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),number_number_of(X_a,Ya)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),Ya)). % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),number_number_of(X_a,Ya)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),Ya)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),Z_2)),Z_2)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int))). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),Z_2)),Z_2)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),zero_zero(int))). % 8.03/8.04 0 [] -linord219039673up_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2)!=zero_zero(X_a)|ti(X_a,A_2)=zero_zero(X_a). % 8.03/8.04 0 [] -linord219039673up_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2)=zero_zero(X_a)|ti(X_a,A_2)!=zero_zero(X_a). % 8.03/8.04 0 [] hAPP(int,int,bit1,K)!=pls. % 8.03/8.04 0 [] pls!=hAPP(int,int,bit1,L). % 8.03/8.04 0 [] hAPP(int,int,bit1,K)!=hAPP(int,int,bit0,L). % 8.03/8.04 0 [] hAPP(int,int,bit0,K)!=hAPP(int,int,bit1,L). % 8.03/8.04 0 [] hAPP(int,int,bit0,K_2)!=pls|K_2=pls. % 8.03/8.04 0 [] hAPP(int,int,bit0,K_2)=pls|K_2!=pls. % 8.03/8.04 0 [] pls!=hAPP(int,int,bit0,L_1)|pls=L_1. % 8.03/8.04 0 [] pls=hAPP(int,int,bit0,L_1)|pls!=L_1. % 8.03/8.04 0 [] hAPP(int,int,bit0,pls)=pls. % 8.03/8.04 0 [] pls=zero_zero(int). % 8.03/8.04 0 [] zero_zero(int)!=one_one(int). % 8.03/8.04 0 [] hAPP(int,int,plus_plus(int,K),pls)=K. % 8.03/8.04 0 [] hAPP(int,int,plus_plus(int,pls),K)=K. % 8.03/8.04 0 [] hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,K)),hAPP(int,int,bit0,L))=hAPP(int,int,bit0,hAPP(int,int,plus_plus(int,K),L)). % 8.03/8.04 0 [] hAPP(int,int,bit0,K)=hAPP(int,int,plus_plus(int,K),K). % 8.03/8.04 0 [] hAPP(int,int,plus_plus(int,Z_1),zero_zero(int))=Z_1. % 8.03/8.04 0 [] hAPP(int,int,plus_plus(int,zero_zero(int)),Z_1)=Z_1. % 8.03/8.04 0 [] -number_semiring(X_a)|number_number_of(X_a,pls)=zero_zero(X_a). % 8.03/8.04 0 [] -number_ring(X_a)|number_number_of(X_a,pls)=zero_zero(X_a). % 8.03/8.04 0 [] -number_ring(X_a)|zero_zero(X_a)=number_number_of(X_a,pls). % 8.03/8.04 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,pls)),A_1)=ti(X_a,A_1). % 8.03/8.04 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),number_number_of(X_a,pls))=ti(X_a,A_1). % 8.03/8.04 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,Wa))!=zero_zero(X_a)|ti(X_a,A_2)=zero_zero(X_a). % 8.03/8.04 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,Wa))!=zero_zero(X_a)|number_number_of(nat,Wa)!=zero_zero(nat). % 8.03/8.04 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,Wa))=zero_zero(X_a)|ti(X_a,A_2)!=zero_zero(X_a)|number_number_of(nat,Wa)=zero_zero(nat). % 8.03/8.04 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V_1)),hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,W_1)),Z_1))=hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,hAPP(int,int,plus_plus(int,V_1),W_1))),Z_1). % 8.03/8.04 0 [] -number_ring(X_a)|hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V_1)),number_number_of(X_a,W_1))=number_number_of(X_a,hAPP(int,int,plus_plus(int,V_1),W_1)). % 8.03/8.04 0 [] -number_ring(X_a)|number_number_of(X_a,hAPP(int,int,plus_plus(int,V_1),W_1))=hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V_1)),number_number_of(X_a,W_1)). % 8.03/8.04 0 [] hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,K)),hAPP(int,int,bit0,L))=hAPP(int,int,bit1,hAPP(int,int,plus_plus(int,K),L)). % 8.03/8.04 0 [] hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,K)),hAPP(int,int,bit1,L))=hAPP(int,int,bit1,hAPP(int,int,plus_plus(int,K),L)). % 8.03/8.04 0 [] hAPP(int,int,bit1,K)=hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),K)),K). % 8.03/8.04 0 [] hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),Z_1)),Z_1)!=zero_zero(int). % 8.03/8.04 0 [] -number_semiring(X_a)|number_number_of(X_a,hAPP(nat,int,semiring_1_of_nat(int),N))=hAPP(nat,X_a,semiring_1_of_nat(X_a),N). % 8.03/8.04 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))|ti(X_a,A_2)!=zero_zero(X_a). % 8.03/8.04 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))|ti(X_a,A_2)=zero_zero(X_a). % 8.03/8.04 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(X_a))). % 8.03/8.04 0 [] -linordered_idom(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,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))|ti(X_a,Xa)!=zero_zero(X_a)|ti(X_a,Ya)!=zero_zero(X_a). % 8.03/8.04 0 [] -linordered_idom(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,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))|ti(X_a,Xa)=zero_zero(X_a). % 8.03/8.04 0 [] -linordered_idom(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,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))|ti(X_a,Ya)=zero_zero(X_a). % 8.03/8.04 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X_a))). % 8.03/8.04 0 [] -number_ring(X_a)|number_number_of(X_a,hAPP(int,int,bit0,W_1))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),number_number_of(X_a,W_1))),number_number_of(X_a,W_1)). % 8.03/8.04 0 [] -number_ring(X_a)|number_number_of(X_a,hAPP(int,int,bit1,W_1))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,W_1))),number_number_of(X_a,W_1)). % 8.03/8.04 0 [] -number_semiring(X_a)|number_number_of(X_a,hAPP(int,int,bit1,pls))=one_one(X_a). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),m1),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))). % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)|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),N)),hAPP(nat,X_a,power_power(X_a,number_number_of(X_a,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))). % 8.03/8.04 0 [] number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))=hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). % 8.03/8.04 0 [] number_number_of(int,hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))=hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))). % 8.03/8.04 0 [] hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))!=zero_zero(real)|Xa=zero_zero(real). % 8.03/8.04 0 [] hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))!=zero_zero(real)|Ya=zero_zero(real). % 8.03/8.04 0 [] hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))=zero_zero(real)|Xa!=zero_zero(real)|Ya!=zero_zero(real). % 8.03/8.04 0 [] -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(nat,X_a,semiring_1_of_nat(X_a),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)). % 8.03/8.04 0 [] -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(nat,X_a,semiring_1_of_nat(X_a),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N))). % 8.03/8.04 0 [] -power(X_a)| -semiring_0(X_a)|N!=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),N)=one_one(X_a). % 8.03/8.04 0 [] -power(X_a)| -semiring_0(X_a)|N=zero_zero(nat)|hAPP(nat,X_a,power_power(X_a,zero_zero(X_a)),N)=zero_zero(X_a). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_2))| -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),A_1),one_one(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_2)),hAPP(nat,X_a,power_power(X_a,A_1),N))). % 8.03/8.04 0 [] -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,plus_plus(X_a,one_one(X_a)),one_one(X_a)))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),I))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,K_2),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),$f1(P_1,K_2,I)))|hBOOL(hAPP(int,bool,P_1,I)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),I))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,K_2),one_one(int))))|hBOOL(hAPP(int,bool,P_1,$f1(P_1,K_2,I)))|hBOOL(hAPP(int,bool,P_1,I)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),I))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,K_2),one_one(int))))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,$f1(P_1,K_2,I)),one_one(int))))|hBOOL(hAPP(int,bool,P_1,I)). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),tn)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))). % 8.03/8.04 0 [] zero_zero(real)!=one_one(real). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_2),J_2)),I_2)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,J_2),I_2)),I_2)). % 8.03/8.04 0 [] number_number_of(int,K)=K. % 8.03/8.04 0 [] Ma=Na|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma)). % 8.03/8.04 0 [] Ma!=Na| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)). % 8.03/8.04 0 [] Ma!=Na| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma)). % 8.03/8.04 0 [] hAPP(nat,nat,plus_plus(nat,M_1),N)=hAPP(nat,nat,plus_plus(nat,N),M_1). % 8.03/8.04 0 [] hAPP(nat,nat,plus_plus(nat,X),hAPP(nat,nat,plus_plus(nat,Y),Z_1))=hAPP(nat,nat,plus_plus(nat,Y),hAPP(nat,nat,plus_plus(nat,X),Z_1)). % 8.03/8.04 0 [] hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,plus_plus(nat,M_1),N)),K)=hAPP(nat,nat,plus_plus(nat,M_1),hAPP(nat,nat,plus_plus(nat,N),K)). % 8.03/8.04 0 [] hAPP(nat,nat,plus_plus(nat,K_2),Ma)!=hAPP(nat,nat,plus_plus(nat,K_2),Na)|Ma=Na. % 8.03/8.04 0 [] hAPP(nat,nat,plus_plus(nat,K_2),Ma)=hAPP(nat,nat,plus_plus(nat,K_2),Na)|Ma!=Na. % 8.03/8.04 0 [] hAPP(nat,nat,plus_plus(nat,Ma),K_2)!=hAPP(nat,nat,plus_plus(nat,Na),K_2)|Ma=Na. % 8.03/8.04 0 [] hAPP(nat,nat,plus_plus(nat,Ma),K_2)=hAPP(nat,nat,plus_plus(nat,Na),K_2)|Ma!=Na. % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,K_2),Ma)),hAPP(nat,nat,plus_plus(nat,K_2),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,K_2),Ma)),hAPP(nat,nat,plus_plus(nat,K_2),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)). % 8.03/8.04 0 [] 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)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_1))|M_1!=N. % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3))|S!=T_3. % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,plus_plus(nat,J_2),M_1))). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),hAPP(nat,nat,plus_plus(nat,M_1),J_2))). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),hAPP(nat,nat,plus_plus(nat,J_2),K))). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),hAPP(nat,nat,plus_plus(nat,J_2),L))). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L))|hAPP(nat,nat,plus_plus(nat,M_1),L)!=hAPP(nat,nat,plus_plus(nat,K),N)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,I_2),J_2)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),K)). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))|Ma=Na|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),Ma))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Na),Ma)). % 8.03/8.04 0 [] N=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))|N!=zero_zero(nat). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),I_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,power_power(nat,I_2),M_1)),hAPP(nat,nat,power_power(nat,I_2),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa))|Na=zero_zero(nat). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa)). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na)))|Na!=zero_zero(nat). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,Ma),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,Ma),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,Ma),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)). % 8.03/8.04 0 [] Na=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)). % 8.03/8.04 0 [] Na!=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na)))|Na=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa)). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na)))|Na!=zero_zero(nat). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),number_number_of(nat,Wa))))|number_number_of(nat,Wa)=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa)). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),number_number_of(nat,Wa))))|number_number_of(nat,Wa)!=zero_zero(nat). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,Xa),number_number_of(nat,Wa))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Xa)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,Va)),number_number_of(nat,V)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Va),V))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,Va)),number_number_of(nat,V)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Va),V)). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,Va)),number_number_of(nat,V)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Va),V)). % 8.03/8.04 0 [] -linordered_idom(X_a)|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)). % 8.03/8.04 0 [] hAPP(nat,nat,plus_plus(nat,M_1),N)!=M_1|N=zero_zero(nat). % 8.03/8.04 0 [] hAPP(nat,nat,plus_plus(nat,Ma),Na)!=zero_zero(nat)|Ma=zero_zero(nat). % 8.03/8.04 0 [] hAPP(nat,nat,plus_plus(nat,Ma),Na)!=zero_zero(nat)|Na=zero_zero(nat). % 8.03/8.04 0 [] hAPP(nat,nat,plus_plus(nat,Ma),Na)=zero_zero(nat)|Ma!=zero_zero(nat)|Na!=zero_zero(nat). % 8.03/8.04 0 [] hAPP(nat,nat,plus_plus(nat,M_1),zero_zero(nat))=M_1. % 8.03/8.04 0 [] hAPP(nat,nat,plus_plus(nat,zero_zero(nat)),N)=N. % 8.03/8.04 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),one_one(nat))=ti(X_a,A_1). % 8.03/8.04 0 [] -semiring_char_0(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma)!=hAPP(nat,X_a,semiring_1_of_nat(X_a),Na)|Ma=Na. % 8.03/8.04 0 [] -semiring_char_0(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma)=hAPP(nat,X_a,semiring_1_of_nat(X_a),Na)|Ma!=Na. % 8.03/8.04 0 [] hAPP(nat,int,semiring_1_of_nat(int),Xa)!=hAPP(nat,int,semiring_1_of_nat(int),Ya)|Xa=Ya. % 8.03/8.04 0 [] hAPP(nat,int,semiring_1_of_nat(int),Xa)=hAPP(nat,int,semiring_1_of_nat(int),Ya)|Xa!=Ya. % 8.03/8.04 0 [] -hBOOL(P_1)|hAPP(nat,int,semiring_1_of_nat(int),Xa)=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),Xa),Ya)). % 8.03/8.04 0 [] hBOOL(P_1)|hAPP(nat,int,semiring_1_of_nat(int),Ya)=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),Xa),Ya)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,Va)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Va)). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,Va)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Va)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Na)). % 8.03/8.04 0 [] -zero_ne_q_one(X_a)|one_one(X_a)!=zero_zero(X_a). % 8.03/8.04 0 [] -zero_ne_q_one(X_a)|zero_zero(X_a)!=one_one(X_a). % 8.03/8.04 0 [] -ring_11004092258visors(X_a)|ti(X_a,A_1)=zero_zero(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),N)!=zero_zero(X_a). % 8.03/8.04 0 [] -monoid_mult(X_a)|hAPP(nat,X_a,power_power(X_a,one_one(X_a)),N)=one_one(X_a). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -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),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)). % 8.03/8.04 0 [] -linordered_semidom(X_a)|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),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))|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))). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -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)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)). % 8.03/8.04 0 [] -semiring_1(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,plus_plus(nat,M_1),N))=hAPP(X_a,X_a,plus_plus(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)). % 8.03/8.04 0 [] -semiring_1(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),one_one(nat))=one_one(X_a). % 8.03/8.04 0 [] -semiring_1(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,power_power(nat,M_1),N))=hAPP(nat,X_a,power_power(X_a,hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1)),N). % 8.03/8.04 0 [] one_one(int)=hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)). % 8.03/8.04 0 [] hAPP(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,plus_plus(nat,X),Y)). % 8.03/8.04 0 [] hAPP(nat,int,power_power(int,hAPP(nat,int,semiring_1_of_nat(int),X)),N)=hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,power_power(nat,X),N)). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1))). % 8.03/8.04 0 [] -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))). % 8.03/8.04 0 [] -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))). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -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)),hAPP(nat,X_a,power_power(X_a,A_1),N))). % 8.03/8.04 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),hAPP(X_a,X_a,plus_plus(X_a,A_1),one_one(X_a)))). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_2))|hAPP(nat,X_a,power_power(X_a,A_2),Ma)!=hAPP(nat,X_a,power_power(X_a,A_2),Na)|Ma=Na. % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_2))|hAPP(nat,X_a,power_power(X_a,A_2),Ma)=hAPP(nat,X_a,power_power(X_a,A_2),Na)|Ma!=Na. % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,B_1),Xa)),hAPP(nat,X_a,power_power(X_a,B_1),Ya)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya)). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,B_1),Xa)),hAPP(nat,X_a,power_power(X_a,B_1),Ya)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Xa),Ya)). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M_1)),hAPP(nat,X_a,power_power(X_a,A_1),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N)),hAPP(nat,X_a,power_power(X_a,A_1),N_2))). % 8.03/8.04 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|hAPP(nat,X_a,power_power(X_a,A_2),Na)!=zero_zero(X_a)|ti(X_a,A_2)=zero_zero(X_a). % 8.03/8.04 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|hAPP(nat,X_a,power_power(X_a,A_2),Na)!=zero_zero(X_a)|Na!=zero_zero(nat). % 8.03/8.04 0 [] -power(X_a)| -mult_zero(X_a)| -no_zero_divisors(X_a)| -zero_ne_q_one(X_a)|hAPP(nat,X_a,power_power(X_a,A_2),Na)=zero_zero(X_a)|ti(X_a,A_2)!=zero_zero(X_a)|Na=zero_zero(nat). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -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)),zero_zero(X_a))). % 8.03/8.04 0 [] -power(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),zero_zero(nat))=one_one(X_a). % 8.03/8.04 0 [] -semiring_1(X_a)|hAPP(nat,X_a,semiring_1_of_nat(X_a),zero_zero(nat))=zero_zero(X_a). % 8.03/8.04 0 [] zero_zero(int)=hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),$f2(K))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))|K=hAPP(nat,int,semiring_1_of_nat(int),$f2(K)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),$f3(I_2,J_2))). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2))|hAPP(nat,nat,plus_plus(nat,I_2),$f3(I_2,J_2))=J_2. % 8.03/8.04 0 [] hAPP(nat,nat,power_power(nat,Xa),Na)!=one_one(nat)|Xa=one_one(nat)|Na=zero_zero(nat). % 8.03/8.04 0 [] hAPP(nat,nat,power_power(nat,Xa),Na)=one_one(nat)|Xa!=one_one(nat). % 8.03/8.04 0 [] hAPP(nat,nat,power_power(nat,Xa),Na)=one_one(nat)|Na!=zero_zero(nat). % 8.03/8.04 0 [] -comm_semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,X),zero_zero(nat))=one_one(X_a). % 8.03/8.04 0 [] -linord219039673up_add(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,plus_plus(X_a,A_2),A_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)). % 8.03/8.04 0 [] -linord219039673up_add(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,plus_plus(X_a,A_2),A_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)). % 8.03/8.04 0 [] -linord219039673up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))). % 8.03/8.04 0 [] -linord219039673up_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))). % 8.03/8.04 0 [] -zero(X_a)|zero_zero(X_a)!=ti(X_a,Xa)|ti(X_a,Xa)=zero_zero(X_a). % 8.03/8.04 0 [] -zero(X_a)|zero_zero(X_a)=ti(X_a,Xa)|ti(X_a,Xa)!=zero_zero(X_a). % 8.03/8.04 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,B),A_1)!=hAPP(X_a,X_a,plus_plus(X_a,C_1),A_1)|ti(X_a,B)=ti(X_a,C_1). % 8.03/8.04 0 [] -cancel146912293up_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),B)!=hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)|ti(X_a,B)=ti(X_a,C_1). % 8.03/8.04 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),B)!=hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)|ti(X_a,B)=ti(X_a,C_1). % 8.03/8.04 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),hAPP(X_a,X_a,plus_plus(X_a,C_1),D))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),D)). % 8.03/8.04 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,B_1),A_2)!=hAPP(X_a,X_a,plus_plus(X_a,C),A_2)|ti(X_a,B_1)=ti(X_a,C). % 8.03/8.04 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,B_1),A_2)=hAPP(X_a,X_a,plus_plus(X_a,C),A_2)|ti(X_a,B_1)!=ti(X_a,C). % 8.03/8.04 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_2),B_1)!=hAPP(X_a,X_a,plus_plus(X_a,A_2),C)|ti(X_a,B_1)=ti(X_a,C). % 8.03/8.04 0 [] -cancel_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_2),B_1)=hAPP(X_a,X_a,plus_plus(X_a,A_2),C)|ti(X_a,B_1)!=ti(X_a,C). % 8.03/8.04 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C_1)=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),B). % 8.03/8.04 0 [] -ab_semigroup_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C_1)=hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,B),C_1)). % 8.03/8.04 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),C_1)=hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,B),C_1)). % 8.03/8.04 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,C_1),D))=hAPP(X_a,X_a,plus_plus(X_a,hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),D). % 8.03/8.04 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),hAPP(X_a,X_a,plus_plus(X_a,C_1),D))=hAPP(X_a,X_a,plus_plus(X_a,C_1),hAPP(X_a,X_a,plus_plus(X_a,A_1),D)). % 8.03/8.04 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)=hAPP(X_a,X_a,plus_plus(X_a,C_1),A_1). % 8.03/8.04 0 [] -one(X_a)|one_one(X_a)!=ti(X_a,Xa)|ti(X_a,Xa)=one_one(X_a). % 8.03/8.04 0 [] -one(X_a)|one_one(X_a)=ti(X_a,Xa)|ti(X_a,Xa)!=one_one(X_a). % 8.03/8.04 0 [] -semiri456707255roduct(X_a)|ti(X_a,B_1)!=hAPP(X_a,X_a,plus_plus(X_a,B_1),A_2)|ti(X_a,A_2)=zero_zero(X_a). % 8.03/8.04 0 [] -semiri456707255roduct(X_a)|ti(X_a,B_1)=hAPP(X_a,X_a,plus_plus(X_a,B_1),A_2)|ti(X_a,A_2)!=zero_zero(X_a). % 8.03/8.04 0 [] -comm_monoid_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1). % 8.03/8.04 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1). % 8.03/8.04 0 [] -monoid_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,A_1),zero_zero(X_a))=ti(X_a,A_1). % 8.03/8.04 0 [] -linord219039673up_add(X_a)|zero_zero(X_a)!=hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2)|ti(X_a,A_2)=zero_zero(X_a). % 8.03/8.04 0 [] -linord219039673up_add(X_a)|zero_zero(X_a)=hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2)|ti(X_a,A_2)!