TSTP Solution File: SWW374+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWW374+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n009.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 : Wed May 31 12:44:50 EDT 2023
% Result : Theorem 9.35s 1.92s
% Output : CNFRefutation 9.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW374+1 : TPTP v8.1.2. Released v5.2.0.
% 0.13/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 10:52:31 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.55/0.76 % Drodi V3.5.1
% 9.35/1.92 % Refutation found
% 9.35/1.92 % SZS status Theorem for theBenchmark: Theorem is valid
% 9.35/1.92 % SZS output start CNFRefutation for theBenchmark
% 9.35/1.92 fof(f3,axiom,(
% 9.35/1.92 (! [V_A_2,V_x_2,T_a] :( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))<=> hBOOL(hAPP(V_A_2,V_x_2)) ) )),
% 9.35/1.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.92 fof(f4,axiom,(
% 9.35/1.92 (! [V_y_2,V_x_2,T_a] :( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2)))<=> V_x_2 = V_y_2 ) )),
% 9.35/1.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.92 fof(f8,axiom,(
% 9.35/1.92 (! [V_b,V_pn] :( c_Com_OWT__bodies=> ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b)=> hBOOL(hAPP(c_Com_OWT,V_b)) ) ) )),
% 9.35/1.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.92 fof(f10,axiom,(
% 9.35/1.92 ( c_Hoare__Mirabelle_Ostate__not__singleton=> (! [B_t] :~ (! [B_s] : B_s = B_t ))) ),
% 9.35/1.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.92 fof(f11,axiom,(
% 9.35/1.92 ( c_Hoare__Mirabelle_Ostate__not__singleton<=> (? [B_s,B_t] : B_s != B_t )) ),
% 9.35/1.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.92 fof(f12,axiom,(
% 9.35/1.92 (! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] :( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2)))<=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))& hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) )),
% 9.35/1.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.92 fof(f13,axiom,(
% 9.35/1.92 (! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] :( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2)))<=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))& hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) )),
% 9.35/1.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.92 fof(f14,axiom,(
% 9.35/1.92 (! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] :( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2)))<=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))& hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) )),
% 9.35/1.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.92 fof(f15,axiom,(
% 9.35/1.92 (! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] :( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__eq_2,V_l_2,V_u_2)))<=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))& hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) )),
% 9.35/1.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.92 fof(f16,axiom,(
% 9.35/1.92 (! [V_k_2,V_less_2,V_i_2,T_a] :( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2)))<=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) )),
% 9.35/1.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.92 fof(f17,axiom,(
% 9.35/1.92 (! [V_k_2,V_less_2,V_i_2,T_a] :( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2)))<=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) )),
% 9.35/1.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.92 fof(f18,axiom,(
% 9.35/1.92 (! [V_k_2,V_less__eq_2,V_i_2,T_a] :( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2)))<=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) )),
% 9.35/1.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.92 fof(f19,axiom,(
% 9.35/1.92 (! [V_k_2,V_less__eq_2,V_i_2,T_a] :( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2)))<=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) )),
% 9.35/1.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.92 fof(f20,axiom,(
% 9.35/1.92 (! [T_b,V_b_2,T_a,V_a_2,V_m_2] :( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2)=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2))) ) )),
% 9.35/1.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.92 fof(f21,axiom,(
% 9.35/1.92 (! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x )),
% 9.35/1.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.92 fof(f22,axiom,(
% 9.35/1.92 (! [V_a_2] :( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(V_a_2)))<=> (? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) )) )),
% 9.35/1.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.92 fof(f27,axiom,(
% 9.35/1.92 (! [V_m_2,T_b,V_a_2,T_a] :( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2)))=> (? [B_b] : hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),B_b) )) )),
% 9.35/1.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.94 fof(f38,axiom,(
% 9.35/1.94 (! [V_pn] :( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom)=> hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(V_pn))) ) )),
% 9.35/1.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.94 fof(f3645,axiom,(
% 9.35/1.94 ( c_Com_OWT__bodies<=> (! [B_x] :( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),B_x),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),B_x)) ) )) ),
% 9.35/1.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.94 fof(f4872,axiom,(
% 9.35/1.94 (! [V_com2_2,V_com1_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1_2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )),
% 9.35/1.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.94 fof(f4968,axiom,(
% 9.35/1.94 (! [V_com_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )),
% 9.35/1.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.94 fof(f5245,hypothesis,(
% 9.35/1.94 c_Hoare__Mirabelle_Ostate__not__singleton ),
% 9.35/1.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.94 fof(f5246,hypothesis,(
% 9.35/1.94 c_Com_OWT__bodies ),
% 9.35/1.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.94 fof(f5248,hypothesis,(
% 9.35/1.94 hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ),
% 9.35/1.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.94 fof(f5249,conjecture,(
% 9.35/1.94 hBOOL(hAPP(c_Com_OWT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)))) ),
% 9.35/1.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.35/1.94 fof(f5250,negated_conjecture,(
% 9.35/1.94 ~(hBOOL(hAPP(c_Com_OWT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)))) )),
% 9.35/1.94 inference(negated_conjecture,[status(cth)],[f5249])).
% 9.35/1.94 fof(f5260,plain,(
% 9.35/1.94 ![V_A_2,V_x_2,T_a]: ((~hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))|hBOOL(hAPP(V_A_2,V_x_2)))&(hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))|~hBOOL(hAPP(V_A_2,V_x_2))))),
% 9.35/1.94 inference(NNF_transformation,[status(esa)],[f3])).
% 9.35/1.94 fof(f5261,plain,(
% 9.35/1.94 (![V_A_2,V_x_2]: ((![T_a]: ~hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)))|hBOOL(hAPP(V_A_2,V_x_2))))&(![V_A_2,V_x_2]: ((![T_a]: hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)))|~hBOOL(hAPP(V_A_2,V_x_2))))),
% 9.35/1.94 inference(miniscoping,[status(esa)],[f5260])).
% 9.35/1.94 fof(f5262,plain,(
% 9.35/1.94 ![X0,X1,X2]: (~hBOOL(hAPP(hAPP(c_member(X0),X1),X2))|hBOOL(hAPP(X2,X1)))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5261])).
% 9.35/1.94 fof(f5263,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hBOOL(hAPP(hAPP(c_member(X0),X1),X2))|~hBOOL(hAPP(X2,X1)))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5261])).
% 9.35/1.94 fof(f5264,plain,(
% 9.35/1.94 ![V_y_2,V_x_2,T_a]: ((~hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2)))|V_x_2=V_y_2)&(hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2)))|~V_x_2=V_y_2))),
% 9.35/1.94 inference(NNF_transformation,[status(esa)],[f4])).
% 9.35/1.94 fof(f5265,plain,(
% 9.35/1.94 (![V_y_2,V_x_2]: ((![T_a]: ~hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))))|V_x_2=V_y_2))&(![V_y_2,V_x_2]: ((![T_a]: hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))))|~V_x_2=V_y_2))),
% 9.35/1.94 inference(miniscoping,[status(esa)],[f5264])).
% 9.35/1.94 fof(f5267,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(c_fequal,X2)))|~X1=X2)),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5265])).
% 9.35/1.94 fof(f5281,plain,(
% 9.35/1.94 ![V_b,V_pn]: (~c_Com_OWT__bodies|(~hAPP(c_Com_Obody,V_pn)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b)|hBOOL(hAPP(c_Com_OWT,V_b))))),
% 9.35/1.94 inference(pre_NNF_transformation,[status(esa)],[f8])).
% 9.35/1.94 fof(f5282,plain,(
% 9.35/1.94 ~c_Com_OWT__bodies|(![V_b]: ((![V_pn]: ~hAPP(c_Com_Obody,V_pn)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b))|hBOOL(hAPP(c_Com_OWT,V_b))))),
% 9.35/1.94 inference(miniscoping,[status(esa)],[f5281])).
% 9.35/1.94 fof(f5283,plain,(
% 9.35/1.94 ![X0,X1]: (~c_Com_OWT__bodies|~hAPP(c_Com_Obody,X0)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1)|hBOOL(hAPP(c_Com_OWT,X1)))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5282])).
% 9.35/1.94 fof(f5285,plain,(
% 9.35/1.94 ~c_Hoare__Mirabelle_Ostate__not__singleton|(![B_t]: ?[B_s]: ~B_s=B_t)),
% 9.35/1.94 inference(pre_NNF_transformation,[status(esa)],[f10])).
