0.11/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.13	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.34	% Computer   : n012.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 960
0.13/0.34	% WCLimit    : 120
0.13/0.34	% DateTime   : Thu Jul  2 06:38:36 EDT 2020
0.13/0.34	% CPUTime    : 
95.35/12.54	% SZS status Theorem
95.35/12.54	
108.47/14.26	% SZS output start Proof
108.47/14.26	Take the following subset of the input axioms:
117.53/15.58	  fof(arity_Int_Oint___Groups_Ocomm__monoid__add, axiom, comm_monoid_add(int)).
117.53/15.58	  fof(arity_Int_Oint___Rings_Oring__1__no__zero__divisors, axiom, ring_11004092258visors(int)).
117.53/15.58	  fof(arity_Int_Oint___Rings_Osemiring__1, axiom, semiring_1(int)).
117.53/15.58	  fof(arity_Nat_Onat___Rings_Ozero__neq__one, axiom, zero_neq_one(nat)).
117.53/15.58	  fof(conj_0, conjecture, 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)).
117.53/15.58	  fof(fact_0_n1pos, axiom, 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))))).
117.53/15.58	  fof(fact_114_less__zeroE, axiom, ![N]: ~hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), N), zero_zero(nat)))).
117.53/15.58	  fof(fact_116_less__not__refl, axiom, ![N]: ~hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), N), N))).
117.53/15.58	  fof(fact_117_not__add__less1, axiom, ![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))).
117.53/15.58	  fof(fact_118_not__add__less2, axiom, ![I_2, J_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))).
117.53/15.58	  fof(fact_119_number__of__is__id, axiom, ![K]: number_number_of(int, K)=K).
117.53/15.58	  fof(fact_120_nat__neq__iff, axiom, ![Na, Ma]: (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), ord_less(nat), Ma), Na))))).
117.53/15.58	  fof(fact_128_less__irrefl__nat, axiom, ![N]: ~hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), N), N))).
117.53/15.58	  fof(fact_129_less__not__refl2, axiom, ![N, M_1]: (N!=M_1 <= hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), N), M_1)))).
117.53/15.58	  fof(fact_130_less__not__refl3, axiom, ![T_3, S]: (S!=T_3 <= hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), S), T_3)))).
117.53/15.58	  fof(fact_137_nat__less__cases, axiom, ![Na, Ma, P_1]: (((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)))) <= (Ma=Na => 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)) <= hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), Ma), Na))))).
117.53/15.58	  fof(fact_139_gr__implies__not0, axiom, ![N, M_1]: (hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), M_1), N)) => zero_zero(nat)!=N)).
117.53/15.58	  fof(fact_141_less__nat__zero__code, axiom, ![N]: ~hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), N), zero_zero(nat)))).
117.53/15.58	  fof(fact_144_neq0__conv, axiom, ![Na]: (hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), Na)) <=> Na!=zero_zero(nat))).
117.53/15.58	  fof(fact_145_not__less0, axiom, ![N]: ~hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), N), zero_zero(nat)))).
117.53/15.58	  fof(fact_162_one__neq__zero, axiom, ![X_a]: (zero_neq_one(X_a) => one_one(X_a)!=zero_zero(X_a))).
117.53/15.58	  fof(fact_163_zero__neq__one, axiom, ![X_a]: (one_one(X_a)!=zero_zero(X_a) <= zero_neq_one(X_a))).
117.53/15.58	  fof(fact_170_of__nat__1, axiom, ![X_a]: (one_one(X_a)=hAPP(nat, X_a, semiring_1_of_nat(X_a), one_one(nat)) <= semiring_1(X_a))).
117.53/15.58	  fof(fact_176_not__one__less__zero, axiom, ![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))))).
117.53/15.58	  fof(fact_184_power__eq__0__iff, axiom, ![X_a]: (![Na, A_2]: (zero_zero(X_a)=hAPP(nat, X_a, power_power(X_a, A_2), Na) <=> (ti(X_a, A_2)=zero_zero(X_a) & Na!=zero_zero(nat))) <= (zero_neq_one(X_a) & (no_zero_divisors(X_a) & (mult_zero(X_a) & power(X_a)))))).
117.53/15.58	  fof(fact_185_of__nat__less__0__iff, axiom, ![X_a]: (linordered_semidom(X_a) => ![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))))).
117.53/15.58	  fof(fact_187_of__nat__0, axiom, ![X_a]: (zero_zero(X_a)=hAPP(nat, X_a, semiring_1_of_nat(X_a), zero_zero(nat)) <= semiring_1(X_a))).
117.53/15.58	  fof(fact_19_zero__is__num__zero, axiom, zero_zero(int)=number_number_of(int, pls)).
117.53/15.58	  fof(fact_215_add__0, axiom, ![X_a]: (comm_monoid_add(X_a) => ![A_1]: ti(X_a, A_1)=hAPP(X_a, X_a, plus_plus(X_a, zero_zero(X_a)), A_1))).
117.53/15.58	  fof(fact_216_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, axiom, ![X_a]: (![A_1]: hAPP(X_a, X_a, plus_plus(X_a, zero_zero(X_a)), A_1)=ti(X_a, A_1) <= comm_semiring_1(X_a))).
117.53/15.58	  fof(fact_226_nat__power__eq__0__iff, axiom, ![Na, Ma]: (hAPP(nat, nat, power_power(nat, Ma), Na)=zero_zero(nat) <=> (Ma=zero_zero(nat) & Na!=zero_zero(nat)))).
117.53/15.58	  fof(fact_254_zless__le, axiom, ![Wa, Z_2]: (hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), Z_2), Wa)) <=> (Wa!=Z_2 & hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), Z_2), Wa))))).
117.53/15.59	  fof(fact_273_not__one__le__zero, axiom, ![X_a]: (~hBOOL(hAPP(X_a, bool, hAPP(X_a, fun(X_a, bool), ord_less_eq(X_a), one_one(X_a)), zero_zero(X_a))) <= linordered_semidom(X_a))).
117.53/15.59	  fof(fact_275_le__number__of__eq__not__less, axiom, ![X_a]: ((linorder(X_a) & number(X_a)) => ![Wa, Va]: (hBOOL(hAPP(X_a, bool, hAPP(X_a, fun(X_a, bool), ord_less_eq(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)))))).
117.53/15.59	  fof(fact_27_int__eq__0__conv, axiom, ![Na]: (zero_zero(int)=hAPP(nat, int, semiring_1_of_nat(int), Na) <=> Na=zero_zero(nat))).
117.53/15.59	  fof(fact_292_zero__zle__int, axiom, ![N]: hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), hAPP(nat, int, semiring_1_of_nat(int), N)))).
117.53/15.59	  fof(fact_29_nat__1__add__1, axiom, 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)))).
117.53/15.59	  fof(fact_312_int__one__le__iff__zero__less, axiom, ![Z_2]: (hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), Z_2)) <=> hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), one_one(int)), Z_2)))).
117.53/15.59	  fof(fact_313_int__le__0__conv, axiom, ![Na]: (hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, semiring_1_of_nat(int), Na)), zero_zero(int))) <=> Na=zero_zero(nat))).
117.53/15.59	  fof(fact_314_succ__Pls, axiom, hAPP(int, int, bit1, pls)=hAPP(int, int, succ, pls)).
