TSTP Solution File: SWV675-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV675-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n014.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 : Thu Aug 31 23:05:51 EDT 2023
% Result : Unsatisfiable 112.75s 14.83s
% Output : Proof 112.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV675-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.34 % Computer : n014.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Aug 29 06:53:45 EDT 2023
% 0.16/0.35 % CPUTime :
% 112.75/14.83 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 112.75/14.83
% 112.75/14.83 % SZS status Unsatisfiable
% 112.75/14.83
% 112.75/14.84 % SZS output start Proof
% 112.75/14.84 Take the following subset of the input axioms:
% 112.75/14.85 fof(cls_Suc__mult__cancel1_0, axiom, ![V_m, V_n, V_k]: (c_HOL_Otimes__class_Otimes(c_Suc(V_k), V_m, tc_nat)!=c_HOL_Otimes__class_Otimes(c_Suc(V_k), V_n, tc_nat) | V_m=V_n)).
% 112.75/14.85 fof(cls_Suc__n__not__le__n_0, axiom, ![V_n2]: ~c_lessequals(c_Suc(V_n2), V_n2, tc_nat)).
% 112.75/14.85 fof(cls_Suc__n__not__n_0, axiom, ![V_n2]: c_Suc(V_n2)!=V_n2).
% 112.75/14.85 fof(cls_Suc__neq__Zero_0, axiom, ![V_m2]: c_Suc(V_m2)!=c_HOL_Ozero__class_Ozero(tc_nat)).
% 112.75/14.85 fof(cls_Zero__neq__Suc_0, axiom, ![V_m2]: c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_m2)).
% 112.75/14.85 fof(cls_abs__not__less__zero_0, axiom, ![T_a, V_a]: (~class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a))).
% 112.75/14.85 fof(cls_conjecture_0, negated_conjecture, c_lessequals(c_Suc(v_y), c_HOL_Ozero__class_Ozero(tc_nat), tc_nat)).
% 112.75/14.85 fof(cls_conjecture_1, negated_conjecture, c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a, t_a), c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(v_y), tc_nat), t_a)!=c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a, c_Suc(v_y), t_a), c_Power_Opower__class_Opower(v_a, c_HOL_Ozero__class_Ozero(tc_nat), t_a), t_a)).
% 112.75/14.85 fof(cls_diff__is__0__eq_1, axiom, ![V_n2, V_m2]: (c_HOL_Ominus__class_Ominus(V_m2, V_n2, tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat) | ~c_lessequals(V_m2, V_n2, tc_nat))).
% 112.75/14.85 fof(cls_even__Suc_0, axiom, ![V_x]: (~c_Parity_Oeven__odd__class_Oeven(V_x, tc_nat) | ~c_Parity_Oeven__odd__class_Oeven(c_Suc(V_x), tc_nat))).
% 112.75/14.85 fof(cls_fact__nonzero__nat_0, axiom, ![V_n2]: c_Fact_Ofact__class_Ofact(V_n2, tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)).
% 112.75/14.85 fof(cls_gcd__pos__nat_0, axiom, ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_GCD_Ogcd__class_Ogcd(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Ozero__class_Ozero(tc_nat), tc_nat), tc_nat)).
% 112.75/14.85 fof(cls_gr__implies__not0_0, axiom, ![V_m2]: ~c_HOL_Oord__class_Oless(V_m2, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat)).
% 112.75/14.85 fof(cls_le__number__of__eq__not__less_0, axiom, ![V_v, V_w, T_a2]: (~class_Orderings_Olinorder(T_a2) | (~class_Int_Onumber(T_a2) | (~c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w, T_a2), c_Int_Onumber__class_Onumber__of(V_v, T_a2), T_a2) | ~c_lessequals(c_Int_Onumber__class_Onumber__of(V_v, T_a2), c_Int_Onumber__class_Onumber__of(V_w, T_a2), T_a2))))).
% 112.75/14.85 fof(cls_less__le__not__le_1, axiom, ![V_y, T_a2, V_x2]: (~class_Orderings_Opreorder(T_a2) | (~c_lessequals(V_y, V_x2, T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_y, T_a2)))).
% 112.75/14.85 fof(cls_less__not__refl_0, axiom, ![V_n2]: ~c_HOL_Oord__class_Oless(V_n2, V_n2, tc_nat)).
% 112.75/14.85 fof(cls_linorder__antisym__conv2_1, axiom, ![T_a2, V_x2]: (~class_Orderings_Olinorder(T_a2) | (~c_lessequals(V_x2, V_x2, T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_x2, T_a2)))).
