TSTP Solution File: SCT159+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SCT159+1 : TPTP v8.1.2. Released v5.2.0.
% 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 : n028.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 14:22:16 EDT 2023
% Result : Theorem 162.19s 21.20s
% Output : Proof 162.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT159+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.33 % Computer : n028.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 15:11:19 EDT 2023
% 0.14/0.34 % CPUTime :
% 162.19/21.20 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 162.19/21.20
% 162.19/21.20 % SZS status Theorem
% 162.19/21.20
% 162.19/21.23 % SZS output start Proof
% 162.19/21.23 Take the following subset of the input axioms:
% 162.19/21.24 fof(arity_HOL__Obool__Orderings_Oord, axiom, class_Orderings_Oord(tc_HOL_Obool)).
% 162.19/21.24 fof(conj_1, conjecture, v_thesis____).
% 162.19/21.24 fof(fact_Ints__odd__nonzero, axiom, ![T_a, V_a_2]: (class_Int_Oring__char__0(T_a) => (c_member(T_a, V_a_2, c_Int_Oring__1__class_OInts(T_a)) => c_Groups_Oplus__class_Oplus(T_a, c_Groups_Oplus__class_Oplus(T_a, c_Groups_Oone__class_Oone(T_a), V_a_2), V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)))).
% 162.19/21.24 fof(fact_Nat_Oadd__0__right, axiom, ![V_m]: c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 162.19/21.24 fof(fact_One__nat__def, axiom, c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 162.19/21.24 fof(fact_Suc__eq__plus1__left, axiom, ![V_n]: hAPP(c_Nat_OSuc, V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), V_n)).
% 162.19/21.24 fof(fact_Suc__n__not__le__n, axiom, ![V_n2]: ~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Nat_OSuc, V_n2), V_n2)).
% 162.19/21.24 fof(fact_Suc__n__not__n, axiom, ![V_n2]: hAPP(c_Nat_OSuc, V_n2)!=V_n2).
% 162.19/21.24 fof(fact_Suc__neq__Zero, axiom, ![V_m2]: hAPP(c_Nat_OSuc, V_m2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 162.19/21.24 fof(fact_Suc__not__Zero, axiom, ![V_m2]: hAPP(c_Nat_OSuc, V_m2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 162.19/21.24 fof(fact_UNIV__not__empty, axiom, ![T_a2]: c_Orderings_Otop__class_Otop(tc_fun(T_a2, tc_HOL_Obool))!=c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool))).
% 162.19/21.24 fof(fact_Zero__neq__Suc, axiom, ![V_m2]: c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc, V_m2)).
% 162.19/21.24 fof(fact_Zero__not__Suc, axiom, ![V_m2]: c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc, V_m2)).
% 162.19/21.24 fof(fact_all__not__in__conv, axiom, ![V_A_2, T_a2]: (![B_x]: ~c_member(T_a2, B_x, V_A_2) <=> V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool)))).
% 162.19/21.24 fof(fact_atLeastLessThan__empty__iff, axiom, ![V_b_2, T_a2, V_a_2_2]: (class_Orderings_Oorder(T_a2) => (c_SetInterval_Oord__class_OatLeastLessThan(T_a2, V_a_2_2, V_b_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool)) <=> ~c_Orderings_Oord__class_Oless(T_a2, V_a_2_2, V_b_2)))).
% 162.19/21.24 fof(fact_atLeastLessThan__empty__iff2, axiom, ![T_a2, V_a_2_2, V_b_2_2]: (class_Orderings_Oorder(T_a2) => (c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastLessThan(T_a2, V_a_2_2, V_b_2_2) <=> ~c_Orderings_Oord__class_Oless(T_a2, V_a_2_2, V_b_2_2)))).
% 162.19/21.24 fof(fact_atLeastatMost__empty__iff, axiom, ![T_a2, V_a_2_2, V_b_2_2]: (class_Orderings_Oorder(T_a2) => (c_SetInterval_Oord__class_OatLeastAtMost(T_a2, V_a_2_2, V_b_2_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool)) <=> ~c_Orderings_Oord__class_Oless__eq(T_a2, V_a_2_2, V_b_2_2)))).
% 162.19/21.24 fof(fact_atLeastatMost__empty__iff2, axiom, ![T_a2, V_a_2_2, V_b_2_2]: (class_Orderings_Oorder(T_a2) => (c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastAtMost(T_a2, V_a_2_2, V_b_2_2) <=> ~c_Orderings_Oord__class_Oless__eq(T_a2, V_a_2_2, V_b_2_2)))).
% 162.19/21.24 fof(fact_card_Oempty, axiom, ![T_a2]: c_Finite__Set_Ocard(T_a2, c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 162.19/21.24 fof(fact_card__Suc__eq, axiom, ![V_k_2, T_a2, V_A_2_2]: (c_Finite__Set_Ocard(T_a2, V_A_2_2)=hAPP(c_Nat_OSuc, V_k_2) <=> ?[B_b, B_B]: (V_A_2_2=c_Set_Oinsert(T_a2, B_b, B_B) & (~c_member(T_a2, B_b, B_B) & (c_Finite__Set_Ocard(T_a2, B_B)=V_k_2 & (V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat) => B_B=c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool)))))))).
% 162.19/21.24 fof(fact_card__UNIV__unit, axiom, c_Finite__Set_Ocard(tc_Product__Type_Ounit, c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit, tc_HOL_Obool)))=c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 162.19/21.24 fof(fact_card__gt__0__iff, axiom, ![T_a2, V_A_2_2]: (c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Finite__Set_Ocard(T_a2, V_A_2_2)) <=> (V_A_2_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool)) & c_Finite__Set_Ofinite(T_a2, V_A_2_2)))).
% 162.19/21.24 fof(fact_emptyE, axiom, ![T_a2, V_a_2_2]: ~c_member(T_a2, V_a_2_2, c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool)))).