117.53/15.59	  fof(fact_320_succ__def, axiom, ![K]: hAPP(int, int, succ, K)=hAPP(int, int, plus_plus(int, K), one_one(int))).
117.53/15.59	  fof(fact_341_nonneg__int__cases, axiom, ![K]: (hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), K)) => ~![N_1]: K!=hAPP(nat, int, semiring_1_of_nat(int), N_1))).
117.53/15.59	  fof(fact_349_nat__less__le, axiom, ![Na, Ma]: ((Na!=Ma & hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less_eq(nat), Ma), Na))) <=> hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), Ma), Na)))).
117.53/15.59	  fof(fact_356_real__less__def, axiom, ![Xa, Ya]: ((Ya!=Xa & hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less_eq(real), Xa), Ya))) <=> hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), Xa), Ya)))).
117.53/15.59	  fof(fact_37_one__is__num__one, axiom, number_number_of(int, hAPP(int, int, bit1, pls))=one_one(int)).
117.53/15.59	  fof(fact_403_order__less__asym, axiom, ![X_a]: (preorder(X_a) => ![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))))).
117.53/15.59	  fof(fact_410_xt1_I9_J, axiom, ![X_a]: (order(X_a) => ![A_1, B]: (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))))).
117.53/15.59	  fof(fact_411_order__less__asym_H, axiom, ![X_a]: (preorder(X_a) => ![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))))).
117.53/15.59	  fof(fact_413_order__less__imp__not__eq2, axiom, ![X_a]: (order(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)))).
117.53/15.59	  fof(fact_414_order__less__imp__not__eq, axiom, ![X_a]: (![X, Y]: (ti(X_a, Y)!=ti(X_a, X) <= hBOOL(hAPP(X_a, bool, hAPP(X_a, fun(X_a, bool), ord_less(X_a), X), Y))) <= order(X_a))).
117.53/15.59	  fof(fact_415_order__less__imp__not__less, axiom, ![X_a]: (preorder(X_a) => ![X, Y]: (~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), X), Y))))).
117.53/15.59	  fof(fact_416_order__less__not__sym, axiom, ![X_a]: (![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))) <= preorder(X_a))).
117.53/15.59	  fof(fact_417_less__imp__neq, axiom, ![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)) <= order(X_a))).
117.53/15.59	  fof(fact_421_not__less__iff__gr__or__eq, axiom, ![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, Ya)=ti(X_a, Xa) | hBOOL(hAPP(X_a, bool, hAPP(X_a, fun(X_a, bool), ord_less(X_a), Ya), Xa)))) <= linorder(X_a))).
117.53/15.59	  fof(fact_422_linorder__neq__iff, axiom, ![X_a]: (![Xa, Ya]: ((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)) <= linorder(X_a))).
117.53/15.59	  fof(fact_423_order__less__irrefl, axiom, ![X_a]: (![X]: ~hBOOL(hAPP(X_a, bool, hAPP(X_a, fun(X_a, bool), ord_less(X_a), X), X)) <= preorder(X_a))).
117.53/15.59	  fof(fact_424_linorder__not__less, axiom, ![X_a]: (![Xa, Ya]: (hBOOL(hAPP(X_a, bool, hAPP(X_a, fun(X_a, bool), ord_less_eq(X_a), Ya), Xa)) <=> ~hBOOL(hAPP(X_a, bool, hAPP(X_a, fun(X_a, bool), ord_less(X_a), Xa), Ya))) <= linorder(X_a))).
117.53/15.59	  fof(fact_425_linorder__not__le, axiom, ![X_a]: (![Xa, Ya]: (~hBOOL(hAPP(X_a, bool, hAPP(X_a, fun(X_a, bool), ord_less_eq(X_a), Xa), Ya)) <=> hBOOL(hAPP(X_a, bool, hAPP(X_a, fun(X_a, bool), ord_less(X_a), Ya), Xa))) <= linorder(X_a))).
117.53/15.59	  fof(fact_427_order__less__le, axiom, ![X_a]: (![Xa, Ya]: ((hBOOL(hAPP(X_a, bool, hAPP(X_a, fun(X_a, bool), ord_less_eq(X_a), Xa), Ya)) & ti(X_a, Ya)!=ti(X_a, Xa)) <=> hBOOL(hAPP(X_a, bool, hAPP(X_a, fun(X_a, bool), ord_less(X_a), Xa), Ya))) <= order(X_a))).
117.53/15.59	  fof(fact_428_less__le__not__le, axiom, ![X_a]: (![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_eq(X_a), Xa), Ya)) & ~hBOOL(hAPP(X_a, bool, hAPP(X_a, fun(X_a, bool), ord_less_eq(X_a), Ya), Xa)))) <= preorder(X_a))).
117.53/15.59	  fof(fact_435_leD, axiom, ![X_a]: (linorder(X_a) => ![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_eq(X_a), Y), X))))).
117.53/15.59	  fof(fact_437_linorder__antisym__conv2, axiom, ![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, Ya)=ti(X_a, Xa)) <= hBOOL(hAPP(X_a, bool, hAPP(X_a, fun(X_a, bool), ord_less_eq(X_a), Xa), Ya))) <= linorder(X_a))).
117.53/15.59	  fof(fact_447_less__fun__def, axiom, ![X_a, X_b]: (![F, G]: ((~hBOOL(hAPP(fun(X_a, X_b), bool, hAPP(fun(X_a, X_b), fun(fun(X_a, X_b), bool), ord_less_eq(fun(X_a, X_b)), G), F)) & hBOOL(hAPP(fun(X_a, X_b), bool, hAPP(fun(X_a, X_b), fun(fun(X_a, X_b), bool), ord_less_eq(fun(X_a, X_b)), F), G))) <=> hBOOL(hAPP(fun(X_a, X_b), bool, hAPP(fun(X_a, X_b), fun(fun(X_a, X_b), bool), ord_less(fun(X_a, X_b)), F), G))) <= ord(X_b))).
117.53/15.59	  fof(fact_449_pinf_I6_J, axiom, ![X_a]: (![T_3]: ?[Z]: ![X_1]: (~hBOOL(hAPP(X_a, bool, hAPP(X_a, fun(X_a, bool), ord_less_eq(X_a), X_1), T_3)) <= hBOOL(hAPP(X_a, bool, hAPP(X_a, fun(X_a, bool), ord_less(X_a), Z), X_1))) <= linorder(X_a))).
117.53/15.59	  fof(fact_456_minf_I8_J, axiom, ![X_a]: (![T_3]: ?[Z]: ![X_1]: (~hBOOL(hAPP(X_a, bool, hAPP(X_a, fun(X_a, bool), ord_less_eq(X_a), T_3), X_1)) <= hBOOL(hAPP(X_a, bool, hAPP(X_a, fun(X_a, bool), ord_less(X_a), X_1), Z))) <= linorder(X_a))).
117.53/15.59	  fof(fact_477_sum__squares__gt__zero__iff, axiom, ![X_a]: (linord581940658strict(X_a) => ![Xa, Ya]: ((zero_zero(X_a)!=ti(X_a, Xa) | zero_zero(X_a)!=ti(X_a, 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))))))).
117.53/15.59	  fof(fact_478_not__sum__squares__lt__zero, axiom, ![X_a]: (![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))) <= linordered_ring(X_a))).