% 112.75/14.85 fof(cls_linorder__neq__iff_1, axiom, ![T_a2, V_x2]: (~class_Orderings_Olinorder(T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_x2, T_a2))).
% 112.75/14.85 fof(cls_linorder__not__le_1, axiom, ![T_a2, V_x2, V_y2]: (~class_Orderings_Olinorder(T_a2) | (~c_lessequals(V_x2, V_y2, T_a2) | ~c_HOL_Oord__class_Oless(V_y2, V_x2, T_a2)))).
% 112.75/14.85 fof(cls_linorder__not__less_1, axiom, ![T_a2, V_x2, V_y2]: (~class_Orderings_Olinorder(T_a2) | (~c_HOL_Oord__class_Oless(V_x2, V_y2, T_a2) | ~c_lessequals(V_y2, V_x2, T_a2)))).
% 112.75/14.85 fof(cls_minus__nat_Odiff__0_0, axiom, ![V_m2]: c_HOL_Ominus__class_Ominus(V_m2, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat)=V_m2).
% 112.75/14.85 fof(cls_mult__is__0_1, axiom, ![V_n2]: c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat), V_n2, tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)).
% 112.75/14.85 fof(cls_n__not__Suc__n_0, axiom, ![V_n2]: V_n2!=c_Suc(V_n2)).
% 112.75/14.85 fof(cls_nat_Osimps_I2_J_0, axiom, ![V_nat_H]: c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_nat_H)).
% 112.75/14.85 fof(cls_nat_Osimps_I3_J_0, axiom, ![V_nat_H2]: c_Suc(V_nat_H2)!=c_HOL_Ozero__class_Ozero(tc_nat)).
% 112.75/14.85 fof(cls_nat__dvd__not__less_0, axiom, ![V_n2, V_m2]: (~c_Ring__and__Field_Odvd__class_Odvd(V_n2, V_m2, tc_nat) | (~c_HOL_Oord__class_Oless(V_m2, V_n2, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_m2, tc_nat)))).
% 112.75/14.85 fof(cls_nat__less__le_1, axiom, ![V_x2]: ~c_HOL_Oord__class_Oless(V_x2, V_x2, tc_nat)).
% 112.75/14.85 fof(cls_neq0__conv_1, axiom, ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Ozero__class_Ozero(tc_nat), tc_nat)).
% 112.75/14.85 fof(cls_not__add__less1_0, axiom, ![V_i, V_j]: ~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i, V_j, tc_nat), V_i, tc_nat)).
% 112.75/14.85 fof(cls_not__add__less2_0, axiom, ![V_i2, V_j2]: ~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j2, V_i2, tc_nat), V_i2, tc_nat)).
% 112.75/14.85 fof(cls_not__less0_0, axiom, ![V_n2]: ~c_HOL_Oord__class_Oless(V_n2, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat)).
% 112.75/14.85 fof(cls_not__less__eq_1, axiom, ![V_n2, V_m2]: (~c_HOL_Oord__class_Oless(V_m2, V_n2, tc_nat) | ~c_HOL_Oord__class_Oless(V_n2, c_Suc(V_m2), tc_nat))).
% 112.75/14.85 fof(cls_not__less__eq__eq_1, axiom, ![V_n2, V_m2]: (~c_lessequals(V_m2, V_n2, tc_nat) | ~c_lessequals(c_Suc(V_n2), V_m2, tc_nat))).
% 112.75/14.85 fof(cls_not__less__iff__gr__or__eq_1, axiom, ![T_a2, V_x2, V_y2]: (~class_Orderings_Olinorder(T_a2) | (~c_HOL_Oord__class_Oless(V_x2, V_y2, T_a2) | ~c_HOL_Oord__class_Oless(V_y2, V_x2, T_a2)))).
% 112.75/14.85 fof(cls_not__one__le__zero_0, axiom, ![T_a2]: (~class_Ring__and__Field_Oordered__semidom(T_a2) | ~c_lessequals(c_HOL_Oone__class_Oone(T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 112.75/14.85 fof(cls_not__one__less__zero_0, axiom, ![T_a2]: (~class_Ring__and__Field_Oordered__semidom(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 112.75/14.85 fof(cls_not__square__less__zero_0, axiom, ![T_a2, V_a2]: (~class_Ring__and__Field_Oordered__ring__strict(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a2, V_a2, T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 112.75/14.85 fof(cls_not__sum__squares__lt__zero_0, axiom, ![T_a2, V_x2, V_y2]: (~class_Ring__and__Field_Oordered__ring__strict(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x2, V_x2, T_a2), c_HOL_Otimes__class_Otimes(V_y2, V_y2, T_a2), T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 112.75/14.85 fof(cls_nz_0, axiom, ~class_Ring__and__Field_Ofield(t_a) | v_a!=c_HOL_Ozero__class_Ozero(t_a)).
