0.05/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.05/0.11	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.10/0.32	% Computer   : n007.cluster.edu
0.10/0.32	% Model      : x86_64 x86_64
0.10/0.32	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.32	% Memory     : 8042.1875MB
0.10/0.32	% OS         : Linux 3.10.0-693.el7.x86_64
0.10/0.32	% CPULimit   : 1200
0.10/0.32	% WCLimit    : 120
0.10/0.32	% DateTime   : Tue Jul 13 16:45:04 EDT 2021
0.10/0.32	% CPUTime    : 
59.34/7.89	% SZS status Theorem
59.34/7.89	
59.83/7.92	% SZS output start Proof
59.83/7.92	Take the following subset of the input axioms:
59.83/7.92	  fof(arity_Int_Oint___Groups_Ocomm__monoid__add, axiom, comm_monoid_add(int)).
59.83/7.92	  fof(arity_Int_Oint___Rings_Oring__1__no__zero__divisors, axiom, ring_11004092258visors(int)).
59.83/7.92	  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)).
59.83/7.92	  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))))).
59.83/7.92	  fof(fact_119_number__of__is__id, axiom, ![K]: K=number_number_of(int, K)).
59.83/7.92	  fof(fact_211_add_Ocomm__neutral, axiom, ![X_a]: (comm_monoid_add(X_a) => ![A_1]: ti(X_a, A_1)=hAPP(X_a, X_a, plus_plus(X_a, A_1), zero_zero(X_a)))).
59.83/7.92	  fof(fact_27_int__eq__0__conv, axiom, ![Na]: (hAPP(nat, int, semiring_1_of_nat(int), Na)=zero_zero(int) <=> zero_zero(nat)=Na)).
59.83/7.92	  fof(fact_320_succ__def, axiom, ![K]: hAPP(int, int, plus_plus(int, K), one_one(int))=hAPP(int, int, succ, K)).
59.83/7.92	  fof(fact_32_rel__simps_I2_J, axiom, ~hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), pls))).
59.83/7.92	  fof(fact_37_one__is__num__one, axiom, number_number_of(int, hAPP(int, int, bit1, pls))=one_one(int)).
59.83/7.92	  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)).
59.83/7.92	  fof(fact_57_bin__less__0__simps_I1_J, axiom, ~hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int)))).
59.83/7.92	  fof(fact_5_zero__eq__power2, axiom, ![X_a]: (ring_11004092258visors(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)))) <=> zero_zero(X_a)=ti(X_a, A_2)))).
59.83/7.92	  fof(fact_73_Pls__def, axiom, pls=zero_zero(int)).
59.83/7.92	  fof(fact_79_zadd__0__right, axiom, ![Z_1]: Z_1=hAPP(int, int, plus_plus(int, Z_1), zero_zero(int))).
59.83/7.92	
59.83/7.92	Now clausify the problem and encode Horn clauses using encoding 3 of
59.83/7.92	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
59.83/7.92	We repeatedly replace C & s=t => u=v by the two clauses:
59.83/7.92	  fresh(y, y, x1...xn) = u
59.83/7.92	  C => fresh(s, t, x1...xn) = v
59.83/7.92	where fresh is a fresh function symbol and x1..xn are the free
59.83/7.92	variables of u and v.
59.83/7.92	A predicate p(X) is encoded as p(X)=true (this is sound, because the
59.83/7.92	input problem has no model of domain size 1).
59.83/7.92	
59.83/7.92	The encoding turns the above axioms into the following unit equations and goals:
59.83/7.92	
59.83/7.92	Axiom 1 (fact_73_Pls__def): pls = zero_zero(int).
59.83/7.92	Axiom 2 (arity_Int_Oint___Rings_Oring__1__no__zero__divisors): ring_11004092258visors(int) = true2.
59.83/7.92	Axiom 3 (arity_Int_Oint___Groups_Ocomm__monoid__add): comm_monoid_add(int) = true2.
59.83/7.92	Axiom 4 (fact_119_number__of__is__id): X = number_number_of(int, X).
59.83/7.92	Axiom 5 (fact_211_add_Ocomm__neutral): fresh384(X, X, Y, Z) = ti(Y, Z).