=zero_zero(X_a). % 8.03/8.04 0 [] -comm_monoid_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)=ti(X_a,A_1). % 8.03/8.04 0 [] -comm_semiring_1(X_a)|hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)=ti(X_a,A_1). % 8.03/8.04 0 [] -monoid_add(X_a)|hAPP(X_a,X_a,plus_plus(X_a,zero_zero(X_a)),A_1)=ti(X_a,A_1). % 8.03/8.04 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)). % 8.03/8.04 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)). % 8.03/8.04 0 [] -ordere223160158up_add(X_a)| -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_1),D))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),D))). % 8.03/8.04 0 [] -ordere223160158up_add(X_a)| -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,plus_plus(X_a,C_1),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B))). % 8.03/8.04 0 [] -ordere223160158up_add(X_a)| -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,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),C_1))). % 8.03/8.04 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_2)),hAPP(X_a,X_a,plus_plus(X_a,C),B_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)). % 8.03/8.04 0 [] -ordere236663937imp_le(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_2)),hAPP(X_a,X_a,plus_plus(X_a,C),B_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)). % 8.03/8.04 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_2),C)),hAPP(X_a,X_a,plus_plus(X_a,B_1),C)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)). % 8.03/8.04 0 [] -ordere236663937imp_le(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_2),C)),hAPP(X_a,X_a,plus_plus(X_a,B_1),C)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)). % 8.03/8.04 0 [] -comm_semiring_1(X_a)|hAPP(nat,X_a,power_power(X_a,X),one_one(nat))=ti(X_a,X). % 8.03/8.04 0 [] hAPP(nat,nat,power_power(nat,Ma),Na)!=zero_zero(nat)|Na!=zero_zero(nat). % 8.03/8.04 0 [] hAPP(nat,nat,power_power(nat,Ma),Na)!=zero_zero(nat)|Ma=zero_zero(nat). % 8.03/8.04 0 [] hAPP(nat,nat,power_power(nat,Ma),Na)=zero_zero(nat)|Na=zero_zero(nat)|Ma!=zero_zero(nat). % 8.03/8.04 0 [] -ordere216010020id_add(X_a)| -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,plus_plus(X_a,A_1),B)),zero_zero(X_a))). % 8.03/8.04 0 [] -ordere216010020id_add(X_a)| -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,plus_plus(X_a,A_1),B))). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),$f4(A_1,N))). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))|hAPP(nat,real,power_power(real,$f4(A_1,N)),N)=A_1. % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1))|hAPP(nat,real,power_power(real,Y_1),N)!=A_1|Y_1=$f4(A_1,N). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),$f5(A_1,N))). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1))|hAPP(nat,real,power_power(real,$f5(A_1,N)),N)=A_1. % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),t)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V_1)),one_one(nat))=one_one(nat). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|hAPP(nat,nat,plus_plus(nat,number_number_of(nat,V_1)),one_one(nat))=number_number_of(nat,hAPP(int,int,succ,V_1)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,V_1))=one_one(nat). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),pls))|hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,V_1))=number_number_of(nat,hAPP(int,int,succ,V_1)). % 8.03/8.04 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_2),C)),hAPP(X_a,X_a,plus_plus(X_a,B_1),C)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B_1)). % 8.03/8.04 0 [] -ordere236663937imp_le(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_2),C)),hAPP(X_a,X_a,plus_plus(X_a,B_1),C)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B_1)). % 8.03/8.04 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_2)),hAPP(X_a,X_a,plus_plus(X_a,C),B_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B_1)). % 8.03/8.04 0 [] -ordere236663937imp_le(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C),A_2)),hAPP(X_a,X_a,plus_plus(X_a,C),B_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B_1)). % 8.03/8.04 0 [] -ordere779506340up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),C_1))). % 8.03/8.04 0 [] -ordere779506340up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B))). % 8.03/8.04 0 [] -ordere779506340up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),D))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),D))). % 8.03/8.04 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),C_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B)). % 8.03/8.04 0 [] -ordere236663937imp_le(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,C_1),A_1)),hAPP(X_a,X_a,plus_plus(X_a,C_1),B)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B)). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),N_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N)),hAPP(nat,X_a,power_power(X_a,A_1),N_2))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K_2)),hAPP(int,int,bit1,L_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),L_1)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K_2)),hAPP(int,int,bit1,L_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),L_1)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),pls)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit0,K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit0,K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,K_2)),hAPP(int,int,bit0,L_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),L_1)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,K_2)),hAPP(int,int,bit0,L_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),L_1)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),zero_zero(int))). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),W_1)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),W_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_1)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),J_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),J_2),K))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),K)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_1),W_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),W_1),Z_1))|Z_1=W_1. % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,Xa)),number_number_of(X_a,Ya)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),Ya)). % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,Xa)),number_number_of(X_a,Ya)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),Ya)). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)). % 8.03/8.04 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),Wa))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_2),Wa)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),Wa))|Z_2!=Wa. % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),Wa))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_2),Wa))|Z_2=Wa. % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),I_2),J_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,K),I_2)),hAPP(int,int,plus_plus(int,K),J_2))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,K_2)),number_number_of(int,L_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),L_1)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,K_2)),number_number_of(int,L_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),L_1)). % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),number_number_of(X_a,Ya)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),Ya)). % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),number_number_of(X_a,Ya)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),Ya)). % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,Xa)),zero_zero(X_a)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),pls)). % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,Xa)),zero_zero(X_a)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),pls)). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),N_2))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),one_one(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N_2)),hAPP(nat,X_a,power_power(X_a,A_1),N))). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,B_1),Xa)),hAPP(nat,X_a,power_power(X_a,B_1),Ya)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Xa),Ya)). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,B_1),Xa)),hAPP(nat,X_a,power_power(X_a,B_1),Ya)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Xa),Ya)). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),M_1)),hAPP(nat,X_a,power_power(X_a,A_1),N)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N)). % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),number_number_of(X_a,Ya)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,pls)),Ya)). % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),number_number_of(X_a,Ya)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,pls)),Ya)). % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,Xa)),one_one(X_a)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),hAPP(int,int,bit1,pls))). % 8.03/8.04 0 [] -number_ring(X_a)| -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,Xa)),one_one(X_a)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Xa),hAPP(int,int,bit1,pls))). % 8.03/8.04 0 [] -linord219039673up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_2)). % 8.03/8.04 0 [] -linord219039673up_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_2)). % 8.03/8.04 0 [] -linord219039673up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2)),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),zero_zero(X_a))). % 8.03/8.04 0 [] -linord219039673up_add(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_2),A_2)),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),zero_zero(X_a))). % 8.03/8.04 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,A_1),B))). % 8.03/8.04 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Xa))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Ya))|hAPP(X_a,X_a,plus_plus(X_a,Xa),Ya)!=zero_zero(X_a)|ti(X_a,Xa)=zero_zero(X_a). % 8.03/8.04 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Xa))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Ya))|hAPP(X_a,X_a,plus_plus(X_a,Xa),Ya)!=zero_zero(X_a)|ti(X_a,Ya)=zero_zero(X_a). % 8.03/8.04 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Xa))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Ya))|hAPP(X_a,X_a,plus_plus(X_a,Xa),Ya)=zero_zero(X_a)|ti(X_a,Xa)!=zero_zero(X_a)|ti(X_a,Ya)!=zero_zero(X_a). % 8.03/8.04 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1))). % 8.03/8.04 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1))). % 8.03/8.04 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),zero_zero(X_a)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),zero_zero(X_a)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),B)),zero_zero(X_a))). % 8.03/8.04 0 [] -ordere223160158up_add(X_a)| -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_e_q(X_a),C_1),D))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),D))). % 8.03/8.04 0 [] -ordere223160158up_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1)),hAPP(X_a,X_a,plus_plus(X_a,B),D))). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),zero_zero(X_a))). % 8.03/8.04 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),one_one(X_a))). % 8.03/8.04 0 [] -number(X_a)| -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,Va)),number_number_of(X_a,Wa)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Wa)),number_number_of(X_a,Va))). % 8.03/8.04 0 [] -number(X_a)| -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),number_number_of(X_a,Va)),number_number_of(X_a,Wa)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),number_number_of(X_a,Wa)),number_number_of(X_a,Va))). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N))). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N)),hAPP(nat,X_a,power_power(X_a,B),N))). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),one_one(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N))). % 8.03/8.04 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M_1))). % 8.03/8.04 0 [] -linordered_semidom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),hAPP(int,int,bit1,K_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K_2)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),hAPP(int,int,bit1,K_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K_2)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,K_2)),hAPP(int,int,bit1,L_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),L_1)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,K_2)),hAPP(int,int,bit1,L_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),L_1)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit1,K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit1,K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),hAPP(int,int,bit0,K_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K_2)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),hAPP(int,int,bit0,K_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K_2)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,K_2)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),pls)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,K_2)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),pls)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),one_one(int))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Y))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,X),Y))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),W_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Z_3),Z_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,W_2),Z_3)),hAPP(int,int,plus_plus(int,W_1),Z_1))). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Z_1))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X_1))| -hBOOL(hAPP(int,bool,P_1,X_1))|hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),$f6(P_1)))). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f7(P_1)))| -hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X1))). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,P_1,$f7(P_1)))| -hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X1))). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f8(P_1)))|hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_1))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,P_1,$f8(P_1)))|hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_1))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X2))|hBOOL(hAPP(int,bool,P_1,X2))| -hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),$f9(P_1)))). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,power_power(int,X),N))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),Z_2))|Z_2=hAPP(int,int,plus_plus(int,Wa),hAPP(nat,int,semiring_1_of_nat(int),$f10(Wa,Z_2))). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),Z_2))|Z_2!=hAPP(int,int,plus_plus(int,Wa),hAPP(nat,int,semiring_1_of_nat(int),N_1)). % 8.03/8.04 0 [] -number_semiring(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))|hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,V_1))=number_number_of(X_a,hAPP(int,int,succ,V_1)). % 8.03/8.04 0 [] -number_semiring(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))|hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V_1)),one_one(X_a))=number_number_of(X_a,hAPP(int,int,succ,V_1)). % 8.03/8.04 0 [] -ordere216010020id_add(X_a)| -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_e_q(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,plus_plus(X_a,A_1),B))). % 8.03/8.04 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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,plus_plus(X_a,A_1),B))). % 8.03/8.04 0 [] -ordere216010020id_add(X_a)| -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_e_q(X_a),B),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1))). % 8.03/8.04 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,plus_plus(X_a,A_1),C_1))). % 8.03/8.04 0 [] -ordere216010020id_add(X_a)| -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_e_q(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,plus_plus(X_a,A_1),B)),zero_zero(X_a))). % 8.03/8.04 0 [] -ordere216010020id_add(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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,plus_plus(X_a,A_1),B)),zero_zero(X_a))). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N)),hAPP(nat,X_a,power_power(X_a,B),N)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)). % 8.03/8.04 0 [] zero_zero(nat)!=number_number_of(nat,Va)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),pls)). % 8.03/8.04 0 [] zero_zero(nat)=number_number_of(nat,Va)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),pls)). % 8.03/8.04 0 [] number_number_of(nat,Va)!=zero_zero(nat)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),pls)). % 8.03/8.04 0 [] number_number_of(nat,Va)=zero_zero(nat)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),pls)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,K_2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K_2)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,K_2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),K_2)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K_2)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),pls)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K_2)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),pls)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K_2)),hAPP(int,int,bit1,L_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),L_1)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K_2)),hAPP(int,int,bit1,L_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),L_1)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit1,K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit1,K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K1),K2)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K_2)),hAPP(int,int,bit0,L_1)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K_2)),hAPP(int,int,bit0,L_1)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_2),L_1)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit0,K2)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit0,K2)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),Z_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_2)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)))|Na=zero_zero(nat). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)))|Na!=zero_zero(nat). % 8.03/8.04 0 [] hAPP(int,int,succ,pls)=hAPP(int,int,bit1,pls). % 8.03/8.04 0 [] hAPP(int,int,succ,hAPP(int,int,bit0,K))=hAPP(int,int,bit1,K). % 8.03/8.04 0 [] hAPP(int,int,succ,hAPP(int,int,bit1,K))=hAPP(int,int,bit0,hAPP(int,int,succ,K)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),Z_2)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Wa),Z_2)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,Wa),one_one(int))),Z_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_2)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,Wa),one_one(int))),Z_2))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_2)). % 8.03/8.04 0 [] -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_e_q(int),hAPP(int,int,plus_plus(int,W_1),one_one(int))),Z_1)). % 8.03/8.04 0 [] hAPP(int,int,succ,K)=hAPP(int,int,plus_plus(int,K),one_one(int)). % 8.03/8.04 0 [] -linordered_semidom(X_a)|hAPP(nat,X_a,power_power(X_a,A_1),N)!=hAPP(nat,X_a,power_power(X_a,B),N)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|ti(X_a,A_1)=ti(X_a,B). % 8.03/8.04 0 [] -number_semiring(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_1))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),V_2))|hAPP(X_a,X_a,plus_plus(X_a,number_number_of(X_a,V_1)),number_number_of(X_a,V_2))=number_number_of(X_a,hAPP(int,int,plus_plus(int,V_1),V_2)). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),Z_1))). % 8.03/8.04 0 [] -number_ring(X_a)|number_number_of(X_a,hAPP(int,int,succ,K))=hAPP(X_a,X_a,plus_plus(X_a,one_one(X_a)),number_number_of(X_a,K)). % 8.03/8.04 0 [] hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L))=hAPP(int,int,bit0,hAPP(int,int,plus_plus(int,K),hAPP(int,int,succ,L))). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -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_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N)),hAPP(nat,X_a,power_power(X_a,B),N))). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). % 8.03/8.04 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y)). % 8.03/8.04 0 [] -linordered_semidom(X_a)|hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))!=hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),X))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))|ti(X_a,X)=ti(X_a,Y). % 8.03/8.04 0 [] -number_ring(X_a)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,V_1)))|hAPP(nat,X_a,semiring_1_of_nat(X_a),number_number_of(nat,V_1))=number_number_of(X_a,V_1). % 8.03/8.04 0 [] -number_ring(X_a)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,V_1)))|hAPP(nat,X_a,semiring_1_of_nat(X_a),number_number_of(nat,V_1))=zero_zero(X_a). % 8.03/8.04 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)). % 8.03/8.04 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Y),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))). % 8.03/8.04 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X_a)))|ti(X_a,Xa)=zero_zero(X_a). % 8.03/8.04 0 [] -linordered_idom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X_a)))|ti(X_a,Ya)=zero_zero(X_a). % 8.03/8.04 0 [] -linordered_idom(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,plus_plus(X_a,hAPP(nat,X_a,power_power(X_a,Xa),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,power_power(X_a,Ya),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X_a)))|ti(X_a,Xa)!=zero_zero(X_a)|ti(X_a,Ya)!=zero_zero(X_a). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),X))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))|X=zero_zero(int)|X=one_one(int). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,N)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit0,N)))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,N)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit1,N)))). % 8.03/8.04 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,pls))). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))|K=hAPP(nat,int,semiring_1_of_nat(int),$f11(K)). % 8.03/8.04 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),K))|K=hAPP(nat,int,semiring_1_of_nat(int),$f12(K)). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N)). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),zero_zero(nat)),N)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Na),zero_zero(nat)))|Na=zero_zero(nat). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Na),zero_zero(nat)))|Na!=zero_zero(nat). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N)). % 8.03/8.04 0 [] M_1!=N|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))|M_1=N|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))|Ma=Na. % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na)). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))|Ma!=Na. % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))|Ma!=Na. % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))|Ma=Na. % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),N)). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M_1)). % 8.03/8.04 0 [] M_1!