% 112.75/14.85 fof(cls_odd__nat__equiv__def2_1, axiom, ![V_xa]: ~c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))), V_xa, tc_nat)), tc_nat)).
% 112.75/14.85 fof(cls_odd__nat__equiv__def_1, axiom, ![V_x2]: (c_Divides_Odiv__class_Omod(V_x2, c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))), tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) | ~c_Parity_Oeven__odd__class_Oeven(V_x2, tc_nat))).
% 112.75/14.85 fof(cls_of__nat__fact__not__zero_0, axiom, ![T_a2, V_n2]: (~class_Nat_Osemiring__char__0(T_a2) | c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(V_n2, tc_nat), T_a2)!=c_HOL_Ozero__class_Ozero(T_a2))).
% 112.75/14.85 fof(cls_of__nat__less__0__iff_0, axiom, ![T_a2, V_m2]: (~class_Ring__and__Field_Oordered__semidom(T_a2) | ~c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m2, T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 112.75/14.85 fof(cls_one__neq__zero_0, axiom, ![T_a2]: (~class_Ring__and__Field_Ozero__neq__one(T_a2) | c_HOL_Oone__class_Oone(T_a2)!=c_HOL_Ozero__class_Ozero(T_a2))).
% 112.75/14.85 fof(cls_order__less__asym_0, axiom, ![T_a2, V_x2, V_y2]: (~class_Orderings_Opreorder(T_a2) | (~c_HOL_Oord__class_Oless(V_y2, V_x2, T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_y2, T_a2)))).
% 112.75/14.85 fof(cls_order__less__asym_H_0, axiom, ![V_b, T_a2, V_a2]: (~class_Orderings_Opreorder(T_a2) | (~c_HOL_Oord__class_Oless(V_b, V_a2, T_a2) | ~c_HOL_Oord__class_Oless(V_a2, V_b, T_a2)))).
% 112.75/14.85 fof(cls_order__less__irrefl_0, axiom, ![T_a2, V_x2]: (~class_Orderings_Opreorder(T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_x2, T_a2))).
% 112.75/14.85 fof(cls_order__less__le_1, axiom, ![T_a2, V_x2]: (~class_Orderings_Oorder(T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_x2, T_a2))).
% 112.75/14.85 fof(cls_power__eq__0__iff_1, axiom, ![T_a2, V_a2]: (~class_Ring__and__Field_Ozero__neq__one(T_a2) | (~class_Ring__and__Field_Ono__zero__divisors(T_a2) | (~class_Ring__and__Field_Omult__zero(T_a2) | (~class_Power_Opower(T_a2) | c_Power_Opower__class_Opower(V_a2, c_HOL_Ozero__class_Ozero(tc_nat), T_a2)!=c_HOL_Ozero__class_Ozero(T_a2)))))).
% 112.75/14.85 fof(cls_power__eq__0__iff__number__of_1, axiom, ![T_a2, V_a2, V_w2]: (~class_Ring__and__Field_Ozero__neq__one(T_a2) | (~class_Ring__and__Field_Ono__zero__divisors(T_a2) | (~class_Ring__and__Field_Omult__zero(T_a2) | (~class_Power_Opower(T_a2) | (c_Int_Onumber__class_Onumber__of(V_w2, tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(V_a2, c_Int_Onumber__class_Onumber__of(V_w2, tc_nat), T_a2)!=c_HOL_Ozero__class_Ozero(T_a2))))))).
% 112.75/14.85 fof(cls_power__le__zero__eq_0, axiom, ![T_a2, V_x2]: (~class_Ring__and__Field_Oordered__idom(T_a2) | ~c_lessequals(c_Power_Opower__class_Opower(V_x2, c_HOL_Ozero__class_Ozero(tc_nat), T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 112.75/14.85 fof(cls_power__le__zero__eq__number__of_0, axiom, ![T_a2, V_x2, V_w2]: (~class_Ring__and__Field_Oordered__idom(T_a2) | (c_Int_Onumber__class_Onumber__of(V_w2, tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat) | ~c_lessequals(c_Power_Opower__class_Opower(V_x2, c_Int_Onumber__class_Onumber__of(V_w2, tc_nat), T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2)))).