117.53/15.59	  fof(fact_47_zadd__commute, axiom, ![Z_1, W_1]: hAPP(int, int, plus_plus(int, Z_1), W_1)=hAPP(int, int, plus_plus(int, W_1), Z_1)).
117.53/15.59	  fof(fact_482_real__sqrt__not__eq__zero, axiom, ![X]: (hAPP(real, real, sqrt, X)!=zero_zero(real) <= hBOOL(hAPP(real, bool, hAPP(real, fun(real, bool), ord_less(real), zero_zero(real)), X)))).
117.53/15.59	  fof(fact_5_zero__eq__power2, axiom, ![X_a]: (![A_2]: (zero_zero(X_a)=ti(X_a, A_2) <=> 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))))) <= ring_11004092258visors(X_a))).
117.53/15.59	  fof(fact_61_int__less__0__conv, axiom, ![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)))).
117.53/15.59	  fof(fact_66_rel__simps_I46_J, axiom, ![K]: hAPP(int, int, bit1, K)!=pls).
117.53/15.59	  fof(fact_67_rel__simps_I39_J, axiom, ![L]: pls!=hAPP(int, int, bit1, L)).
117.53/15.59	  fof(fact_68_rel__simps_I50_J, axiom, ![K, L]: hAPP(int, int, bit1, K)!=hAPP(int, int, bit0, L)).
117.53/15.59	  fof(fact_69_rel__simps_I49_J, axiom, ![K, L]: hAPP(int, int, bit1, L)!=hAPP(int, int, bit0, K)).
117.53/15.59	  fof(fact_80_zadd__0, axiom, ![Z_1]: hAPP(int, int, plus_plus(int, zero_zero(int)), Z_1)=Z_1).
117.53/15.59	  fof(fact_86_power__eq__0__iff__number__of, axiom, ![X_a]: (![A_2, Wa]: ((zero_zero(nat)!=number_number_of(nat, Wa) & ti(X_a, A_2)=zero_zero(X_a)) <=> zero_zero(X_a)=hAPP(nat, X_a, power_power(X_a, A_2), number_number_of(nat, Wa))) <= (power(X_a) & (mult_zero(X_a) & (zero_neq_one(X_a) & no_zero_divisors(X_a)))))).
117.53/15.59	  fof(fact_93_odd__nonzero, axiom, ![Z_1]: hAPP(int, int, plus_plus(int, hAPP(int, int, plus_plus(int, one_one(int)), Z_1)), Z_1)!=zero_zero(int)).
117.53/15.59	  fof(fact_95_zero__less__power2, axiom, ![X_a]: (![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)) <= linordered_idom(X_a))).
117.53/15.59	  fof(fact_96_power2__less__0, axiom, ![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), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))), zero_zero(X_a))) <= linordered_idom(X_a))).
117.53/15.59	  fof(fact_97_sum__power2__gt__zero__iff, axiom, ![X_a]: (linordered_idom(X_a) => ![Xa, Ya]: ((ti(X_a, Xa)!=zero_zero(X_a) | zero_zero(X_a)!=ti(X_a, 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)))))))))).
117.53/15.59	  fof(fact_98_not__sum__power2__lt__zero, axiom, ![X_a]: (![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))) <= linordered_idom(X_a))).
117.53/15.59	
117.53/15.59	Now clausify the problem and encode Horn clauses using encoding 3 of
117.53/15.59	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
117.53/15.59	We repeatedly replace C & s=t => u=v by the two clauses:
117.53/15.59	  fresh(y, y, x1...xn) = u
117.53/15.59	  C => fresh(s, t, x1...xn) = v
117.53/15.59	where fresh is a fresh function symbol and x1..xn are the free
117.53/15.59	variables of u and v.
117.53/15.59	A predicate p(X) is encoded as p(X)=true (this is sound, because the
117.53/15.59	input problem has no model of domain size 1).
117.53/15.59	
117.53/15.59	The encoding turns the above axioms into the following unit equations and goals:
117.53/15.59	
117.53/15.59	Axiom 1 (fact_112_int__gr__induct): fresh477(X, X, Y, Z, W) = hBOOL(hAPP(int, bool, Y, W)).
117.53/15.59	Axiom 2 (fact_150_less__nat__number__of_1): fresh449(X, X, Y, Z) = hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), Z)).
117.53/15.59	Axiom 3 (fact_159_int__if__cong_1): fresh445(X, X, Y, Z, W) = hAPP(nat, int, semiring_1_of_nat(int), Y).
117.53/15.59	Axiom 4 (fact_170_of__nat__1): fresh430(X, X, Y) = one_one(Y).
117.53/15.59	Axiom 5 (fact_187_of__nat__0): fresh421(X, X, Y) = zero_zero(Y).
117.53/15.59	Axiom 6 (fact_18_less__number__of): fresh890(X, X, Y, Z, W) = hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), Z), W)).
117.53/15.59	Axiom 7 (fact_215_add__0): fresh377(X, X, Y, Z) = ti(Y, Z).
117.53/15.59	Axiom 8 (fact_250_zle__trans): fresh341(X, X, Y, Z, W) = hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), Z), Y)).
117.53/15.59	Axiom 9 (fact_252_le__number__of): fresh508(X, X, Y, Z, W) = hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), Z), W)).
117.53/15.59	Axiom 10 (fact_257_le__special_I1_J): fresh526(X, X, Y, Z) = hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), Z)).
117.53/15.60	Axiom 11 (fact_258_le__special_I3_J): fresh567(X, X, Y, Z) = hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), Z), pls)).
117.53/15.60	Axiom 12 (fact_262_le__special_I2_J): fresh604(X, X, Y, Z) = hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit1, pls)), Z)).
117.53/15.60	Axiom 13 (fact_267_add__nonneg__eq__0__iff_2): fresh597(X, X, Y, Z, W) = hAPP(Y, Y, plus_plus(Y, W), Z).
117.53/15.60	Axiom 14 (fact_27_int__eq__0__conv_1): fresh23(X, X, Y) = Y.
117.53/15.60	Axiom 15 (fact_291_transfer__int__nat__quantifiers_I1_J_1): fresh299(X, X, Y, Z) = hBOOL(hAPP(int, bool, Y, Z)).
117.53/15.60	Axiom 16 (fact_295_semiring__1__add__number__of): fresh294(X, X, Y, Z) = hAPP(Y, Y, plus_plus(Y, one_one(Y)), number_number_of(Y, Z)).
117.53/15.60	Axiom 17 (fact_295_semiring__1__add__number__of): fresh293(X, X, Y, Z) = number_number_of(Y, hAPP(int, int, succ, Z)).
117.53/15.60	Axiom 18 (fact_312_int__one__le__iff__zero__less): fresh265(X, X, Y) = true2.
117.53/15.60	Axiom 19 (fact_313_int__le__0__conv_1): fresh19(X, X, Y) = Y.
117.53/15.60	Axiom 20 (fact_341_nonneg__int__cases): fresh32(X, X, Y) = Y.
117.53/15.60	Axiom 21 (fact_50_less__special_I1_J): fresh647(X, X, Y, Z) = hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), Z)).
117.53/15.60	Axiom 22 (fact_5_zero__eq__power2): fresh90(X, X, Y, Z) = ti(Y, Z).