=N|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),J_2),K))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),K)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),M_1))|M_1=N. % 8.03/8.04 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya))|Xa=Ya. % 8.03/8.04 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya)). % 8.03/8.04 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya))|Xa!=Ya. % 8.03/8.04 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya)). % 8.03/8.04 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya))|Xa!=Ya. % 8.03/8.04 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),Ya))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Xa),Ya))|Xa=Ya. % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),hAPP(nat,nat,plus_plus(nat,M_1),N))). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),N),hAPP(nat,nat,plus_plus(nat,N),M_1))). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))|Na=hAPP(nat,nat,plus_plus(nat,Ma),$f13(Ma,Na)). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na))|Na!=hAPP(nat,nat,plus_plus(nat,Ma),K_1). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,K_2),Ma)),hAPP(nat,nat,plus_plus(nat,K_2),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)). % 8.03/8.04 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,K_2),Ma)),hAPP(nat,nat,plus_plus(nat,K_2),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),hAPP(nat,nat,plus_plus(nat,J_2),M_1))). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),hAPP(nat,nat,plus_plus(nat,M_1),J_2))). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),hAPP(nat,nat,plus_plus(nat,J_2),K))). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_2),J_2))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),L))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,I_2),K)),hAPP(nat,nat,plus_plus(nat,J_2),L))). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M_1),K)),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M_1),K)),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N)). % 8.03/8.04 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M_1),K)),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),M_1),N)). % 8.03/8.05 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,M_1),K)),N))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),K),N)). % 8.03/8.05 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),X),Y))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,plus_plus(real,Z_1),X)),hAPP(real,real,plus_plus(real,Z_1),Y))). % 8.03/8.05 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Xa),Ya)). % 8.03/8.05 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Xa)),hAPP(nat,int,semiring_1_of_nat(int),Ya)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Xa),Ya)). % 8.03/8.05 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),Na)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)). % 8.03/8.05 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),Na)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),Ma),Na)). % 8.03/8.05 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,Va)),number_number_of(nat,V)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),V))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),pls)). % 8.03/8.05 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,Va)),number_number_of(nat,V)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),V)). % 8.03/8.05 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,Va)),number_number_of(nat,V)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),Va),pls)). % 8.03/8.05 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),one_one(real)),hAPP(nat,real,power_power(real,number_number_of(real,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))). % 8.03/8.05 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f14(Na,P_1)),Na)). % 8.03/8.05 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I_1),$f14(Na,P_1)))| -hBOOL(hAPP(nat,bool,P_1,I_1)). % 8.03/8.05 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,Na))|hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,plus_plus(nat,$f14(Na,P_1)),one_one(nat)))). % 8.03/8.05 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),Z_1))|Z_1=hAPP(nat,int,semiring_1_of_nat(int),$f15(Z_1)). % 8.03/8.05 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f17(Ma,K_2,F)),$f16(Ma,K_2,F)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,F,Ma)),K_2)),hAPP(nat,nat,F,hAPP(nat,nat,plus_plus(nat,Ma),K_2)))). % 8.03/8.05 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,$f17(Ma,K_2,F))),hAPP(nat,nat,F,$f16(Ma,K_2,F))))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,F,Ma)),K_2)),hAPP(nat,nat,F,hAPP(nat,nat,plus_plus(nat,Ma),K_2)))). % 8.03/8.05 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W_1),W_1)). % 8.03/8.05 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z_1),W_1))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W_1),Z_1)). % 8.03/8.05 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),I_2),J_2))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),J_2),K))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),I_2),K)). % 8.03/8.05 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),Z_1),W_1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),W_1),Z_1))|Z_1=W_1. % 8.03/8.05 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),I))| -hBOOL(hAPP(int,bool,P_1,K_2))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),$f18(P_1,K_2,I)))|hBOOL(hAPP(int,bool,P_1,I)). % 8.03/8.05 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),I))| -hBOOL(hAPP(int,bool,P_1,K_2))|hBOOL(hAPP(int,bool,P_1,$f18(P_1,K_2,I)))|hBOOL(hAPP(int,bool,P_1,I)). % 8.03/8.05 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),K_2),I))| -hBOOL(hAPP(int,bool,P_1,K_2))| -hBOOL(hAPP(int,bool,P_1,hAPP(int,int,plus_plus(int,$f18(P_1,K_2,I)),one_one(int))))|hBOOL(hAPP(int,bool,P_1,I)). % 8.03/8.05 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,Na))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f19(Na,P_1)),Na)). % 8.03/8.05 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,Na))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),$f19(Na,P_1)))| -hBOOL(hAPP(nat,bool,P_1,I_1)). % 8.03/8.05 0 [] hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,P_1,Na))|hBOOL(hAPP(nat,bool,P_1,$f19(Na,P_1))). % 8.03/8.05 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f21(I,J,F)),$f20(I,J,F)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,F,I)),hAPP(nat,nat,F,J))). % 8.03/8.05 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,$f21(I,J,F))),hAPP(nat,nat,F,$f20(I,J,F))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),I),J))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,F,I)),hAPP(nat,nat,F,J))). % 8.03/8.05 0 [] -preorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),X)). % 8.03/8.05 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X)). % 8.03/8.05 0 [] -ord(X_b)| -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,Xa)),hAPP(X_a,X_b,G,Xa))). % 8.03/8.05 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Z_1),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Z_1),X)). % 8.03/8.05 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))|ti(X_a,X)=ti(X_a,Y). % 8.03/8.05 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Z_1)). % 8.03/8.05 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))|ti(X_a,X)=ti(X_a,Y). % 8.03/8.05 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))|ti(X_a,B)!=ti(X_a,C_1)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),A_1)). % 8.03/8.05 0 [] -ord(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))|B!=C_1|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),C_1)). % 8.03/8.05 0 [] -order(X_a)|ti(X_a,A_1)!=ti(X_a,B)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),C_1),A_1)). % 8.03/8.05 0 [] -ord(X_a)|A_1!=B| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),C_1)). % 8.03/8.05 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ya),Xa))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))|ti(X_a,Xa)=ti(X_a,Ya). % 8.03/8.05 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ya),Xa))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))|ti(X_a,Xa)!=ti(X_a,Ya). % 8.03/8.05 0 [] -ord(X_b)| -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,Xa)),hAPP(X_a,X_b,G,Xa))). % 8.03/8.05 0 [] -preorder(X_a)|X!=Y|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y)). % 8.03/8.05 0 [] -order(X_a)|ti(X_a,Xa)!=ti(X_a,Ya)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya)). % 8.03/8.05 0 [] -order(X_a)|ti(X_a,Xa)!=ti(X_a,Ya)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ya),Xa)). % 8.03/8.05 0 [] -order(X_a)|ti(X_a,Xa)=ti(X_a,Ya)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ya),Xa)). % 8.03/8.05 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X)). % 8.03/8.05 0 [] -ord(X_b)| -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))). % 8.03/8.05 0 [] -ord(X_b)|hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,$f22(X_a,X_b,F,G))),hAPP(X_a,X_b,G,$f22(X_a,X_b,F,G)))). % 8.03/8.05 0 [] -linorder(X_a)|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)). % 8.03/8.05 0 [] -preorder(X_a)| -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)). % 8.03/8.05 0 [] -order(X_a)| -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)). % 8.03/8.05 0 [] -preorder(X_a)| -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)). % 8.03/8.05 0 [] -order(X_a)| -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_1)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_1)). % 8.03/8.05 0 [] -ord(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))|B!=C_1|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C_1)). % 8.03/8.05 0 [] -order(X_a)|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_1),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_1)). % 8.03/8.05 0 [] -ord(X_a)|A_1!=B| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C_1)). % 8.03/8.05 0 [] -order(X_a)| -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)). % 8.03/8.05 0 [] -preorder(X_a)| -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)). % 8.03/8.05 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa))|hBOOL(P_1). % 8.03/8.05 0 [] -order(X_a)| -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). % 8.03/8.05 0 [] -order(X_a)| -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). % 8.03/8.05 0 [] -preorder(X_a)| -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)). % 8.03/8.05 0 [] -preorder(X_a)| -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)). % 8.03/8.05 0 [] -order(X_a)| -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). % 8.03/8.05 0 [] -linorder(X_a)|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)). % 8.03/8.05 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))|ti(X_a,Xa)=ti(X_a,Ya). % 8.03/8.05 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))|ti(X_a,Xa)!=ti(X_a,Ya). % 8.03/8.05 0 [] -linorder(X_a)|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)). % 8.03/8.05 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa))|ti(X_a,Xa)=ti(X_a,Ya). % 8.03/8.05 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa)). % 8.03/8.05 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))|ti(X_a,Xa)!=ti(X_a,Ya). % 8.03/8.05 0 [] -linorder(X_a)|ti(X_a,Xa)=ti(X_a,Ya)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa)). % 8.03/8.05 0 [] -linorder(X_a)|ti(X_a,Xa)!=ti(X_a,Ya)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)). % 8.03/8.05 0 [] -linorder(X_a)|ti(X_a,Xa)!=ti(X_a,Ya)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa)). % 8.03/8.05 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X)). % 8.03/8.05 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ya),Xa)). % 8.03/8.05 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ya),Xa)). % 8.03/8.05 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa)). % 8.03/8.05 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa)). % 8.03/8.05 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)). % 8.03/8.05 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya)). % 8.03/8.05 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))|ti(X_a,Xa)!=ti(X_a,Ya). % 8.03/8.05 0 [] -order(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))|ti(X_a,Xa)=ti(X_a,Ya). % 8.03/8.05 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya)). % 8.03/8.05 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ya),Xa)). % 8.03/8.05 0 [] -preorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Ya),Xa)). % 8.03/8.05 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))|ti(X_a,Xa)=ti(X_a,Ya). % 8.03/8.05 0 [] -order(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya)). % 8.03/8.05 0 [] -order(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))|ti(X_a,Xa)!=ti(X_a,Ya). % 8.03/8.05 0 [] -linorder(X_a)|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_e_q(X_a),Y),X)). % 8.03/8.05 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)). % 8.03/8.05 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))|ti(X_a,Xa)=ti(X_a,Ya). % 8.03/8.05 0 [] -linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))|ti(X_a,Xa)!=ti(X_a,Ya). % 8.03/8.05 0 [] -order(X_a)|ti(X_a,A_1)=ti(X_a,B)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)). % 8.03/8.05 0 [] -order(X_a)|ti(X_a,A_1)=ti(X_a,B)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)). % 8.03/8.05 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),X))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)). % 8.03/8.05 0 [] -preorder(X_a)| -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_e_q(X_a),X),Y)). % 8.03/8.05 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))|ti(X_a,Xa)=ti(X_a,Ya). % 8.03/8.05 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Xa),Ya))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))|ti(X_a,Xa)!=ti(X_a,Ya). % 8.03/8.05 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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). % 8.03/8.05 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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)). % 8.03/8.05 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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)). % 8.03/8.05 0 [] -preorder(X_a)| -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_e_q(X_a),Y),Z_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1)). % 8.03/8.05 0 [] -order(X_a)| -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_e_q(X_a),Z_1),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X)). % 8.03/8.05 0 [] -preorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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)). % 8.03/8.05 0 [] -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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)). % 8.03/8.05 0 [] -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))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),$f23(D2,D1))). % 8.03/8.05 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D1))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D2))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),$f23(D2,D1)),D1)). % 8.03/8.05 0 [] -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))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),$f23(D2,D1)),D2)). % 8.03/8.05 0 [] -dense_linorder(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f24(X_a,Z_1,Y)),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1)). % 8.03/8.05 0 [] -dense_linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),$f24(X_a,Z_1,Y)),Z_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1)). % 8.03/8.05 0 [] -ord(X_b)| -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G))|hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G)). % 8.03/8.05 0 [] -ord(X_b)| -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G))| -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),G),F)). % 8.03/8.05 0 [] -ord(X_b)|hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G))| -hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G))|hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),G),F)). % 8.03/8.05 0 [] -ord(X_b)| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,$f25(X_a,X_b,F,G))),hAPP(X_a,X_b,G,$f25(X_a,X_b,F,G))))|hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_e_q(fun(X_a,X_b)),F),G)). % 8.03/8.05 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f26(X_a,T_3)),X_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),T_3)). % 8.03/8.05 0 [] -dense_linorder(X_a)| -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),X),$f27(X_a,Z_1,X,Y)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1)). % 8.03/8.05 0 [] -dense_linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f27(X_a,Z_1,X,Y)),Y))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1)). % 8.03/8.05 0 [] -dense_linorder(X_a)| -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_e_q(X_a),$f27(X_a,Z_1,X,Y)),Z_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),Y),Z_1)). % 8.03/8.05 0 [] -order(X_a)| -order(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C),hAPP(X_a,X_b,F,B_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f28(X_b,X_a,C,F,B_1,A_2)),$f29(X_b,X_a,C,F,B_1,A_2)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C),hAPP(X_a,X_b,F,A_2))). % 8.03/8.05 0 [] -order(X_a)| -order(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C),hAPP(X_a,X_b,F,B_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,$f28(X_b,X_a,C,F,B_1,A_2))),hAPP(X_a,X_b,F,$f29(X_b,X_a,C,F,B_1,A_2))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C),hAPP(X_a,X_b,F,A_2))). % 8.03/8.05 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),$f30(X_a,T_3)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),X_1),T_3)). % 8.03/8.05 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f31(X_a,T_3)),X_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),T_3),X_1)). % 8.03/8.05 0 [] -order(X_a)| -order(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_1),A_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C),hAPP(X_a,X_b,F,B_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),$f32(X_b,X_a,C,F,B_1,A_2)),$f33(X_b,X_a,C,F,B_1,A_2)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C),hAPP(X_a,X_b,F,A_2))). % 8.03/8.05 0 [] -order(X_a)| -order(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_1),A_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C),hAPP(X_a,X_b,F,B_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,$f32(X_b,X_a,C,F,B_1,A_2))),hAPP(X_a,X_b,F,$f33(X_b,X_a,C,F,B_1,A_2))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C),hAPP(X_a,X_b,F,A_2))). % 8.03/8.05 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,B_1)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),$f35(X_a,X_b,F,C,A_2,B_1)),$f34(X_a,X_b,F,C,A_2,B_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,A_2)),C)). % 8.03/8.05 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,B_1)),C))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,$f35(X_a,X_b,F,C,A_2,B_1))),hAPP(X_a,X_b,F,$f34(X_a,X_b,F,C,A_2,B_1))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,A_2)),C)). % 8.03/8.05 0 [] -linorder(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),$f36(X_a,T_3)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),T_3),X_1)). % 8.03/8.05 0 [] -order(X_a)| -ord(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_b,X_a,F,B_1)),A_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C),B_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),$f37(X_b,X_a,C,F,B_1,A_2)),$f38(X_b,X_a,C,F,B_1,A_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C)),A_2)). % 8.03/8.05 0 [] -order(X_a)| -ord(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_b,X_a,F,B_1)),A_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C),B_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,$f37(X_b,X_a,C,F,B_1,A_2))),hAPP(X_b,X_a,F,$f38(X_b,X_a,C,F,B_1,A_2))))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C)),A_2)). % 8.03/8.05 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,B_1)),C))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),$f40(X_a,X_b,F,C,A_2,B_1)),$f39(X_a,X_b,F,C,A_2,B_1)))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,A_2)),C)). % 8.03/8.05 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B_1))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,B_1)),C))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),hAPP(X_a,X_b,F,$f40(X_a,X_b,F,C,A_2,B_1))),hAPP(X_a,X_b,F,$f39(X_a,X_b,F,C,A_2,B_1))))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,A_2)),C)). % 8.03/8.05 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,B_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_1),C))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),$f42(X_a,X_b,C,A_2,F,B_1)),$f41(X_a,X_b,C,A_2,F,B_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,C))). % 8.03/8.05 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,B_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),B_1),C))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_b,X_a,F,$f42(X_a,X_b,C,A_2,F,B_1))),hAPP(X_b,X_a,F,$f41(X_a,X_b,C,A_2,F,B_1))))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,C))). % 8.03/8.05 0 [] -order(X_a)| -order(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,B_1)),A_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C),B_1))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),$f43(X_b,X_a,C,F,B_1,A_2)),$f44(X_b,X_a,C,F,B_1,A_2)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C)),A_2)). % 8.03/8.05 0 [] -order(X_a)| -order(X_b)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,B_1)),A_2))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_e_q(X_b),C),B_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_b,X_a,F,$f43(X_b,X_a,C,F,B_1,A_2))),hAPP(X_b,X_a,F,$f44(X_b,X_a,C,F,B_1,A_2))))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C)),A_2)). % 8.03/8.05 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),hAPP(X_b,X_a,F,B_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_1),C))|hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),$f46(X_a,X_b,C,A_2,F,B_1)),$f45(X_a,X_b,C,A_2,F,B_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,C))). % 8.03/8.05 0 [] -order(X_b)| -order(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),hAPP(X_b,X_a,F,B_1)))| -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_1),C))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,$f46(X_a,X_b,C,A_2,F,B_1))),hAPP(X_b,X_a,F,$f45(X_a,X_b,C,A_2,F,B_1))))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,C))). % 8.03/8.05 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,Y),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))). % 8.03/8.05 0 [] hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,A_1),B)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,A_1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)),B))),hAPP(nat,int,power_power(int,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). % 8.03/8.05 0 [] hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit1,K)),L)=hAPP(int,int,plus_plus(int,hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),L))),L). % 8.03/8.05 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B)))| -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_e_q(X_a),A_1),B)). % 8.03/8.05 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),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_e_q(X_a),A_1),B)). % 8.03/8.05 0 [] -linord20386208strict(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),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)). % 8.03/8.05 0 [] -linordered_semiring(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),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)). % 8.03/8.05 0 [] -linord20386208strict(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_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)). % 8.03/8.05 0 [] -linordered_semiring(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_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),C_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)). % 8.03/8.05 0 [] -linord20386208strict(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_1),B))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D))| -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_e_q(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),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D))). % 8.03/8.05 0 [] -linord20386208strict(X_a)| -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_e_q(X_a),C_1),D))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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_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),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D))). % 8.03/8.05 0 [] -linord20386208strict(X_a)| -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_1),D))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),zero_zero(X_a)),A_1))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(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),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D))). % 8.03/8.05 0 [] -linord20386208strict(X_a)| -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_1),D))| -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_e_q(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),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D))). % 8.03/8.05 0 [] -linord581940658strict(X_a)| -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_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_1),A_2)). % 8.03/8.05 0 [] -linord581940658strict(X_a)| -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_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),B_1),A_2)). % 8.03/8.05 0 [] -linord581940658strict(X_a)| -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_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B_1)). % 8.03/8.05 0 [] -linord581940658strict(X_a)| -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_e_q(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_e_q(X_a),A_2),B_1)). % 8.03/8.05 0 [] -linord581940658strict(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,plus_plus(X_a,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),Xa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ya),Ya))))|ti(X_a,Xa)!