59.83/7.92	Axiom 6 (fact_5_zero__eq__power2): fresh90(X, X, Y, Z) = zero_zero(Y).
59.83/7.92	Axiom 7 (fact_5_zero__eq__power2): fresh89(X, X, Y, Z) = ti(Y, Z).
59.83/7.92	Axiom 8 (fact_94_number__of__int): fresh63(X, X, Y, Z) = hAPP(nat, Y, semiring_1_of_nat(Y), Z).
59.83/7.92	Axiom 9 (fact_27_int__eq__0__conv): fresh313(zero_zero(nat), X, X) = hAPP(nat, int, semiring_1_of_nat(int), X).
59.83/7.92	Axiom 10 (fact_291_transfer__int__nat__quantifiers_I1_J_1): fresh299(X, X, Y, Z) = hBOOL(hAPP(int, bool, Y, Z)).
59.83/7.92	Axiom 11 (fact_267_add__nonneg__eq__0__iff_2): fresh757(X, X, Y, Z, W) = hAPP(Y, Y, plus_plus(Y, W), Z).
59.83/7.92	Axiom 12 (fact_47_zadd__commute): hAPP(int, int, plus_plus(int, X), Y) = hAPP(int, int, plus_plus(int, Y), X).
59.83/7.92	Axiom 13 (fact_99_number__of__Bit0): fresh62(X, X, Y, Z) = number_number_of(Y, hAPP(int, int, bit0, Z)).
59.83/7.92	Axiom 14 (fact_37_one__is__num__one): number_number_of(int, hAPP(int, int, bit1, pls)) = one_one(int).
59.83/7.92	Axiom 15 (fact_211_add_Ocomm__neutral): fresh384(comm_monoid_add(X), true2, X, Y) = hAPP(X, X, plus_plus(X, Y), zero_zero(X)).
59.83/7.92	Axiom 16 (fact_79_zadd__0__right): X = hAPP(int, int, plus_plus(int, X), zero_zero(int)).
59.83/7.92	Axiom 17 (fact_320_succ__def): hAPP(int, int, plus_plus(int, X), one_one(int)) = hAPP(int, int, succ, X).
59.83/7.92	Axiom 18 (fact_18_less__number__of): fresh686(X, X, Y, Z, W) = hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), Z), W)).
59.83/7.92	Axiom 19 (fact_50_less__special_I1_J): fresh874(X, X, Y, Z) = hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), Z)).
59.83/7.92	Axiom 20 (fact_5_zero__eq__power2_1): fresh881(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)))).
59.83/7.92	Axiom 21 (fact_5_zero__eq__power2): fresh89(ring_11004092258visors(X), true2, X, Y) = fresh90(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).
59.83/7.92	Axiom 22 (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.
60.25/7.96	Axiom 23 (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).
60.25/7.96	
60.25/7.96	Lemma 24: hAPP(int, int, bit1, pls) = one_one(int).
60.25/7.96	Proof:
60.25/7.96	  hAPP(int, int, bit1, pls)
60.25/7.96	= { by axiom 4 (fact_119_number__of__is__id) }
60.25/7.96	  number_number_of(int, hAPP(int, int, bit1, pls))
60.25/7.96	= { by axiom 14 (fact_37_one__is__num__one) }
60.25/7.96	  one_one(int)
60.25/7.96	
60.25/7.96	Lemma 25: fresh63(Y, Y, int, X) = fresh313(zero_zero(nat), X, X).
60.25/7.96	Proof:
60.25/7.96	  fresh63(Y, Y, int, X)
60.25/7.96	= { by axiom 8 (fact_94_number__of__int) }
60.25/7.96	  hAPP(nat, int, semiring_1_of_nat(int), X)
60.25/7.96	= { by axiom 9 (fact_27_int__eq__0__conv) R->L }
60.25/7.96	  fresh313(zero_zero(nat), X, X)
60.25/7.96	
60.25/7.96	Lemma 26: fresh757(W, W, int, Z, Y) = fresh757(X, X, int, Y, Z).