% 9.35/1.94 fof(f5286,plain,(
% 9.35/1.94 ~c_Hoare__Mirabelle_Ostate__not__singleton|(![B_t]: ~sk0_1(B_t)=B_t)),
% 9.35/1.94 inference(skolemization,[status(esa)],[f5285])).
% 9.35/1.94 fof(f5287,plain,(
% 9.35/1.94 ![X0]: (~c_Hoare__Mirabelle_Ostate__not__singleton|~sk0_1(X0)=X0)),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5286])).
% 9.35/1.94 fof(f5288,plain,(
% 9.35/1.94 (~c_Hoare__Mirabelle_Ostate__not__singleton|(?[B_s,B_t]: ~B_s=B_t))&(c_Hoare__Mirabelle_Ostate__not__singleton|(![B_s,B_t]: B_s=B_t))),
% 9.35/1.94 inference(NNF_transformation,[status(esa)],[f11])).
% 9.35/1.94 fof(f5289,plain,(
% 9.35/1.94 (~c_Hoare__Mirabelle_Ostate__not__singleton|~sk0_2=sk0_3)&(c_Hoare__Mirabelle_Ostate__not__singleton|(![B_s,B_t]: B_s=B_t))),
% 9.35/1.94 inference(skolemization,[status(esa)],[f5288])).
% 9.35/1.94 fof(f5290,plain,(
% 9.35/1.94 ~c_Hoare__Mirabelle_Ostate__not__singleton|~sk0_2=sk0_3),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5289])).
% 9.35/1.94 fof(f5292,plain,(
% 9.35/1.94 ![V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a]: ((~hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2)))|(hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))&hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))))&(hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2)))|(~hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))|~hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)))))),
% 9.35/1.94 inference(NNF_transformation,[status(esa)],[f12])).
% 9.35/1.94 fof(f5293,plain,(
% 9.35/1.94 (![V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2]: ((![T_a]: ~hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2))))|(hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))&hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)))))&(![V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2]: ((![T_a]: hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2))))|(~hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))|~hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)))))),
% 9.35/1.94 inference(miniscoping,[status(esa)],[f5292])).
% 9.35/1.94 fof(f5296,plain,(
% 9.35/1.94 ![X0,X1,X2,X3,X4,X5]: (hBOOL(hAPP(hAPP(c_member(X0),X1),c_SetInterval_Oord_OgreaterThanAtMost(X0,X2,X3,X4,X5)))|~hBOOL(hAPP(hAPP(X3,X4),X1))|~hBOOL(hAPP(hAPP(X2,X1),X5)))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5293])).
% 9.35/1.94 fof(f5297,plain,(
% 9.35/1.94 ![V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a]: ((~hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2)))|(hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))&hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))))&(hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2)))|(~hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))|~hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)))))),
% 9.35/1.94 inference(NNF_transformation,[status(esa)],[f13])).
% 9.35/1.94 fof(f5298,plain,(
% 9.35/1.94 (![V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2]: ((![T_a]: ~hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2))))|(hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))&hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)))))&(![V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2]: ((![T_a]: hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2))))|(~hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))|~hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)))))),
% 9.35/1.94 inference(miniscoping,[status(esa)],[f5297])).
% 9.35/1.94 fof(f5301,plain,(
% 9.35/1.94 ![X0,X1,X2,X3,X4,X5]: (hBOOL(hAPP(hAPP(c_member(X0),X1),c_SetInterval_Oord_OatLeastLessThan(X0,X2,X3,X4,X5)))|~hBOOL(hAPP(hAPP(X2,X4),X1))|~hBOOL(hAPP(hAPP(X3,X1),X5)))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5298])).
% 9.35/1.94 fof(f5302,plain,(
% 9.35/1.94 ![V_u_2,V_l_2,V_less_2,V_i_2,T_a]: ((~hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2)))|(hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))&hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))))&(hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2)))|(~hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))|~hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)))))),
% 9.35/1.94 inference(NNF_transformation,[status(esa)],[f14])).
% 9.35/1.94 fof(f5303,plain,(
% 9.35/1.94 (![V_u_2,V_l_2,V_less_2,V_i_2]: ((![T_a]: ~hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2))))|(hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))&hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)))))&(![V_u_2,V_l_2,V_less_2,V_i_2]: ((![T_a]: hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2))))|(~hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))|~hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)))))),
% 9.35/1.94 inference(miniscoping,[status(esa)],[f5302])).
% 9.35/1.94 fof(f5306,plain,(
% 9.35/1.94 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(hAPP(c_member(X0),X1),c_SetInterval_Oord_OgreaterThanLessThan(X0,X2,X3,X4)))|~hBOOL(hAPP(hAPP(X2,X3),X1))|~hBOOL(hAPP(hAPP(X2,X1),X4)))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5303])).
% 9.35/1.94 fof(f5307,plain,(
% 9.35/1.94 ![V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a]: ((~hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__eq_2,V_l_2,V_u_2)))|(hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))&hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))))&(hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__eq_2,V_l_2,V_u_2)))|(~hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))|~hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)))))),
% 9.35/1.94 inference(NNF_transformation,[status(esa)],[f15])).
% 9.35/1.94 fof(f5308,plain,(
% 9.35/1.94 (![V_u_2,V_l_2,V_less__eq_2,V_i_2]: ((![T_a]: ~hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__eq_2,V_l_2,V_u_2))))|(hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))&hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)))))&(![V_u_2,V_l_2,V_less__eq_2,V_i_2]: ((![T_a]: hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__eq_2,V_l_2,V_u_2))))|(~hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))|~hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)))))),
% 9.35/1.94 inference(miniscoping,[status(esa)],[f5307])).
% 9.35/1.94 fof(f5311,plain,(
% 9.35/1.94 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(hAPP(c_member(X0),X1),c_SetInterval_Oord_OatLeastAtMost(X0,X2,X3,X4)))|~hBOOL(hAPP(hAPP(X2,X3),X1))|~hBOOL(hAPP(hAPP(X2,X1),X4)))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5308])).
% 9.35/1.94 fof(f5312,plain,(
% 9.35/1.94 ![V_k_2,V_less_2,V_i_2,T_a]: ((~hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2)))|hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)))&(hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2)))|~hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2))))),
% 9.35/1.94 inference(NNF_transformation,[status(esa)],[f16])).
% 9.35/1.94 fof(f5313,plain,(
% 9.35/1.94 (![V_k_2,V_less_2,V_i_2]: ((![T_a]: ~hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))))|hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2))))&(![V_k_2,V_less_2,V_i_2]: ((![T_a]: hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))))|~hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2))))),
% 9.35/1.94 inference(miniscoping,[status(esa)],[f5312])).
% 9.35/1.94 fof(f5315,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hBOOL(hAPP(hAPP(c_member(X0),X1),c_SetInterval_Oord_OgreaterThan(X0,X2,X3)))|~hBOOL(hAPP(hAPP(X2,X3),X1)))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5313])).
% 9.35/1.94 fof(f5316,plain,(
% 9.35/1.94 ![V_k_2,V_less_2,V_i_2,T_a]: ((~hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2)))|hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)))&(hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2)))|~hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2))))),
% 9.35/1.94 inference(NNF_transformation,[status(esa)],[f17])).
% 9.35/1.94 fof(f5317,plain,(
% 9.35/1.94 (![V_k_2,V_less_2,V_i_2]: ((![T_a]: ~hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))))|hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2))))&(![V_k_2,V_less_2,V_i_2]: ((![T_a]: hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))))|~hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2))))),
% 9.35/1.94 inference(miniscoping,[status(esa)],[f5316])).
% 9.35/1.94 fof(f5319,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hBOOL(hAPP(hAPP(c_member(X0),X1),c_SetInterval_Oord_OlessThan(X0,X2,X3)))|~hBOOL(hAPP(hAPP(X2,X1),X3)))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5317])).
% 9.35/1.94 fof(f5320,plain,(
% 9.35/1.94 ![V_k_2,V_less__eq_2,V_i_2,T_a]: ((~hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2)))|hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)))&(hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2)))|~hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2))))),
% 9.35/1.94 inference(NNF_transformation,[status(esa)],[f18])).
% 9.35/1.94 fof(f5321,plain,(
% 9.35/1.94 (![V_k_2,V_less__eq_2,V_i_2]: ((![T_a]: ~hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2))))|hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2))))&(![V_k_2,V_less__eq_2,V_i_2]: ((![T_a]: hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2))))|~hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2))))),
% 9.35/1.94 inference(miniscoping,[status(esa)],[f5320])).