=zero_zero(X_a)|ti(X_a,Ya)!=zero_zero(X_a). % 8.03/8.05 0 [] -linord581940658strict(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,plus_plus(X_a,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),Xa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ya),Ya))))|ti(X_a,Xa)=zero_zero(X_a). % 8.03/8.05 0 [] -linord581940658strict(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,plus_plus(X_a,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa),Xa)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ya),Ya))))|ti(X_a,Ya)=zero_zero(X_a). % 8.03/8.05 0 [] -linordered_ring(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(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))). % 8.03/8.05 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,power_power(X_a,A_1),N)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,power_power(X_a,A_1),N)))). % 8.03/8.05 0 [] -linordered_semidom(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_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),A_1),hAPP(nat,X_a,power_power(X_a,A_1),N)))). % 8.03/8.05 0 [] -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)),hAPP(real,real,sqrt,X))). % 8.03/8.05 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X))|hAPP(real,real,sqrt,X)!=zero_zero(real). % 8.03/8.05 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,Xa)),zero_zero(real)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),zero_zero(real))). % 8.03/8.05 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,Xa)),zero_zero(real)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),zero_zero(real))). % 8.03/8.05 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,Ya)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Ya)). % 8.03/8.05 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,Ya)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Ya)). % 8.03/8.05 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,Xa)),one_one(real)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),one_one(real))). % 8.03/8.05 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,Xa)),one_one(real)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Xa),one_one(real))). % 8.03/8.05 0 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,Ya)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Ya)). % 8.03/8.05 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,Ya)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Ya)). % 8.03/8.05 0 [] -linord581940658strict(X_a)| -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_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),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B))). % 8.03/8.05 0 [] -linord581940658strict(X_a)| -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_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),A_1),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1))). % 8.03/8.05 0 [] -linord893533164strict(X_a)| -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_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),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B))). % 8.03/8.05 0 [] -linord20386208strict(X_a)| -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_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),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B))). % 8.03/8.05 0 [] -linord20386208strict(X_a)| -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_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),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C_1))). % 8.03/8.05 0 [] -linord581940658strict(X_a)| -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))). % 8.03/8.05 0 [] -linord20386208strict(X_a)| -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))). % 8.03/8.05 0 [] -linord581940658strict(X_a)| -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_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B_1)))|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)). % 8.03/8.05 0 [] -linord581940658strict(X_a)| -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_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B_1)))| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)). % 8.03/8.05 0 [] -linord20386208strict(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),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)). % 8.03/8.05 0 [] -preorder(T_1)|preorder(fun(T_2,T_1)). % 8.03/8.05 0 [] -order(T_1)|order(fun(T_2,T_1)). % 8.03/8.05 0 [] -ord(T_1)|ord(fun(T_2,T_1)). % 8.03/8.05 0 [] semiri456707255roduct(int). % 8.03/8.05 0 [] ordere223160158up_add(int). % 8.03/8.05 0 [] ordere236663937imp_le(int). % 8.03/8.05 0 [] linord893533164strict(int). % 8.03/8.05 0 [] linord20386208strict(int). % 8.03/8.05 0 [] ordere779506340up_add(int). % 8.03/8.05 0 [] ordere216010020id_add(int). % 8.03/8.05 0 [] linord219039673up_add(int). % 8.03/8.05 0 [] cancel146912293up_add(int). % 8.03/8.05 0 [] ring_11004092258visors(int). % 8.03/8.05 0 [] linord581940658strict(int). % 8.03/8.05 0 [] cancel_semigroup_add(int). % 8.03/8.05 0 [] linordered_semiring(int). % 8.03/8.05 0 [] linordered_semidom(int). % 8.03/8.05 0 [] ab_semigroup_add(int). % 8.03/8.05 0 [] no_zero_divisors(int). % 8.03/8.05 0 [] comm_monoid_add(int). % 8.03/8.05 0 [] linordered_ring(int). % 8.03/8.05 0 [] linordered_idom(int). % 8.03/8.05 0 [] comm_semiring_1(int). % 8.03/8.05 0 [] semiring_char_0(int). % 8.03/8.05 0 [] number_semiring(int). % 8.03/8.05 0 [] zero_ne_q_one(int). % 8.03/8.05 0 [] preorder(int). % 8.03/8.05 0 [] linorder(int). % 8.03/8.05 0 [] monoid_mult(int). % 8.03/8.05 0 [] monoid_add(int). % 8.03/8.05 0 [] semiring_1(int). % 8.03/8.05 0 [] semiring_0(int). % 8.03/8.05 0 [] mult_zero(int). % 8.03/8.05 0 [] order(int). % 8.03/8.05 0 [] ring_char_0(int). % 8.03/8.05 0 [] number_ring(int). % 8.03/8.05 0 [] ord(int). % 8.03/8.05 0 [] power(int). % 8.03/8.05 0 [] zero(int). % 8.03/8.05 0 [] number(int). % 8.03/8.05 0 [] one(int). % 8.03/8.05 0 [] semiri456707255roduct(nat). % 8.03/8.05 0 [] ordere223160158up_add(nat). % 8.03/8.05 0 [] ordere236663937imp_le(nat). % 8.03/8.05 0 [] linord893533164strict(nat). % 8.03/8.05 0 [] linord20386208strict(nat). % 8.03/8.05 0 [] ordere779506340up_add(nat). % 8.03/8.05 0 [] ordere216010020id_add(nat). % 8.03/8.05 0 [] cancel146912293up_add(nat). % 8.03/8.05 0 [] cancel_semigroup_add(nat). % 8.03/8.05 0 [] linordered_semiring(nat). % 8.03/8.05 0 [] linordered_semidom(nat). % 8.03/8.05 0 [] ab_semigroup_add(nat). % 8.03/8.05 0 [] no_zero_divisors(nat). % 8.03/8.05 0 [] comm_monoid_add(nat). % 8.03/8.05 0 [] comm_semiring_1(nat). % 8.03/8.05 0 [] semiring_char_0(nat). % 8.03/8.05 0 [] number_semiring(nat). % 8.03/8.05 0 [] zero_ne_q_one(nat). % 8.03/8.05 0 [] preorder(nat). % 8.03/8.05 0 [] linorder(nat). % 8.03/8.05 0 [] monoid_mult(nat). % 8.03/8.05 0 [] monoid_add(nat). % 8.03/8.05 0 [] semiring_1(nat). % 8.03/8.05 0 [] semiring_0(nat). % 8.03/8.05 0 [] mult_zero(nat). % 8.03/8.05 0 [] order(nat). % 8.03/8.05 0 [] ord(nat). % 8.03/8.05 0 [] power(nat). % 8.03/8.05 0 [] zero(nat). % 8.03/8.05 0 [] number(nat). % 8.03/8.05 0 [] one(nat). % 8.03/8.05 0 [] preorder(bool). % 8.03/8.05 0 [] order(bool). % 8.03/8.05 0 [] ord(bool). % 8.03/8.05 0 [] semiri456707255roduct(real). % 8.03/8.05 0 [] ordere223160158up_add(real). % 8.03/8.05 0 [] ordere236663937imp_le(real). % 8.03/8.05 0 [] linord893533164strict(real). % 8.03/8.05 0 [] linord20386208strict(real). % 8.03/8.05 0 [] ordere779506340up_add(real). % 8.03/8.05 0 [] ordere216010020id_add(real). % 8.03/8.05 0 [] linord219039673up_add(real). % 8.03/8.05 0 [] cancel146912293up_add(real). % 8.03/8.05 0 [] ring_11004092258visors(real). % 8.03/8.05 0 [] linord581940658strict(real). % 8.03/8.05 0 [] cancel_semigroup_add(real). % 8.03/8.05 0 [] linordered_semiring(real). % 8.03/8.05 0 [] linordered_semidom(real). % 8.03/8.05 0 [] dense_linorder(real). % 8.03/8.05 0 [] ab_semigroup_add(real). % 8.03/8.05 0 [] no_zero_divisors(real). % 8.03/8.05 0 [] comm_monoid_add(real). % 8.03/8.05 0 [] linordered_ring(real). % 8.03/8.05 0 [] linordered_idom(real). % 8.03/8.05 0 [] comm_semiring_1(real). % 8.03/8.05 0 [] semiring_char_0(real). % 8.03/8.05 0 [] number_semiring(real). % 8.03/8.05 0 [] zero_ne_q_one(real). % 8.03/8.05 0 [] preorder(real). % 8.03/8.05 0 [] linorder(real). % 8.03/8.05 0 [] monoid_mult(real). % 8.03/8.05 0 [] monoid_add(real). % 8.03/8.05 0 [] semiring_1(real). % 8.03/8.05 0 [] semiring_0(real). % 8.03/8.05 0 [] mult_zero(real). % 8.03/8.05 0 [] order(real). % 8.03/8.05 0 [] ring_char_0(real). % 8.03/8.05 0 [] number_ring(real). % 8.03/8.05 0 [] ord(real). % 8.03/8.05 0 [] power(real). % 8.03/8.05 0 [] zero(real). % 8.03/8.05 0 [] number(real). % 8.03/8.05 0 [] one(real). % 8.03/8.05 0 [] ti(T,ti(T,A))=ti(T,A). % 8.03/8.05 0 [] 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). % 8.03/8.05 0 [] 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). % 8.03/8.05 0 [] ti(bool,P)=fTrue|ti(bool,P)=fFalse. % 8.03/8.05 0 [] hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=zero_zero(int). % 8.03/8.05 end_of_list. % 8.03/8.05 % 8.03/8.05 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7. % 8.03/8.05 % 8.03/8.05 This ia a non-Horn set with equality. The strategy will be % 8.03/8.05 Knuth-Bendix, ordered hyper_res, factoring, and unit % 8.03/8.05 deletion, with positive clauses in sos and nonpositive % 8.03/8.05 clauses in usable. % 8.03/8.05 % 8.03/8.05 dependent: set(knuth_bendix). % 8.03/8.05 dependent: set(anl_eq). % 8.03/8.05 dependent: set(para_from). % 8.03/8.05 dependent: set(para_into). % 8.03/8.05 dependent: clear(para_from_right). % 8.03/8.05 dependent: clear(para_into_right). % 8.03/8.05 dependent: set(para_from_vars). % 8.03/8.05 dependent: set(eq_units_both_ways). % 8.03/8.05 dependent: set(dynamic_demod_all). % 8.03/8.05 dependent: set(dynamic_demod). % 8.03/8.05 dependent: set(order_eq). % 8.03/8.05 dependent: set(back_demod). % 8.03/8.05 dependent: set(lrpo). % 8.03/8.05 dependent: set(hyper_res). % 8.03/8.05 dependent: set(unit_deletion). % 8.03/8.05 dependent: set(factor). % 8.03/8.05 % 8.03/8.05 ------------> process usable: % 8.03/8.05 ** KEPT (pick-wt=9): 1 [] -one(A)|ti(A,one_one(A))=one_one(A). % 8.03/8.05 ** KEPT (pick-wt=11): 2 [] -monoid_add(A)|plus_plus(A,ti(A,B))=plus_plus(A,B). % 8.03/8.05 ** KEPT (pick-wt=13): 3 [] -monoid_add(A)|ti(fun(A,A),plus_plus(A,B))=plus_plus(A,B). % 8.03/8.05 ** KEPT (pick-wt=11): 4 [] -ab_semigroup_add(A)|plus_plus(A,ti(A,B))=plus_plus(A,B). % 8.03/8.05 ** KEPT (pick-wt=13): 5 [] -ab_semigroup_add(A)|ti(fun(A,A),plus_plus(A,B))=plus_plus(A,B). % 8.03/8.05 ** KEPT (pick-wt=11): 6 [] -cancel_semigroup_add(A)|plus_plus(A,ti(A,B))=plus_plus(A,B). % 8.03/8.05 ** KEPT (pick-wt=13): 7 [] -cancel_semigroup_add(A)|ti(fun(A,A),plus_plus(A,B))=plus_plus(A,B). % 8.03/8.05 ** KEPT (pick-wt=13): 8 [] -linordered_semiring(A)|ti(fun(A,fun(A,A)),times_times(A))=times_times(A). % 8.03/8.05 ** KEPT (pick-wt=9): 9 [] -zero(A)|ti(A,zero_zero(A))=zero_zero(A). % 8.03/8.05 ** KEPT (pick-wt=11): 10 [] -number(A)|number_number_of(A,ti(int,B))=number_number_of(A,B). % 8.03/8.05 ** KEPT (pick-wt=11): 11 [] -number(A)|ti(A,number_number_of(A,B))=number_number_of(A,B). % 8.03/8.05 ** KEPT (pick-wt=11): 12 [] -semiring_1(A)|ti(fun(nat,A),semiring_1_of_nat(A))=semiring_1_of_nat(A). % 8.03/8.05 ** KEPT (pick-wt=13): 13 [] -ord(A)|ti(fun(A,fun(A,bool)),ord_less(A))=ord_less(A). % 8.03/8.05 ** KEPT (pick-wt=13): 14 [] -ord(A)|ti(fun(A,fun(A,bool)),ord_less_e_q(A))=ord_less_e_q(A). % 8.03/8.05 ** KEPT (pick-wt=11): 15 [] -power(A)|power_power(A,ti(A,B))=power_power(A,B). % 8.03/8.05 ** KEPT (pick-wt=13): 16 [] -power(A)|ti(fun(nat,A),power_power(A,B))=power_power(A,B). % 8.03/8.05 ** KEPT (pick-wt=17): 17 [] -ord(A)|hAPP(B,A,ti(fun(B,A),C),D)=hAPP(B,A,C,D). % 8.03/8.05 ** KEPT (pick-wt=15): 18 [] -ord(A)|hAPP(B,A,C,ti(B,D))=hAPP(B,A,C,D). % 8.03/8.05 ** KEPT (pick-wt=15): 19 [] -ord(A)|ti(A,hAPP(B,A,C,D))=hAPP(B,A,C,D). % 8.03/8.05 ** KEPT (pick-wt=17): 20 [] -power(A)|hAPP(nat,A,ti(fun(nat,A),B),C)=hAPP(nat,A,B,C). % 8.03/8.05 ** KEPT (pick-wt=15): 21 [] -power(A)|hAPP(nat,A,B,ti(nat,C))=hAPP(nat,A,B,C). % 8.03/8.05 ** KEPT (pick-wt=15): 22 [] -power(A)|ti(A,hAPP(nat,A,B,C))=hAPP(nat,A,B,C). % 8.03/8.05 ** KEPT (pick-wt=6): 23 [] -hBOOL(ti(bool,A))|hBOOL(A). % 8.03/8.05 ** KEPT (pick-wt=6): 24 [] hBOOL(ti(bool,A))| -hBOOL(A). % 8.03/8.05 ** KEPT (pick-wt=50): 25 [] -linordered_idom(A)|hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))!=zero_zero(A)|ti(A,B)=zero_zero(A). % 8.03/8.05 ** KEPT (pick-wt=50): 26 [] -linordered_idom(A)|hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))!=zero_zero(A)|ti(A,C)=zero_zero(A). % 8.03/8.05 ** KEPT (pick-wt=56): 27 [] -linordered_idom(A)|hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))=zero_zero(A)|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A). % 8.03/8.05 ** KEPT (pick-wt=23): 28 [] -semiring_1(A)|hAPP(nat,A,power_power(A,one_one(A)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=one_one(A). % 8.03/8.06 ** KEPT (pick-wt=23): 29 [] -semiring_1(A)|hAPP(nat,A,power_power(A,zero_zero(A)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=zero_zero(A). % 8.03/8.06 ** KEPT (pick-wt=28): 30 [] -ring_11004092258visors(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))!=zero_zero(A)|ti(A,B)=zero_zero(A). % 8.03/8.06 ** KEPT (pick-wt=28): 31 [] -ring_11004092258visors(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=zero_zero(A)|ti(A,B)!=zero_zero(A). % 8.03/8.06 ** KEPT (pick-wt=26): 32 [] -number_ring(A)|hAPP(A,A,plus_plus(A,one_one(A)),number_number_of(A,B))=number_number_of(A,hAPP(int,int,plus_plus(int,hAPP(int,int,bit1,pls)),B)). % 8.03/8.06 ** KEPT (pick-wt=26): 33 [] -number_ring(A)|hAPP(A,A,plus_plus(A,number_number_of(A,B)),one_one(A))=number_number_of(A,hAPP(int,int,plus_plus(int,B),hAPP(int,int,bit1,pls))). % 8.03/8.06 ** KEPT (pick-wt=23): 34 [] -number_ring(A)|hAPP(A,A,plus_plus(A,one_one(A)),one_one(A))=number_number_of(A,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))). % 8.03/8.06 ** KEPT (pick-wt=23): 35 [] -number_semiring(A)|hAPP(A,A,plus_plus(A,one_one(A)),one_one(A))=number_number_of(A,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))). % 8.03/8.06 ** KEPT (pick-wt=23): 36 [] -power(A)| -semiring_0(A)|number_number_of(nat,B)!=zero_zero(nat)|hAPP(nat,A,power_power(A,zero_zero(A)),number_number_of(nat,B))=one_one(A). % 8.03/8.06 ** KEPT (pick-wt=23): 37 [] -power(A)| -semiring_0(A)|number_number_of(nat,B)=zero_zero(nat)|hAPP(nat,A,power_power(A,zero_zero(A)),number_number_of(nat,B))=zero_zero(A). % 8.03/8.06 ** KEPT (pick-wt=12): 38 [] -number_ring(A)|one_one(A)=number_number_of(A,hAPP(int,int,bit1,pls)). % 8.03/8.06 Following clause subsumed by 38 during input processing: 0 [flip.2] -number_ring(A)|one_one(A)=number_number_of(A,hAPP(int,int,bit1,pls)). % 8.03/8.06 ** KEPT (pick-wt=30): 39 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,A)),number_number_of(int,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.03/8.06 ** KEPT (pick-wt=30): 40 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),number_number_of(int,A)),number_number_of(int,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.03/8.06 ** KEPT (pick-wt=34): 41 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),number_number_of(A,C)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). % 8.03/8.06 ** KEPT (pick-wt=34): 42 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),number_number_of(A,C)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). % 8.03/8.06 ** KEPT (pick-wt=13): 43 [] hAPP(nat,int,semiring_1_of_nat(int),A)!=zero_zero(int)|A=zero_zero(nat). % 8.03/8.06 ** KEPT (pick-wt=13): 44 [] hAPP(nat,int,semiring_1_of_nat(int),A)=zero_zero(int)|A!=zero_zero(nat). % 8.03/8.06 ** KEPT (pick-wt=34): 45 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,A)),hAPP(int,int,bit1,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.03/8.06 ** KEPT (pick-wt=34): 46 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,A)),hAPP(int,int,bit1,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.03/8.06 Following clause subsumed by 45 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,A)),hAPP(int,int,bit1,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.03/8.06 Following clause subsumed by 46 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,A)),hAPP(int,int,bit1,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.03/8.06 ** KEPT (pick-wt=13): 47 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)). % 8.03/8.06 ** KEPT (pick-wt=34): 48 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,A)),hAPP(int,int,bit0,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.03/8.06 ** KEPT (pick-wt=34): 49 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,A)),hAPP(int,int,bit0,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.03/8.06 Following clause subsumed by 48 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,A)),hAPP(int,int,bit0,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.03/8.06 Following clause subsumed by 49 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,A)),hAPP(int,int,bit0,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.03/8.06 ** KEPT (pick-wt=38): 50 [] -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,plus_plus(int,A),C)),hAPP(int,int,plus_plus(int,B),C))). % 8.03/8.06 ** KEPT (pick-wt=28): 51 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls))|hAPP(nat,nat,plus_plus(nat,number_number_of(nat,A)),number_number_of(nat,B))=number_number_of(nat,B). % 8.03/8.06 ** KEPT (pick-wt=41): 52 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls))|hAPP(nat,nat,plus_plus(nat,number_number_of(nat,A)),number_number_of(nat,B))=number_number_of(nat,A). % 8.03/8.06 ** KEPT (pick-wt=14): 53 [] -number_ring(A)| -ring_char_0(A)|number_number_of(A,B)!=number_number_of(A,C)|B=C. % 8.03/8.06 ** KEPT (pick-wt=14): 54 [] -number_ring(A)| -ring_char_0(A)|number_number_of(A,B)=number_number_of(A,C)|B!=C. % 8.03/8.06 ** KEPT (pick-wt=16): 55 [] -number(A)|number_number_of(A,B)!=ti(A,C)|ti(A,C)=number_number_of(A,B). % 8.03/8.06 ** KEPT (pick-wt=16): 56 [] -number(A)|number_number_of(A,B)=ti(A,C)|ti(A,C)!=number_number_of(A,B). % 8.03/8.06 ** KEPT (pick-wt=14): 57 [] hAPP(int,int,bit1,A)!=hAPP(int,int,bit1,B)|A=B. % 8.03/8.06 ** KEPT (pick-wt=14): 58 [] hAPP(int,int,bit1,A)=hAPP(int,int,bit1,B)|A!=B. % 8.03/8.06 ** KEPT (pick-wt=14): 59 [] hAPP(int,int,bit0,A)!=hAPP(int,int,bit0,B)|A=B. % 8.03/8.06 ** KEPT (pick-wt=14): 60 [] hAPP(int,int,bit0,A)=hAPP(int,int,bit0,B)|A!=B. % 8.03/8.06 ** KEPT (pick-wt=36): 61 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(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))). % 8.03/8.06 ** KEPT (pick-wt=36): 62 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(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))). % 8.03/8.06 ** KEPT (pick-wt=16): 63 [] hAPP(nat,int,semiring_1_of_nat(int),A)!=hAPP(nat,int,semiring_1_of_nat(int),B)|A=B. % 8.03/8.06 ** KEPT (pick-wt=16): 64 [] hAPP(nat,int,semiring_1_of_nat(int),A)=hAPP(nat,int,semiring_1_of_nat(int),B)|A!