60.25/7.96	Proof:
60.25/7.96	  fresh757(W, W, int, Z, Y)
60.25/7.96	= { by axiom 11 (fact_267_add__nonneg__eq__0__iff_2) }
60.25/7.96	  hAPP(int, int, plus_plus(int, Y), Z)
60.25/7.96	= { by axiom 12 (fact_47_zadd__commute) R->L }
60.25/7.96	  hAPP(int, int, plus_plus(int, Z), Y)
60.25/7.96	= { by axiom 11 (fact_267_add__nonneg__eq__0__iff_2) R->L }
60.25/7.96	  fresh757(X, X, int, Y, Z)
60.25/7.96	
60.25/7.96	Lemma 27: fresh299(X, X, hAPP(int, fun(int, bool), ord_less(int), Y), Z) = fresh686(W, W, V, Y, Z).
60.25/7.96	Proof:
60.25/7.96	  fresh299(X, X, hAPP(int, fun(int, bool), ord_less(int), Y), Z)
60.25/7.96	= { by axiom 10 (fact_291_transfer__int__nat__quantifiers_I1_J_1) }
60.25/7.96	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), Y), Z))
60.25/7.96	= { by axiom 18 (fact_18_less__number__of) R->L }
60.25/7.96	  fresh686(W, W, V, Y, Z)
60.25/7.96	
60.25/7.96	Lemma 28: fresh686(X, X, Y, pls, Z) = fresh874(W, W, V, Z).
60.25/7.96	Proof:
60.25/7.96	  fresh686(X, X, Y, pls, Z)
60.25/7.96	= { by lemma 27 R->L }
60.25/7.96	  fresh299(U, U, hAPP(int, fun(int, bool), ord_less(int), pls), Z)
60.25/7.96	= { by axiom 10 (fact_291_transfer__int__nat__quantifiers_I1_J_1) }
60.25/7.96	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), Z))
60.25/7.96	= { by axiom 19 (fact_50_less__special_I1_J) R->L }
60.25/7.96	  fresh874(W, W, V, Z)
60.25/7.96	
60.25/7.96	Lemma 29: fresh757(X, X, int, hAPP(int, int, bit1, pls), Y) = hAPP(int, int, succ, Y).
60.25/7.96	Proof:
60.25/7.96	  fresh757(X, X, int, hAPP(int, int, bit1, pls), Y)
60.25/7.96	= { by lemma 24 }
60.25/7.96	  fresh757(X, X, int, one_one(int), Y)
60.25/7.96	= { by axiom 11 (fact_267_add__nonneg__eq__0__iff_2) }
60.25/7.96	  hAPP(int, int, plus_plus(int, Y), one_one(int))
60.25/7.96	= { by axiom 17 (fact_320_succ__def) }
60.25/7.96	  hAPP(int, int, succ, Y)
60.25/7.96	
60.25/7.96	Lemma 30: hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int))) = fresh874(X, X, Y, pls).
60.25/7.96	Proof:
60.25/7.96	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int)))
60.25/7.96	= { by axiom 10 (fact_291_transfer__int__nat__quantifiers_I1_J_1) R->L }
60.25/7.96	  fresh299(V, V, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int))
60.25/7.96	= { by lemma 27 }
60.25/7.96	  fresh686(Z, Z, W, pls, zero_zero(int))
60.25/7.96	= { by lemma 28 }
60.25/7.96	  fresh874(X, X, Y, zero_zero(int))
60.25/7.96	= { by axiom 1 (fact_73_Pls__def) R->L }
60.25/7.96	  fresh874(X, X, Y, pls)
60.25/7.96	
60.25/7.96	Lemma 31: hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int))) = true2.