% 9.35/1.94 fof(f5323,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hBOOL(hAPP(hAPP(c_member(X0),X1),c_SetInterval_Oord_OatLeast(X0,X2,X3)))|~hBOOL(hAPP(hAPP(X2,X3),X1)))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5321])).
% 9.35/1.94 fof(f5324,plain,(
% 9.35/1.94 ![V_k_2,V_less__eq_2,V_i_2,T_a]: ((~hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2)))|hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)))&(hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2)))|~hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2))))),
% 9.35/1.94 inference(NNF_transformation,[status(esa)],[f19])).
% 9.35/1.94 fof(f5325,plain,(
% 9.35/1.94 (![V_k_2,V_less__eq_2,V_i_2]: ((![T_a]: ~hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2))))|hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2))))&(![V_k_2,V_less__eq_2,V_i_2]: ((![T_a]: hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2))))|~hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2))))),
% 9.35/1.94 inference(miniscoping,[status(esa)],[f5324])).
% 9.35/1.94 fof(f5327,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hBOOL(hAPP(hAPP(c_member(X0),X1),c_SetInterval_Oord_OatMost(X0,X2,X3)))|~hBOOL(hAPP(hAPP(X2,X1),X3)))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5325])).
% 9.35/1.94 fof(f5328,plain,(
% 9.35/1.94 ![T_b,V_b_2,T_a,V_a_2,V_m_2]: (~hAPP(V_m_2,V_a_2)=hAPP(c_Option_Ooption_OSome(T_a),V_b_2)|hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2))))),
% 9.35/1.94 inference(pre_NNF_transformation,[status(esa)],[f20])).
% 9.35/1.94 fof(f5329,plain,(
% 9.35/1.94 ![T_a,V_a_2,V_m_2]: ((![V_b_2]: ~hAPP(V_m_2,V_a_2)=hAPP(c_Option_Ooption_OSome(T_a),V_b_2))|(![T_b]: hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2)))))),
% 9.35/1.94 inference(miniscoping,[status(esa)],[f5328])).
% 9.35/1.94 fof(f5330,plain,(
% 9.35/1.94 ![X0,X1,X2,X3,X4]: (~hAPP(X0,X1)=hAPP(c_Option_Ooption_OSome(X2),X3)|hBOOL(hAPP(hAPP(c_member(X4),X1),c_Map_Odom(X4,X2,X0))))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5329])).
% 9.35/1.94 fof(f5331,plain,(
% 9.35/1.94 ![X0,X1]: (hAPP(c_Option_Othe(X0),hAPP(c_Option_Ooption_OSome(X0),X1))=X1)),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f21])).
% 9.35/1.94 fof(f5332,plain,(
% 9.35/1.94 ![V_a_2]: ((~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(V_a_2)))|(?[B_y]: hAPP(c_Com_Obody,V_a_2)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y)))&(hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(V_a_2)))|(![B_y]: ~hAPP(c_Com_Obody,V_a_2)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y))))),
% 9.35/1.94 inference(NNF_transformation,[status(esa)],[f22])).
% 9.35/1.94 fof(f5333,plain,(
% 9.35/1.94 (![V_a_2]: (~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(V_a_2)))|(?[B_y]: hAPP(c_Com_Obody,V_a_2)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y))))&(![V_a_2]: (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(V_a_2)))|(![B_y]: ~hAPP(c_Com_Obody,V_a_2)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y))))),
% 9.35/1.94 inference(miniscoping,[status(esa)],[f5332])).
% 9.35/1.94 fof(f5334,plain,(
% 9.35/1.94 (![V_a_2]: (~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(V_a_2)))|hAPP(c_Com_Obody,V_a_2)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sk0_4(V_a_2))))&(![V_a_2]: (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(V_a_2)))|(![B_y]: ~hAPP(c_Com_Obody,V_a_2)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y))))),
% 9.35/1.94 inference(skolemization,[status(esa)],[f5333])).
% 9.35/1.94 fof(f5335,plain,(
% 9.35/1.94 ![X0]: (~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X0)))|hAPP(c_Com_Obody,X0)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sk0_4(X0)))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5334])).
% 9.35/1.94 fof(f5336,plain,(
% 9.35/1.94 ![X0,X1]: (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X0)))|~hAPP(c_Com_Obody,X0)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5334])).
% 9.35/1.94 fof(f5351,plain,(
% 9.35/1.94 ![V_m_2,T_b,V_a_2,T_a]: (~hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2)))|(?[B_b]: hAPP(V_m_2,V_a_2)=hAPP(c_Option_Ooption_OSome(T_b),B_b)))),
% 9.35/1.94 inference(pre_NNF_transformation,[status(esa)],[f27])).
% 9.35/1.94 fof(f5352,plain,(
% 9.35/1.94 ![V_m_2,T_b,V_a_2]: ((![T_a]: ~hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2))))|(?[B_b]: hAPP(V_m_2,V_a_2)=hAPP(c_Option_Ooption_OSome(T_b),B_b)))),
% 9.35/1.94 inference(miniscoping,[status(esa)],[f5351])).
% 9.35/1.94 fof(f5353,plain,(
% 9.35/1.94 ![V_m_2,T_b,V_a_2]: ((![T_a]: ~hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2))))|hAPP(V_m_2,V_a_2)=hAPP(c_Option_Ooption_OSome(T_b),sk0_5(V_a_2,T_b,V_m_2)))),
% 9.35/1.94 inference(skolemization,[status(esa)],[f5352])).
% 9.35/1.94 fof(f5354,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (~hBOOL(hAPP(hAPP(c_member(X0),X1),c_Map_Odom(X0,X2,X3)))|hAPP(X3,X1)=hAPP(c_Option_Ooption_OSome(X2),sk0_5(X1,X2,X3)))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5353])).
% 9.35/1.94 fof(f5380,plain,(
% 9.35/1.94 ![V_pn]: (hAPP(c_Com_Obody,V_pn)=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(V_pn))))),
% 9.35/1.94 inference(pre_NNF_transformation,[status(esa)],[f38])).
% 9.35/1.94 fof(f5381,plain,(
% 9.35/1.94 ![X0]: (hAPP(c_Com_Obody,X0)=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X0))))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5380])).
% 9.35/1.94 fof(f16177,plain,(
% 9.35/1.94 c_Com_OWT__bodies<=>(![B_x]: (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),B_x),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),B_x))))),
% 9.35/1.94 inference(pre_NNF_transformation,[status(esa)],[f3645])).
% 9.35/1.94 fof(f16178,plain,(
% 9.35/1.94 (~c_Com_OWT__bodies|(![B_x]: (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),B_x),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),B_x)))))&(c_Com_OWT__bodies|(?[B_x]: (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),B_x),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))&~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),B_x)))))),
% 9.35/1.94 inference(NNF_transformation,[status(esa)],[f16177])).
% 9.35/1.94 fof(f16179,plain,(
% 9.35/1.94 (~c_Com_OWT__bodies|(![B_x]: (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),B_x),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),B_x)))))&(c_Com_OWT__bodies|(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),sk0_322),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))&~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),sk0_322))))),
% 9.35/1.94 inference(skolemization,[status(esa)],[f16178])).
% 9.35/1.94 fof(f16180,plain,(
% 9.35/1.94 ![X0]: (~c_Com_OWT__bodies|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),X0),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),X0)))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f16179])).
% 9.35/1.94 fof(f19397,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X0,X1,X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f4872])).
% 9.35/1.94 fof(f19625,plain,(
% 9.35/1.94 ![X0,X1]: (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X0,X1))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f4968])).
% 9.35/1.94 fof(f19977,plain,(
% 9.35/1.94 c_Hoare__Mirabelle_Ostate__not__singleton),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5245])).
% 9.35/1.94 fof(f19978,plain,(
% 9.35/1.94 c_Com_OWT__bodies),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5246])).
% 9.35/1.94 fof(f19980,plain,(
% 9.35/1.94 hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5248])).
% 9.35/1.94 fof(f19981,plain,(
% 9.35/1.94 ~hBOOL(hAPP(c_Com_OWT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))))),
% 9.35/1.94 inference(cnf_transformation,[status(esa)],[f5250])).
% 9.35/1.94 fof(f20222,plain,(
% 9.35/1.94 spl0_0 <=> c_Com_OWT__bodies),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f20224,plain,(
% 9.35/1.94 ~c_Com_OWT__bodies|spl0_0),
% 9.35/1.94 inference(component_clause,[status(thm)],[f20222])).