% 162.19/21.24 fof(fact_empty__iff, axiom, ![V_c_2, T_a2]: ~c_member(T_a2, V_c_2, c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool)))).
% 162.19/21.24 fof(fact_empty__not__insert, axiom, ![T_a2, V_A_2_2, V_a_2_2]: c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool))!=c_Set_Oinsert(T_a2, V_a_2_2, V_A_2_2)).
% 162.19/21.24 fof(fact_empty__subsetI, axiom, ![T_a2, V_A_2_2]: c_Orderings_Oord__class_Oless__eq(tc_fun(T_a2, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool)), V_A_2_2)).
% 162.19/21.24 fof(fact_equalityI, axiom, ![V_B_2, T_a2, V_A_2_2]: (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a2, tc_HOL_Obool), V_A_2_2, V_B_2) => (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a2, tc_HOL_Obool), V_B_2, V_A_2_2) => V_A_2_2=V_B_2))).
% 162.19/21.24 fof(fact_equals0D, axiom, ![T_a2, V_A_2_2, V_a_2_2]: (V_A_2_2=c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool)) => ~c_member(T_a2, V_a_2_2, V_A_2_2))).
% 162.19/21.24 fof(fact_ex__in__conv, axiom, ![T_a2, V_A_2_2]: (?[B_x2]: c_member(T_a2, B_x2, V_A_2_2) <=> V_A_2_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool)))).
% 162.19/21.24 fof(fact_gr__implies__not0, axiom, ![V_n2, V_m2]: (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m2, V_n2) => V_n2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 162.19/21.24 fof(fact_infinite__UNIV__nat, axiom, ~c_Finite__Set_Ofinite(tc_Nat_Onat, c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))).
% 162.19/21.24 fof(fact_insert__not__empty, axiom, ![T_a2, V_A_2_2, V_a_2_2]: c_Set_Oinsert(T_a2, V_a_2_2, V_A_2_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool))).
% 162.19/21.24 fof(fact_leD, axiom, ![V_x, V_y, T_a2]: (class_Orderings_Olinorder(T_a2) => (c_Orderings_Oord__class_Oless__eq(T_a2, V_y, V_x) => ~c_Orderings_Oord__class_Oless(T_a2, V_x, V_y)))).
% 162.19/21.24 fof(fact_le__fun__def, axiom, ![V_g_2, V_f_2, T_b, T_a2]: (class_Orderings_Oord(T_b) => (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a2, T_b), V_f_2, V_g_2) <=> ![B_x2]: c_Orderings_Oord__class_Oless__eq(T_b, hAPP(V_f_2, B_x2), hAPP(V_g_2, B_x2))))).
% 162.19/21.24 fof(fact_less__fun__def, axiom, ![T_a2, V_f_2_2, T_b2, V_g_2_2]: (class_Orderings_Oord(T_b2) => (c_Orderings_Oord__class_Oless(tc_fun(T_a2, T_b2), V_f_2_2, V_g_2_2) <=> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a2, T_b2), V_f_2_2, V_g_2_2) & ~c_Orderings_Oord__class_Oless__eq(tc_fun(T_a2, T_b2), V_g_2_2, V_f_2_2))))).
% 162.19/21.24 fof(fact_less__imp__neq, axiom, ![T_a2, V_x2, V_y2]: (class_Orderings_Oorder(T_a2) => (c_Orderings_Oord__class_Oless(T_a2, V_x2, V_y2) => V_x2!=V_y2))).
% 162.19/21.24 fof(fact_less__irrefl__nat, axiom, ![V_n2]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n2, V_n2)).
% 162.19/21.24 fof(fact_less__le__not__le, axiom, ![V_x_2, V_y_2, T_a2]: (class_Orderings_Opreorder(T_a2) => (c_Orderings_Oord__class_Oless(T_a2, V_x_2, V_y_2) <=> (c_Orderings_Oord__class_Oless__eq(T_a2, V_x_2, V_y_2) & ~c_Orderings_Oord__class_Oless__eq(T_a2, V_y_2, V_x_2))))).
% 162.19/21.24 fof(fact_less__nat__zero__code, axiom, ![V_n2]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n2, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 162.19/21.24 fof(fact_less__not__refl, axiom, ![V_n2]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n2, V_n2)).
% 162.19/21.24 fof(fact_less__not__refl2, axiom, ![V_n2, V_m2]: (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n2, V_m2) => V_m2!=V_n2)).
% 162.19/21.24 fof(fact_less__not__refl3, axiom, ![V_t, V_s]: (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_s, V_t) => V_s!=V_t)).
% 162.19/21.24 fof(fact_less__zeroE, axiom, ![V_n2]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n2, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 162.19/21.24 fof(fact_linorder__antisym__conv2, axiom, ![T_a2, V_x_2_2, V_y_2_2]: (class_Orderings_Olinorder(T_a2) => (c_Orderings_Oord__class_Oless__eq(T_a2, V_x_2_2, V_y_2_2) => (~c_Orderings_Oord__class_Oless(T_a2, V_x_2_2, V_y_2_2) <=> V_x_2_2=V_y_2_2)))).
% 162.19/21.24 fof(fact_linorder__neq__iff, axiom, ![T_a2, V_x_2_2, V_y_2_2]: (class_Orderings_Olinorder(T_a2) => (V_x_2_2!=V_y_2_2 <=> (c_Orderings_Oord__class_Oless(T_a2, V_x_2_2, V_y_2_2) | c_Orderings_Oord__class_Oless(T_a2, V_y_2_2, V_x_2_2))))).
% 162.19/21.24 fof(fact_linorder__not__le, axiom, ![T_a2, V_x_2_2, V_y_2_2]: (class_Orderings_Olinorder(T_a2) => (~c_Orderings_Oord__class_Oless__eq(T_a2, V_x_2_2, V_y_2_2) <=> c_Orderings_Oord__class_Oless(T_a2, V_y_2_2, V_x_2_2)))).