60.25/7.96	Proof:
60.25/7.96	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int)))
60.25/7.96	= { by lemma 30 }
60.25/7.96	  fresh874(X, X, Y, pls)
60.25/7.96	= { by axiom 1 (fact_73_Pls__def) }
60.25/7.96	  fresh874(X, X, Y, zero_zero(int))
60.25/7.96	= { by axiom 6 (fact_5_zero__eq__power2) R->L }
60.25/7.96	  fresh874(X, X, Y, fresh90(pls, pls, int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))))
60.25/7.96	= { by axiom 1 (fact_73_Pls__def) }
60.25/7.96	  fresh874(X, X, Y, fresh90(pls, zero_zero(int), int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))))
60.25/7.96	= { by axiom 23 (conj_0) R->L }
60.25/7.96	  fresh874(X, X, Y, fresh90(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(zero_zero(nat), n, n))))
60.25/7.96	= { by axiom 11 (fact_267_add__nonneg__eq__0__iff_2) R->L }
60.25/7.96	  fresh874(X, X, Y, fresh90(pls, hAPP(nat, int, power_power(int, fresh757(Z, Z, int, hAPP(nat, int, semiring_1_of_nat(int), n), one_one(int))), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))), int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))))
60.25/7.96	= { by axiom 8 (fact_94_number__of__int) R->L }
60.25/7.96	  fresh874(X, X, Y, fresh90(pls, hAPP(nat, int, power_power(int, fresh757(Z, Z, int, fresh63(W, W, int, n), one_one(int))), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))), int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))))
60.25/7.96	= { by lemma 24 R->L }
60.25/7.96	  fresh874(X, X, Y, fresh90(pls, hAPP(nat, int, power_power(int, fresh757(Z, Z, int, fresh63(W, W, int, n), hAPP(int, int, bit1, pls))), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))), int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))))
60.25/7.96	= { by axiom 13 (fact_99_number__of__Bit0) R->L }
60.25/7.96	  fresh874(X, X, Y, fresh90(pls, hAPP(nat, int, power_power(int, fresh757(Z, Z, int, fresh63(W, W, int, n), hAPP(int, int, bit1, pls))), fresh62(V, V, nat, hAPP(int, int, bit1, pls))), int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))))
60.25/7.96	= { by lemma 26 R->L }
60.25/7.96	  fresh874(X, X, Y, fresh90(pls, hAPP(nat, int, power_power(int, fresh757(U, U, int, hAPP(int, int, bit1, pls), fresh63(W, W, int, n))), fresh62(V, V, nat, hAPP(int, int, bit1, pls))), int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))))
60.25/7.96	= { by lemma 29 }
60.25/7.96	  fresh874(X, X, Y, fresh90(pls, hAPP(nat, int, power_power(int, hAPP(int, int, succ, fresh63(W, W, int, n))), fresh62(V, V, nat, hAPP(int, int, bit1, pls))), int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))))
60.25/7.96	= { by lemma 25 }
60.25/7.96	  fresh874(X, X, Y, fresh90(pls, hAPP(nat, int, power_power(int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))), fresh62(V, V, nat, hAPP(int, int, bit1, pls))), int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))))
60.25/7.96	= { by axiom 13 (fact_99_number__of__Bit0) }
60.25/7.96	  fresh874(X, X, Y, fresh90(pls, hAPP(nat, int, power_power(int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))), int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))))
60.25/7.96	= { by axiom 20 (fact_5_zero__eq__power2_1) R->L }
60.25/7.96	  fresh874(X, X, Y, fresh90(pls, fresh881(ring_11004092258visors(int), true2, int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))), int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))))
60.25/7.96	= { by axiom 1 (fact_73_Pls__def) }
60.25/7.96	  fresh874(X, X, Y, fresh90(zero_zero(int), fresh881(ring_11004092258visors(int), true2, int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))), int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))))
60.25/7.96	= { by axiom 20 (fact_5_zero__eq__power2_1) }
60.25/7.96	  fresh874(X, X, Y, fresh90(zero_zero(int), hAPP(nat, int, power_power(int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))), number_number_of(nat, hAPP(int, int, bit0, hAPP(int, int, bit1, pls)))), int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))))