=B. % 8.03/8.06 ** KEPT (pick-wt=33): 65 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),zero_zero(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)). % 8.03/8.06 ** KEPT (pick-wt=33): 66 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),zero_zero(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)). % 8.03/8.06 ** KEPT (pick-wt=33): 67 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),number_number_of(A,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)). % 8.03/8.06 ** KEPT (pick-wt=33): 68 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),number_number_of(A,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)). % 8.03/8.06 ** KEPT (pick-wt=30): 69 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,A)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). % 8.03/8.06 ** KEPT (pick-wt=30): 70 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,A)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). % 8.03/8.06 ** KEPT (pick-wt=34): 71 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,A)),hAPP(int,int,bit0,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.03/8.06 ** KEPT (pick-wt=34): 72 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,A)),hAPP(int,int,bit0,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.03/8.06 Following clause subsumed by 71 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,A)),hAPP(int,int,bit0,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.03/8.06 Following clause subsumed by 72 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,A)),hAPP(int,int,bit0,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.03/8.06 ** KEPT (pick-wt=30): 73 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,A)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). % 8.03/8.06 ** KEPT (pick-wt=30): 74 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,A)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). % 8.03/8.06 ** KEPT (pick-wt=30): 75 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). % 8.03/8.06 ** KEPT (pick-wt=30): 76 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). % 8.03/8.06 ** KEPT (pick-wt=32): 77 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,A)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). % 8.03/8.06 ** KEPT (pick-wt=32): 78 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,A)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). % 8.03/8.06 ** KEPT (pick-wt=14): 79 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),zero_zero(int))). % 8.03/8.06 ** KEPT (pick-wt=32): 80 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,A)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). % 8.03/8.06 ** KEPT (pick-wt=32): 81 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,A)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). % 8.03/8.06 ** KEPT (pick-wt=36): 82 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,plus_plus(int,B),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|A=B. % 8.03/8.06 ** KEPT (pick-wt=33): 83 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,plus_plus(int,B),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.03/8.06 ** KEPT (pick-wt=23): 84 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,plus_plus(int,B),one_one(int))))|A!=B. % 8.03/8.06 ** KEPT (pick-wt=19): 85 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),zero_zero(int))). % 8.03/8.06 ** KEPT (pick-wt=37): 86 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),one_one(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,bit1,pls))). % 8.03/8.06 ** KEPT (pick-wt=37): 87 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,B)),one_one(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,bit1,pls))). % 8.03/8.06 ** KEPT (pick-wt=37): 88 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),number_number_of(A,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),B)). % 8.03/8.06 ** KEPT (pick-wt=37): 89 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),number_number_of(A,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),B)). % 8.03/8.06 ** KEPT (pick-wt=41): 90 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),A)),A)),zero_zero(int)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). % 8.03/8.06 ** KEPT (pick-wt=41): 91 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),A)),A)),zero_zero(int)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). % 8.03/8.06 ** KEPT (pick-wt=18): 92 [] -linord219039673up_add(A)|hAPP(A,A,plus_plus(A,B),B)!=zero_zero(A)|ti(A,B)=zero_zero(A). % 8.03/8.06 ** KEPT (pick-wt=18): 93 [] -linord219039673up_add(A)|hAPP(A,A,plus_plus(A,B),B)=zero_zero(A)|ti(A,B)!=zero_zero(A). % 8.03/8.06 ** KEPT (pick-wt=7): 94 [] hAPP(int,int,bit1,A)!=pls. % 8.03/8.06 Following clause subsumed by 94 during input processing: 0 [flip.1] hAPP(int,int,bit1,A)!=pls. % 8.03/8.06 ** KEPT (pick-wt=11): 95 [] hAPP(int,int,bit1,A)!=hAPP(int,int,bit0,B). % 8.03/8.06 ** KEPT (pick-wt=11): 96 [] hAPP(int,int,bit0,A)!=hAPP(int,int,bit1,B). % 8.03/8.06 ** KEPT (pick-wt=10): 97 [] hAPP(int,int,bit0,A)!=pls|A=pls. % 8.03/8.06 ** KEPT (pick-wt=10): 98 [] hAPP(int,int,bit0,A)=pls|A!=pls. % 8.03/8.06 ** KEPT (pick-wt=10): 100 [copy,99,flip.1] hAPP(int,int,bit0,A)!=pls|pls=A. % 8.03/8.06 ** KEPT (pick-wt=10): 102 [copy,101,flip.1] hAPP(int,int,bit0,A)=pls|pls!=A. % 8.03/8.06 ** KEPT (pick-wt=5): 103 [] zero_zero(int)!=one_one(int). % 8.03/8.06 ** KEPT (pick-wt=8): 105 [copy,104,flip.2] -number_semiring(A)|zero_zero(A)=number_number_of(A,pls). % 8.03/8.06 ** KEPT (pick-wt=8): 107 [copy,106,flip.2] -number_ring(A)|zero_zero(A)=number_number_of(A,pls). % 8.03/8.06 Following clause subsumed by 107 during input processing: 0 [] -number_ring(A)|zero_zero(A)=number_number_of(A,pls). % 8.03/8.06 ** KEPT (pick-wt=15): 109 [copy,108,flip.2] -number_ring(A)|ti(A,B)=hAPP(A,A,plus_plus(A,number_number_of(A,pls)),B). % 8.03/8.06 ** KEPT (pick-wt=15): 111 [copy,110,flip.2] -number_ring(A)|ti(A,B)=hAPP(A,A,plus_plus(A,B),number_number_of(A,pls)). % 8.03/8.06 ** KEPT (pick-wt=26): 112 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,C))!=zero_zero(A)|ti(A,B)=zero_zero(A). % 8.03/8.06 ** KEPT (pick-wt=26): 113 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,C))!=zero_zero(A)|number_number_of(nat,C)!=zero_zero(nat). % 8.03/8.06 ** KEPT (pick-wt=32): 114 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,C))=zero_zero(A)|ti(A,B)!=zero_zero(A)|number_number_of(nat,C)=zero_zero(nat). % 8.03/8.06 ** KEPT (pick-wt=35): 116 [copy,115,flip.2] -number_ring(A)|hAPP(A,A,plus_plus(A,number_number_of(A,hAPP(int,int,plus_plus(int,B),C))),D)=hAPP(A,A,plus_plus(A,number_number_of(A,B)),hAPP(A,A,plus_plus(A,number_number_of(A,C)),D)). % 8.03/8.06 ** KEPT (pick-wt=23): 117 [] -number_ring(A)|hAPP(A,A,plus_plus(A,number_number_of(A,B)),number_number_of(A,C))=number_number_of(A,hAPP(int,int,plus_plus(int,B),C)). % 8.03/8.06 ** KEPT (pick-wt=23): 118 [] -number_ring(A)|number_number_of(A,hAPP(int,int,plus_plus(int,B),C))=hAPP(A,A,plus_plus(A,number_number_of(A,B)),number_number_of(A,C)). % 8.03/8.06 ** KEPT (pick-wt=17): 119 [] hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),A)),A)!=zero_zero(int). % 8.03/8.06 ** KEPT (pick-wt=17): 120 [] -number_semiring(A)|number_number_of(A,hAPP(nat,int,semiring_1_of_nat(int),B))=hAPP(nat,A,semiring_1_of_nat(A),B). % 8.03/8.06 ** KEPT (pick-wt=38): 121 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))|ti(A,B)!=zero_zero(A). % 8.03/8.06 ** KEPT (pick-wt=38): 122 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))|ti(A,B)=zero_zero(A). % 8.03/8.06 ** KEPT (pick-wt=32): 123 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(A))). % 8.03/8.06 ** KEPT (pick-wt=66): 124 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A). % 8.03/8.06 ** KEPT (pick-wt=60): 125 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))|ti(A,B)=zero_zero(A). % 8.03/8.06 ** KEPT (pick-wt=60): 126 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))|ti(A,C)=zero_zero(A). % 8.03/8.06 ** KEPT (pick-wt=54): 127 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A))). % 8.03/8.06 ** KEPT (pick-wt=28): 129 [copy,128,flip.2] -number_ring(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,zero_zero(A)),number_number_of(A,B))),number_number_of(A,B))=number_number_of(A,hAPP(int,int,bit0,B)). % 8.03/8.06 ** KEPT (pick-wt=28): 131 [copy,130,flip.2] -number_ring(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,one_one(A)),number_number_of(A,B))),number_number_of(A,B))=number_number_of(A,hAPP(int,int,bit1,B)). % 8.03/8.06 ** KEPT (pick-wt=12): 133 [copy,132,flip.2] -number_semiring(A)|one_one(A)=number_number_of(A,hAPP(int,int,bit1,pls)). % 8.03/8.06 ** KEPT (pick-wt=38): 134 [] -number_ring(A)| -linordered_idom(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,power_power(A,number_number_of(A,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))). % 8.03/8.06 ** KEPT (pick-wt=46): 135 [] hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))!=zero_zero(real)|A=zero_zero(real). % 8.03/8.06 ** KEPT (pick-wt=46): 136 [] hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))!=zero_zero(real)|B=zero_zero(real). % 8.03/8.06 ** KEPT (pick-wt=50): 137 [] hAPP(real,real,plus_plus(real,hAPP(nat,real,power_power(real,A),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,power_power(real,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))=zero_zero(real)|A!=zero_zero(real)|B!=zero_zero(real). % 8.03/8.06 ** KEPT (pick-wt=35): 138 [] -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)). % 8.03/8.06 ** KEPT (pick-wt=35): 139 [] -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)). % 8.03/8.06 ** KEPT (pick-wt=50): 140 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(nat,A,power_power(A,B),C))). % 8.03/8.06 ** KEPT (pick-wt=19): 141 [] -power(A)| -semiring_0(A)|B!=zero_zero(nat)|hAPP(nat,A,power_power(A,zero_zero(A)),B)=one_one(A). % 8.03/8.06 ** KEPT (pick-wt=19): 142 [] -power(A)| -semiring_0(A)|B=zero_zero(nat)|hAPP(nat,A,power_power(A,zero_zero(A)),B)=zero_zero(A). % 8.03/8.06 ** KEPT (pick-wt=68): 143 [] -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),zero_zero(A)),D))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),one_one(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,D),C)),hAPP(nat,A,power_power(A,D),B))). % 8.03/8.06 ** KEPT (pick-wt=24): 144 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,one_one(A)),one_one(A)))). % 8.03/8.06 ** KEPT (pick-wt=48): 145 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,C,hAPP(int,int,plus_plus(int,A),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),$f1(C,A,B)))|hBOOL(hAPP(int,bool,C,B)). % 8.03/8.06 ** KEPT (pick-wt=41): 146 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,C,hAPP(int,int,plus_plus(int,A),one_one(int))))|hBOOL(hAPP(int,bool,C,$f1(C,A,B)))|hBOOL(hAPP(int,bool,C,B)). % 8.03/8.06 ** KEPT (pick-wt=48): 147 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))| -hBOOL(hAPP(int,bool,C,hAPP(int,int,plus_plus(int,A),one_one(int))))| -hBOOL(hAPP(int,bool,C,hAPP(int,int,plus_plus(int,$f1(C,A,B)),one_one(int))))|hBOOL(hAPP(int,bool,C,B)). % 8.03/8.06 ** KEPT (pick-wt=14): 148 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))). % 8.03/8.06 ** KEPT (pick-wt=5): 149 [] zero_zero(real)!=one_one(real). % 8.03/8.06 ** KEPT (pick-wt=13): 150 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),A)). % 8.03/8.06 ** KEPT (pick-wt=19): 151 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,A),B)),A)). % 8.03/8.06 ** KEPT (pick-wt=19): 152 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,A),B)),B)). % 8.03/8.06 ** KEPT (pick-wt=16): 153 [] A!=B| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). % 8.03/8.06 ** KEPT (pick-wt=16): 154 [] A!=B| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). % 8.03/8.06 ** KEPT (pick-wt=18): 155 [] hAPP(nat,nat,plus_plus(nat,A),B)!=hAPP(nat,nat,plus_plus(nat,A),C)|B=C. % 8.03/8.06 ** KEPT (pick-wt=18): 156 [] hAPP(nat,nat,plus_plus(nat,A),B)=hAPP(nat,nat,plus_plus(nat,A),C)|B!=C. % 8.03/8.06 ** KEPT (pick-wt=18): 157 [] hAPP(nat,nat,plus_plus(nat,A),B)!=hAPP(nat,nat,plus_plus(nat,C),B)|A=C. % 8.03/8.06 ** KEPT (pick-wt=18): 158 [] hAPP(nat,nat,plus_plus(nat,A),B)=hAPP(nat,nat,plus_plus(nat,C),B)|A!=C. % 8.03/8.06 ** KEPT (pick-wt=38): 159 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,A),B)),hAPP(nat,nat,plus_plus(nat,A),C)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). % 8.03/8.06 ** KEPT (pick-wt=38): 160 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,A),B)),hAPP(nat,nat,plus_plus(nat,A),C)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). % 8.03/8.06 Following clause subsumed by 150 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),A)). % 8.03/8.06 Following clause subsumed by 154 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|B!=A. % 8.03/8.06 Following clause subsumed by 153 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|A!=B. % 8.03/8.06 ** KEPT (pick-wt=32): 161 [] -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),A),hAPP(nat,nat,plus_plus(nat,B),C))). % 8.03/8.06 ** KEPT (pick-wt=32): 162 [] -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),A),hAPP(nat,nat,plus_plus(nat,C),B))). % 8.03/8.06 ** KEPT (pick-wt=38): 163 [] -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,plus_plus(nat,A),C)),hAPP(nat,nat,plus_plus(nat,B),C))). % 8.03/8.06 ** KEPT (pick-wt=51): 164 [] -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,plus_plus(nat,A),C)),hAPP(nat,nat,plus_plus(nat,B),D))). % 8.03/8.06 ** KEPT (pick-wt=41): 165 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hAPP(nat,nat,plus_plus(nat,C),B)!=hAPP(nat,nat,plus_plus(nat,A),D)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)). % 8.03/8.06 ** KEPT (pick-wt=32): 166 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,plus_plus(nat,A),B)),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). % 8.03/8.06 ** KEPT (pick-wt=17): 167 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|B!=zero_zero(nat). % 8.03/8.06 ** KEPT (pick-wt=52): 168 [] -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),hAPP(nat,nat,power_power(nat,A),B)),hAPP(nat,nat,power_power(nat,A),C)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). % 8.03/8.06 Following clause subsumed by 148 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))). % 8.03/8.06 ** KEPT (pick-wt=38): 169 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A))|B=zero_zero(nat). % 8.03/8.06 ** KEPT (pick-wt=34): 170 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). % 8.03/8.06 ** KEPT (pick-wt=24): 171 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B)))|B!=zero_zero(nat). % 8.03/8.06 ** KEPT (pick-wt=48): 172 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(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)). % 8.03/8.06 Following clause subsumed by 161 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,A),B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). % 8.03/8.06 Following clause subsumed by 162 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,plus_plus(nat,A),B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)). % 8.03/8.06 Following clause subsumed by 154 during input processing: 0 [] A!=zero_zero(nat)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). % 8.03/8.06 Following clause subsumed by 148 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))). % 8.03/8.06 Following clause subsumed by 169 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B)))|B=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). % 8.03/8.06 Following clause subsumed by 171 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B)))|B!=zero_zero(nat). % 8.03/8.06 Following clause subsumed by 170 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),B)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). % 8.03/8.06 ** KEPT (pick-wt=36): 173 [] -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)). % 8.03/8.06 ** KEPT (pick-wt=36): 174 [] 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)). % 8.03/8.06 Following clause subsumed by 169 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),number_number_of(nat,B))))|number_number_of(nat,B)=zero_zero(nat)|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). % 8.03/8.06 Following clause subsumed by 171 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),number_number_of(nat,B))))|number_number_of(nat,B)!=zero_zero(nat). % 8.03/8.06 Following clause subsumed by 170 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,A),number_number_of(nat,B))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). % 8.03/8.06 Following clause subsumed by 173 during input processing: 0 [] -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)). % 8.03/8.06 Following clause subsumed by 174 during input processing: 0 [] 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)). % 8.03/8.06 ** KEPT (pick-wt=43): 175 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,A)),number_number_of(nat,B)))| -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),pls),B)). % 8.03/8.06 ** KEPT (pick-wt=30): 176 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,A)),number_number_of(nat,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.03/8.06 ** KEPT (pick-wt=43): 177 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),number_number_of(nat,A)),number_number_of(nat,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.03/8.06 ** KEPT (pick-wt=35): 178 [] -linordered_idom(A)|ti(A,B)=ti(A,C)|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)). % 8.03/8.06 ** KEPT (pick-wt=13): 179 [] hAPP(nat,nat,plus_plus(nat,A),B)!=A|B=zero_zero(nat). % 8.03/8.06 ** KEPT (pick-wt=14): 180 [] hAPP(nat,nat,plus_plus(nat,A),B)!=zero_zero(nat)|A=zero_zero(nat). % 8.03/8.06 ** KEPT (pick-wt=14): 181 [] hAPP(nat,nat,plus_plus(nat,A),B)!=zero_zero(nat)|B=zero_zero(nat). % 8.03/8.06 ** KEPT (pick-wt=18): 182 [] hAPP(nat,nat,plus_plus(nat,A),B)=zero_zero(nat)|A!=zero_zero(nat)|B!=zero_zero(nat). % 8.03/8.06 ** KEPT (pick-wt=14): 183 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,B),one_one(nat))=ti(A,B). % 8.03/8.06 ** KEPT (pick-wt=18): 184 [] -semiring_char_0(A)|hAPP(nat,A,semiring_1_of_nat(A),B)!=hAPP(nat,A,semiring_1_of_nat(A),C)|B=C. % 8.03/8.06 ** KEPT (pick-wt=18): 185 [] -semiring_char_0(A)|hAPP(nat,A,semiring_1_of_nat(A),B)=hAPP(nat,A,semiring_1_of_nat(A),C)|B!=C. % 8.03/8.06 Following clause subsumed by 63 during input processing: 0 [] hAPP(nat,int,semiring_1_of_nat(int),A)!=hAPP(nat,int,semiring_1_of_nat(int),B)|A=B. % 8.03/8.06 Following clause subsumed by 64 during input processing: 0 [] hAPP(nat,int,semiring_1_of_nat(int),A)=hAPP(nat,int,semiring_1_of_nat(int),B)|A!=B. % 8.03/8.06 ** KEPT (pick-wt=34): 187 [copy,186,flip.2] -hBOOL(A)|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),A),B),C))=hAPP(nat,int,semiring_1_of_nat(int),B). % 8.03/8.06 ** KEPT (pick-wt=29): 188 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). % 8.03/8.06 ** KEPT (pick-wt=29): 189 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)). % 8.03/8.06 ** KEPT (pick-wt=33): 190 [] -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)). % 8.03/8.06 ** KEPT (pick-wt=33): 191 [] 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)). % 8.03/8.06 ** KEPT (pick-wt=7): 193 [copy,192,flip.2] -zero_ne_q_one(A)|zero_zero(A)!=one_one(A). % 8.03/8.06 Following clause subsumed by 193 during input processing: 0 [] -zero_ne_q_one(A)|zero_zero(A)!=one_one(A). % 8.03/8.06 ** KEPT (pick-wt=18): 194 [] -ring_11004092258visors(A)|ti(A,B)=zero_zero(A)|hAPP(nat,A,power_power(A,B),C)!=zero_zero(A). % 8.03/8.06 ** KEPT (pick-wt=13): 195 [] -monoid_mult(A)|hAPP(nat,A,power_power(A,one_one(A)),B)=one_one(A). % 8.03/8.06 ** KEPT (pick-wt=38): 196 [] -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)). % 8.03/8.06 ** KEPT (pick-wt=38): 197 [] -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)). % 8.03/8.06 Following clause subsumed by 197 during input processing: 0 [] -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))). % 8.03/8.06 Following clause subsumed by 196 during input processing: 0 [] -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)). % 8.03/8.06 ** KEPT (pick-wt=32): 198 [] -semiring_1(A)|hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,plus_plus(nat,B),C))=hAPP(A,A,plus_plus(A,hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C)). % 8.03/8.06 ** KEPT (pick-wt=12): 199 [] -semiring_1(A)|hAPP(nat,A,semiring_1_of_nat(A),one_one(nat))=one_one(A). % 8.03/8.06 ** KEPT (pick-wt=27): 200 [] -semiring_1(A)|hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,power_power(nat,B),C))=hAPP(nat,A,power_power(A,hAPP(nat,A,semiring_1_of_nat(A),B)),C). % 8.03/8.06 ** KEPT (pick-wt=48): 201 [] -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,plus_plus(A,B),D))). % 8.03/8.06 ** KEPT (pick-wt=17): 202 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),zero_zero(A))). % 8.03/8.06 ** KEPT (pick-wt=17): 203 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),one_one(A))). % 8.03/8.06 ** KEPT (pick-wt=36): 204 [] -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),zero_zero(A)),hAPP(nat,A,power_power(A,B),C))). % 8.03/8.06 ** KEPT (pick-wt=22): 205 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,plus_plus(A,B),one_one(A)))). % 8.03/8.06 ** KEPT (pick-wt=34): 206 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))|hAPP(nat,A,power_power(A,B),C)!=hAPP(nat,A,power_power(A,B),D)|C=D. % 8.03/8.06 ** KEPT (pick-wt=34): 207 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B))|hAPP(nat,A,power_power(A,B),C)=hAPP(nat,A,power_power(A,B),D)|C!=D. % 8.03/8.06 ** KEPT (pick-wt=54): 208 [] -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),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)). % 8.03/8.06 ** KEPT (pick-wt=54): 209 [] -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),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)). % 8.03/8.06 Following clause subsumed by 208 during input processing: 0 [] -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),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)). % 8.03/8.06 Following clause subsumed by 209 during input processing: 0 [] -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),one_one(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,D),B)),hAPP(nat,A,power_power(A,D),C))). % 8.03/8.06 ** KEPT (pick-wt=24): 210 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|hAPP(nat,A,power_power(A,B),C)!=zero_zero(A)|ti(A,B)=zero_zero(A). % 8.03/8.06 ** KEPT (pick-wt=22): 211 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|hAPP(nat,A,power_power(A,B),C)!=zero_zero(A)|C!=zero_zero(nat). % 8.03/8.06 ** KEPT (pick-wt=28): 212 [] -power(A)| -mult_zero(A)| -no_zero_divisors(A)| -zero_ne_q_one(A)|hAPP(nat,A,power_power(A,B),C)=zero_zero(A)|ti(A,B)!=zero_zero(A)|C=zero_zero(nat). % 8.03/8.06 ** KEPT (pick-wt=21): 213 [] -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))). % 8.03/8.06 ** KEPT (pick-wt=13): 214 [] -power(A)|hAPP(nat,A,power_power(A,B),zero_zero(nat))=one_one(A). % 8.03/8.06 ** KEPT (pick-wt=12): 215 [] -semiring_1(A)|hAPP(nat,A,semiring_1_of_nat(A),zero_zero(nat))=zero_zero(A). % 8.03/8.06 ** KEPT (pick-wt=29): 216 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),$f2(A))). % 8.03/8.06 ** KEPT (pick-wt=23): 218 [copy,217,flip.2] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A))|hAPP(nat,int,semiring_1_of_nat(int),$f2(A))=A. % 8.03/8.06 ** KEPT (pick-wt=29): 219 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),$f3(A,B))). % 8.03/8.06 ** KEPT (pick-wt=24): 220 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|hAPP(nat,nat,plus_plus(nat,A),$f3(A,B))=B. % 8.03/8.06 ** KEPT (pick-wt=18): 221 [] hAPP(nat,nat,power_power(nat,A),B)!