% 112.75/14.85 fof(cls_power__less__zero__eq_0, axiom, ![T_a2, V_x2, V_n2]: (~class_Ring__and__Field_Oordered__idom(T_a2) | (~c_Parity_Oeven__odd__class_Oeven(V_n2, tc_nat) | ~c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x2, V_n2, T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2)))).
% 112.75/14.85 fof(cls_power__less__zero__eq__number__of_0, axiom, ![T_a2, V_x2, V_w2]: (~class_Ring__and__Field_Oordered__idom(T_a2) | (~c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w2, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x2, c_Int_Onumber__class_Onumber__of(V_w2, tc_nat), T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2)))).
% 112.75/14.85 fof(cls_sum__squares__gt__zero__iff_0, axiom, ![T_a2]: (~class_Ring__and__Field_Oordered__ring__strict(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a2), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2), c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2), T_a2), T_a2))).
% 112.75/14.85 fof(cls_xt1_I9_J_0, axiom, ![T_a2, V_a2, V_b2]: (~class_Orderings_Oorder(T_a2) | (~c_HOL_Oord__class_Oless(V_a2, V_b2, T_a2) | ~c_HOL_Oord__class_Oless(V_b2, V_a2, T_a2)))).
% 112.75/14.85 fof(cls_zero__less__abs__iff_0, axiom, ![T_a2]: (~class_OrderedGroup_Opordered__ab__group__add__abs(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a2), c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a2), T_a2), T_a2))).
% 112.75/14.85 fof(cls_zero__neq__one_0, axiom, ![T_a2]: (~class_Ring__and__Field_Ozero__neq__one(T_a2) | c_HOL_Ozero__class_Ozero(T_a2)!=c_HOL_Oone__class_Oone(T_a2))).
% 112.75/14.85
% 112.75/14.85 Now clausify the problem and encode Horn clauses using encoding 3 of
% 112.75/14.85 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 112.75/14.85 We repeatedly replace C & s=t => u=v by the two clauses:
% 112.75/14.85 fresh(y, y, x1...xn) = u
% 112.75/14.85 C => fresh(s, t, x1...xn) = v
% 112.75/14.85 where fresh is a fresh function symbol and x1..xn are the free
% 112.75/14.85 variables of u and v.
% 112.75/14.85 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 112.75/14.85 input problem has no model of domain size 1).
% 112.75/14.85
% 112.75/14.85 The encoding turns the above axioms into the following unit equations and goals:
% 112.75/14.85
% 112.75/14.85 Axiom 1 (cls_mult__is__0_1): c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat), X, tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat).
% 112.75/14.85 Axiom 2 (cls_minus__nat_Odiff__0_0): c_HOL_Ominus__class_Ominus(X, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) = X.
% 112.75/14.85 Axiom 3 (cls_diff__is__0__eq_1): fresh764(X, X, Y, Z) = c_HOL_Ozero__class_Ozero(tc_nat).
% 112.75/14.85 Axiom 4 (cls_Suc__mult__cancel1_0): fresh5(X, X, Y, Z) = Z.
% 112.75/14.85 Axiom 5 (cls_conjecture_0): c_lessequals(c_Suc(v_y), c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) = true2.
% 112.75/14.85 Axiom 6 (cls_diff__is__0__eq_1): fresh764(c_lessequals(X, Y, tc_nat), true2, X, Y) = c_HOL_Ominus__class_Ominus(X, Y, tc_nat).
% 112.75/14.85 Axiom 7 (cls_Suc__mult__cancel1_0): fresh5(c_HOL_Otimes__class_Otimes(c_Suc(X), Y, tc_nat), c_HOL_Otimes__class_Otimes(c_Suc(X), Z, tc_nat), Y, Z) = Y.
% 112.75/14.85
% 112.75/14.85 Lemma 8: c_Suc(v_y) = c_HOL_Ozero__class_Ozero(tc_nat).