60.25/7.96	= { by axiom 21 (fact_5_zero__eq__power2) R->L }
60.25/7.96	  fresh874(X, X, Y, fresh89(ring_11004092258visors(int), true2, int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))))
60.25/7.96	= { by axiom 2 (arity_Int_Oint___Rings_Oring__1__no__zero__divisors) }
60.25/7.96	  fresh874(X, X, Y, fresh89(true2, true2, int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))))
60.25/7.96	= { by axiom 7 (fact_5_zero__eq__power2) }
60.25/7.96	  fresh874(X, X, Y, ti(int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))))
60.25/7.96	= { by axiom 5 (fact_211_add_Ocomm__neutral) R->L }
60.25/7.96	  fresh874(X, X, Y, fresh384(true2, true2, int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))))
60.25/7.96	= { by axiom 3 (arity_Int_Oint___Groups_Ocomm__monoid__add) R->L }
60.25/7.96	  fresh874(X, X, Y, fresh384(comm_monoid_add(int), true2, int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))))
60.25/7.96	= { by axiom 15 (fact_211_add_Ocomm__neutral) }
60.25/7.96	  fresh874(X, X, Y, hAPP(int, int, plus_plus(int, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n))), zero_zero(int)))
60.25/7.96	= { by axiom 16 (fact_79_zadd__0__right) R->L }
60.25/7.96	  fresh874(X, X, Y, hAPP(int, int, succ, fresh313(zero_zero(nat), n, n)))
60.25/7.96	= { by lemma 25 R->L }
60.25/7.96	  fresh874(X, X, Y, hAPP(int, int, succ, fresh63(T, T, int, n)))
60.25/7.96	= { by lemma 29 R->L }
60.25/7.96	  fresh874(X, X, Y, fresh757(S, S, int, hAPP(int, int, bit1, pls), fresh63(T, T, int, n)))
60.25/7.96	= { by lemma 26 }
60.25/7.96	  fresh874(X, X, Y, fresh757(X2, X2, int, fresh63(T, T, int, n), hAPP(int, int, bit1, pls)))
60.25/7.96	= { by lemma 24 }
60.25/7.96	  fresh874(X, X, Y, fresh757(X2, X2, int, fresh63(T, T, int, n), one_one(int)))
60.25/7.96	= { by axiom 8 (fact_94_number__of__int) }
60.25/7.96	  fresh874(X, X, Y, fresh757(X2, X2, int, hAPP(nat, int, semiring_1_of_nat(int), n), one_one(int)))
60.25/7.96	= { by axiom 11 (fact_267_add__nonneg__eq__0__iff_2) }
60.25/7.96	  fresh874(X, X, Y, hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n)))
60.25/7.96	= { by lemma 28 R->L }
60.25/7.96	  fresh686(Y2, Y2, Z2, pls, hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n)))
60.25/7.96	= { by axiom 1 (fact_73_Pls__def) }
60.25/7.96	  fresh686(Y2, Y2, Z2, zero_zero(int), hAPP(int, int, plus_plus(int, one_one(int)), hAPP(nat, int, semiring_1_of_nat(int), n)))
60.25/7.96	= { by lemma 27 R->L }
60.25/7.96	  fresh299(W2, W2, 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)))
60.25/7.96	= { by axiom 10 (fact_291_transfer__int__nat__quantifiers_I1_J_1) }
60.25/7.96	  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))))
60.25/7.96	= { by axiom 22 (fact_0_n1pos) }
60.25/7.96	  true2
60.25/7.96	
60.25/7.96	Goal 1 (fact_32_rel__simps_I2_J): hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), pls)) = true2.
60.25/7.96	Proof:
60.25/7.96	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), pls))
60.25/7.96	= { by axiom 10 (fact_291_transfer__int__nat__quantifiers_I1_J_1) R->L }
60.25/7.96	  fresh299(X, X, hAPP(int, fun(int, bool), ord_less(int), pls), pls)
60.25/7.96	= { by lemma 27 }
60.25/7.96	  fresh686(Y, Y, Z, pls, pls)
60.25/7.96	= { by lemma 28 }
60.25/7.96	  fresh874(W, W, V, pls)
60.25/7.96	= { by lemma 30 R->L }
60.25/7.96	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int)))
60.25/7.96	= { by lemma 31 }
60.25/7.96	  true2
60.25/7.96	
60.25/7.96	Goal 2 (fact_57_bin__less__0__simps_I1_J): hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int))) = true2.
60.25/7.96	Proof:
60.25/7.96	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int)))
60.25/7.96	= { by lemma 31 }
60.25/7.96	  true2
60.25/7.96	% SZS output end Proof
60.25/7.96	
60.25/7.96	RESULT: Theorem (the conjecture is true).
60.25/7.99	EOF