% 162.19/21.24 fof(fact_linorder__not__less, axiom, ![T_a2, V_x_2_2, V_y_2_2]: (class_Orderings_Olinorder(T_a2) => (~c_Orderings_Oord__class_Oless(T_a2, V_x_2_2, V_y_2_2) <=> c_Orderings_Oord__class_Oless__eq(T_a2, V_y_2_2, V_x_2_2)))).
% 162.19/21.24 fof(fact_mem__def, axiom, ![T_a2, V_x_2_2, V_A_2_2]: (c_member(T_a2, V_x_2_2, V_A_2_2) <=> hBOOL(hAPP(V_A_2_2, V_x_2_2)))).
% 162.19/21.24 fof(fact_n__not__Suc__n, axiom, ![V_n2]: V_n2!=hAPP(c_Nat_OSuc, V_n2)).
% 162.19/21.24 fof(fact_nat_Osimps_I2_J, axiom, ![V_nat_H]: c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc, V_nat_H)).
% 162.19/21.24 fof(fact_nat_Osimps_I3_J, axiom, ![V_nat_H_1]: hAPP(c_Nat_OSuc, V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 162.19/21.24 fof(fact_nat__less__cases, axiom, ![V_P_2, V_n_2, V_m_2]: ((c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) => hBOOL(hAPP(hAPP(V_P_2, V_n_2), V_m_2))) => ((V_m_2=V_n_2 => hBOOL(hAPP(hAPP(V_P_2, V_n_2), V_m_2))) => ((c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2) => hBOOL(hAPP(hAPP(V_P_2, V_n_2), V_m_2))) => hBOOL(hAPP(hAPP(V_P_2, V_n_2), V_m_2)))))).
% 162.19/21.24 fof(fact_nat__less__le, axiom, ![V_n_2_2, V_m_2_2]: (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2_2, V_n_2_2) <=> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m_2_2, V_n_2_2) & V_m_2_2!=V_n_2_2))).
% 162.19/21.24 fof(fact_nat__neq__iff, axiom, ![V_n_2_2, V_m_2_2]: (V_m_2_2!=V_n_2_2 <=> (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2_2, V_n_2_2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2_2, V_m_2_2)))).
% 162.19/21.24 fof(fact_neq0__conv, axiom, ![V_n_2_2]: (V_n_2_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n_2_2))).
% 162.19/21.24 fof(fact_not__add__less1, axiom, ![V_j, V_i]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_i, V_j), V_i)).
% 162.19/21.24 fof(fact_not__add__less2, axiom, ![V_j2, V_i2]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_j2, V_i2), V_i2)).
% 162.19/21.24 fof(fact_not__less0, axiom, ![V_n2]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n2, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 162.19/21.24 fof(fact_not__less__eq, axiom, ![V_n_2_2, V_m_2_2]: (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2_2, V_n_2_2) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2_2, hAPP(c_Nat_OSuc, V_m_2_2)))).
% 162.19/21.24 fof(fact_not__less__eq__eq, axiom, ![V_n_2_2, V_m_2_2]: (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m_2_2, V_n_2_2) <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Nat_OSuc, V_n_2_2), V_m_2_2))).
% 162.19/21.24 fof(fact_not__less__iff__gr__or__eq, axiom, ![T_a2, V_x_2_2, V_y_2_2]: (class_Orderings_Olinorder(T_a2) => (~c_Orderings_Oord__class_Oless(T_a2, V_x_2_2, V_y_2_2) <=> (c_Orderings_Oord__class_Oless(T_a2, V_y_2_2, V_x_2_2) | V_x_2_2=V_y_2_2)))).
% 162.19/21.24 fof(fact_not__one__le__zero, axiom, ![T_a2]: (class_Rings_Olinordered__semidom(T_a2) => ~c_Orderings_Oord__class_Oless__eq(T_a2, c_Groups_Oone__class_Oone(T_a2), c_Groups_Ozero__class_Ozero(T_a2)))).
% 162.19/21.24 fof(fact_not__one__less__zero, axiom, ![T_a2]: (class_Rings_Olinordered__semidom(T_a2) => ~c_Orderings_Oord__class_Oless(T_a2, c_Groups_Oone__class_Oone(T_a2), c_Groups_Ozero__class_Ozero(T_a2)))).
% 162.19/21.24 fof(fact_not__psubset__empty, axiom, ![T_a2, V_A_2_2]: ~c_Orderings_Oord__class_Oless(tc_fun(T_a2, tc_HOL_Obool), V_A_2_2, c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool)))).
% 162.19/21.24 fof(fact_one__neq__zero, axiom, ![T_a2]: (class_Rings_Ozero__neq__one(T_a2) => c_Groups_Oone__class_Oone(T_a2)!=c_Groups_Ozero__class_Ozero(T_a2))).
% 162.19/21.24 fof(fact_order__less__asym, axiom, ![T_a2, V_x2, V_y2]: (class_Orderings_Opreorder(T_a2) => (c_Orderings_Oord__class_Oless(T_a2, V_x2, V_y2) => ~c_Orderings_Oord__class_Oless(T_a2, V_y2, V_x2)))).
% 162.19/21.24 fof(fact_order__less__asym_H, axiom, ![V_b, V_a, T_a2]: (class_Orderings_Opreorder(T_a2) => (c_Orderings_Oord__class_Oless(T_a2, V_a, V_b) => ~c_Orderings_Oord__class_Oless(T_a2, V_b, V_a)))).
% 162.19/21.24 fof(fact_order__less__imp__not__eq, axiom, ![T_a2, V_x2, V_y2]: (class_Orderings_Oorder(T_a2) => (c_Orderings_Oord__class_Oless(T_a2, V_x2, V_y2) => V_x2!=V_y2))).