117.53/15.60	Axiom 23 (fact_5_zero__eq__power2): fresh89(X, X, Y, Z) = zero_zero(Y).
117.53/15.60	Axiom 24 (fact_5_zero__eq__power2_1): fresh547(X, X, Y, Z) = fresh548(zero_zero(Y), ti(Y, Z), Y, Z).
117.53/15.60	Axiom 25 (fact_8_one__add__one__is__two): fresh63(X, X, Y) = hAPP(Y, Y, plus_plus(Y, one_one(Y)), one_one(Y)).
117.53/15.60	Axiom 26 (fact_94_number__of__int): fresh62(X, X, Y, Z) = hAPP(nat, Y, semiring_1_of_nat(Y), Z).
117.53/15.60	Axiom 27 (fact_99_number__of__Bit0): fresh61(X, X, Y, Z) = number_number_of(Y, hAPP(int, int, bit0, Z)).
117.53/15.60	Axiom 28 (fact_119_number__of__is__id): number_number_of(int, X) = X.
117.53/15.60	Axiom 29 (fact_341_nonneg__int__cases): fresh32(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), X)), true2, X) = hAPP(nat, int, semiring_1_of_nat(int), sK39_fact_341_nonneg__int__cases_N_1(X)).
117.53/15.60	Axiom 30 (arity_Int_Oint___Rings_Osemiring__1): semiring_1(int) = true2.
117.53/15.60	Axiom 31 (fact_216_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J): fresh376(comm_semiring_1(X), true2, X, Y) = hAPP(X, X, plus_plus(X, zero_zero(X)), Y).
117.53/15.60	Axiom 32 (fact_187_of__nat__0): fresh421(semiring_1(X), true2, X) = hAPP(nat, X, semiring_1_of_nat(X), zero_zero(nat)).
117.53/15.60	Axiom 33 (fact_215_add__0): fresh377(comm_monoid_add(X), true2, X, Y) = hAPP(X, X, plus_plus(X, zero_zero(X)), Y).
117.53/15.60	Axiom 34 (fact_170_of__nat__1): fresh430(semiring_1(X), true2, X) = hAPP(nat, X, semiring_1_of_nat(X), one_one(nat)).
117.53/15.60	Axiom 35 (fact_314_succ__Pls): hAPP(int, int, bit1, pls) = hAPP(int, int, succ, pls).
117.53/15.60	Axiom 36 (arity_Nat_Onat___Rings_Ozero__neq__one): zero_neq_one(nat) = true2.
117.53/15.60	Axiom 37 (fact_27_int__eq__0__conv_1): fresh23(zero_zero(int), hAPP(nat, int, semiring_1_of_nat(int), X), X) = zero_zero(nat).
117.53/15.60	Axiom 38 (fact_27_int__eq__0__conv): fresh313(X, zero_zero(nat), X) = hAPP(nat, int, semiring_1_of_nat(int), X).
117.53/15.60	Axiom 39 (fact_37_one__is__num__one): number_number_of(int, hAPP(int, int, bit1, pls)) = one_one(int).
117.53/15.60	Axiom 40 (fact_292_zero__zle__int): hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), hAPP(nat, int, semiring_1_of_nat(int), X))) = true2.
117.53/15.60	Axiom 41 (fact_0_n1pos): 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)))) = true2.
117.53/15.60	Axiom 42 (fact_313_int__le__0__conv_1): fresh19(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, semiring_1_of_nat(int), X)), zero_zero(int))), true2, X) = zero_zero(nat).
117.53/15.60	Axiom 43 (fact_312_int__one__le__iff__zero__less): fresh265(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), X)), true2, X) = hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), one_one(int)), X)).
117.53/15.60	Axiom 44 (fact_47_zadd__commute): hAPP(int, int, plus_plus(int, X), Y) = hAPP(int, int, plus_plus(int, Y), X).
117.53/15.60	Axiom 45 (fact_29_nat__1__add__1): 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))).
117.53/15.60	Axiom 46 (fact_80_zadd__0): hAPP(int, int, plus_plus(int, zero_zero(int)), X) = X.
117.53/15.60	Axiom 47 (arity_Int_Oint___Groups_Ocomm__monoid__add): comm_monoid_add(int) = true2.
117.53/15.60	Axiom 48 (fact_320_succ__def): hAPP(int, int, succ, X) = hAPP(int, int, plus_plus(int, X), one_one(int)).
117.53/15.60	Axiom 49 (fact_5_zero__eq__power2_1): fresh547(ring_11004092258visors(X), true2, X, Y) = hAPP(nat, X, power_power(X, Y), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))).
117.53/15.60	Axiom 50 (fact_5_zero__eq__power2): fresh90(ring_11004092258visors(X), true2, X, Y) = fresh89(zero_zero(X), hAPP(nat, X, power_power(X, Y), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))), X, Y).
117.53/15.60	Axiom 51 (arity_Int_Oint___Rings_Oring__1__no__zero__divisors): ring_11004092258visors(int) = true2.
117.53/15.60	Axiom 52 (fact_19_zero__is__num__zero): zero_zero(int) = number_number_of(int, pls).
117.53/15.62	Axiom 53 (conj_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).
117.53/15.62	
117.53/15.62	Lemma 54: zero_zero(int) = pls.
117.53/15.62	Proof:
117.53/15.62	  zero_zero(int)
117.53/15.62	= { by axiom 52 (fact_19_zero__is__num__zero) }
117.53/15.62	  number_number_of(int, pls)
117.53/15.62	= { by axiom 28 (fact_119_number__of__is__id) }
117.53/15.62	  pls
117.53/15.62	
117.53/15.62	Lemma 55: fresh445(?, ?, X, ?, ?) = fresh62(?, ?, int, X).
117.53/15.62	Proof:
117.53/15.62	  fresh445(?, ?, X, ?, ?)
117.53/15.62	= { by axiom 3 (fact_159_int__if__cong_1) }
117.53/15.62	  hAPP(nat, int, semiring_1_of_nat(int), X)
117.53/15.62	= { by axiom 26 (fact_94_number__of__int) }
117.53/15.62	  fresh62(?, ?, int, X)
117.53/15.62	
117.53/15.62	Lemma 56: fresh477(?, ?, hAPP(int, fun(int, bool), ord_less_eq(int), Z), ?, Y) = fresh341(?, ?, Y, Z, ?).
117.53/15.62	Proof:
117.53/15.62	  fresh477(?, ?, hAPP(int, fun(int, bool), ord_less_eq(int), Z), ?, Y)
117.53/15.62	= { by axiom 1 (fact_112_int__gr__induct) }
117.53/15.62	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), Z), Y))
117.53/15.62	= { by axiom 8 (fact_250_zle__trans) }
117.53/15.62	  fresh341(?, ?, Y, Z, ?)
117.53/15.62	
117.53/15.62	Lemma 57: fresh341(?, ?, W, Z, ?) = fresh508(?, ?, ?, Z, W).
117.53/15.62	Proof:
117.53/15.62	  fresh341(?, ?, W, Z, ?)