% 9.35/1.94 fof(f20225,plain,(
% 9.35/1.94 spl0_1 <=> ~hAPP(c_Com_Obody,X0)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1)|hBOOL(hAPP(c_Com_OWT,X1))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f20226,plain,(
% 9.35/1.94 ![X0,X1]: (~hAPP(c_Com_Obody,X0)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1)|hBOOL(hAPP(c_Com_OWT,X1))|~spl0_1)),
% 9.35/1.94 inference(component_clause,[status(thm)],[f20225])).
% 9.35/1.94 fof(f20228,plain,(
% 9.35/1.94 ~spl0_0|spl0_1),
% 9.35/1.94 inference(split_clause,[status(thm)],[f5283,f20222,f20225])).
% 9.35/1.94 fof(f20229,plain,(
% 9.35/1.94 spl0_2 <=> c_Hoare__Mirabelle_Ostate__not__singleton),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f20231,plain,(
% 9.35/1.94 ~c_Hoare__Mirabelle_Ostate__not__singleton|spl0_2),
% 9.35/1.94 inference(component_clause,[status(thm)],[f20229])).
% 9.35/1.94 fof(f20232,plain,(
% 9.35/1.94 spl0_3 <=> ~sk0_1(X0)=X0),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f20235,plain,(
% 9.35/1.94 ~spl0_2|spl0_3),
% 9.35/1.94 inference(split_clause,[status(thm)],[f5287,f20229,f20232])).
% 9.35/1.94 fof(f20236,plain,(
% 9.35/1.94 spl0_4 <=> sk0_2=sk0_3),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f20239,plain,(
% 9.35/1.94 ~spl0_2|~spl0_4),
% 9.35/1.94 inference(split_clause,[status(thm)],[f5290,f20229,f20236])).
% 9.35/1.94 fof(f20262,plain,(
% 9.35/1.94 spl0_11 <=> ~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),X0),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),X0))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f20263,plain,(
% 9.35/1.94 ![X0]: (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),X0),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),X0))|~spl0_11)),
% 9.35/1.94 inference(component_clause,[status(thm)],[f20262])).
% 9.35/1.94 fof(f20265,plain,(
% 9.35/1.94 ~spl0_0|spl0_11),
% 9.35/1.94 inference(split_clause,[status(thm)],[f16180,f20222,f20262])).
% 9.35/1.94 fof(f20266,plain,(
% 9.35/1.94 spl0_12 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),sk0_322),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f20267,plain,(
% 9.35/1.94 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),sk0_322),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))|~spl0_12),
% 9.35/1.94 inference(component_clause,[status(thm)],[f20266])).
% 9.35/1.94 fof(f20270,plain,(
% 9.35/1.94 spl0_13 <=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),sk0_322))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f20271,plain,(
% 9.35/1.94 hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),sk0_322))|~spl0_13),
% 9.35/1.94 inference(component_clause,[status(thm)],[f20270])).
% 9.35/1.94 fof(f20272,plain,(
% 9.35/1.94 ~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),sk0_322))|spl0_13),
% 9.35/1.94 inference(component_clause,[status(thm)],[f20270])).
% 9.35/1.94 fof(f20287,plain,(
% 9.35/1.94 ![X0,X1]: (hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(c_fequal,X1))))),
% 9.35/1.94 inference(destructive_equality_resolution,[status(esa)],[f5267])).
% 9.35/1.94 fof(f20394,plain,(
% 9.35/1.94 hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),sk0_322))|~spl0_11|~spl0_12),
% 9.35/1.94 inference(resolution,[status(thm)],[f20263,f20267])).
% 9.35/1.94 fof(f20395,plain,(
% 9.35/1.94 $false|spl0_13|~spl0_11|~spl0_12),
% 9.35/1.94 inference(forward_subsumption_resolution,[status(thm)],[f20394,f20272])).
% 9.35/1.94 fof(f20396,plain,(
% 9.35/1.94 spl0_13|~spl0_11|~spl0_12),
% 9.35/1.94 inference(contradiction_clause,[status(thm)],[f20395])).
% 9.35/1.94 fof(f20397,plain,(
% 9.35/1.94 $false|spl0_2),
% 9.35/1.94 inference(forward_subsumption_resolution,[status(thm)],[f20231,f19977])).
% 9.35/1.94 fof(f20398,plain,(
% 9.35/1.94 spl0_2),
% 9.35/1.94 inference(contradiction_clause,[status(thm)],[f20397])).
% 9.35/1.94 fof(f20399,plain,(
% 9.35/1.94 $false|spl0_0),
% 9.35/1.94 inference(forward_subsumption_resolution,[status(thm)],[f20224,f19978])).
% 9.35/1.94 fof(f20400,plain,(
% 9.35/1.94 spl0_0),
% 9.35/1.94 inference(contradiction_clause,[status(thm)],[f20399])).
% 9.35/1.94 fof(f20902,plain,(
% 9.35/1.94 hBOOL(hAPP(c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody),v_pn))),
% 9.35/1.94 inference(resolution,[status(thm)],[f5262,f19980])).
% 9.35/1.94 fof(f20903,plain,(
% 9.35/1.94 ![X0]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f5263,f20271])).
% 9.35/1.94 fof(f21006,plain,(
% 9.35/1.94 ![X0]: (hBOOL(hAPP(hAPP(c_member(X0),v_pn),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))))),
% 9.35/1.94 inference(resolution,[status(thm)],[f20902,f5263])).
% 9.35/1.94 fof(f21720,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,X1,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT),X2)))|~hBOOL(hAPP(hAPP(X1,sk0_322),X2))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f5296,f20271])).
% 9.35/1.94 fof(f21773,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))),c_SetInterval_Oord_OgreaterThanAtMost(X0,X1,c_member(X2),sk0_322,X3)))|~hBOOL(hAPP(hAPP(X1,hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))),X3))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f5296,f20903])).
% 9.35/1.94 fof(f21781,plain,(
% 9.35/1.94 ![X0,X1,X2,X3,X4,X5]: (hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_SetInterval_Oord_OgreaterThanAtMost(X0,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X3)),X4)))|~hBOOL(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X5,X2,X3)))|~hBOOL(hAPP(hAPP(X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X4)))),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f19397,f5296])).
% 9.35/1.94 fof(f21785,plain,(
% 9.35/1.94 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_SetInterval_Oord_OgreaterThanAtMost(X0,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2),X3)))|~hBOOL(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X4,X2)))|~hBOOL(hAPP(hAPP(X1,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3)))),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f19625,f5296])).
% 9.35/1.94 fof(f21826,plain,(
% 9.35/1.94 ![X0,X1,X2,X3,X4,X5]: (hBOOL(hAPP(hAPP(c_member(X0),X1),c_SetInterval_Oord_OgreaterThanAtMost(X0,X2,c_Option_Othe(X3),hAPP(c_Option_Ooption_OSome(X3),X4),X5)))|~hBOOL(hAPP(X4,X1))|~hBOOL(hAPP(hAPP(X2,X1),X5)))),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f5331,f5296])).
% 9.35/1.94 fof(f21908,plain,(
% 9.35/1.94 ![X0,X1]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT),hAPP(c_fequal,sk0_322))))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f21720,f20287])).
% 9.35/1.94 fof(f21911,plain,(
% 9.35/1.94 ![X0,X1]: (hBOOL(hAPP(c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT),hAPP(c_fequal,sk0_322)),sk0_322))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f21908,f5262])).
% 9.35/1.94 fof(f21917,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X1,c_member(X2),c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT),hAPP(c_fequal,sk0_322))))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f21911,f5263])).
% 9.35/1.94 fof(f22129,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),c_SetInterval_Oord_OatLeastLessThan(X0,X1,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),X2,sk0_322)))|~hBOOL(hAPP(hAPP(X1,X2),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f5301,f20271])).
% 9.35/1.94 fof(f22197,plain,(
% 9.35/1.94 ![X0,X1,X2,X3,X4,X5]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeastLessThan(X0,X1,c_member(X2),X3,c_SetInterval_Oord_OgreaterThanAtMost(X4,c_member(X5),c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT),hAPP(c_fequal,sk0_322)))))|~hBOOL(hAPP(hAPP(X1,X3),sk0_322))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f5301,f21917])).
% 9.35/1.94 fof(f22198,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeastLessThan(X0,X1,c_member(X2),X3,hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))|~hBOOL(hAPP(hAPP(X1,X3),sk0_322))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f5301,f20903])).
