TSTP Solution File: SCT137+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SCT137+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 : n001.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 14:22:12 EDT 2023
% Result : Theorem 68.66s 9.34s
% Output : Proof 69.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SCT137+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n001.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 24 16:36:26 EDT 2023
% 0.14/0.36 % CPUTime :
% 68.66/9.34 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 68.66/9.34
% 68.66/9.34 % SZS status Theorem
% 68.66/9.34
% 68.66/9.34 % SZS output start Proof
% 68.66/9.34 Take the following subset of the input axioms:
% 68.66/9.36 fof(fact_Lin__irrefl, axiom, ![V_ba_2, V_aa_2, V_L_2]: (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), V_L_2), c_Arrow__Order__Mirabelle_OLin)) => (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_aa_2), V_ba_2)), V_L_2)) => ~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_ba_2), V_aa_2)), V_L_2))))).
% 68.66/9.36 fof(fact_Nil2__notin__lex, axiom, ![T_a, V_r_2, V_xs_2]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a), tc_List_Olist(T_a))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a), tc_List_Olist(T_a)), V_xs_2), c_List_Olist_ONil(T_a))), c_List_Olex(T_a, V_r_2)))).
% 68.66/9.36 fof(fact_Nil__notin__lex, axiom, ![V_ys_2, T_a2, V_r_2_2]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a2), tc_List_Olist(T_a2))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a2), tc_List_Olist(T_a2)), c_List_Olist_ONil(T_a2)), V_ys_2)), c_List_Olex(T_a2, V_r_2_2)))).
% 68.66/9.36 fof(fact_dropWhile__eq__Cons__conv, axiom, ![V_y_2, V_Pa_2, T_a2, V_ys_2_2, V_xs_2_2]: (c_List_OdropWhile(T_a2, V_Pa_2, V_xs_2_2)=hAPP(hAPP(c_List_Olist_OCons(T_a2), V_y_2), V_ys_2_2) <=> (V_xs_2_2=hAPP(hAPP(c_List_Oappend(T_a2), c_List_OtakeWhile(T_a2, V_Pa_2, V_xs_2_2)), hAPP(hAPP(c_List_Olist_OCons(T_a2), V_y_2), V_ys_2_2)) & ~hBOOL(hAPP(V_Pa_2, V_y_2))))).
% 68.66/9.36 fof(fact_impossible__Cons, axiom, ![V_xs, V_x, V_ys, T_a2]: (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_Osize__class_Osize(tc_List_Olist(T_a2), V_xs), c_Nat_Osize__class_Osize(tc_List_Olist(T_a2), V_ys)) => V_xs!=hAPP(hAPP(c_List_Olist_OCons(T_a2), V_x), V_ys))).
% 68.66/9.36 fof(fact_in__measures_I1_J, axiom, ![V_x_2, T_a2, V_y_2_2]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(T_a2, T_a2)), hAPP(hAPP(c_Product__Type_OPair(T_a2, T_a2), V_x_2), V_y_2_2)), c_List_Omeasures(T_a2, c_List_Olist_ONil(tc_fun(T_a2, tc_Nat_Onat)))))).
% 68.66/9.36 fof(fact_in__mkbot, axiom, ![V_z_2, V_x_2_2, V_y_2_2, V_L_2_2]: (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_x_2_2), V_y_2_2)), c_Arrow__Order__Mirabelle_Omkbot(V_L_2_2, V_z_2))) <=> (V_y_2_2!=V_z_2 & ((V_x_2_2=V_z_2 => V_x_2_2!=V_y_2_2) & (V_x_2_2!=V_z_2 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_x_2_2), V_y_2_2)), V_L_2_2))))))).
% 68.66/9.36 fof(fact_in__mktop, axiom, ![V_x_2_2, V_y_2_2, V_z_2_2, V_L_2_2]: (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_x_2_2), V_y_2_2)), c_Arrow__Order__Mirabelle_Omktop(V_L_2_2, V_z_2_2))) <=> (V_x_2_2!=V_z_2_2 & ((V_y_2_2=V_z_2_2 => V_x_2_2!=V_y_2_2) & (V_y_2_2!=V_z_2_2 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_x_2_2), V_y_2_2)), V_L_2_2))))))).