117.53/15.62	= { by lemma 56 }
117.53/15.62	  fresh477(?, ?, hAPP(int, fun(int, bool), ord_less_eq(int), Z), ?, W)
117.53/15.62	= { by axiom 1 (fact_112_int__gr__induct) }
117.53/15.62	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), Z), W))
117.53/15.62	= { by axiom 9 (fact_252_le__number__of) }
117.53/15.62	  fresh508(?, ?, ?, Z, W)
117.53/15.62	
117.53/15.62	Lemma 58: fresh508(?, ?, ?, pls, Z) = fresh526(?, ?, ?, Z).
117.53/15.62	Proof:
117.53/15.62	  fresh508(?, ?, ?, pls, Z)
117.53/15.62	= { by lemma 57 }
117.53/15.62	  fresh341(?, ?, Z, pls, ?)
117.53/15.62	= { by lemma 56 }
117.53/15.62	  fresh477(?, ?, hAPP(int, fun(int, bool), ord_less_eq(int), pls), ?, Z)
117.53/15.62	= { by axiom 1 (fact_112_int__gr__induct) }
117.53/15.62	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), pls), Z))
117.53/15.62	= { by axiom 10 (fact_257_le__special_I1_J) }
117.53/15.62	  fresh526(?, ?, ?, Z)
117.53/15.62	
117.53/15.62	Lemma 59: fresh477(?, ?, X, ?, Y) = fresh299(?, ?, X, Y).
117.53/15.62	Proof:
117.53/15.62	  fresh477(?, ?, X, ?, Y)
117.53/15.62	= { by axiom 1 (fact_112_int__gr__induct) }
117.53/15.62	  hBOOL(hAPP(int, bool, X, Y))
117.53/15.62	= { by axiom 15 (fact_291_transfer__int__nat__quantifiers_I1_J_1) }
117.53/15.62	  fresh299(?, ?, X, Y)
117.53/15.62	
117.53/15.62	Lemma 60: fresh299(?, ?, hAPP(int, fun(int, bool), ord_less_eq(int), X), Y) = fresh508(?, ?, ?, X, Y).
117.53/15.62	Proof:
117.53/15.62	  fresh299(?, ?, hAPP(int, fun(int, bool), ord_less_eq(int), X), Y)
117.53/15.62	= { by lemma 59 }
117.53/15.62	  fresh477(?, ?, hAPP(int, fun(int, bool), ord_less_eq(int), X), ?, Y)
117.53/15.62	= { by axiom 1 (fact_112_int__gr__induct) }
117.53/15.62	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), X), Y))
117.53/15.62	= { by axiom 8 (fact_250_zle__trans) }
117.53/15.62	  fresh341(?, ?, Y, X, ?)
117.53/15.62	= { by lemma 57 }
117.84/15.64	  fresh508(?, ?, ?, X, Y)
117.84/15.64	
117.84/15.64	Lemma 61: zero_zero(nat) = sK39_fact_341_nonneg__int__cases_N_1(pls).
117.84/15.64	Proof:
117.84/15.64	  zero_zero(nat)
117.84/15.64	= { by axiom 37 (fact_27_int__eq__0__conv_1) }
117.84/15.64	  fresh23(zero_zero(int), hAPP(nat, int, semiring_1_of_nat(int), sK39_fact_341_nonneg__int__cases_N_1(pls)), sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by lemma 54 }
117.84/15.64	  fresh23(pls, hAPP(nat, int, semiring_1_of_nat(int), sK39_fact_341_nonneg__int__cases_N_1(pls)), sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by axiom 29 (fact_341_nonneg__int__cases) }
117.84/15.64	  fresh23(pls, fresh32(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), pls)), true2, pls), sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by axiom 15 (fact_291_transfer__int__nat__quantifiers_I1_J_1) }
117.84/15.64	  fresh23(pls, fresh32(fresh299(?, ?, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), pls), true2, pls), sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by lemma 60 }
117.84/15.64	  fresh23(pls, fresh32(fresh508(?, ?, ?, zero_zero(int), pls), true2, pls), sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by lemma 54 }
117.84/15.64	  fresh23(pls, fresh32(fresh508(?, ?, ?, pls, pls), true2, pls), sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by lemma 58 }
117.84/15.64	  fresh23(pls, fresh32(fresh526(?, ?, ?, pls), true2, pls), sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by lemma 54 }
117.84/15.64	  fresh23(pls, fresh32(fresh526(?, ?, ?, zero_zero(int)), true2, pls), sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by axiom 5 (fact_187_of__nat__0) }
117.84/15.64	  fresh23(pls, fresh32(fresh526(?, ?, ?, fresh421(true2, true2, int)), true2, pls), sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by axiom 30 (arity_Int_Oint___Rings_Osemiring__1) }
117.84/15.64	  fresh23(pls, fresh32(fresh526(?, ?, ?, fresh421(semiring_1(int), true2, int)), true2, pls), sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by axiom 32 (fact_187_of__nat__0) }
117.84/15.64	  fresh23(pls, fresh32(fresh526(?, ?, ?, hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat))), true2, pls), sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by axiom 26 (fact_94_number__of__int) }
117.84/15.64	  fresh23(pls, fresh32(fresh526(?, ?, ?, fresh62(?, ?, int, zero_zero(nat))), true2, pls), sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by lemma 58 }
117.84/15.64	  fresh23(pls, fresh32(fresh508(?, ?, ?, pls, fresh62(?, ?, int, zero_zero(nat))), true2, pls), sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by lemma 54 }
117.84/15.64	  fresh23(pls, fresh32(fresh508(?, ?, ?, zero_zero(int), fresh62(?, ?, int, zero_zero(nat))), true2, pls), sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by lemma 55 }
117.84/15.64	  fresh23(pls, fresh32(fresh508(?, ?, ?, zero_zero(int), fresh445(?, ?, zero_zero(nat), ?, ?)), true2, pls), sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by lemma 60 }
117.84/15.64	  fresh23(pls, fresh32(fresh299(?, ?, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), fresh445(?, ?, zero_zero(nat), ?, ?)), true2, pls), sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by axiom 3 (fact_159_int__if__cong_1) }
117.84/15.64	  fresh23(pls, fresh32(fresh299(?, ?, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat))), true2, pls), sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by axiom 15 (fact_291_transfer__int__nat__quantifiers_I1_J_1) }
117.84/15.64	  fresh23(pls, fresh32(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), zero_zero(int)), hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat)))), true2, pls), sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by axiom 40 (fact_292_zero__zle__int) }
117.84/15.64	  fresh23(pls, fresh32(true2, true2, pls), sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by axiom 20 (fact_341_nonneg__int__cases) }
117.84/15.64	  fresh23(pls, pls, sK39_fact_341_nonneg__int__cases_N_1(pls))
117.84/15.64	= { by axiom 14 (fact_27_int__eq__0__conv_1) }
117.84/15.64	  sK39_fact_341_nonneg__int__cases_N_1(pls)
117.84/15.64	
117.84/15.64	Lemma 62: fresh597(?, ?, int, one_one(int), X) = hAPP(int, int, succ, X).
117.84/15.64	Proof:
117.84/15.64	  fresh597(?, ?, int, one_one(int), X)
117.84/15.64	= { by axiom 13 (fact_267_add__nonneg__eq__0__iff_2) }
117.84/15.64	  hAPP(int, int, plus_plus(int, X), one_one(int))
117.84/15.64	= { by axiom 48 (fact_320_succ__def) }
117.84/15.64	  hAPP(int, int, succ, X)
117.84/15.64	
117.84/15.64	Lemma 63: fresh597(?, ?, int, Y, X) = fresh597(?, ?, int, X, Y).