% 162.19/21.24 fof(fact_order__less__imp__not__eq2, axiom, ![T_a2, V_x2, V_y2]: (class_Orderings_Oorder(T_a2) => (c_Orderings_Oord__class_Oless(T_a2, V_x2, V_y2) => V_y2!=V_x2))).
% 162.19/21.24 fof(fact_order__less__imp__not__less, axiom, ![T_a2, V_x2, V_y2]: (class_Orderings_Opreorder(T_a2) => (c_Orderings_Oord__class_Oless(T_a2, V_x2, V_y2) => ~c_Orderings_Oord__class_Oless(T_a2, V_y2, V_x2)))).
% 162.19/21.24 fof(fact_order__less__irrefl, axiom, ![T_a2, V_x2]: (class_Orderings_Opreorder(T_a2) => ~c_Orderings_Oord__class_Oless(T_a2, V_x2, V_x2))).
% 162.19/21.24 fof(fact_order__less__le, axiom, ![T_a2, V_x_2_2, V_y_2_2]: (class_Orderings_Oorder(T_a2) => (c_Orderings_Oord__class_Oless(T_a2, V_x_2_2, V_y_2_2) <=> (c_Orderings_Oord__class_Oless__eq(T_a2, V_x_2_2, V_y_2_2) & V_x_2_2!=V_y_2_2)))).
% 162.19/21.24 fof(fact_order__less__not__sym, axiom, ![T_a2, V_x2, V_y2]: (class_Orderings_Opreorder(T_a2) => (c_Orderings_Oord__class_Oless(T_a2, V_x2, V_y2) => ~c_Orderings_Oord__class_Oless(T_a2, V_y2, V_x2)))).
% 162.19/21.24 fof(fact_pigeonhole, axiom, ![T_a2, V_A_2_2, V_f_2_2, T_b2]: (c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Finite__Set_Ocard(T_a2, c_Set_Oimage(T_b2, T_a2, V_f_2_2, V_A_2_2)), c_Finite__Set_Ocard(T_b2, V_A_2_2)) => ~c_Fun_Oinj__on(T_b2, T_a2, V_f_2_2, V_A_2_2))).
% 162.19/21.24 fof(fact_psubset__eq, axiom, ![T_a2, V_A_2_2, V_B_2_2]: (c_Orderings_Oord__class_Oless(tc_fun(T_a2, tc_HOL_Obool), V_A_2_2, V_B_2_2) <=> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a2, tc_HOL_Obool), V_A_2_2, V_B_2_2) & V_A_2_2!=V_B_2_2))).
% 162.19/21.24 fof(fact_singletonE, axiom, ![T_a2, V_a_2_2, V_b_2_2]: (c_member(T_a2, V_b_2_2, c_Set_Oinsert(T_a2, V_a_2_2, c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool)))) => V_b_2_2=V_a_2_2)).
% 162.19/21.24 fof(fact_subset__UNIV, axiom, ![T_a2, V_A_2_2]: c_Orderings_Oord__class_Oless__eq(tc_fun(T_a2, tc_HOL_Obool), V_A_2_2, c_Orderings_Otop__class_Otop(tc_fun(T_a2, tc_HOL_Obool)))).
% 162.19/21.24 fof(fact_subset__empty, axiom, ![T_a2, V_A_2_2]: (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a2, tc_HOL_Obool), V_A_2_2, c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool))) <=> V_A_2_2=c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_HOL_Obool)))).
% 162.19/21.24 fof(fact_top1I, axiom, ![T_a2, V_x_2_2]: hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a2, tc_HOL_Obool)), V_x_2_2))).
% 162.19/21.24 fof(fact_xt1_I9_J, axiom, ![T_a2, V_b2, V_a2]: (class_Orderings_Oorder(T_a2) => (c_Orderings_Oord__class_Oless(T_a2, V_b2, V_a2) => ~c_Orderings_Oord__class_Oless(T_a2, V_a2, V_b2)))).
% 162.19/21.24 fof(fact_zero__neq__one, axiom, ![T_a2]: (class_Rings_Ozero__neq__one(T_a2) => c_Groups_Ozero__class_Ozero(T_a2)!=c_Groups_Oone__class_Oone(T_a2))).
% 162.19/21.24 fof(help_c__fFalse__1, axiom, ~hBOOL(c_fFalse)).
% 162.19/21.24
% 162.19/21.24 Now clausify the problem and encode Horn clauses using encoding 3 of
% 162.19/21.24 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 162.19/21.24 We repeatedly replace C & s=t => u=v by the two clauses:
% 162.19/21.24 fresh(y, y, x1...xn) = u
% 162.19/21.24 C => fresh(s, t, x1...xn) = v
% 162.19/21.24 where fresh is a fresh function symbol and x1..xn are the free
% 162.19/21.24 variables of u and v.
% 162.19/21.24 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 162.19/21.24 input problem has no model of domain size 1).
% 162.19/21.24
% 162.19/21.24 The encoding turns the above axioms into the following unit equations and goals:
% 162.19/21.24
% 162.19/21.24 Axiom 1 (arity_HOL__Obool__Orderings_Oord): class_Orderings_Oord(tc_HOL_Obool) = true2.
% 162.19/21.24 Axiom 2 (fact_One__nat__def): c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 162.19/21.24 Axiom 3 (fact_Nat_Oadd__0__right): c_Groups_Oplus__class_Oplus(tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X.
% 162.19/21.24 Axiom 4 (fact_Suc__eq__plus1__left): hAPP(c_Nat_OSuc, X) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), X).
% 162.19/21.24 Axiom 5 (fact_equalityI): fresh64(X, X, Y, Z) = Y.
% 162.19/21.24 Axiom 6 (fact_subset__empty_1): fresh58(X, X, Y, Z) = Y.
% 162.19/21.24 Axiom 7 (fact_singletonE): fresh4(X, X, Y, Z) = Y.