% 9.35/1.94 fof(f22547,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeastLessThan(X0,c_Option_Othe(X1),c_member(X2),hAPP(c_Option_Ooption_OSome(X1),X3),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))|~hBOOL(hAPP(X3,sk0_322))|~spl0_13)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f5331,f22198])).
% 9.35/1.94 fof(f22630,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),c_SetInterval_Oord_OatLeastLessThan(X0,c_Option_Othe(X1),c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_Option_Ooption_OSome(X1),X2),sk0_322)))|~hBOOL(hAPP(X2,hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))|~spl0_13)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f5331,f22129])).
% 9.35/1.94 fof(f23044,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))),c_SetInterval_Oord_OgreaterThanLessThan(X0,c_member(X1),sk0_322,X2)))|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))),X2))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f5306,f20903])).
% 9.35/1.94 fof(f23330,plain,(
% 9.35/1.94 ![X0,X1,X2,X3,X4,X5]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeastLessThan(X0,c_Option_Othe(X1),c_member(X2),hAPP(c_Option_Ooption_OSome(X1),X3),c_SetInterval_Oord_OgreaterThanAtMost(X4,c_member(X5),c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT),hAPP(c_fequal,sk0_322)))))|~hBOOL(hAPP(X3,sk0_322))|~spl0_13)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f5331,f22197])).
% 9.35/1.94 fof(f23458,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),X2),sk0_322)))|~hBOOL(hAPP(X2,hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f21826,f20271])).
% 9.35/1.94 fof(f23553,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),X3),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))|~hBOOL(hAPP(X3,sk0_322))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f21826,f20903])).
% 9.35/1.94 fof(f23554,plain,(
% 9.35/1.94 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(hAPP(c_member(X0),X1),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X2),c_Option_Othe(X3),hAPP(c_Option_Ooption_OSome(X3),X4),hAPP(c_fequal,X1))))|~hBOOL(hAPP(X4,X1)))),
% 9.35/1.94 inference(resolution,[status(thm)],[f21826,f20287])).
% 9.35/1.94 fof(f24029,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))),c_SetInterval_Oord_OatLeastAtMost(X0,c_member(X1),sk0_322,X2)))|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))),X2))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f5311,f20903])).
% 9.35/1.94 fof(f25047,plain,(
% 9.35/1.94 ![X0]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThan(X0,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f5315,f20271])).
% 9.35/1.94 fof(f25211,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hBOOL(hAPP(hAPP(c_member(X0),X1),c_SetInterval_Oord_OgreaterThan(X0,c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),X3))))|~hBOOL(hAPP(X3,X1)))),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f5331,f5315])).
% 9.35/1.94 fof(f25212,plain,(
% 9.35/1.94 ![X0]: (hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),c_SetInterval_Oord_OlessThan(X0,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),sk0_322)))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f5319,f20271])).
% 9.35/1.94 fof(f25376,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Option_Ooption_OSome(X1),X2)),c_SetInterval_Oord_OlessThan(X0,c_Option_Othe(X1),X3)))|~hBOOL(hAPP(X2,X3)))),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f5331,f5319])).
% 9.35/1.94 fof(f25650,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),X3),c_SetInterval_Oord_OgreaterThan(X1,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))|~hBOOL(hAPP(X3,sk0_322))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f25047,f21826])).
% 9.35/1.94 fof(f25652,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeastLessThan(X0,X1,c_member(X2),X3,c_SetInterval_Oord_OgreaterThan(X2,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))|~hBOOL(hAPP(hAPP(X1,X3),sk0_322))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f25047,f5301])).
% 9.35/1.94 fof(f25669,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),X3),c_SetInterval_Oord_OlessThan(X1,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),sk0_322))))|~hBOOL(hAPP(X3,hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f25212,f21826])).
% 9.35/1.94 fof(f26454,plain,(
% 9.35/1.94 ![X0]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeast(X0,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f5323,f20271])).
% 9.35/1.94 fof(f26633,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hBOOL(hAPP(hAPP(c_member(X0),X1),c_SetInterval_Oord_OatLeast(X0,c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),X3))))|~hBOOL(hAPP(X3,X1)))),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f5331,f5323])).
% 9.35/1.94 fof(f26854,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),X3),c_SetInterval_Oord_OatLeast(X1,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))|~hBOOL(hAPP(X3,sk0_322))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f26454,f21826])).
% 9.35/1.94 fof(f27769,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Option_Ooption_OSome(X1),X2)),c_SetInterval_Oord_OatMost(X0,c_Option_Othe(X1),X3)))|~hBOOL(hAPP(X2,X3)))),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f5331,f5327])).
% 9.35/1.94 fof(f27819,plain,(
% 9.35/1.94 ![X0]: (hAPP(c_Com_Obody,X0)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sk0_4(X0))|hAPP(c_Com_Obody,X0)=c_Option_Ooption_ONone(tc_Com_Ocom))),
% 9.35/1.94 inference(resolution,[status(thm)],[f5335,f5381])).
% 9.35/1.94 fof(f28370,plain,(
% 9.35/1.94 ![X0]: (hAPP(c_Com_Obody,X0)=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(c_Com_OWT,sk0_4(X0)))|~spl0_1)),
% 9.35/1.94 inference(resolution,[status(thm)],[f27819,f20226])).
% 9.35/1.94 fof(f28372,plain,(
% 9.35/1.94 ![X0,X1]: (hAPP(c_Com_Obody,X0)=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X1),X0),c_Map_Odom(X1,tc_Com_Ocom,c_Com_Obody))))),
% 9.35/1.94 inference(resolution,[status(thm)],[f27819,f5330])).
% 9.35/1.94 fof(f28377,plain,(
% 9.35/1.94 ![X0]: (hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X0))=sk0_4(X0)|hAPP(c_Com_Obody,X0)=c_Option_Ooption_ONone(tc_Com_Ocom))),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f27819,f5331])).
% 9.35/1.94 fof(f28403,plain,(
% 9.35/1.94 spl0_17 <=> hBOOL(hAPP(c_Com_OWT,sk0_4(v_pn)))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28405,plain,(
% 9.35/1.94 ~hBOOL(hAPP(c_Com_OWT,sk0_4(v_pn)))|spl0_17),
% 9.35/1.94 inference(component_clause,[status(thm)],[f28403])).
% 9.35/1.94 fof(f28406,plain,(
% 9.35/1.94 spl0_18 <=> hAPP(c_Com_Obody,v_pn)=c_Option_Ooption_ONone(tc_Com_Ocom)),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28407,plain,(
% 9.35/1.94 hAPP(c_Com_Obody,v_pn)=c_Option_Ooption_ONone(tc_Com_Ocom)|~spl0_18),
% 9.35/1.94 inference(component_clause,[status(thm)],[f28406])).
% 9.35/1.94 fof(f28409,plain,(
% 9.35/1.94 ~hBOOL(hAPP(c_Com_OWT,sk0_4(v_pn)))|hAPP(c_Com_Obody,v_pn)=c_Option_Ooption_ONone(tc_Com_Ocom)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f28377,f19981])).
% 9.35/1.94 fof(f28410,plain,(
% 9.35/1.94 ~spl0_17|spl0_18),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28409,f28403,f28406])).
% 9.35/1.94 fof(f28553,plain,(
% 9.35/1.94 spl0_19 <=> hAPP(c_Com_Obody,hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))=c_Option_Ooption_ONone(tc_Com_Ocom)),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28556,plain,(
% 9.35/1.94 spl0_20 <=> hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))),c_SetInterval_Oord_OatLeastAtMost(X0,c_member(X1),sk0_322,c_Map_Odom(X1,tc_Com_Ocom,c_Com_Obody))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28559,plain,(
% 9.35/1.94 ![X0,X1]: (hAPP(c_Com_Obody,hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))),c_SetInterval_Oord_OatLeastAtMost(X0,c_member(X1),sk0_322,c_Map_Odom(X1,tc_Com_Ocom,c_Com_Obody))))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f28372,f24029])).
% 9.35/1.94 fof(f28560,plain,(
% 9.35/1.94 spl0_19|spl0_20|~spl0_13),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28559,f28553,f28556,f20270])).
% 9.35/1.94 fof(f28561,plain,(
% 9.35/1.94 spl0_21 <=> hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))),c_SetInterval_Oord_OgreaterThanLessThan(X0,c_member(X1),sk0_322,c_Map_Odom(X1,tc_Com_Ocom,c_Com_Obody))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28564,plain,(
% 9.35/1.94 ![X0,X1]: (hAPP(c_Com_Obody,hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))),c_SetInterval_Oord_OgreaterThanLessThan(X0,c_member(X1),sk0_322,c_Map_Odom(X1,tc_Com_Ocom,c_Com_Obody))))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f28372,f23044])).