117.84/15.64	Proof:
117.84/15.64	  fresh597(?, ?, int, Y, X)
117.84/15.64	= { by axiom 13 (fact_267_add__nonneg__eq__0__iff_2) }
117.84/15.64	  hAPP(int, int, plus_plus(int, X), Y)
117.84/15.64	= { by axiom 44 (fact_47_zadd__commute) }
117.84/15.64	  hAPP(int, int, plus_plus(int, Y), X)
117.84/15.64	= { by axiom 13 (fact_267_add__nonneg__eq__0__iff_2) }
117.84/15.64	  fresh597(?, ?, int, X, Y)
117.84/15.64	
117.84/15.64	Lemma 64: fresh293(?, ?, int, X) = fresh294(?, ?, int, X).
117.84/15.64	Proof:
117.84/15.64	  fresh293(?, ?, int, X)
117.84/15.64	= { by axiom 28 (fact_119_number__of__is__id) }
117.84/15.64	  fresh293(?, ?, int, number_number_of(int, X))
117.84/15.64	= { by axiom 17 (fact_295_semiring__1__add__number__of) }
117.84/15.64	  number_number_of(int, hAPP(int, int, succ, number_number_of(int, X)))
117.84/15.64	= { by axiom 28 (fact_119_number__of__is__id) }
117.84/15.64	  hAPP(int, int, succ, number_number_of(int, X))
117.84/15.64	= { by lemma 62 }
117.84/15.64	  fresh597(?, ?, int, one_one(int), number_number_of(int, X))
117.84/15.64	= { by lemma 63 }
117.84/15.64	  fresh597(?, ?, int, number_number_of(int, X), one_one(int))
117.84/15.64	= { by axiom 13 (fact_267_add__nonneg__eq__0__iff_2) }
117.84/15.64	  hAPP(int, int, plus_plus(int, one_one(int)), number_number_of(int, X))
117.84/15.64	= { by axiom 16 (fact_295_semiring__1__add__number__of) }
117.84/15.64	  fresh294(?, ?, int, X)
117.84/15.64	
117.84/15.64	Lemma 65: fresh547(X, X, Y, Z) = fresh547(?, ?, Y, Z).
117.84/15.64	Proof:
117.84/15.64	  fresh547(X, X, Y, Z)
117.84/15.64	= { by axiom 24 (fact_5_zero__eq__power2_1) }
117.84/15.64	  fresh548(zero_zero(Y), ti(Y, Z), Y, Z)
117.84/15.64	= { by axiom 24 (fact_5_zero__eq__power2_1) }
117.84/15.64	  fresh547(?, ?, Y, Z)
117.84/15.64	
117.84/15.64	Lemma 66: hAPP(int, int, succ, pls) = one_one(int).
117.84/15.64	Proof:
117.84/15.64	  hAPP(int, int, succ, pls)
117.84/15.64	= { by axiom 35 (fact_314_succ__Pls) }
117.84/15.64	  hAPP(int, int, bit1, pls)
117.84/15.64	= { by axiom 28 (fact_119_number__of__is__id) }
117.84/15.64	  number_number_of(int, hAPP(int, int, bit1, pls))
117.84/15.64	= { by axiom 39 (fact_37_one__is__num__one) }
117.84/15.64	  one_one(int)
117.84/15.64	
117.84/15.64	Lemma 67: fresh61(?, ?, nat, one_one(int)) = fresh63(?, ?, nat).
117.84/15.64	Proof:
117.84/15.64	  fresh61(?, ?, nat, one_one(int))
117.84/15.64	= { by lemma 66 }
117.84/15.64	  fresh61(?, ?, nat, hAPP(int, int, succ, pls))
117.84/15.64	= { by axiom 35 (fact_314_succ__Pls) }
117.84/15.64	  fresh61(?, ?, nat, hAPP(int, int, bit1, pls))
117.84/15.64	= { by axiom 27 (fact_99_number__of__Bit0) }
117.84/15.64	  number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))
117.84/15.64	= { by axiom 45 (fact_29_nat__1__add__1) }
117.84/15.64	  hAPP(nat, nat, plus_plus(nat, one_one(nat)), one_one(nat))
117.84/15.64	= { by axiom 25 (fact_8_one__add__one__is__two) }
117.84/15.64	  fresh63(?, ?, nat)
117.84/15.64	
117.84/15.64	Lemma 68: hAPP(nat, X, power_power(X, Y), fresh63(?, ?, nat)) = fresh547(ring_11004092258visors(X), true2, X, Y).
117.84/15.64	Proof:
117.84/15.64	  hAPP(nat, X, power_power(X, Y), fresh63(?, ?, nat))
117.84/15.64	= { by lemma 67 }
117.84/15.64	  hAPP(nat, X, power_power(X, Y), fresh61(?, ?, nat, one_one(int)))
117.84/15.64	= { by lemma 66 }
117.84/15.64	  hAPP(nat, X, power_power(X, Y), fresh61(?, ?, nat, hAPP(int, int, succ, pls)))
117.84/15.64	= { by axiom 35 (fact_314_succ__Pls) }
117.84/15.64	  hAPP(nat, X, power_power(X, Y), fresh61(?, ?, nat, hAPP(int, int, bit1, pls)))
117.84/15.64	= { by axiom 27 (fact_99_number__of__Bit0) }
117.84/15.64	  hAPP(nat, X, power_power(X, Y), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls))))
117.84/15.64	= { by axiom 49 (fact_5_zero__eq__power2_1) }
117.84/15.64	  fresh547(ring_11004092258visors(X), true2, X, Y)
117.84/15.64	
117.84/15.64	Lemma 69: fresh597(?, ?, X, Y, zero_zero(X)) = fresh376(comm_semiring_1(X), true2, X, Y).
117.84/15.64	Proof:
117.84/15.64	  fresh597(?, ?, X, Y, zero_zero(X))
117.84/15.64	= { by axiom 13 (fact_267_add__nonneg__eq__0__iff_2) }
117.84/15.64	  hAPP(X, X, plus_plus(X, zero_zero(X)), Y)
117.84/15.64	= { by axiom 31 (fact_216_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) }
117.84/15.64	  fresh376(comm_semiring_1(X), true2, X, Y)
117.84/15.64	
117.84/15.64	Lemma 70: fresh62(?, ?, int, X) = fresh313(X, zero_zero(nat), X).
117.84/15.64	Proof:
117.84/15.64	  fresh62(?, ?, int, X)
117.84/15.64	= { by axiom 26 (fact_94_number__of__int) }
117.84/15.64	  hAPP(nat, int, semiring_1_of_nat(int), X)
117.84/15.64	= { by axiom 38 (fact_27_int__eq__0__conv) }
117.84/15.64	  fresh313(X, zero_zero(nat), X)
117.84/15.64	
117.84/15.64	Lemma 71: fresh890(?, ?, ?, pls, X) = fresh449(?, ?, ?, X).
117.84/15.64	Proof:
117.84/15.64	  fresh890(?, ?, ?, pls, X)
117.84/15.64	= { by axiom 6 (fact_18_less__number__of) }
117.84/15.64	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), X))
117.84/15.64	= { by axiom 2 (fact_150_less__nat__number__of_1) }
117.84/15.64	  fresh449(?, ?, ?, X)
117.84/15.64	
117.84/15.64	Lemma 72: fresh299(?, ?, hAPP(int, fun(int, bool), ord_less(int), X), Y) = fresh890(?, ?, ?, X, Y).