=one_one(nat)|A=one_one(nat)|B=zero_zero(nat). % 8.03/8.06 ** KEPT (pick-wt=14): 222 [] hAPP(nat,nat,power_power(nat,A),B)=one_one(nat)|A!=one_one(nat). % 8.03/8.06 ** KEPT (pick-wt=14): 223 [] hAPP(nat,nat,power_power(nat,A),B)=one_one(nat)|B!=zero_zero(nat). % 8.03/8.06 ** KEPT (pick-wt=13): 224 [] -comm_semiring_1(A)|hAPP(nat,A,power_power(A,B),zero_zero(nat))=one_one(A). % 8.03/8.06 ** KEPT (pick-wt=36): 225 [] -linord219039673up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,B),B)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)). % 8.03/8.06 ** KEPT (pick-wt=36): 226 [] -linord219039673up_add(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,B),B)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)). % 8.03/8.06 ** KEPT (pick-wt=36): 227 [] -linord219039673up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(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))). % 8.03/8.06 ** KEPT (pick-wt=36): 228 [] -linord219039673up_add(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(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))). % 8.03/8.06 ** KEPT (pick-wt=14): 229 [] -zero(A)|zero_zero(A)!=ti(A,B)|ti(A,B)=zero_zero(A). % 8.03/8.06 ** KEPT (pick-wt=14): 230 [] -zero(A)|zero_zero(A)=ti(A,B)|ti(A,B)!=zero_zero(A). % 8.03/8.06 ** KEPT (pick-wt=24): 231 [] -cancel_semigroup_add(A)|hAPP(A,A,plus_plus(A,B),C)!=hAPP(A,A,plus_plus(A,D),C)|ti(A,B)=ti(A,D). % 8.03/8.06 ** KEPT (pick-wt=24): 232 [] -cancel146912293up_add(A)|hAPP(A,A,plus_plus(A,B),C)!=hAPP(A,A,plus_plus(A,B),D)|ti(A,C)=ti(A,D). % 8.03/8.06 ** KEPT (pick-wt=24): 233 [] -cancel_semigroup_add(A)|hAPP(A,A,plus_plus(A,B),C)!=hAPP(A,A,plus_plus(A,B),D)|ti(A,C)=ti(A,D). % 8.03/8.06 ** KEPT (pick-wt=41): 234 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,D),E))=hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),D)),hAPP(A,A,plus_plus(A,C),E)). % 8.03/8.06 Following clause subsumed by 231 during input processing: 0 [] -cancel_semigroup_add(A)|hAPP(A,A,plus_plus(A,B),C)!=hAPP(A,A,plus_plus(A,D),C)|ti(A,B)=ti(A,D). % 8.03/8.06 ** KEPT (pick-wt=24): 235 [] -cancel_semigroup_add(A)|hAPP(A,A,plus_plus(A,B),C)=hAPP(A,A,plus_plus(A,D),C)|ti(A,B)!=ti(A,D). % 8.03/8.07 Following clause subsumed by 233 during input processing: 0 [] -cancel_semigroup_add(A)|hAPP(A,A,plus_plus(A,B),C)!=hAPP(A,A,plus_plus(A,B),D)|ti(A,C)=ti(A,D). % 8.03/8.07 ** KEPT (pick-wt=24): 236 [] -cancel_semigroup_add(A)|hAPP(A,A,plus_plus(A,B),C)=hAPP(A,A,plus_plus(A,B),D)|ti(A,C)!=ti(A,D). % 8.03/8.07 ** KEPT (pick-wt=29): 237 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),C)),D)=hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),D)),C). % 8.03/8.07 ** KEPT (pick-wt=29): 238 [] -ab_semigroup_add(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),C)),D)=hAPP(A,A,plus_plus(A,B),hAPP(A,A,plus_plus(A,C),D)). % 8.03/8.07 ** KEPT (pick-wt=29): 239 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),C)),D)=hAPP(A,A,plus_plus(A,B),hAPP(A,A,plus_plus(A,C),D)). % 8.03/8.07 Following clause subsumed by 239 during input processing: 0 [flip.2] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,hAPP(A,A,plus_plus(A,B),C)),D)=hAPP(A,A,plus_plus(A,B),hAPP(A,A,plus_plus(A,C),D)). % 8.03/8.07 ** KEPT (pick-wt=29): 240 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,B),hAPP(A,A,plus_plus(A,C),D))=hAPP(A,A,plus_plus(A,C),hAPP(A,A,plus_plus(A,B),D)). % 8.03/8.07 ** KEPT (pick-wt=17): 241 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,B),C)=hAPP(A,A,plus_plus(A,C),B). % 8.03/8.07 ** KEPT (pick-wt=14): 242 [] -one(A)|one_one(A)!=ti(A,B)|ti(A,B)=one_one(A). % 8.03/8.07 ** KEPT (pick-wt=14): 243 [] -one(A)|one_one(A)=ti(A,B)|ti(A,B)!=one_one(A). % 8.03/8.07 ** KEPT (pick-wt=19): 244 [] -semiri456707255roduct(A)|ti(A,B)!=hAPP(A,A,plus_plus(A,B),C)|ti(A,C)=zero_zero(A). % 8.03/8.07 ** KEPT (pick-wt=19): 245 [] -semiri456707255roduct(A)|ti(A,B)=hAPP(A,A,plus_plus(A,B),C)|ti(A,C)!=zero_zero(A). % 8.03/8.07 ** KEPT (pick-wt=14): 246 [] -comm_monoid_add(A)|hAPP(A,A,plus_plus(A,B),zero_zero(A))=ti(A,B). % 8.03/8.07 ** KEPT (pick-wt=14): 247 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,B),zero_zero(A))=ti(A,B). % 8.03/8.07 ** KEPT (pick-wt=14): 248 [] -monoid_add(A)|hAPP(A,A,plus_plus(A,B),zero_zero(A))=ti(A,B). % 8.03/8.07 ** KEPT (pick-wt=18): 249 [] -linord219039673up_add(A)|zero_zero(A)!=hAPP(A,A,plus_plus(A,B),B)|ti(A,B)=zero_zero(A). % 8.03/8.07 ** KEPT (pick-wt=18): 250 [] -linord219039673up_add(A)|zero_zero(A)=hAPP(A,A,plus_plus(A,B),B)|ti(A,B)!=zero_zero(A). % 8.03/8.07 ** KEPT (pick-wt=14): 251 [] -comm_monoid_add(A)|hAPP(A,A,plus_plus(A,zero_zero(A)),B)=ti(A,B). % 8.03/8.07 ** KEPT (pick-wt=14): 252 [] -comm_semiring_1(A)|hAPP(A,A,plus_plus(A,zero_zero(A)),B)=ti(A,B). % 8.03/8.07 ** KEPT (pick-wt=14): 253 [] -monoid_add(A)|hAPP(A,A,plus_plus(A,zero_zero(A)),B)=ti(A,B). % 8.03/8.07 ** KEPT (pick-wt=40): 254 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,B),D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)). % 8.03/8.07 ** KEPT (pick-wt=40): 255 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,D),C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)). % 8.03/8.07 ** KEPT (pick-wt=53): 256 [] -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,plus_plus(A,B),D)),hAPP(A,A,plus_plus(A,C),E))). % 8.03/8.07 ** KEPT (pick-wt=40): 257 [] -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,plus_plus(A,D),B)),hAPP(A,A,plus_plus(A,D),C))). % 8.03/8.07 ** KEPT (pick-wt=40): 258 [] -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,plus_plus(A,B),D)),hAPP(A,A,plus_plus(A,C),D))). % 8.03/8.07 Following clause subsumed by 254 during input processing: 0 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,B),D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)). % 8.03/8.07 ** KEPT (pick-wt=40): 259 [] -ordere236663937imp_le(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,B),D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)). % 8.03/8.07 Following clause subsumed by 255 during input processing: 0 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,D),C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)). % 8.03/8.07 ** KEPT (pick-wt=40): 260 [] -ordere236663937imp_le(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,D),C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)). % 8.03/8.07 ** KEPT (pick-wt=14): 261 [] -comm_semiring_1(A)|hAPP(nat,A,power_power(A,B),one_one(nat))=ti(A,B). % 8.03/8.07 ** KEPT (pick-wt=14): 262 [] hAPP(nat,nat,power_power(nat,A),B)!=zero_zero(nat)|B!=zero_zero(nat). % 8.03/8.07 ** KEPT (pick-wt=14): 263 [] hAPP(nat,nat,power_power(nat,A),B)!=zero_zero(nat)|A=zero_zero(nat). % 8.03/8.07 ** KEPT (pick-wt=18): 264 [] hAPP(nat,nat,power_power(nat,A),B)=zero_zero(nat)|B=zero_zero(nat)|A!=zero_zero(nat). % 8.03/8.07 ** KEPT (pick-wt=50): 265 [] -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,plus_plus(A,B),C)),zero_zero(A))). % 8.03/8.07 ** KEPT (pick-wt=50): 266 [] -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,plus_plus(A,B),C))). % 8.03/8.07 ** KEPT (pick-wt=44): 267 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),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)),$f4(B,A))). % 8.03/8.07 ** KEPT (pick-wt=39): 268 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B))|hAPP(nat,real,power_power(real,$f4(B,A)),A)=B. % 8.03/8.07 ** KEPT (pick-wt=56): 269 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C))|hAPP(nat,real,power_power(real,C),A)!=B|C=$f4(B,A). % 8.10/8.07 ** KEPT (pick-wt=44): 270 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),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)),$f5(B,A))). % 8.10/8.07 ** KEPT (pick-wt=39): 271 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B))|hAPP(nat,real,power_power(real,$f5(B,A)),A)=B. % 8.10/8.07 ** KEPT (pick-wt=26): 272 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls))|hAPP(nat,nat,plus_plus(nat,number_number_of(nat,A)),one_one(nat))=one_one(nat). % 8.10/8.07 ** KEPT (pick-wt=26): 273 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls))|hAPP(nat,nat,plus_plus(nat,one_one(nat)),number_number_of(nat,A))=one_one(nat). % 8.10/8.07 ** KEPT (pick-wt=40): 274 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,D),C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),D)). % 8.10/8.07 ** KEPT (pick-wt=40): 275 [] -ordere236663937imp_le(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,D),C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),D)). % 8.10/8.07 ** KEPT (pick-wt=40): 276 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,B),D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D)). % 8.10/8.07 ** KEPT (pick-wt=40): 277 [] -ordere236663937imp_le(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,B),D)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D)). % 8.10/8.07 ** KEPT (pick-wt=40): 278 [] -ordere779506340up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,B),D)),hAPP(A,A,plus_plus(A,C),D))). % 8.10/8.07 ** KEPT (pick-wt=40): 279 [] -ordere779506340up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,D),B)),hAPP(A,A,plus_plus(A,D),C))). % 8.10/8.07 ** KEPT (pick-wt=53): 280 [] -ordere779506340up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),E))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,B),D)),hAPP(A,A,plus_plus(A,C),E))). % 8.10/8.07 Following clause subsumed by 274 during input processing: 0 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,D),C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),D)). % 8.10/8.07 Following clause subsumed by 276 during input processing: 0 [] -ordere236663937imp_le(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,B),C)),hAPP(A,A,plus_plus(A,B),D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D)). % 8.10/8.07 ** KEPT (pick-wt=54): 281 [] -linordered_semidom(A)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),one_one(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,D),B)),hAPP(nat,A,power_power(A,D),C))). % 8.10/8.07 ** KEPT (pick-wt=34): 282 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,A)),hAPP(int,int,bit1,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 ** KEPT (pick-wt=34): 283 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,A)),hAPP(int,int,bit1,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 Following clause subsumed by 282 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,A)),hAPP(int,int,bit1,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 Following clause subsumed by 283 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,A)),hAPP(int,int,bit1,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 ** KEPT (pick-wt=34): 284 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,A)),hAPP(int,int,bit0,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 ** KEPT (pick-wt=34): 285 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,A)),hAPP(int,int,bit0,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 Following clause subsumed by 284 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,A)),hAPP(int,int,bit0,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 Following clause subsumed by 285 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,A)),hAPP(int,int,bit0,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 ** KEPT (pick-wt=39): 286 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),C))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),C)). % 8.10/8.07 ** KEPT (pick-wt=29): 287 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),A))|A=B. % 8.10/8.07 ** KEPT (pick-wt=34): 288 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),number_number_of(A,C)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),C)). % 8.10/8.07 ** KEPT (pick-wt=34): 289 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),number_number_of(A,C)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),C)). % 8.10/8.07 ** KEPT (pick-wt=38): 290 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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_e_q(nat),B),C)). % 8.10/8.07 ** KEPT (pick-wt=38): 291 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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_e_q(nat),B),C)). % 8.10/8.07 ** KEPT (pick-wt=26): 292 [] -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_e_q(int),A),B)). % 8.10/8.07 ** KEPT (pick-wt=16): 293 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B))|A!=B. % 8.10/8.07 ** KEPT (pick-wt=29): 294 [] 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_e_q(int),A),B))|A=B. % 8.10/8.07 ** KEPT (pick-wt=38): 295 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,C),A)),hAPP(int,int,plus_plus(int,C),B))). % 8.10/8.07 ** KEPT (pick-wt=30): 296 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,A)),number_number_of(int,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 ** KEPT (pick-wt=30): 297 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),number_number_of(int,A)),number_number_of(int,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 ** KEPT (pick-wt=33): 298 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),number_number_of(A,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),B)). % 8.10/8.07 ** KEPT (pick-wt=33): 299 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),number_number_of(A,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),B)). % 8.10/8.07 ** KEPT (pick-wt=33): 300 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),zero_zero(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),pls)). % 8.10/8.07 ** KEPT (pick-wt=33): 301 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),zero_zero(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),pls)). % 8.10/8.07 ** KEPT (pick-wt=68): 302 [] -linordered_semidom(A)| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),D))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),one_one(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,D),C)),hAPP(nat,A,power_power(A,D),B))). % 8.10/8.07 ** KEPT (pick-wt=54): 303 [] -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_e_q(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),C),D)). % 8.10/8.07 ** KEPT (pick-wt=54): 304 [] -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_e_q(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),C),D)). % 8.10/8.07 Following clause subsumed by 303 during input processing: 0 [] -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_e_q(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,B),D)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),C),D)). % 8.10/8.07 ** KEPT (pick-wt=37): 305 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),one_one(A)),number_number_of(A,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,pls)),B)). % 8.10/8.07 ** KEPT (pick-wt=37): 306 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),one_one(A)),number_number_of(A,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,pls)),B)). % 8.10/8.07 ** KEPT (pick-wt=37): 307 [] -number_ring(A)| -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),one_one(A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),hAPP(int,int,bit1,pls))). % 8.10/8.07 ** KEPT (pick-wt=37): 308 [] -number_ring(A)| -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),one_one(A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),B),hAPP(int,int,bit1,pls))). % 8.10/8.07 ** KEPT (pick-wt=36): 309 [] -linord219039673up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(A,A,plus_plus(A,B),B)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B)). % 8.10/8.07 ** KEPT (pick-wt=36): 310 [] -linord219039673up_add(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(A,A,plus_plus(A,B),B)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B)). % 8.10/8.07 ** KEPT (pick-wt=36): 311 [] -linord219039673up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,B),B)),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),zero_zero(A))). % 8.10/8.07 ** KEPT (pick-wt=36): 312 [] -linord219039673up_add(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,B),B)),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),zero_zero(A))). % 8.10/8.07 ** KEPT (pick-wt=50): 313 [] -ordere216010020id_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(A,A,plus_plus(A,B),C))). % 8.10/8.07 ** KEPT (pick-wt=46): 314 [] -ordere216010020id_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|hAPP(A,A,plus_plus(A,B),C)!=zero_zero(A)|ti(A,B)=zero_zero(A). % 8.10/8.07 ** KEPT (pick-wt=46): 315 [] -ordere216010020id_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|hAPP(A,A,plus_plus(A,B),C)!=zero_zero(A)|ti(A,C)=zero_zero(A). % 8.10/8.07 ** KEPT (pick-wt=52): 316 [] -ordere216010020id_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|hAPP(A,A,plus_plus(A,B),C)=zero_zero(A)|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A). % 8.10/8.07 ** KEPT (pick-wt=48): 317 [] -ordere216010020id_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),hAPP(A,A,plus_plus(A,B),D))). % 8.10/8.07 ** KEPT (pick-wt=48): 318 [] -ordere216010020id_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),hAPP(A,A,plus_plus(A,D),B))). % 8.10/8.07 ** KEPT (pick-wt=50): 319 [] -ordere216010020id_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),zero_zero(A)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,B),C)),zero_zero(A))). % 8.10/8.07 ** KEPT (pick-wt=53): 320 [] -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_e_q(A),D),E))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),D)),hAPP(A,A,plus_plus(A,C),E))). % 8.10/8.07 ** KEPT (pick-wt=53): 321 [] -ordere223160158up_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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,plus_plus(A,B),D)),hAPP(A,A,plus_plus(A,C),E))). % 8.10/8.07 ** KEPT (pick-wt=17): 322 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),one_one(A)),zero_zero(A))). % 8.10/8.07 ** KEPT (pick-wt=17): 323 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),one_one(A))). % 8.10/8.07 ** KEPT (pick-wt=38): 324 [] -number(A)| -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),number_number_of(A,C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,C)),number_number_of(A,B))). % 8.10/8.07 ** KEPT (pick-wt=38): 325 [] -number(A)| -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),number_number_of(A,B)),number_number_of(A,C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),number_number_of(A,C)),number_number_of(A,B))). % 8.10/8.07 ** KEPT (pick-wt=36): 326 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),C))). % 8.10/8.07 ** KEPT (pick-wt=54): 327 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,B),D)),hAPP(nat,A,power_power(A,C),D))). % 8.10/8.07 ** KEPT (pick-wt=36): 328 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),one_one(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),one_one(A)),hAPP(nat,A,power_power(A,B),C))). % 8.10/8.07 ** KEPT (pick-wt=21): 329 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))). % 8.10/8.07 Following clause subsumed by 329 during input processing: 0 [] -linordered_semidom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))). % 8.10/8.07 ** KEPT (pick-wt=30): 330 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),hAPP(int,int,bit1,A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),A)). % 8.10/8.07 ** KEPT (pick-wt=30): 331 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),hAPP(int,int,bit1,A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),A)). % 8.10/8.07 ** KEPT (pick-wt=34): 332 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,A)),hAPP(int,int,bit1,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 ** KEPT (pick-wt=34): 333 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,A)),hAPP(int,int,bit1,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 Following clause subsumed by 332 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,A)),hAPP(int,int,bit1,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 Following clause subsumed by 333 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,A)),hAPP(int,int,bit1,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 ** KEPT (pick-wt=30): 334 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),hAPP(int,int,bit0,A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),A)). % 8.10/8.07 ** KEPT (pick-wt=30): 335 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),hAPP(int,int,bit0,A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),A)). % 8.10/8.07 ** KEPT (pick-wt=30): 336 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,A)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)). % 8.10/8.07 ** KEPT (pick-wt=30): 337 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit0,A)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)). % 8.10/8.07 ** KEPT (pick-wt=48): 338 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(int,int,plus_plus(int,A),B))). % 8.10/8.07 ** KEPT (pick-wt=51): 339 [] -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_e_q(int),C),D))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,A),C)),hAPP(int,int,plus_plus(int,B),D))). % 8.10/8.07 ** KEPT (pick-wt=32): 340 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,B,A))|hBOOL(hAPP(int,bool,B,hAPP(nat,int,semiring_1_of_nat(int),$f6(B)))). % 8.10/8.07 ** KEPT (pick-wt=26): 341 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),$f7(A)))| -hBOOL(hAPP(int,bool,A,hAPP(nat,int,semiring_1_of_nat(int),B))). % 8.10/8.07 ** KEPT (pick-wt=18): 342 [] hBOOL(hAPP(int,bool,A,$f7(A)))| -hBOOL(hAPP(int,bool,A,hAPP(nat,int,semiring_1_of_nat(int),B))). % 8.10/8.07 ** KEPT (pick-wt=18): 343 [] -hBOOL(hAPP(int,bool,A,$f8(A)))|hBOOL(hAPP(int,bool,A,hAPP(nat,int,semiring_1_of_nat(int),B))). % 8.10/8.07 ** KEPT (pick-wt=32): 344 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|hBOOL(hAPP(int,bool,B,A))| -hBOOL(hAPP(int,bool,B,hAPP(nat,int,semiring_1_of_nat(int),$f9(B)))). % 8.10/8.07 ** KEPT (pick-wt=34): 345 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),hAPP(nat,int,power_power(int,A),B))). % 8.10/8.07 ** KEPT (pick-wt=29): 347 [copy,346,flip.2] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))|hAPP(int,int,plus_plus(int,A),hAPP(nat,int,semiring_1_of_nat(int),$f10(A,B)))=B. % 8.10/8.07 ** KEPT (pick-wt=27): 348 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))|B!