% 162.19/21.24 Axiom 8 (fact_card_Oempty): c_Finite__Set_Ocard(X, c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 162.19/21.24 Axiom 9 (fact_card__UNIV__unit): c_Finite__Set_Ocard(tc_Product__Type_Ounit, c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 162.19/21.24 Axiom 10 (fact_card__Suc__eq_2): fresh417(X, X, Y, Z, W) = c_Orderings_Obot__class_Obot(tc_fun(W, tc_HOL_Obool)).
% 162.19/21.24 Axiom 11 (fact_card__Suc__eq_2): fresh416(X, X, Y, Z, W) = b_b2(Y, Z, W).
% 162.19/21.24 Axiom 12 (fact_mem__def): fresh229(X, X, Y, Z, W) = true2.
% 162.19/21.24 Axiom 13 (fact_equalityI): fresh65(X, X, Y, Z, W) = Z.
% 162.19/21.24 Axiom 14 (fact_card__Suc__eq_4): fresh12(X, X, Y, Z, W) = Z.
% 162.19/21.24 Axiom 15 (fact_top1I): hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), Y)) = true2.
% 162.19/21.24 Axiom 16 (fact_le__fun__def): fresh260(X, X, Y, Z, W, V) = c_Orderings_Oord__class_Oless__eq(tc_fun(W, V), Z, Y).
% 162.19/21.24 Axiom 17 (fact_le__fun__def): fresh259(X, X, Y, Z, W, V) = true2.
% 162.19/21.24 Axiom 18 (fact_le__fun__def_1): fresh257(X, X, Y, Z, W, V) = true2.
% 162.19/21.24 Axiom 19 (fact_card__Plus): fresh420(X, X, Y, Z, W, V) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Finite__Set_Ocard(V, W), c_Finite__Set_Ocard(Z, Y)).
% 162.19/21.24 Axiom 20 (fact_le__fun__def_1): fresh258(X, X, Y, Z, W, V, U) = c_Orderings_Oord__class_Oless__eq(V, hAPP(Z, U), hAPP(Y, U)).
% 162.19/21.24 Axiom 21 (fact_subset__UNIV): c_Orderings_Oord__class_Oless__eq(tc_fun(X, tc_HOL_Obool), Y, c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool))) = true2.
% 162.19/21.24 Axiom 22 (fact_empty__subsetI): c_Orderings_Oord__class_Oless__eq(tc_fun(X, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)), Y) = true2.
% 162.19/21.24 Axiom 23 (fact_mem__def): fresh229(hBOOL(hAPP(X, Y)), true2, X, Y, Z) = c_member(Z, Y, X).
% 162.19/21.24 Axiom 24 (fact_card__Suc__eq_2): fresh416(c_Finite__Set_Ocard(X, Y), hAPP(c_Nat_OSuc, Z), Z, Y, X) = fresh417(Z, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), Z, Y, X).
% 162.19/21.24 Axiom 25 (fact_card__Suc__eq_4): fresh12(c_Finite__Set_Ocard(X, Y), hAPP(c_Nat_OSuc, Z), Z, Y, X) = c_Set_Oinsert(X, b_b(Z, Y, X), b_b2(Z, Y, X)).
% 162.19/21.24 Axiom 26 (fact_equalityI): fresh65(c_Orderings_Oord__class_Oless__eq(tc_fun(X, tc_HOL_Obool), Y, Z), true2, Z, Y, X) = fresh64(c_Orderings_Oord__class_Oless__eq(tc_fun(X, tc_HOL_Obool), Z, Y), true2, Z, Y).
% 162.19/21.24 Axiom 27 (fact_le__fun__def_1): fresh258(class_Orderings_Oord(X), true2, Y, Z, W, X, V) = fresh257(c_Orderings_Oord__class_Oless__eq(tc_fun(W, X), Z, Y), true2, Y, Z, X, V).
% 162.19/21.24 Axiom 28 (fact_subset__empty_1): fresh58(c_Orderings_Oord__class_Oless__eq(tc_fun(X, tc_HOL_Obool), Y, c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool))), true2, Y, X) = c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)).
% 162.19/21.24 Axiom 29 (fact_singletonE): fresh4(c_member(X, Y, c_Set_Oinsert(X, Z, c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)))), true2, Z, Y) = Y.
% 162.19/21.24 Axiom 30 (fact_le__fun__def): fresh260(class_Orderings_Oord(X), true2, Y, Z, W, X) = fresh259(c_Orderings_Oord__class_Oless__eq(X, hAPP(Z, b_x16(Y, Z, X)), hAPP(Y, b_x16(Y, Z, X))), true2, Y, Z, W, X).
% 162.19/21.24
% 162.19/21.24 Lemma 31: fresh259(fresh258(X, X, Y, Z, W, V, b_x16(Y, Z, V)), true2, Y, Z, U, V) = fresh260(class_Orderings_Oord(V), true2, Y, Z, U, V).
% 162.19/21.24 Proof:
% 162.19/21.24 fresh259(fresh258(X, X, Y, Z, W, V, b_x16(Y, Z, V)), true2, Y, Z, U, V)
% 162.19/21.24 = { by axiom 20 (fact_le__fun__def_1) }
% 162.19/21.24 fresh259(c_Orderings_Oord__class_Oless__eq(V, hAPP(Z, b_x16(Y, Z, V)), hAPP(Y, b_x16(Y, Z, V))), true2, Y, Z, U, V)
% 162.19/21.24 = { by axiom 30 (fact_le__fun__def) R->L }
% 162.19/21.24 fresh260(class_Orderings_Oord(V), true2, Y, Z, U, V)
% 162.19/21.24
% 162.19/21.24 Lemma 32: c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)).