% 68.66/9.36 fof(fact_irrefl__def, axiom, ![T_a2, V_r_2_2]: (c_Relation_Oirrefl(T_a2, V_r_2_2) <=> ![B_x]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(T_a2, T_a2)), hAPP(hAPP(c_Product__Type_OPair(T_a2, T_a2), B_x), B_x)), V_r_2_2)))).
% 68.66/9.36 fof(fact_leD, axiom, ![V_y, T_a2, V_x2]: (class_Orderings_Olinorder(T_a2) => (c_Orderings_Oord__class_Oless__eq(T_a2, V_y, V_x2) => ~c_Orderings_Oord__class_Oless(T_a2, V_x2, V_y)))).
% 68.66/9.36 fof(fact_less__fun__def, axiom, ![V_g_2, V_f_2, T_b, T_a2]: (class_Orderings_Oord(T_b) => (c_Orderings_Oord__class_Oless(tc_fun(T_a2, T_b), V_f_2, V_g_2) <=> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a2, T_b), V_f_2, V_g_2) & ~c_Orderings_Oord__class_Oless__eq(tc_fun(T_a2, T_b), V_g_2, V_f_2))))).
% 68.66/9.36 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))).
% 68.66/9.36 fof(fact_less__irrefl__nat, axiom, ![V_n]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_n)).
% 68.66/9.36 fof(fact_less__le__not__le, axiom, ![T_a2, V_x_2_2, V_y_2_2]: (class_Orderings_Opreorder(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) & ~c_Orderings_Oord__class_Oless__eq(T_a2, V_y_2_2, V_x_2_2))))).
% 68.66/9.36 fof(fact_less__not__refl, axiom, ![V_n2]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n2, V_n2)).
% 68.66/9.36 fof(fact_less__not__refl2, axiom, ![V_m, V_n2]: (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n2, V_m) => V_m!=V_n2)).
% 68.66/9.36 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)).
% 68.66/9.36 fof(fact_lexord__Nil__right, axiom, ![T_a2, V_x_2_2, V_r_2_2]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a2), tc_List_Olist(T_a2))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a2), tc_List_Olist(T_a2)), V_x_2_2), c_List_Olist_ONil(T_a2))), c_List_Olexord(T_a2, V_r_2_2)))).
% 68.66/9.36 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)))).
% 68.66/9.36 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))))).
% 68.66/9.36 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)))).
% 68.66/9.36 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)))).
% 68.66/9.36 fof(fact_list_Osimps_I2_J, axiom, ![V_list_H, V_a_H, T_a2]: c_List_Olist_ONil(T_a2)!=hAPP(hAPP(c_List_Olist_OCons(T_a2), V_a_H), V_list_H)).
% 68.66/9.36 fof(fact_list_Osimps_I3_J, axiom, ![T_a2, V_list_H2, V_a_H2]: hAPP(hAPP(c_List_Olist_OCons(T_a2), V_a_H2), V_list_H2)!=c_List_Olist_ONil(T_a2)).
% 68.66/9.36 fof(fact_nat__less__cases, axiom, ![V_n_2, V_m_2, V_Pa_2_2]: ((c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) => hBOOL(hAPP(hAPP(V_Pa_2_2, V_n_2), V_m_2))) => ((V_m_2=V_n_2 => hBOOL(hAPP(hAPP(V_Pa_2_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_Pa_2_2, V_n_2), V_m_2))) => hBOOL(hAPP(hAPP(V_Pa_2_2, V_n_2), V_m_2)))))).
% 68.66/9.36 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))).
% 68.66/9.36 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)))).
% 68.66/9.36 fof(fact_not__Cons__self, axiom, ![T_a2, V_x2, V_xs2]: V_xs2!=hAPP(hAPP(c_List_Olist_OCons(T_a2), V_x2), V_xs2)).
% 68.66/9.36 fof(fact_not__Cons__self2, axiom, ![T_a2, V_x2, V_xs2]: hAPP(hAPP(c_List_Olist_OCons(T_a2), V_x2), V_xs2)!=V_xs2).