=hAPP(int,int,plus_plus(int,A),hAPP(nat,int,semiring_1_of_nat(int),C)). % 8.10/8.07 ** KEPT (pick-wt=33): 349 [] -number_semiring(A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),B))|hAPP(A,A,plus_plus(A,one_one(A)),number_number_of(A,B))=number_number_of(A,hAPP(int,int,succ,B)). % 8.10/8.07 ** KEPT (pick-wt=33): 350 [] -number_semiring(A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),B))|hAPP(A,A,plus_plus(A,number_number_of(A,B)),one_one(A))=number_number_of(A,hAPP(int,int,succ,B)). % 8.10/8.07 ** KEPT (pick-wt=50): 351 [] -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_e_q(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,plus_plus(A,B),C))). % 8.10/8.07 ** KEPT (pick-wt=50): 352 [] -ordere216010020id_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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,plus_plus(A,B),C))). % 8.10/8.07 ** KEPT (pick-wt=48): 353 [] -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_e_q(A),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,plus_plus(A,B),D))). % 8.10/8.07 ** KEPT (pick-wt=48): 354 [] -ordere216010020id_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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,plus_plus(A,B),D))). % 8.10/8.07 ** KEPT (pick-wt=50): 355 [] -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_e_q(A),C),zero_zero(A)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,plus_plus(A,B),C)),zero_zero(A))). % 8.10/8.07 ** KEPT (pick-wt=50): 356 [] -ordere216010020id_add(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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,plus_plus(A,B),C)),zero_zero(A))). % 8.10/8.07 ** KEPT (pick-wt=54): 357 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),C)),hAPP(nat,A,power_power(A,D),C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)). % 8.10/8.07 ** KEPT (pick-wt=19): 358 [] zero_zero(nat)!=number_number_of(nat,A)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)). % 8.10/8.07 ** KEPT (pick-wt=19): 359 [] zero_zero(nat)=number_number_of(nat,A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)). % 8.10/8.07 ** KEPT (pick-wt=19): 360 [] number_number_of(nat,A)!=zero_zero(nat)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)). % 8.10/8.07 ** KEPT (pick-wt=19): 361 [] number_number_of(nat,A)=zero_zero(nat)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)). % 8.10/8.07 ** KEPT (pick-wt=30): 362 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),A)). % 8.10/8.07 ** KEPT (pick-wt=30): 363 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,A)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),A)). % 8.10/8.07 ** KEPT (pick-wt=30): 364 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,A)),pls))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). % 8.10/8.07 ** KEPT (pick-wt=30): 365 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,A)),pls))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). % 8.10/8.07 ** KEPT (pick-wt=34): 366 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,A)),hAPP(int,int,bit1,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 ** KEPT (pick-wt=34): 367 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,A)),hAPP(int,int,bit1,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 Following clause subsumed by 366 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,A)),hAPP(int,int,bit1,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 Following clause subsumed by 367 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,A)),hAPP(int,int,bit1,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 ** KEPT (pick-wt=34): 368 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,A)),hAPP(int,int,bit0,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.10/8.07 ** KEPT (pick-wt=34): 369 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,A)),hAPP(int,int,bit0,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.10/8.07 Following clause subsumed by 368 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,A)),hAPP(int,int,bit0,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.10/8.07 Following clause subsumed by 369 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,bit1,A)),hAPP(int,int,bit0,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.10/8.07 ** KEPT (pick-wt=28): 370 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). % 8.10/8.07 ** KEPT (pick-wt=28): 371 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),one_one(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). % 8.10/8.07 ** KEPT (pick-wt=23): 372 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),A)),zero_zero(int)))|A=zero_zero(nat). % 8.10/8.07 ** KEPT (pick-wt=23): 373 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(nat,int,semiring_1_of_nat(int),A)),zero_zero(int)))|A!=zero_zero(nat). % 8.10/8.07 ** KEPT (pick-wt=33): 374 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,plus_plus(int,B),one_one(int))))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 ** KEPT (pick-wt=33): 375 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,plus_plus(int,B),one_one(int))))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 ** KEPT (pick-wt=33): 376 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,A),one_one(int))),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.10/8.07 ** KEPT (pick-wt=33): 377 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),hAPP(int,int,plus_plus(int,A),one_one(int))),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). % 8.10/8.07 Following clause subsumed by 377 during input processing: 0 [] -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_e_q(int),hAPP(int,int,plus_plus(int,A),one_one(int))),B)). % 8.10/8.07 ** KEPT (pick-wt=66): 378 [] -linordered_semidom(A)|hAPP(nat,A,power_power(A,B),C)!=hAPP(nat,A,power_power(A,D),C)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),D))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C))|ti(A,B)=ti(A,D). % 8.10/8.07 ** KEPT (pick-wt=49): 379 [] -number_semiring(A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),B))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),pls),C))|hAPP(A,A,plus_plus(A,number_number_of(A,B)),number_number_of(A,C))=number_number_of(A,hAPP(int,int,plus_plus(int,B),C)). % 8.10/8.07 ** KEPT (pick-wt=35): 380 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),A))). % 8.10/8.07 ** KEPT (pick-wt=20): 381 [] -number_ring(A)|number_number_of(A,hAPP(int,int,succ,B))=hAPP(A,A,plus_plus(A,one_one(A)),number_number_of(A,B)). % 8.10/8.07 ** KEPT (pick-wt=68): 382 [] -linordered_semidom(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_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),D)),hAPP(nat,A,power_power(A,C),D))). % 8.10/8.07 ** KEPT (pick-wt=32): 383 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). % 8.10/8.07 ** KEPT (pick-wt=74): 384 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C)). % 8.10/8.07 ** KEPT (pick-wt=72): 385 [] -linordered_semidom(A)|hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))!=hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|ti(A,B)=ti(A,C). % 8.10/8.07 ** KEPT (pick-wt=30): 386 [] -number_ring(A)| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,B)))|hAPP(nat,A,semiring_1_of_nat(A),number_number_of(nat,B))=number_number_of(A,B). % 8.10/8.07 ** KEPT (pick-wt=29): 387 [] -number_ring(A)|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,B)))|hAPP(nat,A,semiring_1_of_nat(A),number_number_of(nat,B))=zero_zero(A). % 8.10/8.07 Following clause subsumed by 357 during input processing: 0 [] -linordered_semidom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)). % 8.10/8.07 ** KEPT (pick-wt=54): 388 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),zero_zero(A)),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))). % 8.10/8.07 ** KEPT (pick-wt=60): 389 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A)))|ti(A,B)=zero_zero(A). % 8.10/8.07 ** KEPT (pick-wt=60): 390 [] -linordered_idom(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A)))|ti(A,C)=zero_zero(A). % 8.10/8.07 ** KEPT (pick-wt=66): 391 [] -linordered_idom(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(A,A,plus_plus(A,hAPP(nat,A,power_power(A,B),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,power_power(A,C),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A)))|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A). % 8.10/8.07 ** KEPT (pick-wt=45): 392 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),number_number_of(int,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))|A=zero_zero(int)|A=one_one(int). % 8.10/8.07 ** KEPT (pick-wt=36): 393 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit0,A)))). % 8.10/8.07 ** KEPT (pick-wt=36): 394 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,A)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),number_number_of(int,hAPP(int,int,bit1,A)))). % 8.10/8.07 ** KEPT (pick-wt=23): 396 [copy,395,flip.2] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|hAPP(nat,int,semiring_1_of_nat(int),$f11(A))=A. % 8.10/8.07 ** KEPT (pick-wt=23): 398 [copy,397,flip.2] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|hAPP(nat,int,semiring_1_of_nat(int),$f12(A))=A. % 8.10/8.07 ** KEPT (pick-wt=18): 399 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),zero_zero(nat)))|A=zero_zero(nat). % 8.10/8.07 ** KEPT (pick-wt=18): 400 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),zero_zero(nat)))|A!=zero_zero(nat). % 8.10/8.07 ** KEPT (pick-wt=26): 401 [] -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_e_q(nat),A),B)). % 8.10/8.07 ** KEPT (pick-wt=16): 402 [] A!=B|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B)). % 8.10/8.07 ** KEPT (pick-wt=29): 403 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))|A=B|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). % 8.10/8.07 Following clause subsumed by 401 during input processing: 0 [] -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_e_q(nat),A),B)). % 8.10/8.07 Following clause subsumed by 403 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|A=B. % 8.10/8.07 Following clause subsumed by 401 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). % 8.10/8.07 Following clause subsumed by 402 during input processing: 0 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))|A!=B. % 8.10/8.07 Following clause subsumed by 401 during input processing: 0 [] -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_e_q(nat),A),B)). % 8.10/8.07 Following clause subsumed by 153 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B))|A!=B. % 8.10/8.07 Following clause subsumed by 403 during input processing: 0 [] 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_e_q(nat),A),B))|A=B. % 8.10/8.07 Following clause subsumed by 402 during input processing: 0 [] A!=B|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B)). % 8.10/8.07 ** KEPT (pick-wt=39): 404 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),C)). % 8.10/8.07 ** KEPT (pick-wt=29): 405 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),A))|A=B. % 8.10/8.07 ** KEPT (pick-wt=29): 406 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),A),B))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B))|A=B. % 8.10/8.07 ** KEPT (pick-wt=26): 407 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),A),B))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). % 8.10/8.07 ** KEPT (pick-wt=16): 408 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),A),B))|A!=B. % 8.10/8.07 Following clause subsumed by 407 during input processing: 0 [] -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_e_q(real),A),B)). % 8.10/8.07 ** KEPT (pick-wt=16): 409 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B))|A!=B. % 8.10/8.07 Following clause subsumed by 406 during input processing: 0 [] 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_e_q(real),A),B))|A=B. % 8.10/8.07 ** KEPT (pick-wt=24): 411 [copy,410,flip.2] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))|hAPP(nat,nat,plus_plus(nat,A),$f13(A,B))=B. % 8.10/8.07 ** KEPT (pick-wt=22): 412 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))|B!=hAPP(nat,nat,plus_plus(nat,A),C). % 8.10/8.07 ** KEPT (pick-wt=38): 413 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,A),B)),hAPP(nat,nat,plus_plus(nat,A),C)))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C)). % 8.10/8.07 ** KEPT (pick-wt=38): 414 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,A),B)),hAPP(nat,nat,plus_plus(nat,A),C)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C)). % 8.10/8.07 ** KEPT (pick-wt=32): 415 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),hAPP(nat,nat,plus_plus(nat,B),C))). % 8.10/8.07 ** KEPT (pick-wt=32): 416 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),hAPP(nat,nat,plus_plus(nat,C),B))). % 8.10/8.07 ** KEPT (pick-wt=38): 417 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,A),C)),hAPP(nat,nat,plus_plus(nat,B),C))). % 8.10/8.07 ** KEPT (pick-wt=51): 418 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),C),D))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,A),C)),hAPP(nat,nat,plus_plus(nat,B),D))). % 8.10/8.07 ** KEPT (pick-wt=32): 419 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,A),B)),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C)). % 8.10/8.07 ** KEPT (pick-wt=32): 420 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,A),B)),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),C)). % 8.10/8.07 Following clause subsumed by 420 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,A),B)),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),C)). % 8.10/8.07 Following clause subsumed by 419 during input processing: 0 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,A),B)),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C)). % 8.10/8.07 ** KEPT (pick-wt=38): 421 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),A),B))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),hAPP(real,real,plus_plus(real,C),A)),hAPP(real,real,plus_plus(real,C),B))). % 8.10/8.07 ** KEPT (pick-wt=36): 422 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(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_e_q(nat),A),B)). % 8.10/8.07 ** KEPT (pick-wt=36): 423 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(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_e_q(nat),A),B)). % 8.10/8.07 Following clause subsumed by 422 during input processing: 0 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(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_e_q(nat),A),B)). % 8.10/8.07 Following clause subsumed by 423 during input processing: 0 [] hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(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_e_q(nat),A),B)). % 8.10/8.07 ** KEPT (pick-wt=43): 424 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,A)),number_number_of(nat,B)))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)). % 8.10/8.07 ** KEPT (pick-wt=30): 425 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,A)),number_number_of(nat,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B)). % 8.10/8.07 ** KEPT (pick-wt=30): 426 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),number_number_of(nat,A)),number_number_of(nat,B)))| -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),pls)). % 8.10/8.07 ** KEPT (pick-wt=28): 427 [] hBOOL(hAPP(nat,bool,A,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,A,B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f14(B,A)),B)). % 8.10/8.07 ** KEPT (pick-wt=34): 428 [] hBOOL(hAPP(nat,bool,A,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,A,B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),C),$f14(B,A)))| -hBOOL(hAPP(nat,bool,A,C)). % 8.10/8.07 ** KEPT (pick-wt=28): 429 [] hBOOL(hAPP(nat,bool,A,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,A,B))|hBOOL(hAPP(nat,bool,A,hAPP(nat,nat,plus_plus(nat,$f14(B,A)),one_one(nat)))). % 8.10/8.07 ** KEPT (pick-wt=23): 431 [copy,430,flip.2] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),zero_zero(int)),A))|hAPP(nat,int,semiring_1_of_nat(int),$f15(A))=A. % 8.10/8.07 ** KEPT (pick-wt=60): 432 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,A,$f17(B,C,A))),hAPP(nat,nat,A,$f16(B,C,A))))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,plus_plus(nat,hAPP(nat,nat,A,B)),C)),hAPP(nat,nat,A,hAPP(nat,nat,plus_plus(nat,B),C)))). % 8.10/8.07 ** KEPT (pick-wt=39): 433 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),A),B))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),B),C))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),A),C)). % 8.10/8.07 ** KEPT (pick-wt=29): 434 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),A),B))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_e_q(real),B),A))|A=B. % 8.10/8.08 ** KEPT (pick-wt=41): 435 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))| -hBOOL(hAPP(int,bool,C,A))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),$f18(C,A,B)))|hBOOL(hAPP(int,bool,C,B)). % 8.10/8.08 ** KEPT (pick-wt=34): 436 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))| -hBOOL(hAPP(int,bool,C,A))|hBOOL(hAPP(int,bool,C,$f18(C,A,B)))|hBOOL(hAPP(int,bool,C,B)). % 8.10/8.08 ** KEPT (pick-wt=41): 437 [] -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_e_q(int),A),B))| -hBOOL(hAPP(int,bool,C,A))| -hBOOL(hAPP(int,bool,C,hAPP(int,int,plus_plus(int,$f18(C,A,B)),one_one(int))))|hBOOL(hAPP(int,bool,C,B)). % 8.10/8.08 ** KEPT (pick-wt=28): 438 [] hBOOL(hAPP(nat,bool,A,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,A,B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),$f19(B,A)),B)). % 8.10/8.08 ** KEPT (pick-wt=34): 439 [] hBOOL(hAPP(nat,bool,A,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,A,B))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),$f19(B,A)))| -hBOOL(hAPP(nat,bool,A,C)). % 8.10/8.08 ** KEPT (pick-wt=21): 440 [] hBOOL(hAPP(nat,bool,A,zero_zero(nat)))| -hBOOL(hAPP(nat,bool,A,B))|hBOOL(hAPP(nat,bool,A,$f19(B,A))). % 8.10/8.08 ** KEPT (pick-wt=53): 441 [] hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),$f21(A,B,C)),$f20(A,B,C)))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),A),B))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,C,A)),hAPP(nat,nat,C,B))). % 8.10/8.08 ** KEPT (pick-wt=61): 442 [] -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,A,$f21(B,C,A))),hAPP(nat,nat,A,$f20(B,C,A))))| -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),B),C))|hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_e_q(nat),hAPP(nat,nat,A,B)),hAPP(nat,nat,A,C))). % 8.10/8.08 ** KEPT (pick-wt=15): 443 [] -preorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),B)). % 8.10/8.08 ** KEPT (pick-wt=28): 444 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B)). % 8.10/8.08 ** KEPT (pick-wt=44): 445 [] -ord(A)| -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_e_q(fun(B,A)),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(B,A,C,E)),hAPP(B,A,D,E))). % 8.10/8.08 ** KEPT (pick-wt=41): 446 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),C)). % 8.10/8.08 ** KEPT (pick-wt=35): 447 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B))|ti(A,C)=ti(A,B). % 8.10/8.08 ** KEPT (pick-wt=41): 448 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),D)). % 8.10/8.08 Following clause subsumed by 447 during input processing: 0 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B))|ti(A,B)=ti(A,C). % 8.10/8.08 ** KEPT (pick-wt=35): 449 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|ti(A,B)!=ti(A,D)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),C)). % 8.10/8.08 ** KEPT (pick-wt=31): 450 [] -ord(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|C!=D|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),D)). % 8.10/8.08 ** KEPT (pick-wt=35): 451 [] -order(A)|ti(A,B)!=ti(A,C)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),D),B)). % 8.10/8.08 ** KEPT (pick-wt=31): 452 [] -ord(A)|B!=C| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),D)). % 8.10/8.08 Following clause subsumed by 447 during input processing: 0 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B))|ti(A,C)=ti(A,B). % 8.10/8.08 ** KEPT (pick-wt=35): 453 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B))|ti(A,C)!=ti(A,B). % 8.10/8.08 Following clause subsumed by 445 during input processing: 0 [] -ord(A)| -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_e_q(fun(B,A)),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(B,A,C,E)),hAPP(B,A,D,E))). % 8.10/8.08 ** KEPT (pick-wt=18): 454 [] -preorder(A)|B!=C|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C)). % 8.10/8.08 ** KEPT (pick-wt=22): 455 [] -order(A)|ti(A,B)!=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C)). % 8.10/8.08 ** KEPT (pick-wt=22): 456 [] -order(A)|ti(A,B)!=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B)). % 8.10/8.08 Following clause subsumed by 447 during input processing: 0 [] -order(A)|ti(A,B)=ti(A,C)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B)). % 8.10/8.08 Following clause subsumed by 444 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B)). % 8.10/8.08 Following clause subsumed by 445 during input processing: 0 [] -ord(A)| -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_e_q(fun(B,A)),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(B,A,C,E)),hAPP(B,A,D,E))). % 8.10/8.08 ** KEPT (pick-wt=52): 457 [] -ord(A)|hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_e_q(fun(B,A)),C),D))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(B,A,C,$f22(B,A,C,D))),hAPP(B,A,D,$f22(B,A,C,D)))). % 8.10/8.08 ** KEPT (pick-wt=35): 458 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)). % 8.10/8.08 ** KEPT (pick-wt=28): 459 [] -preorder(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)). % 8.10/8.08 ** KEPT (pick-wt=41): 460 [] -order(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),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)). % 8.10/8.08 ** KEPT (pick-wt=41): 461 [] -preorder(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),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)). % 8.10/8.08 ** KEPT (pick-wt=35): 462 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)!=ti(A,D)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)). % 8.10/8.08 ** KEPT (pick-wt=31): 463 [] -ord(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|C!=D|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)). % 8.10/8.08 ** KEPT (pick-wt=35): 464 [] -order(A)|ti(A,B)!=ti(A,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(A),D),B)). % 8.10/8.08 ** KEPT (pick-wt=31): 465 [] -ord(A)|B!=C| -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),D)). % 8.10/8.08 ** KEPT (pick-wt=28): 466 [] -order(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)). % 8.10/8.08 Following clause subsumed by 459 during input processing: 0 [] -preorder(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)). % 8.10/8.08 Following clause subsumed by 459 during input processing: 0 [] -preorder(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))|hBOOL(D). % 8.10/8.08 ** KEPT (pick-wt=22): 467 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,C)!=ti(A,B). % 8.10/8.08 ** KEPT (pick-wt=22): 468 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)!