% 9.35/1.94 fof(f28565,plain,(
% 9.35/1.94 spl0_19|spl0_21|~spl0_13),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28564,f28553,f28561,f20270])).
% 9.35/1.94 fof(f28570,plain,(
% 9.35/1.94 ![X0,X1]: (hAPP(c_Com_Obody,X0)=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(c_Map_Odom(X1,tc_Com_Ocom,c_Com_Obody),X0)))),
% 9.35/1.94 inference(resolution,[status(thm)],[f28372,f5262])).
% 9.35/1.94 fof(f28572,plain,(
% 9.35/1.94 spl0_22 <=> hAPP(c_Com_Obody,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Option_Ooption_ONone(tc_Com_Ocom)),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28573,plain,(
% 9.35/1.94 hAPP(c_Com_Obody,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Option_Ooption_ONone(tc_Com_Ocom)|~spl0_22),
% 9.35/1.94 inference(component_clause,[status(thm)],[f28572])).
% 9.35/1.94 fof(f28575,plain,(
% 9.35/1.94 spl0_23 <=> hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2),c_Map_Odom(X1,tc_Com_Ocom,c_Com_Obody))))|~hBOOL(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X3,X2)))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28578,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hAPP(c_Com_Obody,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2),c_Map_Odom(X1,tc_Com_Ocom,c_Com_Obody))))|~hBOOL(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X3,X2))))),
% 9.35/1.94 inference(resolution,[status(thm)],[f28372,f21785])).
% 9.35/1.94 fof(f28579,plain,(
% 9.35/1.94 spl0_22|spl0_23),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28578,f28572,f28575])).
% 9.35/1.94 fof(f28580,plain,(
% 9.35/1.94 spl0_24 <=> hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X3)),c_Map_Odom(X1,tc_Com_Ocom,c_Com_Obody))))|~hBOOL(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X4,X2,X3)))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28583,plain,(
% 9.35/1.94 ![X0,X1,X2,X3,X4]: (hAPP(c_Com_Obody,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X3)),c_Map_Odom(X1,tc_Com_Ocom,c_Com_Obody))))|~hBOOL(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X4,X2,X3))))),
% 9.35/1.94 inference(resolution,[status(thm)],[f28372,f21781])).
% 9.35/1.94 fof(f28584,plain,(
% 9.35/1.94 spl0_22|spl0_24),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28583,f28572,f28580])).
% 9.35/1.94 fof(f28586,plain,(
% 9.35/1.94 spl0_25 <=> hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_member(X2),sk0_322,c_Map_Odom(X1,tc_Com_Ocom,c_Com_Obody))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28589,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hAPP(c_Com_Obody,hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_member(X2),sk0_322,c_Map_Odom(X1,tc_Com_Ocom,c_Com_Obody))))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f28372,f21773])).
% 9.35/1.94 fof(f28590,plain,(
% 9.35/1.94 spl0_19|spl0_25|~spl0_13),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28589,f28553,f28586,f20270])).
% 9.35/1.94 fof(f28591,plain,(
% 9.35/1.94 spl0_26 <=> hAPP(c_Com_Obody,sk0_322)=c_Option_Ooption_ONone(tc_Com_Ocom)),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28592,plain,(
% 9.35/1.94 hAPP(c_Com_Obody,sk0_322)=c_Option_Ooption_ONone(tc_Com_Ocom)|~spl0_26),
% 9.35/1.94 inference(component_clause,[status(thm)],[f28591])).
% 9.35/1.94 fof(f28594,plain,(
% 9.35/1.94 spl0_27 <=> hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT),c_Map_Odom(X1,tc_Com_Ocom,c_Com_Obody))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28597,plain,(
% 9.35/1.94 ![X0,X1]: (hAPP(c_Com_Obody,sk0_322)=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT),c_Map_Odom(X1,tc_Com_Ocom,c_Com_Obody))))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f28372,f21720])).
% 9.35/1.94 fof(f28598,plain,(
% 9.35/1.94 spl0_26|spl0_27|~spl0_13),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28597,f28591,f28594,f20270])).
% 9.35/1.94 fof(f28616,plain,(
% 9.35/1.94 spl0_28 <=> hAPP(c_Com_Obody,hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))=c_Option_Ooption_ONone(tc_Com_Ocom)),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28619,plain,(
% 9.35/1.94 spl0_29 <=> hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),c_Map_Odom(X3,tc_Com_Ocom,c_Com_Obody)),c_SetInterval_Oord_OlessThan(X1,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),sk0_322))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28622,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hAPP(c_Com_Obody,hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),c_Map_Odom(X3,tc_Com_Ocom,c_Com_Obody)),c_SetInterval_Oord_OlessThan(X1,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),sk0_322))))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f28570,f25669])).
% 9.35/1.94 fof(f28623,plain,(
% 9.35/1.94 spl0_28|spl0_29|~spl0_13),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28622,f28616,f28619,f20270])).
% 9.35/1.94 fof(f28624,plain,(
% 9.35/1.94 spl0_30 <=> hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),c_Map_Odom(X2,tc_Com_Ocom,c_Com_Obody)),sk0_322)))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28627,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hAPP(c_Com_Obody,hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),c_Map_Odom(X2,tc_Com_Ocom,c_Com_Obody)),sk0_322)))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f28570,f23458])).
% 9.35/1.94 fof(f28628,plain,(
% 9.35/1.94 spl0_28|spl0_30|~spl0_13),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28627,f28616,f28624,f20270])).
% 9.35/1.94 fof(f28629,plain,(
% 9.35/1.94 spl0_31 <=> hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),c_SetInterval_Oord_OatLeastLessThan(X0,c_Option_Othe(X1),c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_Option_Ooption_OSome(X1),c_Map_Odom(X2,tc_Com_Ocom,c_Com_Obody)),sk0_322)))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28632,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hAPP(c_Com_Obody,hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),c_SetInterval_Oord_OatLeastLessThan(X0,c_Option_Othe(X1),c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_Option_Ooption_OSome(X1),c_Map_Odom(X2,tc_Com_Ocom,c_Com_Obody)),sk0_322)))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f28570,f22630])).
% 9.35/1.94 fof(f28633,plain,(
% 9.35/1.94 spl0_28|spl0_31|~spl0_13),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28632,f28616,f28629,f20270])).
% 9.35/1.94 fof(f28634,plain,(
% 9.35/1.94 spl0_32 <=> hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),c_Map_Odom(X3,tc_Com_Ocom,c_Com_Obody)),c_SetInterval_Oord_OgreaterThan(X1,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28637,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hAPP(c_Com_Obody,sk0_322)=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),c_Map_Odom(X3,tc_Com_Ocom,c_Com_Obody)),c_SetInterval_Oord_OgreaterThan(X1,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f28570,f25650])).
% 9.35/1.94 fof(f28638,plain,(
% 9.35/1.94 spl0_26|spl0_32|~spl0_13),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28637,f28591,f28634,f20270])).
% 9.35/1.94 fof(f28639,plain,(
% 9.35/1.94 spl0_33 <=> hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeastLessThan(X0,c_Option_Othe(X1),c_member(X2),hAPP(c_Option_Ooption_OSome(X1),c_Map_Odom(X3,tc_Com_Ocom,c_Com_Obody)),c_SetInterval_Oord_OgreaterThanAtMost(X4,c_member(X5),c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT),hAPP(c_fequal,sk0_322)))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28642,plain,(
% 9.35/1.94 ![X0,X1,X2,X3,X4,X5]: (hAPP(c_Com_Obody,sk0_322)=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeastLessThan(X0,c_Option_Othe(X1),c_member(X2),hAPP(c_Option_Ooption_OSome(X1),c_Map_Odom(X3,tc_Com_Ocom,c_Com_Obody)),c_SetInterval_Oord_OgreaterThanAtMost(X4,c_member(X5),c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT),hAPP(c_fequal,sk0_322)))))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f28570,f23330])).
% 9.35/1.94 fof(f28643,plain,(
% 9.35/1.94 spl0_26|spl0_33|~spl0_13),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28642,f28591,f28639,f20270])).