% 112.75/14.85 Proof:
% 112.75/14.85 c_Suc(v_y)
% 112.75/14.85 = { by axiom 2 (cls_minus__nat_Odiff__0_0) R->L }
% 112.75/14.85 c_HOL_Ominus__class_Ominus(c_Suc(v_y), c_HOL_Ozero__class_Ozero(tc_nat), tc_nat)
% 112.75/14.85 = { by axiom 6 (cls_diff__is__0__eq_1) R->L }
% 112.75/14.85 fresh764(c_lessequals(c_Suc(v_y), c_HOL_Ozero__class_Ozero(tc_nat), tc_nat), true2, c_Suc(v_y), c_HOL_Ozero__class_Ozero(tc_nat))
% 112.75/14.85 = { by axiom 5 (cls_conjecture_0) }
% 112.75/14.85 fresh764(true2, true2, c_Suc(v_y), c_HOL_Ozero__class_Ozero(tc_nat))
% 112.75/14.85 = { by axiom 3 (cls_diff__is__0__eq_1) }
% 112.75/14.85 c_HOL_Ozero__class_Ozero(tc_nat)
% 112.75/14.85
% 112.75/14.85 Lemma 9: Y = X.
% 112.75/14.85 Proof:
% 112.75/14.85 Y
% 112.75/14.85 = { by axiom 4 (cls_Suc__mult__cancel1_0) R->L }
% 112.75/14.85 fresh5(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Ozero__class_Ozero(tc_nat), X, Y)
% 112.75/14.85 = { by axiom 1 (cls_mult__is__0_1) R->L }
% 112.75/14.85 fresh5(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat), Y, tc_nat), X, Y)
% 112.75/14.85 = { by lemma 8 R->L }
% 112.75/14.85 fresh5(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Otimes__class_Otimes(c_Suc(v_y), Y, tc_nat), X, Y)
% 112.75/14.85 = { by axiom 1 (cls_mult__is__0_1) R->L }
% 112.75/14.85 fresh5(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat), X, tc_nat), c_HOL_Otimes__class_Otimes(c_Suc(v_y), Y, tc_nat), X, Y)
% 112.75/14.85 = { by lemma 8 R->L }
% 112.75/14.85 fresh5(c_HOL_Otimes__class_Otimes(c_Suc(v_y), X, tc_nat), c_HOL_Otimes__class_Otimes(c_Suc(v_y), Y, tc_nat), X, Y)
% 112.75/14.85 = { by axiom 7 (cls_Suc__mult__cancel1_0) }
% 112.75/14.85 X
% 112.75/14.85
% 112.75/14.85 Goal 1 (true_equals_false): true = false.
% 112.75/14.85 Proof:
% 112.75/14.85 true
% 112.75/14.85 = { by lemma 9 }
% 112.75/14.85 false
% 112.75/14.85
% 112.75/14.85 Goal 2 (cls_conjecture_1): c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a, t_a), c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(v_y), tc_nat), t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a, c_Suc(v_y), t_a), c_Power_Opower__class_Opower(v_a, c_HOL_Ozero__class_Ozero(tc_nat), t_a), t_a).
% 112.75/14.85 Proof:
% 112.75/14.85 c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a, t_a), c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(v_y), tc_nat), t_a)
% 112.75/14.85 = { by lemma 9 }
% 112.75/14.85 c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a, c_Suc(v_y), t_a), c_Power_Opower__class_Opower(v_a, c_HOL_Ozero__class_Ozero(tc_nat), t_a), t_a)
% 112.75/14.85
% 112.75/14.85 Goal 3 (cls_nz_0): tuple6(v_a, class_Ring__and__Field_Ofield(t_a)) = tuple6(c_HOL_Ozero__class_Ozero(t_a), true2).
% 112.75/14.85 Proof:
% 112.75/14.85 tuple6(v_a, class_Ring__and__Field_Ofield(t_a))
% 112.75/14.85 = { by lemma 9 }
% 112.75/14.85 tuple6(c_HOL_Ozero__class_Ozero(t_a), true2)
% 112.75/14.85
% 112.75/14.85 Goal 4 (cls_neq0__conv_1): c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) = true2.
% 112.75/14.85 Proof:
% 112.75/14.85 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Ozero__class_Ozero(tc_nat), tc_nat)
% 112.75/14.85 = { by lemma 9 }
% 112.75/14.85 true2
% 112.75/14.85
% 112.75/14.85 Goal 5 (cls_gcd__pos__nat_0): c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_GCD_Ogcd__class_Ogcd(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Ozero__class_Ozero(tc_nat), tc_nat), tc_nat) = true2.
% 112.75/14.85 Proof:
% 112.75/14.85 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_GCD_Ogcd__class_Ogcd(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Ozero__class_Ozero(tc_nat), tc_nat), tc_nat)
% 112.75/14.85 = { by lemma 9 }
% 112.75/14.85 true2
% 112.75/14.85 % SZS output end Proof
% 112.75/14.85
% 112.75/14.85 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------