% 162.19/21.25 Proof:
% 162.19/21.25 c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool))
% 162.19/21.25 = { by axiom 6 (fact_subset__empty_1) R->L }
% 162.19/21.25 fresh58(true2, true2, c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), X)
% 162.19/21.25 = { by axiom 17 (fact_le__fun__def) R->L }
% 162.19/21.25 fresh58(fresh259(true2, true2, c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), X, tc_HOL_Obool), true2, c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), X)
% 162.19/21.25 = { by axiom 18 (fact_le__fun__def_1) R->L }
% 162.19/21.25 fresh58(fresh259(fresh257(true2, true2, c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), tc_HOL_Obool, b_x16(c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), tc_HOL_Obool)), true2, c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), X, tc_HOL_Obool), true2, c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), X)
% 162.19/21.25 = { by axiom 22 (fact_empty__subsetI) R->L }
% 162.19/21.25 fresh58(fresh259(fresh257(c_Orderings_Oord__class_Oless__eq(tc_fun(Y, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool))), true2, c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), tc_HOL_Obool, b_x16(c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), tc_HOL_Obool)), true2, c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), X, tc_HOL_Obool), true2, c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), X)
% 162.19/21.25 = { by axiom 27 (fact_le__fun__def_1) R->L }
% 162.19/21.25 fresh58(fresh259(fresh258(class_Orderings_Oord(tc_HOL_Obool), true2, c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), Y, tc_HOL_Obool, b_x16(c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), tc_HOL_Obool)), true2, c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), X, tc_HOL_Obool), true2, c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), X)
% 162.19/21.25 = { by axiom 1 (arity_HOL__Obool__Orderings_Oord) }
% 162.19/21.25 fresh58(fresh259(fresh258(true2, true2, c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), Y, tc_HOL_Obool, b_x16(c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), tc_HOL_Obool)), true2, c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), X, tc_HOL_Obool), true2, c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), X)
% 162.19/21.25 = { by lemma 31 }
% 162.19/21.25 fresh58(fresh260(class_Orderings_Oord(tc_HOL_Obool), true2, c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), X, tc_HOL_Obool), true2, c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), X)
% 162.19/21.25 = { by axiom 1 (arity_HOL__Obool__Orderings_Oord) }
% 162.19/21.25 fresh58(fresh260(true2, true2, c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), X, tc_HOL_Obool), true2, c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), X)
% 162.19/21.25 = { by axiom 16 (fact_le__fun__def) }
% 162.19/21.25 fresh58(c_Orderings_Oord__class_Oless__eq(tc_fun(X, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool))), true2, c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)), X)
% 162.19/21.25 = { by axiom 28 (fact_subset__empty_1) }
% 162.19/21.25 c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool))
% 162.19/21.25
% 162.19/21.25 Lemma 33: fresh4(c_member(X, Y, c_Set_Oinsert(X, Z, c_Orderings_Obot__class_Obot(tc_fun(W, tc_HOL_Obool)))), true2, Z, Y) = Y.
% 162.19/21.25 Proof:
% 162.19/21.25 fresh4(c_member(X, Y, c_Set_Oinsert(X, Z, c_Orderings_Obot__class_Obot(tc_fun(W, tc_HOL_Obool)))), true2, Z, Y)
% 162.19/21.25 = { by lemma 32 }
% 162.19/21.25 fresh4(c_member(X, Y, c_Set_Oinsert(X, Z, c_Orderings_Obot__class_Obot(tc_fun(X, tc_HOL_Obool)))), true2, Z, Y)
% 162.19/21.25 = { by axiom 29 (fact_singletonE) }
% 162.19/21.25 Y
% 162.19/21.25
% 162.19/21.25 Lemma 34: c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)) = c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)).
% 162.19/21.25 Proof:
% 162.19/21.25 c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool))
% 162.19/21.25 = { by axiom 13 (fact_equalityI) R->L }
% 162.19/21.25 fresh65(true2, true2, c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), X)
% 162.19/21.25 = { by axiom 21 (fact_subset__UNIV) R->L }
% 162.19/21.25 fresh65(c_Orderings_Oord__class_Oless__eq(tc_fun(X, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool))), true2, c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), X)
% 162.19/21.25 = { by axiom 26 (fact_equalityI) }
% 162.19/21.25 fresh64(c_Orderings_Oord__class_Oless__eq(tc_fun(X, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool))), true2, c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)))
% 162.19/21.25 = { by axiom 16 (fact_le__fun__def) R->L }
% 162.19/21.25 fresh64(fresh260(true2, true2, c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), X, tc_HOL_Obool), true2, c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)))
% 162.19/21.25 = { by axiom 1 (arity_HOL__Obool__Orderings_Oord) R->L }
% 162.19/21.25 fresh64(fresh260(class_Orderings_Oord(tc_HOL_Obool), true2, c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), X, tc_HOL_Obool), true2, c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)))
% 162.19/21.25 = { by lemma 31 R->L }
% 162.19/21.25 fresh64(fresh259(fresh258(Z, Z, c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), W, tc_HOL_Obool, b_x16(c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_HOL_Obool)), true2, c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), X, tc_HOL_Obool), true2, c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)))
% 162.19/21.25 = { by axiom 20 (fact_le__fun__def_1) }
% 162.19/21.25 fresh64(fresh259(c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool, hAPP(c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), b_x16(c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), b_x16(c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_HOL_Obool))), true2, c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), X, tc_HOL_Obool), true2, c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)))
% 162.19/21.25 = { by axiom 20 (fact_le__fun__def_1) R->L }
% 162.19/21.25 fresh64(fresh259(fresh258(true2, true2, c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), Y, tc_HOL_Obool, b_x16(c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_HOL_Obool)), true2, c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), X, tc_HOL_Obool), true2, c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)))
% 162.19/21.25 = { by axiom 1 (arity_HOL__Obool__Orderings_Oord) R->L }
% 162.19/21.25 fresh64(fresh259(fresh258(class_Orderings_Oord(tc_HOL_Obool), true2, c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), Y, tc_HOL_Obool, b_x16(c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_HOL_Obool)), true2, c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), X, tc_HOL_Obool), true2, c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)))
% 162.19/21.25 = { by axiom 27 (fact_le__fun__def_1) }
% 162.19/21.25 fresh64(fresh259(fresh257(c_Orderings_Oord__class_Oless__eq(tc_fun(Y, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool))), true2, c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_HOL_Obool, b_x16(c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_HOL_Obool)), true2, c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), X, tc_HOL_Obool), true2, c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)))
% 162.19/21.25 = { by axiom 21 (fact_subset__UNIV) }
% 162.19/21.25 fresh64(fresh259(fresh257(true2, true2, c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_HOL_Obool, b_x16(c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_HOL_Obool)), true2, c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), X, tc_HOL_Obool), true2, c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)))
% 162.19/21.25 = { by axiom 18 (fact_le__fun__def_1) }
% 162.19/21.25 fresh64(fresh259(true2, true2, c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), X, tc_HOL_Obool), true2, c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)))
% 162.19/21.25 = { by axiom 17 (fact_le__fun__def) }
% 162.19/21.25 fresh64(true2, true2, c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(Y, tc_HOL_Obool)))
% 162.19/21.25 = { by axiom 5 (fact_equalityI) }
% 162.19/21.25 c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool))
% 162.19/21.25
% 162.19/21.25 Lemma 35: c_Set_Oinsert(tc_Product__Type_Ounit, b_b(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit), c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)).