% 68.66/9.36 fof(fact_not__Nil__listrel1, axiom, ![T_a2, V_xs_2_2, V_r_2_2]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a2), tc_List_Olist(T_a2))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a2), tc_List_Olist(T_a2)), c_List_Olist_ONil(T_a2)), V_xs_2_2)), c_List_Olistrel1(T_a2, V_r_2_2)))).
% 68.66/9.36 fof(fact_not__add__less2, axiom, ![V_j, V_i]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_j, V_i), V_i)).
% 68.66/9.36 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)))).
% 68.66/9.36 fof(fact_not__listrel1__Nil, axiom, ![T_a2, V_xs_2_2, V_r_2_2]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a2), tc_List_Olist(T_a2))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a2), tc_List_Olist(T_a2)), V_xs_2_2), c_List_Olist_ONil(T_a2))), c_List_Olistrel1(T_a2, V_r_2_2)))).
% 68.66/9.36 fof(fact_nth__length__takeWhile, axiom, ![V_Pa_2_2, T_a2, V_xs_2_2]: (c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_Osize__class_Osize(tc_List_Olist(T_a2), c_List_OtakeWhile(T_a2, V_Pa_2_2, V_xs_2_2)), c_Nat_Osize__class_Osize(tc_List_Olist(T_a2), V_xs_2_2)) => ~hBOOL(hAPP(V_Pa_2_2, c_List_Onth(T_a2, V_xs_2_2, c_Nat_Osize__class_Osize(tc_List_Olist(T_a2), c_List_OtakeWhile(T_a2, V_Pa_2_2, V_xs_2_2))))))).
% 68.66/9.36 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)))).
% 68.66/9.36 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)))).
% 68.66/9.37 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))).
% 68.66/9.37 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))).
% 68.66/9.37 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)))).
% 68.66/9.37 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))).
% 68.66/9.37 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)))).
% 68.66/9.37 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)))).
% 68.66/9.37 fof(fact_psubset__eq, axiom, ![V_B_2, V_A_2, T_a2]: (c_Orderings_Oord__class_Oless(tc_fun(T_a2, tc_HOL_Obool), V_A_2, V_B_2) <=> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a2, tc_HOL_Obool), V_A_2, V_B_2) & V_A_2!=V_B_2))).
% 68.66/9.37 fof(fact_snoc__eq__iff__butlast, axiom, ![T_a2, V_x_2_2, V_ys_2_2, V_xs_2_2]: (hAPP(hAPP(c_List_Oappend(T_a2), V_xs_2_2), hAPP(hAPP(c_List_Olist_OCons(T_a2), V_x_2_2), c_List_Olist_ONil(T_a2)))=V_ys_2_2 <=> (V_ys_2_2!=c_List_Olist_ONil(T_a2) & (c_List_Obutlast(T_a2, V_ys_2_2)=V_xs_2_2 & c_List_Olast(T_a2, V_ys_2_2)=V_x_2_2)))).
% 68.66/9.37 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)))).
% 69.36/9.37 fof(help_c__COMBI__1, axiom, ![V_P, T_a2]: hAPP(c_COMBI(T_a2), V_P)=V_P).
% 69.36/9.37 fof(help_c__COMBS__1, axiom, ![V_R_2, T_c, V_Q_2, V_Pa_2_2, T_a2, T_b2]: hAPP(hAPP(hAPP(c_COMBS(T_b2, T_c, T_a2), V_Pa_2_2), V_Q_2), V_R_2)=hAPP(hAPP(V_Pa_2_2, V_R_2), hAPP(V_Q_2, V_R_2))).
% 69.36/9.37 fof(help_c__fNot__1, axiom, ![V_Pa_2_2]: (~hBOOL(hAPP(c_fNot, V_Pa_2_2)) | ~hBOOL(V_Pa_2_2))).