% 9.35/1.94 fof(f28644,plain,(
% 9.35/1.94 spl0_34 <=> hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),c_Map_Odom(X3,tc_Com_Ocom,c_Com_Obody)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28647,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hAPP(c_Com_Obody,sk0_322)=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),c_Map_Odom(X3,tc_Com_Ocom,c_Com_Obody)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f28570,f23553])).
% 9.35/1.94 fof(f28648,plain,(
% 9.35/1.94 spl0_26|spl0_34|~spl0_13),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28647,f28591,f28644,f20270])).
% 9.35/1.94 fof(f28649,plain,(
% 9.35/1.94 spl0_35 <=> hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeastLessThan(X0,c_Option_Othe(X1),c_member(X2),hAPP(c_Option_Ooption_OSome(X1),c_Map_Odom(X3,tc_Com_Ocom,c_Com_Obody)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28652,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hAPP(c_Com_Obody,sk0_322)=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeastLessThan(X0,c_Option_Othe(X1),c_member(X2),hAPP(c_Option_Ooption_OSome(X1),c_Map_Odom(X3,tc_Com_Ocom,c_Com_Obody)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f28570,f22547])).
% 9.35/1.94 fof(f28653,plain,(
% 9.35/1.94 spl0_26|spl0_35|~spl0_13),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28652,f28591,f28649,f20270])).
% 9.35/1.94 fof(f28658,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hAPP(c_Com_Obody,X0)=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X1),X0),c_Map_Odom(X2,tc_Com_Ocom,c_Com_Obody))))),
% 9.35/1.94 inference(resolution,[status(thm)],[f28570,f5263])).
% 9.35/1.94 fof(f28662,plain,(
% 9.35/1.94 spl0_36 <=> hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))),c_SetInterval_Oord_OatLeastAtMost(X0,c_member(X1),sk0_322,c_Map_Odom(X2,tc_Com_Ocom,c_Com_Obody))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28665,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hAPP(c_Com_Obody,hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))),c_SetInterval_Oord_OatLeastAtMost(X0,c_member(X1),sk0_322,c_Map_Odom(X2,tc_Com_Ocom,c_Com_Obody))))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f28658,f24029])).
% 9.35/1.94 fof(f28666,plain,(
% 9.35/1.94 spl0_19|spl0_36|~spl0_13),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28665,f28553,f28662,f20270])).
% 9.35/1.94 fof(f28667,plain,(
% 9.35/1.94 spl0_37 <=> hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))),c_SetInterval_Oord_OgreaterThanLessThan(X0,c_member(X1),sk0_322,c_Map_Odom(X2,tc_Com_Ocom,c_Com_Obody))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28670,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hAPP(c_Com_Obody,hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))),c_SetInterval_Oord_OgreaterThanLessThan(X0,c_member(X1),sk0_322,c_Map_Odom(X2,tc_Com_Ocom,c_Com_Obody))))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f28658,f23044])).
% 9.35/1.94 fof(f28671,plain,(
% 9.35/1.94 spl0_19|spl0_37|~spl0_13),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28670,f28553,f28667,f20270])).
% 9.35/1.94 fof(f28678,plain,(
% 9.35/1.94 spl0_38 <=> hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2),c_Map_Odom(X3,tc_Com_Ocom,c_Com_Obody))))|~hBOOL(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X4,X2)))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28681,plain,(
% 9.35/1.94 ![X0,X1,X2,X3,X4]: (hAPP(c_Com_Obody,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2),c_Map_Odom(X3,tc_Com_Ocom,c_Com_Obody))))|~hBOOL(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X4,X2))))),
% 9.35/1.94 inference(resolution,[status(thm)],[f28658,f21785])).
% 9.35/1.94 fof(f28682,plain,(
% 9.35/1.94 spl0_22|spl0_38),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28681,f28572,f28678])).
% 9.35/1.94 fof(f28683,plain,(
% 9.35/1.94 spl0_39 <=> hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X3)),c_Map_Odom(X4,tc_Com_Ocom,c_Com_Obody))))|~hBOOL(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X5,X2,X3)))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28686,plain,(
% 9.35/1.94 ![X0,X1,X2,X3,X4,X5]: (hAPP(c_Com_Obody,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X3)),c_Map_Odom(X4,tc_Com_Ocom,c_Com_Obody))))|~hBOOL(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X5,X2,X3))))),
% 9.35/1.94 inference(resolution,[status(thm)],[f28658,f21781])).
% 9.35/1.94 fof(f28687,plain,(
% 9.35/1.94 spl0_22|spl0_39),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28686,f28572,f28683])).
% 9.35/1.94 fof(f28689,plain,(
% 9.35/1.94 spl0_40 <=> hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_member(X2),sk0_322,c_Map_Odom(X3,tc_Com_Ocom,c_Com_Obody))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28692,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hAPP(c_Com_Obody,hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT))),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_member(X2),sk0_322,c_Map_Odom(X3,tc_Com_Ocom,c_Com_Obody))))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f28658,f21773])).
% 9.35/1.94 fof(f28693,plain,(
% 9.35/1.94 spl0_19|spl0_40|~spl0_13),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28692,f28553,f28689,f20270])).
% 9.35/1.94 fof(f28694,plain,(
% 9.35/1.94 spl0_41 <=> hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT),c_Map_Odom(X2,tc_Com_Ocom,c_Com_Obody))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f28697,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hAPP(c_Com_Obody,sk0_322)=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT),c_Map_Odom(X2,tc_Com_Ocom,c_Com_Obody))))|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f28658,f21720])).
% 9.35/1.94 fof(f28698,plain,(
% 9.35/1.94 spl0_26|spl0_41|~spl0_13),
% 9.35/1.94 inference(split_clause,[status(thm)],[f28697,f28591,f28694,f20270])).
% 9.35/1.94 fof(f29079,plain,(
% 9.35/1.94 spl0_43 <=> hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),c_Com_Obody),c_SetInterval_Oord_OgreaterThan(X1,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29082,plain,(
% 9.35/1.94 spl0_44 <=> hBOOL(c_Option_Ooption_ONone(tc_Com_Ocom))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29085,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),c_Com_Obody),c_SetInterval_Oord_OgreaterThan(X1,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))|~hBOOL(c_Option_Ooption_ONone(tc_Com_Ocom))|~spl0_13|~spl0_26)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f28592,f25650])).
% 9.35/1.94 fof(f29086,plain,(
% 9.35/1.94 spl0_43|~spl0_44|~spl0_13|~spl0_26),
% 9.35/1.94 inference(split_clause,[status(thm)],[f29085,f29079,f29082,f20270,f28591])).
% 9.35/1.94 fof(f29087,plain,(
% 9.35/1.94 spl0_45 <=> hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeastLessThan(X0,c_Option_Othe(X1),c_member(X2),hAPP(c_Option_Ooption_OSome(X1),c_Com_Obody),c_SetInterval_Oord_OgreaterThanAtMost(X3,c_member(X4),c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT),hAPP(c_fequal,sk0_322)))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29090,plain,(
% 9.35/1.94 ![X0,X1,X2,X3,X4]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeastLessThan(X0,c_Option_Othe(X1),c_member(X2),hAPP(c_Option_Ooption_OSome(X1),c_Com_Obody),c_SetInterval_Oord_OgreaterThanAtMost(X3,c_member(X4),c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT),hAPP(c_fequal,sk0_322)))))|~hBOOL(c_Option_Ooption_ONone(tc_Com_Ocom))|~spl0_13|~spl0_26)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f28592,f23330])).
% 9.35/1.94 fof(f29091,plain,(
% 9.35/1.94 spl0_45|~spl0_44|~spl0_13|~spl0_26),
% 9.35/1.94 inference(split_clause,[status(thm)],[f29090,f29087,f29082,f20270,f28591])).
% 9.35/1.94 fof(f29092,plain,(
% 9.35/1.94 spl0_46 <=> hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),c_Com_Obody),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29095,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),c_Com_Obody),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))|~hBOOL(c_Option_Ooption_ONone(tc_Com_Ocom))|~spl0_13|~spl0_26)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f28592,f23553])).
% 9.35/1.94 fof(f29096,plain,(
% 9.35/1.94 spl0_46|~spl0_44|~spl0_13|~spl0_26),
% 9.35/1.94 inference(split_clause,[status(thm)],[f29095,f29092,f29082,f20270,f28591])).