% 162.19/21.25 Proof:
% 162.19/21.25 c_Set_Oinsert(tc_Product__Type_Ounit, b_b(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit), c_Orderings_Obot__class_Obot(tc_fun(Y, tc_HOL_Obool)))
% 162.19/21.25 = { by lemma 32 }
% 162.19/21.25 c_Set_Oinsert(tc_Product__Type_Ounit, b_b(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit), c_Orderings_Obot__class_Obot(tc_fun(tc_Product__Type_Ounit, tc_HOL_Obool)))
% 162.19/21.25 = { by axiom 10 (fact_card__Suc__eq_2) R->L }
% 162.19/21.25 c_Set_Oinsert(tc_Product__Type_Ounit, b_b(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit), fresh417(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit, tc_HOL_Obool)), tc_Product__Type_Ounit))
% 162.19/21.25 = { by axiom 24 (fact_card__Suc__eq_2) R->L }
% 162.19/21.25 c_Set_Oinsert(tc_Product__Type_Ounit, b_b(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit), fresh416(c_Finite__Set_Ocard(tc_Product__Type_Ounit, c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit, tc_HOL_Obool))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit, tc_HOL_Obool)), tc_Product__Type_Ounit))
% 162.19/21.25 = { by axiom 2 (fact_One__nat__def) R->L }
% 162.19/21.25 c_Set_Oinsert(tc_Product__Type_Ounit, b_b(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit), fresh416(c_Finite__Set_Ocard(tc_Product__Type_Ounit, c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit, tc_HOL_Obool))), c_Groups_Oone__class_Oone(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit, tc_HOL_Obool)), tc_Product__Type_Ounit))
% 162.19/21.25 = { by axiom 9 (fact_card__UNIV__unit) }
% 162.19/21.25 c_Set_Oinsert(tc_Product__Type_Ounit, b_b(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit), fresh416(c_Groups_Oone__class_Oone(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit, tc_HOL_Obool)), tc_Product__Type_Ounit))
% 162.19/21.25 = { by axiom 11 (fact_card__Suc__eq_2) }
% 162.19/21.25 c_Set_Oinsert(tc_Product__Type_Ounit, b_b(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit), b_b2(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit, tc_HOL_Obool)), tc_Product__Type_Ounit))
% 162.19/21.25 = { by lemma 34 R->L }
% 162.19/21.25 c_Set_Oinsert(tc_Product__Type_Ounit, b_b(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit), b_b2(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit))
% 162.19/21.25 = { by axiom 25 (fact_card__Suc__eq_4) R->L }
% 162.19/21.25 fresh12(c_Finite__Set_Ocard(tc_Product__Type_Ounit, c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit)
% 162.19/21.25 = { by axiom 3 (fact_Nat_Oadd__0__right) R->L }
% 162.19/21.25 fresh12(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Finite__Set_Ocard(tc_Product__Type_Ounit, c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit)
% 162.19/21.25 = { by axiom 8 (fact_card_Oempty) R->L }
% 162.19/21.25 fresh12(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Finite__Set_Ocard(tc_Product__Type_Ounit, c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool))), c_Finite__Set_Ocard(Z, c_Orderings_Obot__class_Obot(tc_fun(Z, tc_HOL_Obool)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit)
% 162.19/21.25 = { by axiom 19 (fact_card__Plus) R->L }
% 162.19/21.25 fresh12(fresh420(W, W, c_Orderings_Obot__class_Obot(tc_fun(Z, tc_HOL_Obool)), Z, c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit)
% 162.19/21.25 = { by lemma 34 }
% 162.19/21.25 fresh12(fresh420(W, W, c_Orderings_Obot__class_Obot(tc_fun(Z, tc_HOL_Obool)), Z, c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit, tc_HOL_Obool)), tc_Product__Type_Ounit), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit)
% 162.19/21.25 = { by axiom 19 (fact_card__Plus) }
% 162.19/21.25 fresh12(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Finite__Set_Ocard(tc_Product__Type_Ounit, c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit, tc_HOL_Obool))), c_Finite__Set_Ocard(Z, c_Orderings_Obot__class_Obot(tc_fun(Z, tc_HOL_Obool)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit)
% 162.19/21.25 = { by axiom 9 (fact_card__UNIV__unit) }
% 162.19/21.25 fresh12(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_Finite__Set_Ocard(Z, c_Orderings_Obot__class_Obot(tc_fun(Z, tc_HOL_Obool)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit)
% 162.19/21.25 = { by axiom 4 (fact_Suc__eq__plus1__left) R->L }
% 162.19/21.25 fresh12(hAPP(c_Nat_OSuc, c_Finite__Set_Ocard(Z, c_Orderings_Obot__class_Obot(tc_fun(Z, tc_HOL_Obool)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit)
% 162.19/21.25 = { by axiom 8 (fact_card_Oempty) }
% 162.19/21.25 fresh12(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit)
% 162.19/21.25 = { by axiom 2 (fact_One__nat__def) R->L }
% 162.19/21.25 fresh12(c_Groups_Oone__class_Oone(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit)
% 162.19/21.25 = { by axiom 2 (fact_One__nat__def) R->L }
% 162.19/21.25 fresh12(c_Groups_Oone__class_Oone(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool)), tc_Product__Type_Ounit)
% 162.19/21.25 = { by axiom 14 (fact_card__Suc__eq_4) }
% 162.19/21.25 c_Orderings_Otop__class_Otop(tc_fun(X, tc_HOL_Obool))
% 162.19/21.25
% 162.19/21.25 Lemma 36: c_member(X, Y, c_Orderings_Otop__class_Otop(tc_fun(Z, tc_HOL_Obool))) = true2.