% 69.36/9.37
% 69.36/9.37 Now clausify the problem and encode Horn clauses using encoding 3 of
% 69.36/9.37 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 69.36/9.37 We repeatedly replace C & s=t => u=v by the two clauses:
% 69.36/9.37 fresh(y, y, x1...xn) = u
% 69.36/9.37 C => fresh(s, t, x1...xn) = v
% 69.36/9.37 where fresh is a fresh function symbol and x1..xn are the free
% 69.36/9.37 variables of u and v.
% 69.36/9.37 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 69.36/9.37 input problem has no model of domain size 1).
% 69.36/9.37
% 69.36/9.37 The encoding turns the above axioms into the following unit equations and goals:
% 69.36/9.37
% 69.36/9.37 Axiom 1 (help_c__COMBI__1): hAPP(c_COMBI(X), Y) = Y.
% 69.36/9.37 Axiom 2 (help_c__COMBS__1): hAPP(hAPP(hAPP(c_COMBS(X, Y, Z), W), V), U) = hAPP(hAPP(W, U), hAPP(V, U)).
% 69.36/9.37
% 69.36/9.37 Goal 1 (fact_not__Cons__self): X = hAPP(hAPP(c_List_Olist_OCons(Y), Z), X).
% 69.36/9.37 The goal is true when:
% 69.36/9.37 X = hAPP(hAPP(hAPP(c_COMBS(V, U, T), hAPP(c_COMBS(X, Y, Z), c_List_Olist_OCons(W))), c_COMBI(S)), hAPP(hAPP(c_COMBS(V, U, T), hAPP(c_COMBS(X, Y, Z), c_List_Olist_OCons(W))), c_COMBI(S)))
% 69.36/9.37 Y = W
% 69.36/9.37 Z = hAPP(hAPP(c_COMBS(V, U, T), hAPP(c_COMBS(X, Y, Z), c_List_Olist_OCons(W))), c_COMBI(S))
% 69.36/9.37
% 69.36/9.37 Proof:
% 69.36/9.37 hAPP(hAPP(hAPP(c_COMBS(V, U, T), hAPP(c_COMBS(X, Y, Z), c_List_Olist_OCons(W))), c_COMBI(S)), hAPP(hAPP(c_COMBS(V, U, T), hAPP(c_COMBS(X, Y, Z), c_List_Olist_OCons(W))), c_COMBI(S)))
% 69.36/9.37 = { by axiom 2 (help_c__COMBS__1) }
% 69.36/9.37 hAPP(hAPP(hAPP(c_COMBS(X, Y, Z), c_List_Olist_OCons(W)), hAPP(hAPP(c_COMBS(V, U, T), hAPP(c_COMBS(X, Y, Z), c_List_Olist_OCons(W))), c_COMBI(S))), hAPP(c_COMBI(S), hAPP(hAPP(c_COMBS(V, U, T), hAPP(c_COMBS(X, Y, Z), c_List_Olist_OCons(W))), c_COMBI(S))))
% 69.36/9.37 = { by axiom 1 (help_c__COMBI__1) }
% 69.36/9.37 hAPP(hAPP(hAPP(c_COMBS(X, Y, Z), c_List_Olist_OCons(W)), hAPP(hAPP(c_COMBS(V, U, T), hAPP(c_COMBS(X, Y, Z), c_List_Olist_OCons(W))), c_COMBI(S))), hAPP(hAPP(c_COMBS(V, U, T), hAPP(c_COMBS(X, Y, Z), c_List_Olist_OCons(W))), c_COMBI(S)))
% 69.36/9.37 = { by axiom 2 (help_c__COMBS__1) }
% 69.36/9.37 hAPP(hAPP(c_List_Olist_OCons(W), hAPP(hAPP(c_COMBS(V, U, T), hAPP(c_COMBS(X, Y, Z), c_List_Olist_OCons(W))), c_COMBI(S))), hAPP(hAPP(hAPP(c_COMBS(V, U, T), hAPP(c_COMBS(X, Y, Z), c_List_Olist_OCons(W))), c_COMBI(S)), hAPP(hAPP(c_COMBS(V, U, T), hAPP(c_COMBS(X, Y, Z), c_List_Olist_OCons(W))), c_COMBI(S))))
% 69.36/9.37 % SZS output end Proof
% 69.36/9.37
% 69.36/9.37 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------