117.84/15.64	Proof:
117.84/15.64	  fresh299(?, ?, hAPP(int, fun(int, bool), ord_less(int), X), Y)
117.84/15.64	= { by lemma 59 }
117.84/15.64	  fresh477(?, ?, hAPP(int, fun(int, bool), ord_less(int), X), ?, Y)
117.84/15.64	= { by axiom 1 (fact_112_int__gr__induct) }
117.84/15.64	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), X), Y))
117.84/15.64	= { by axiom 6 (fact_18_less__number__of) }
117.84/15.65	  fresh890(?, ?, ?, X, Y)
117.84/15.65	
117.84/15.65	Lemma 73: fresh449(?, ?, ?, X) = fresh647(?, ?, ?, X).
117.84/15.65	Proof:
117.84/15.65	  fresh449(?, ?, ?, X)
117.84/15.65	= { by lemma 71 }
117.84/15.65	  fresh890(?, ?, ?, pls, X)
117.84/15.65	= { by lemma 72 }
117.84/15.65	  fresh299(?, ?, hAPP(int, fun(int, bool), ord_less(int), pls), X)
117.84/15.65	= { by axiom 15 (fact_291_transfer__int__nat__quantifiers_I1_J_1) }
117.84/15.65	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), X))
117.84/15.65	= { by axiom 21 (fact_50_less__special_I1_J) }
117.84/15.65	  fresh647(?, ?, ?, X)
117.84/15.65	
117.84/15.65	Lemma 74: fresh508(?, ?, ?, one_one(int), X) = fresh604(?, ?, ?, X).
117.84/15.65	Proof:
117.84/15.65	  fresh508(?, ?, ?, one_one(int), X)
117.84/15.65	= { by lemma 66 }
117.84/15.65	  fresh508(?, ?, ?, hAPP(int, int, succ, pls), X)
117.84/15.65	= { by axiom 35 (fact_314_succ__Pls) }
117.84/15.65	  fresh508(?, ?, ?, hAPP(int, int, bit1, pls), X)
117.84/15.65	= { by lemma 57 }
117.84/15.65	  fresh341(?, ?, X, hAPP(int, int, bit1, pls), ?)
117.84/15.65	= { by lemma 56 }
117.84/15.65	  fresh477(?, ?, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit1, pls)), ?, X)
117.84/15.65	= { by axiom 1 (fact_112_int__gr__induct) }
117.84/15.65	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(int, int, bit1, pls)), X))
117.84/15.65	= { by axiom 12 (fact_262_le__special_I2_J) }
117.84/15.65	  fresh604(?, ?, ?, X)
117.84/15.65	
117.84/15.65	Lemma 75: fresh508(?, ?, ?, Z, pls) = fresh567(?, ?, ?, Z).
117.84/15.65	Proof:
117.84/15.65	  fresh508(?, ?, ?, Z, pls)
117.84/15.65	= { by lemma 57 }
117.84/15.65	  fresh341(?, ?, pls, Z, ?)
117.84/15.65	= { by lemma 56 }
117.84/15.65	  fresh477(?, ?, hAPP(int, fun(int, bool), ord_less_eq(int), Z), ?, pls)
117.84/15.65	= { by axiom 1 (fact_112_int__gr__induct) }
117.84/15.65	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), Z), pls))
117.84/15.65	= { by axiom 11 (fact_258_le__special_I3_J) }
125.03/16.94	  fresh567(?, ?, ?, Z)
125.03/16.94	
125.03/16.94	Goal 1 (fact_163_zero__neq__one): tuple6(one_one(X), zero_neq_one(X)) = tuple6(zero_zero(X), true2).
125.03/16.94	The goal is true when:
125.03/16.94	  X = nat
125.03/16.94	
125.03/16.94	Proof:
125.03/16.94	  tuple6(one_one(nat), zero_neq_one(nat))
125.03/16.94	= { by axiom 19 (fact_313_int__le__0__conv_1) }
125.03/16.94	  tuple6(fresh19(true2, true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by axiom 18 (fact_312_int__one__le__iff__zero__less) }
125.03/16.94	  tuple6(fresh19(fresh265(true2, true2, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by axiom 41 (fact_0_n1pos) }
125.03/16.94	  tuple6(fresh19(fresh265(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)))), true2, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by axiom 15 (fact_291_transfer__int__nat__quantifiers_I1_J_1) }
125.03/16.94	  tuple6(fresh19(fresh265(fresh299(?, ?, 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))), true2, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by axiom 13 (fact_267_add__nonneg__eq__0__iff_2) }
125.03/16.94	  tuple6(fresh19(fresh265(fresh299(?, ?, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), fresh597(?, ?, int, hAPP(nat, int, semiring_1_of_nat(int), n), one_one(int))), true2, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by axiom 3 (fact_159_int__if__cong_1) }
125.03/16.94	  tuple6(fresh19(fresh265(fresh299(?, ?, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), fresh597(?, ?, int, fresh445(?, ?, n, ?, ?), one_one(int))), true2, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by lemma 72 }
125.03/16.94	  tuple6(fresh19(fresh265(fresh890(?, ?, ?, zero_zero(int), fresh597(?, ?, int, fresh445(?, ?, n, ?, ?), one_one(int))), true2, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by lemma 54 }
125.03/16.94	  tuple6(fresh19(fresh265(fresh890(?, ?, ?, pls, fresh597(?, ?, int, fresh445(?, ?, n, ?, ?), one_one(int))), true2, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by lemma 55 }
125.03/16.94	  tuple6(fresh19(fresh265(fresh890(?, ?, ?, pls, fresh597(?, ?, int, fresh62(?, ?, int, n), one_one(int))), true2, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by lemma 71 }
125.03/16.94	  tuple6(fresh19(fresh265(fresh449(?, ?, ?, fresh597(?, ?, int, fresh62(?, ?, int, n), one_one(int))), true2, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by lemma 73 }
125.03/16.94	  tuple6(fresh19(fresh265(fresh647(?, ?, ?, fresh597(?, ?, int, fresh62(?, ?, int, n), one_one(int))), true2, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by lemma 63 }
125.03/16.94	  tuple6(fresh19(fresh265(fresh647(?, ?, ?, fresh597(?, ?, int, one_one(int), fresh62(?, ?, int, n))), true2, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by lemma 62 }
125.03/16.94	  tuple6(fresh19(fresh265(fresh647(?, ?, ?, hAPP(int, int, succ, fresh62(?, ?, int, n))), true2, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by lemma 70 }
125.03/16.94	  tuple6(fresh19(fresh265(fresh647(?, ?, ?, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by lemma 73 }
125.03/16.94	  tuple6(fresh19(fresh265(fresh449(?, ?, ?, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by lemma 71 }
125.03/16.94	  tuple6(fresh19(fresh265(fresh890(?, ?, ?, pls, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by lemma 54 }
125.03/16.94	  tuple6(fresh19(fresh265(fresh890(?, ?, ?, zero_zero(int), hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by lemma 72 }
125.03/16.94	  tuple6(fresh19(fresh265(fresh299(?, ?, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by axiom 15 (fact_291_transfer__int__nat__quantifiers_I1_J_1) }
125.03/16.94	  tuple6(fresh19(fresh265(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by axiom 43 (fact_312_int__one__le__iff__zero__less) }
125.03/16.94	  tuple6(fresh19(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), one_one(int)), hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.94	= { by axiom 15 (fact_291_transfer__int__nat__quantifiers_I1_J_1) }
125.03/16.95	  tuple6(fresh19(fresh299(?, ?, hAPP(int, fun(int, bool), ord_less_eq(int), one_one(int)), hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 60 }
125.03/16.95	  tuple6(fresh19(fresh508(?, ?, ?, one_one(int), hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 74 }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 46 (fact_80_zadd__0) }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, hAPP(int, int, plus_plus(int, zero_zero(int)), hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 33 (fact_215_add__0) }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh377(comm_monoid_add(int), true2, int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 47 (arity_Int_Oint___Groups_Ocomm__monoid__add) }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh377(true2, true2, int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 7 (fact_215_add__0) }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, ti(int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 22 (fact_5_zero__eq__power2) }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh90(true2, true2, int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 51 (arity_Int_Oint___Rings_Oring__1__no__zero__divisors) }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh90(ring_11004092258visors(int), true2, int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 50 (fact_5_zero__eq__power2) }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(zero_zero(int), hAPP(nat, int, power_power(int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 54 }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, hAPP(nat, int, power_power(int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 27 (fact_99_number__of__Bit0) }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, hAPP(nat, int, power_power(int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), fresh61(?, ?, nat, hAPP(int, int, bit1, pls))), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 35 (fact_314_succ__Pls) }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, hAPP(nat, int, power_power(int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), fresh61(?, ?, nat, hAPP(int, int, succ, pls))), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 66 }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, hAPP(nat, int, power_power(int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), fresh61(?, ?, nat, one_one(int))), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 67 }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, hAPP(nat, int, power_power(int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), fresh63(?, ?, nat)), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 68 }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, fresh547(ring_11004092258visors(int), true2, int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 51 (arity_Int_Oint___Rings_Oring__1__no__zero__divisors) }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, fresh547(true2, true2, int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 65 }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, fresh547(?, ?, int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n))), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 70 }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, fresh547(?, ?, int, hAPP(int, int, succ, fresh62(?, ?, int, n))), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 55 }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, fresh547(?, ?, int, hAPP(int, int, succ, fresh445(?, ?, n, ?, ?))), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 62 }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, fresh547(?, ?, int, fresh597(?, ?, int, one_one(int), fresh445(?, ?, n, ?, ?))), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 63 }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, fresh547(?, ?, int, fresh597(?, ?, int, fresh445(?, ?, n, ?, ?), one_one(int))), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 65 }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, fresh547(true2, true2, int, fresh597(?, ?, int, fresh445(?, ?, n, ?, ?), one_one(int))), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 51 (arity_Int_Oint___Rings_Oring__1__no__zero__divisors) }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, fresh547(ring_11004092258visors(int), true2, int, fresh597(?, ?, int, fresh445(?, ?, n, ?, ?), one_one(int))), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 68 }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, hAPP(nat, int, power_power(int, fresh597(?, ?, int, fresh445(?, ?, n, ?, ?), one_one(int))), fresh63(?, ?, nat)), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 3 (fact_159_int__if__cong_1) }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, hAPP(nat, int, power_power(int, fresh597(?, ?, int, hAPP(nat, int, semiring_1_of_nat(int), n), one_one(int))), fresh63(?, ?, nat)), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 13 (fact_267_add__nonneg__eq__0__iff_2) }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, hAPP(nat, int, power_power(int, hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n))), fresh63(?, ?, nat)), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 67 }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, hAPP(nat, int, power_power(int, hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n))), fresh61(?, ?, nat, one_one(int))), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 66 }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, hAPP(nat, int, power_power(int, hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n))), fresh61(?, ?, nat, hAPP(int, int, succ, pls))), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 35 (fact_314_succ__Pls) }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, hAPP(nat, int, power_power(int, hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n))), fresh61(?, ?, nat, hAPP(int, int, bit1, pls))), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 27 (fact_99_number__of__Bit0) }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, 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)))), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 53 (conj_0) }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, zero_zero(int), int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 54 }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, fresh89(pls, pls, int, hAPP(int, int, succ, fresh313(n, zero_zero(nat), n)))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 23 (fact_5_zero__eq__power2) }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, zero_zero(int)), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 54 }
125.03/16.95	  tuple6(fresh19(fresh604(?, ?, ?, pls), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 74 }
125.03/16.95	  tuple6(fresh19(fresh508(?, ?, ?, one_one(int), pls), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 75 }
125.03/16.95	  tuple6(fresh19(fresh567(?, ?, ?, one_one(int)), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 4 (fact_170_of__nat__1) }
125.03/16.95	  tuple6(fresh19(fresh567(?, ?, ?, fresh430(true2, true2, int)), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 30 (arity_Int_Oint___Rings_Osemiring__1) }
125.03/16.95	  tuple6(fresh19(fresh567(?, ?, ?, fresh430(semiring_1(int), true2, int)), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 34 (fact_170_of__nat__1) }
125.03/16.95	  tuple6(fresh19(fresh567(?, ?, ?, hAPP(nat, int, semiring_1_of_nat(int), one_one(nat))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 26 (fact_94_number__of__int) }
125.03/16.95	  tuple6(fresh19(fresh567(?, ?, ?, fresh62(?, ?, int, one_one(nat))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 75 }
125.03/16.95	  tuple6(fresh19(fresh508(?, ?, ?, fresh62(?, ?, int, one_one(nat)), pls), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 55 }
125.03/16.95	  tuple6(fresh19(fresh508(?, ?, ?, fresh445(?, ?, one_one(nat), ?, ?), pls), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 54 }
125.03/16.95	  tuple6(fresh19(fresh508(?, ?, ?, fresh445(?, ?, one_one(nat), ?, ?), zero_zero(int)), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by lemma 60 }
125.03/16.95	  tuple6(fresh19(fresh299(?, ?, hAPP(int, fun(int, bool), ord_less_eq(int), fresh445(?, ?, one_one(nat), ?, ?)), zero_zero(int)), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 3 (fact_159_int__if__cong_1) }
125.03/16.95	  tuple6(fresh19(fresh299(?, ?, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, semiring_1_of_nat(int), one_one(nat))), zero_zero(int)), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 15 (fact_291_transfer__int__nat__quantifiers_I1_J_1) }
125.03/16.95	  tuple6(fresh19(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, semiring_1_of_nat(int), one_one(nat))), zero_zero(int))), true2, one_one(nat)), zero_neq_one(nat))
125.03/16.95	= { by axiom 42 (fact_313_int__le__0__conv_1) }
125.03/16.95	  tuple6(zero_zero(nat), zero_neq_one(nat))
125.03/16.95	= { by axiom 36 (arity_Nat_Onat___Rings_Ozero__neq__one) }
125.03/16.95	  tuple6(zero_zero(nat), true2)
125.03/16.95	% SZS output end Proof
125.03/16.95	
125.03/16.95	RESULT: Theorem (the conjecture is true).
125.03/16.99	EOF