% 162.19/21.25 Proof:
% 162.19/21.25 c_member(X, Y, c_Orderings_Otop__class_Otop(tc_fun(Z, tc_HOL_Obool)))
% 162.19/21.25 = { by axiom 23 (fact_mem__def) R->L }
% 162.19/21.25 fresh229(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(Z, tc_HOL_Obool)), Y)), true2, c_Orderings_Otop__class_Otop(tc_fun(Z, tc_HOL_Obool)), Y, X)
% 162.19/21.25 = { by axiom 15 (fact_top1I) }
% 162.19/21.25 fresh229(true2, true2, c_Orderings_Otop__class_Otop(tc_fun(Z, tc_HOL_Obool)), Y, X)
% 162.19/21.25 = { by axiom 12 (fact_mem__def) }
% 162.19/21.25 true2
% 162.19/21.25
% 162.19/21.25 Lemma 37: Y = X.
% 162.19/21.25 Proof:
% 162.19/21.25 Y
% 162.19/21.25 = { by lemma 33 R->L }
% 162.19/21.25 fresh4(c_member(tc_Product__Type_Ounit, Y, c_Set_Oinsert(tc_Product__Type_Ounit, b_b(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(Z, tc_HOL_Obool)), tc_Product__Type_Ounit), c_Orderings_Obot__class_Obot(tc_fun(V, tc_HOL_Obool)))), true2, b_b(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(Z, tc_HOL_Obool)), tc_Product__Type_Ounit), Y)
% 162.19/21.25 = { by lemma 35 }
% 162.19/21.25 fresh4(c_member(tc_Product__Type_Ounit, Y, c_Orderings_Otop__class_Otop(tc_fun(Z, tc_HOL_Obool))), true2, b_b(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(Z, tc_HOL_Obool)), tc_Product__Type_Ounit), Y)
% 162.19/21.25 = { by lemma 36 }
% 162.19/21.25 fresh4(true2, true2, b_b(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(Z, tc_HOL_Obool)), tc_Product__Type_Ounit), Y)
% 162.19/21.25 = { by axiom 7 (fact_singletonE) }
% 162.19/21.25 b_b(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(Z, tc_HOL_Obool)), tc_Product__Type_Ounit)
% 162.19/21.25 = { by axiom 7 (fact_singletonE) R->L }
% 162.19/21.25 fresh4(true2, true2, b_b(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(Z, tc_HOL_Obool)), tc_Product__Type_Ounit), X)
% 162.19/21.25 = { by lemma 36 R->L }
% 162.19/21.25 fresh4(c_member(tc_Product__Type_Ounit, X, c_Orderings_Otop__class_Otop(tc_fun(Z, tc_HOL_Obool))), true2, b_b(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(Z, tc_HOL_Obool)), tc_Product__Type_Ounit), X)
% 162.19/21.25 = { by lemma 35 R->L }
% 162.19/21.25 fresh4(c_member(tc_Product__Type_Ounit, X, c_Set_Oinsert(tc_Product__Type_Ounit, b_b(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(Z, tc_HOL_Obool)), tc_Product__Type_Ounit), c_Orderings_Obot__class_Obot(tc_fun(W, tc_HOL_Obool)))), true2, b_b(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(Z, tc_HOL_Obool)), tc_Product__Type_Ounit), X)
% 162.19/21.25 = { by lemma 33 }
% 162.19/21.25 X
% 162.19/21.25
% 162.19/21.25 Goal 1 (true_equals_false): true = false.
% 162.19/21.25 Proof:
% 162.19/21.25 true
% 162.19/21.25 = { by lemma 37 }
% 162.19/21.25 false
% 162.19/21.25
% 162.19/21.25 Goal 2 (conj_1): v_thesis____ = true2.
% 162.19/21.25 Proof:
% 162.19/21.25 v_thesis____
% 162.19/21.25 = { by lemma 37 }
% 162.19/21.25 true2
% 162.19/21.25
% 162.19/21.25 Goal 3 (help_c__fFalse__1): hBOOL(c_fFalse) = true2.
% 162.19/21.25 Proof:
% 162.19/21.25 hBOOL(c_fFalse)
% 162.19/21.25 = { by lemma 37 }
% 162.19/21.25 true2
% 162.19/21.25
% 162.19/21.25 Goal 4 (fact_infinite__UNIV__nat): c_Finite__Set_Ofinite(tc_Nat_Onat, c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = true2.
% 162.19/21.25 Proof:
% 162.19/21.25 c_Finite__Set_Ofinite(tc_Nat_Onat, c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))
% 162.19/21.25 = { by lemma 37 }
% 162.19/21.25 true2
% 162.19/21.25 % SZS output end Proof
% 162.19/21.25
% 162.19/21.25 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------