=ti(A,C). % 8.10/8.08 Following clause subsumed by 459 during input processing: 0 [] -preorder(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)). % 8.10/8.08 Following clause subsumed by 459 during input processing: 0 [] -preorder(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)). % 8.10/8.08 Following clause subsumed by 468 during input processing: 0 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)!=ti(A,C). % 8.10/8.08 Following clause subsumed by 458 during input processing: 0 [] -linorder(A)|ti(A,B)=ti(A,C)|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)). % 8.10/8.08 Following clause subsumed by 458 during input processing: 0 [] -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). % 8.10/8.08 ** KEPT (pick-wt=35): 469 [] -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). % 8.10/8.08 Following clause subsumed by 458 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)). % 8.10/8.08 Following clause subsumed by 458 during input processing: 0 [] -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). % 8.10/8.08 ** KEPT (pick-wt=28): 470 [] -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)). % 8.10/8.08 ** KEPT (pick-wt=22): 471 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)!=ti(A,C). % 8.10/8.08 Following clause subsumed by 458 during input processing: 0 [] -linorder(A)|ti(A,B)=ti(A,C)|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)). % 8.10/8.08 Following clause subsumed by 471 during input processing: 0 [] -linorder(A)|ti(A,B)!=ti(A,C)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)). % 8.10/8.08 ** KEPT (pick-wt=22): 472 [] -linorder(A)|ti(A,B)!=ti(A,C)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)). % 8.10/8.08 ** KEPT (pick-wt=15): 473 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),B)). % 8.10/8.08 ** KEPT (pick-wt=28): 474 [] -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_e_q(A),C),B)). % 8.10/8.08 ** KEPT (pick-wt=28): 475 [] -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_e_q(A),C),B)). % 8.10/8.08 Following clause subsumed by 474 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)). % 8.10/8.08 Following clause subsumed by 475 during input processing: 0 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)). % 8.10/8.08 Following clause subsumed by 474 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)). % 8.10/8.08 ** KEPT (pick-wt=28): 476 [] -order(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_e_q(A),B),C)). % 8.10/8.08 Following clause subsumed by 468 during input processing: 0 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)!=ti(A,C). % 8.10/8.08 ** KEPT (pick-wt=35): 477 [] -order(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_e_q(A),B),C))|ti(A,B)=ti(A,C). % 8.10/8.08 ** KEPT (pick-wt=28): 478 [] -preorder(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_e_q(A),B),C)). % 8.10/8.08 ** KEPT (pick-wt=28): 479 [] -preorder(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_e_q(A),C),B)). % 8.10/8.08 ** KEPT (pick-wt=41): 480 [] -preorder(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_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B)). % 8.10/8.08 Following clause subsumed by 477 during input processing: 0 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)=ti(A,C). % 8.10/8.08 Following clause subsumed by 476 during input processing: 0 [] -order(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)). % 8.10/8.08 Following clause subsumed by 455 during input processing: 0 [] -order(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|ti(A,B)!=ti(A,C). % 8.10/8.08 Following clause subsumed by 474 during input processing: 0 [] -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_e_q(A),C),B)). % 8.10/8.08 Following clause subsumed by 474 during input processing: 0 [] -linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)). % 8.10/8.08 ** KEPT (pick-wt=35): 481 [] -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_e_q(A),B),C))|ti(A,B)=ti(A,C). % 8.10/8.08 ** KEPT (pick-wt=35): 482 [] -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_e_q(A),B),C))|ti(A,B)!=ti(A,C). % 8.10/8.08 Following clause subsumed by 477 during input processing: 0 [] -order(A)|ti(A,B)=ti(A,C)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)). % 8.10/8.08 ** KEPT (pick-wt=35): 483 [] -order(A)|ti(A,B)=ti(A,C)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)). % 8.10/8.08 Following clause subsumed by 475 during input processing: 0 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)). % 8.10/8.08 Following clause subsumed by 478 during input processing: 0 [] -preorder(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_e_q(A),B),C)). % 8.10/8.08 Following clause subsumed by 481 during input processing: 0 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)=ti(A,C). % 8.10/8.08 Following clause subsumed by 471 during input processing: 0 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)!=ti(A,C). % 8.10/8.08 Following clause subsumed by 477 during input processing: 0 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|ti(A,B)=ti(A,C). % 8.10/8.08 Following clause subsumed by 477 during input processing: 0 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|ti(A,B)=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)). % 8.10/8.08 Following clause subsumed by 483 during input processing: 0 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))|ti(A,C)=ti(A,B)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)). % 8.10/8.08 ** KEPT (pick-wt=41): 484 [] -preorder(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_e_q(A),C),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)). % 8.10/8.08 ** KEPT (pick-wt=41): 485 [] -order(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_e_q(A),D),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)). % 8.10/8.08 ** KEPT (pick-wt=41): 486 [] -preorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -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),D)). % 8.10/8.08 ** KEPT (pick-wt=41): 487 [] -order(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)). % 8.10/8.08 ** KEPT (pick-wt=44): 488 [] -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)),$f23(B,A))). % 8.10/8.08 ** KEPT (pick-wt=43): 489 [] -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),$f23(B,A)),A)). % 8.10/8.08 ** KEPT (pick-wt=43): 490 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),$f23(B,A)),B)). % 8.10/8.08 ** KEPT (pick-wt=31): 491 [] -dense_linorder(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),$f24(A,B,C)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B)). % 8.10/8.08 ** KEPT (pick-wt=31): 492 [] -dense_linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),$f24(A,B,C)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B)). % 8.10/8.08 ** KEPT (pick-wt=44): 493 [] -ord(A)| -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less(fun(B,A)),C),D))|hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_e_q(fun(B,A)),C),D)). % 8.10/8.08 ** KEPT (pick-wt=44): 494 [] -ord(A)| -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less(fun(B,A)),C),D))| -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_e_q(fun(B,A)),D),C)). % 8.10/8.08 ** KEPT (pick-wt=65): 495 [] -ord(A)|hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less(fun(B,A)),C),D))| -hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_e_q(fun(B,A)),C),D))|hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_e_q(fun(B,A)),D),C)). % 8.10/8.08 ** KEPT (pick-wt=52): 496 [] -ord(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(B,A,C,$f25(B,A,C,D))),hAPP(B,A,D,$f25(B,A,C,D))))|hBOOL(hAPP(fun(B,A),bool,hAPP(fun(B,A),fun(fun(B,A),bool),ord_less_e_q(fun(B,A)),C),D)). % 8.10/8.08 ** KEPT (pick-wt=30): 497 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),$f26(A,B)),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B)). % 8.10/8.08 ** KEPT (pick-wt=45): 498 [] -dense_linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),$f27(A,D,B,C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D)). % 8.10/8.08 ** KEPT (pick-wt=45): 499 [] -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),$f27(A,D,B,C)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D)). % 8.10/8.08 ** KEPT (pick-wt=45): 500 [] -dense_linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),$f27(A,D,B,C)),D))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D)). % 8.10/8.08 ** KEPT (pick-wt=76): 501 [] -order(A)| -order(B)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D))| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less_e_q(B),E),hAPP(A,B,F,C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),$f28(B,A,E,F,C,D)),$f29(B,A,E,F,C,D)))|hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),E),hAPP(A,B,F,D))). % 8.10/8.08 ** KEPT (pick-wt=84): 502 [] -order(A)| -order(B)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D))| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less_e_q(B),E),hAPP(A,B,F,C)))| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),hAPP(A,B,F,$f28(B,A,E,F,C,D))),hAPP(A,B,F,$f29(B,A,E,F,C,D))))|hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),E),hAPP(A,B,F,D))). % 8.10/8.08 ** KEPT (pick-wt=30): 503 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),$f30(A,C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C)). % 8.10/8.08 ** KEPT (pick-wt=30): 504 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),$f31(A,B)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),B),C)). % 8.10/8.08 ** KEPT (pick-wt=76): 505 [] -order(A)| -order(B)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D))| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),E),hAPP(A,B,F,C)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),$f32(B,A,E,F,C,D)),$f33(B,A,E,F,C,D)))|hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),E),hAPP(A,B,F,D))). % 8.10/8.08 ** KEPT (pick-wt=84): 506 [] -order(A)| -order(B)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),D))| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),E),hAPP(A,B,F,C)))| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less_e_q(B),hAPP(A,B,F,$f32(B,A,E,F,C,D))),hAPP(A,B,F,$f33(B,A,E,F,C,D))))|hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),E),hAPP(A,B,F,D))). % 8.10/8.08 ** KEPT (pick-wt=76): 507 [] -order(A)| -order(B)| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),C),D))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(B,A,E,D)),F))|hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),$f35(B,A,E,F,C,D)),$f34(B,A,E,F,C,D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(B,A,E,C)),F)). % 8.10/8.08 ** KEPT (pick-wt=84): 508 [] -order(A)| -order(B)| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),C),D))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(B,A,E,D)),F))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(B,A,E,$f35(B,A,E,F,C,D))),hAPP(B,A,E,$f34(B,A,E,F,C,D))))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(B,A,E,C)),F)). % 8.10/8.08 ** KEPT (pick-wt=30): 509 [] -linorder(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),$f36(A,C)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),C),B)). % 8.10/8.08 ** KEPT (pick-wt=76): 510 [] -order(A)| -ord(B)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(B,A,C,D)),E))| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),F),D))|hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),$f37(B,A,F,C,D,E)),$f38(B,A,F,C,D,E)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(B,A,C,F)),E)). % 8.10/8.08 ** KEPT (pick-wt=84): 511 [] -order(A)| -ord(B)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(B,A,C,D)),E))| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),F),D))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(B,A,C,$f37(B,A,F,C,D,E))),hAPP(B,A,C,$f38(B,A,F,C,D,E))))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(B,A,C,F)),E)). % 8.10/8.08 ** KEPT (pick-wt=76): 512 [] -order(A)| -order(B)| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less_e_q(B),C),D))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(B,A,E,D)),F))|hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less_e_q(B),$f40(B,A,E,F,C,D)),$f39(B,A,E,F,C,D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(B,A,E,C)),F)). % 8.10/8.08 ** KEPT (pick-wt=84): 513 [] -order(A)| -order(B)| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less_e_q(B),C),D))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(B,A,E,D)),F))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(B,A,E,$f40(B,A,E,F,C,D))),hAPP(B,A,E,$f39(B,A,E,F,C,D))))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(B,A,E,C)),F)). % 8.10/8.08 ** KEPT (pick-wt=76): 514 [] -order(A)| -order(B)| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),C),hAPP(A,B,D,E)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),E),F))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),$f42(B,A,F,C,D,E)),$f41(B,A,F,C,D,E)))|hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),C),hAPP(A,B,D,F))). % 8.10/8.08 ** KEPT (pick-wt=84): 515 [] -order(A)| -order(B)| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),C),hAPP(A,B,D,E)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),E),F))| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less_e_q(B),hAPP(A,B,D,$f42(B,A,F,C,D,E))),hAPP(A,B,D,$f41(B,A,F,C,D,E))))|hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),C),hAPP(A,B,D,F))). % 8.10/8.08 ** KEPT (pick-wt=76): 516 [] -order(A)| -order(B)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(B,A,C,D)),E))| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less_e_q(B),F),D))|hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less_e_q(B),$f43(B,A,F,C,D,E)),$f44(B,A,F,C,D,E)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(B,A,C,F)),E)). % 8.10/8.08 ** KEPT (pick-wt=84): 517 [] -order(A)| -order(B)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(B,A,C,D)),E))| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less_e_q(B),F),D))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(A),hAPP(B,A,C,$f43(B,A,F,C,D,E))),hAPP(B,A,C,$f44(B,A,F,C,D,E))))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(B,A,C,F)),E)). % 8.10/8.08 ** KEPT (pick-wt=76): 518 [] -order(A)| -order(B)| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less_e_q(B),C),hAPP(A,B,D,E)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),E),F))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),$f46(B,A,F,C,D,E)),$f45(B,A,F,C,D,E)))|hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),C),hAPP(A,B,D,F))). % 8.10/8.08 ** KEPT (pick-wt=84): 519 [] -order(A)| -order(B)| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less_e_q(B),C),hAPP(A,B,D,E)))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),E),F))| -hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),hAPP(A,B,D,$f46(B,A,F,C,D,E))),hAPP(A,B,D,$f45(B,A,F,C,D,E))))|hBOOL(hAPP(B,bool,hAPP(B,fun(B,bool),ord_less(B),C),hAPP(A,B,D,F))). % 8.10/8.08 ** KEPT (pick-wt=64): 520 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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_e_q(A),C),D)). % 8.10/8.08 ** KEPT (pick-wt=64): 521 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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_e_q(A),B),D)). % 8.10/8.08 ** KEPT (pick-wt=64): 522 [] -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_e_q(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)). % 8.10/8.08 ** KEPT (pick-wt=64): 523 [] -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_e_q(A),zero_zero(A)),B))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)). % 8.10/8.08 ** KEPT (pick-wt=64): 524 [] -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_e_q(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)). % 8.10/8.08 ** KEPT (pick-wt=64): 525 [] -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_e_q(A),zero_zero(A)),C))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)). % 8.10/8.08 ** KEPT (pick-wt=91): 526 [] -linord20386208strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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_e_q(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))). % 8.10/8.08 ** KEPT (pick-wt=91): 527 [] -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_e_q(A),D),E))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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))). % 8.10/8.08 ** KEPT (pick-wt=91): 528 [] -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_e_q(A),zero_zero(A)),B))| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_e_q(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))). % 8.10/8.08 ** KEPT (pick-wt=91): 529 [] -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_e_q(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))). % 8.10/8.08 ** KEPT (pick-wt=64): 530 [] -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_e_q(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_e_q(A),D),C)). % 8.10/8.08 ** KEPT (pick-wt=64): 531 [] -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_e_q(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_e_q(A),D),C)). % 8.10/8.08 ** KEPT (pick-wt=64): 532 [] -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_e_q(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_e_q(A),C),D)). % 8.10/8.08 ** KEPT (pick-wt=64): 533 [] -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_e_q(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_e_q(A),C),D)). % 8.10/8.08 ** KEPT (pick-wt=56): 534 [] -linord581940658strict(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(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))))|ti(A,B)!=zero_zero(A)|ti(A,C)!=zero_zero(A). % 8.10/8.08 ** KEPT (pick-wt=50): 535 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(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))))|ti(A,B)=zero_zero(A). % 8.10/8.08 ** KEPT (pick-wt=50): 536 [] -linord581940658strict(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(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))))|ti(A,C)=zero_zero(A). % 8.10/8.08 ** KEPT (pick-wt=44): 537 [] -linordered_ring(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(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))). % 8.10/8.08 ** KEPT (pick-wt=52): 538 [] -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),hAPP(nat,A,power_power(A,B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,power_power(A,B),C)))). % 8.10/8.08 ** KEPT (pick-wt=47): 539 [] -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)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,power_power(A,B),C)))). % 8.10/8.08 ** KEPT (pick-wt=32): 540 [] -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)),hAPP(real,real,sqrt,A))). % 8.10/8.08 ** KEPT (pick-wt=22): 541 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A))|hAPP(real,real,sqrt,A)!=zero_zero(real). % 8.10/8.08 ** KEPT (pick-wt=32): 542 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,A)),zero_zero(real)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). % 8.10/8.09 ** KEPT (pick-wt=32): 543 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,A)),zero_zero(real)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). % 8.10/8.09 ** KEPT (pick-wt=32): 544 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,A)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). % 8.10/8.09 Following clause subsumed by 540 during input processing: 0 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,A)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). % 8.10/8.09 ** KEPT (pick-wt=32): 545 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,A)),one_one(real)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))). % 8.10/8.09 ** KEPT (pick-wt=32): 546 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,A)),one_one(real)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))). % 8.10/8.09 ** KEPT (pick-wt=32): 547 [] -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,A)))|hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)). % 8.10/8.09 ** KEPT (pick-wt=32): 548 [] hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,A)))| -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)). % 8.10/8.09 ** KEPT (pick-wt=64): 549 [] -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))). % 8.10/8.09 ** KEPT (pick-wt=64): 550 [] -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))). % 8.10/8.09 ** KEPT (pick-wt=64): 551 [] -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))). % 8.10/8.09 ** KEPT (pick-wt=64): 552 [] -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))). % 8.10/8.09 ** KEPT (pick-wt=64): 553 [] -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))). % 8.10/8.09 ** KEPT (pick-wt=55): 554 [] -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))). % 8.10/8.09 ** KEPT (pick-wt=55): 555 [] -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))). % 8.10/8.09 ** KEPT (pick-wt=64): 556 [] -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_t % 8.10/8.09 Search stopped in tp_alloc by max_mem option. % 8.10/8.09 imes(A),B),D)))|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)). % 8.10/8.09 Following clause subsumed by 549 during input processing: 0 [] -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)). % 8.10/8.09 ** KEPT (pick-wt=55): 557 [] -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)). % 8.10/8.09 ** KEPT (pick-wt=6): 558 [] -preorder(A)|preorder(fun(B,A)). % 8.10/8.09 ** KEPT (pick-wt=6): 559 [] -order(A)|order(fun(B,A)). % 8.10/8.09 ** KEPT (pick-wt=6): 560 [] -ord(A)|ord(fun(B,A)). % 8.10/8.09 Following clause subsumed by 96 during input processing: 0 [copy,95,flip.1] hAPP(int,int,bit0,A)!=hAPP(int,int,bit1,B). % 8.10/8.09 Following clause subsumed by 95 during input processing: 0 [copy,96,flip.1] hAPP(int,int,bit1,A)!=hAPP(int,int,bit0,B). % 8.10/8.09 ** KEPT (pick-wt=17): 562 [copy,119,flip.1] zero_zero(int)!=hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),A)),A). % 8.10/8.09 141 back subsumes 36. % 8.10/8.09 142 back subsumes 37. % 8.10/8.09 194 back subsumes 30. % 8.10/8.09 % 8.10/8.09 Search stopped in tp_alloc by max_mem option. % 8.10/8.09 % 8.10/8.09 ============ end of search ============ % 8.10/8.09 % 8.10/8.09 -------------- statistics ------------- % 8.10/8.09 clauses given 0 % 8.10/8.09 clauses generated 13 % 8.10/8.09 clauses kept 553 % 8.10/8.09 clauses forward subsumed 105 % 8.10/8.09 clauses back subsumed 3 % 8.10/8.09 Kbytes malloced 11718 % 8.10/8.09 % 8.10/8.09 ----------- times (seconds) ----------- % 8.10/8.09 user CPU time 0.14 (0 hr, 0 min, 0 sec) % 8.10/8.09 system CPU time 0.00 (0 hr, 0 min, 0 sec) % 8.10/8.09 wall-clock time 8 (0 hr, 0 min, 8 sec) % 8.10/8.09 % 8.10/8.09 Process 22232 finished Wed Jul 27 09:51:03 2022 % 8.10/8.09 Otter interrupted % 8.10/8.09 PROOF NOT FOUND %------------------------------------------------------------------------------