% 9.35/1.94 fof(f29097,plain,(
% 9.35/1.94 spl0_47 <=> hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeastLessThan(X0,c_Option_Othe(X1),c_member(X2),hAPP(c_Option_Ooption_OSome(X1),c_Com_Obody),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29100,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeastLessThan(X0,c_Option_Othe(X1),c_member(X2),hAPP(c_Option_Ooption_OSome(X1),c_Com_Obody),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))|~hBOOL(c_Option_Ooption_ONone(tc_Com_Ocom))|~spl0_13|~spl0_26)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f28592,f22547])).
% 9.35/1.94 fof(f29101,plain,(
% 9.35/1.94 spl0_47|~spl0_44|~spl0_13|~spl0_26),
% 9.35/1.94 inference(split_clause,[status(thm)],[f29100,f29097,f29082,f20270,f28591])).
% 9.35/1.94 fof(f29103,plain,(
% 9.35/1.94 spl0_48 <=> hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Option_Ooption_OSome(X1),c_Com_Obody)),c_SetInterval_Oord_OatMost(X0,c_Option_Othe(X1),sk0_322)))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29106,plain,(
% 9.35/1.94 ![X0,X1]: (hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Option_Ooption_OSome(X1),c_Com_Obody)),c_SetInterval_Oord_OatMost(X0,c_Option_Othe(X1),sk0_322)))|~hBOOL(c_Option_Ooption_ONone(tc_Com_Ocom))|~spl0_26)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f28592,f27769])).
% 9.35/1.94 fof(f29107,plain,(
% 9.35/1.94 spl0_48|~spl0_44|~spl0_26),
% 9.35/1.94 inference(split_clause,[status(thm)],[f29106,f29103,f29082,f28591])).
% 9.35/1.94 fof(f29108,plain,(
% 9.35/1.94 spl0_49 <=> hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeastLessThan(X0,c_Com_Obody,c_member(X1),sk0_322,c_SetInterval_Oord_OgreaterThan(X1,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29111,plain,(
% 9.35/1.94 spl0_50 <=> hBOOL(hAPP(c_Option_Ooption_ONone(tc_Com_Ocom),sk0_322))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29114,plain,(
% 9.35/1.94 ![X0,X1]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeastLessThan(X0,c_Com_Obody,c_member(X1),sk0_322,c_SetInterval_Oord_OgreaterThan(X1,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))|~hBOOL(hAPP(c_Option_Ooption_ONone(tc_Com_Ocom),sk0_322))|~spl0_13|~spl0_26)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f28592,f25652])).
% 9.35/1.94 fof(f29115,plain,(
% 9.35/1.94 spl0_49|~spl0_50|~spl0_13|~spl0_26),
% 9.35/1.94 inference(split_clause,[status(thm)],[f29114,f29108,f29111,f20270,f28591])).
% 9.35/1.94 fof(f29117,plain,(
% 9.35/1.94 spl0_51 <=> hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeast(X0,c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),c_Com_Obody))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29120,plain,(
% 9.35/1.94 ![X0,X1]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeast(X0,c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),c_Com_Obody))))|~hBOOL(c_Option_Ooption_ONone(tc_Com_Ocom))|~spl0_26)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f28592,f26633])).
% 9.35/1.94 fof(f29121,plain,(
% 9.35/1.94 spl0_51|~spl0_44|~spl0_26),
% 9.35/1.94 inference(split_clause,[status(thm)],[f29120,f29117,f29082,f28591])).
% 9.35/1.94 fof(f29124,plain,(
% 9.35/1.94 spl0_52 <=> hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Option_Ooption_OSome(X1),c_Com_Obody)),c_SetInterval_Oord_OlessThan(X0,c_Option_Othe(X1),sk0_322)))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29127,plain,(
% 9.35/1.94 ![X0,X1]: (hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_Option_Ooption_OSome(X1),c_Com_Obody)),c_SetInterval_Oord_OlessThan(X0,c_Option_Othe(X1),sk0_322)))|~hBOOL(c_Option_Ooption_ONone(tc_Com_Ocom))|~spl0_26)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f28592,f25376])).
% 9.35/1.94 fof(f29128,plain,(
% 9.35/1.94 spl0_52|~spl0_44|~spl0_26),
% 9.35/1.94 inference(split_clause,[status(thm)],[f29127,f29124,f29082,f28591])).
% 9.35/1.94 fof(f29129,plain,(
% 9.35/1.94 spl0_53 <=> hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThan(X0,c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),c_Com_Obody))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29132,plain,(
% 9.35/1.94 ![X0,X1]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThan(X0,c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),c_Com_Obody))))|~hBOOL(c_Option_Ooption_ONone(tc_Com_Ocom))|~spl0_26)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f28592,f25211])).
% 9.35/1.94 fof(f29133,plain,(
% 9.35/1.94 spl0_53|~spl0_44|~spl0_26),
% 9.35/1.94 inference(split_clause,[status(thm)],[f29132,f29129,f29082,f28591])).
% 9.35/1.94 fof(f29136,plain,(
% 9.35/1.94 spl0_54 <=> hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),c_Com_Obody),hAPP(c_fequal,sk0_322))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29139,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),c_Com_Obody),hAPP(c_fequal,sk0_322))))|~hBOOL(c_Option_Ooption_ONone(tc_Com_Ocom))|~spl0_26)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f28592,f23554])).
% 9.35/1.94 fof(f29140,plain,(
% 9.35/1.94 spl0_54|~spl0_44|~spl0_26),
% 9.35/1.94 inference(split_clause,[status(thm)],[f29139,f29136,f29082,f28591])).
% 9.35/1.94 fof(f29145,plain,(
% 9.35/1.94 spl0_55 <=> hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeastLessThan(X0,c_Com_Obody,c_member(X1),sk0_322,c_SetInterval_Oord_OgreaterThanAtMost(X2,c_member(X3),c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT),hAPP(c_fequal,sk0_322)))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29148,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeastLessThan(X0,c_Com_Obody,c_member(X1),sk0_322,c_SetInterval_Oord_OgreaterThanAtMost(X2,c_member(X3),c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT),hAPP(c_fequal,sk0_322)))))|~hBOOL(hAPP(c_Option_Ooption_ONone(tc_Com_Ocom),sk0_322))|~spl0_13|~spl0_26)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f28592,f22197])).
% 9.35/1.94 fof(f29149,plain,(
% 9.35/1.94 spl0_55|~spl0_50|~spl0_13|~spl0_26),
% 9.35/1.94 inference(split_clause,[status(thm)],[f29148,f29145,f29111,f20270,f28591])).
% 9.35/1.94 fof(f29151,plain,(
% 9.35/1.94 spl0_56 <=> hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),c_SetInterval_Oord_OatLeastLessThan(X0,c_Com_Obody,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),sk0_322,sk0_322)))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29154,plain,(
% 9.35/1.94 spl0_57 <=> hBOOL(hAPP(c_Option_Ooption_ONone(tc_Com_Ocom),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29157,plain,(
% 9.35/1.94 ![X0]: (hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),c_SetInterval_Oord_OatLeastLessThan(X0,c_Com_Obody,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),sk0_322,sk0_322)))|~hBOOL(hAPP(c_Option_Ooption_ONone(tc_Com_Ocom),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))|~spl0_13|~spl0_26)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f28592,f22129])).
% 9.35/1.94 fof(f29158,plain,(
% 9.35/1.94 spl0_56|~spl0_57|~spl0_13|~spl0_26),
% 9.35/1.94 inference(split_clause,[status(thm)],[f29157,f29151,f29154,f20270,f28591])).
% 9.35/1.94 fof(f29159,plain,(
% 9.35/1.94 spl0_58 <=> hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeastLessThan(X0,c_Com_Obody,c_member(X1),sk0_322,hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29162,plain,(
% 9.35/1.94 ![X0,X1]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OatLeastLessThan(X0,c_Com_Obody,c_member(X1),sk0_322,hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))|~hBOOL(hAPP(c_Option_Ooption_ONone(tc_Com_Ocom),sk0_322))|~spl0_13|~spl0_26)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f28592,f22198])).
% 9.35/1.94 fof(f29163,plain,(
% 9.35/1.94 spl0_58|~spl0_50|~spl0_13|~spl0_26),
% 9.35/1.94 inference(split_clause,[status(thm)],[f29162,f29159,f29111,f20270,f28591])).
% 9.35/1.94 fof(f29169,plain,(
% 9.35/1.94 spl0_59 <=> hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_Com_Obody))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29172,plain,(
% 9.35/1.94 ![X0]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_Com_Obody))|~hBOOL(c_Option_Ooption_ONone(tc_Com_Ocom))|~spl0_26)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f28592,f5263])).
% 9.35/1.94 fof(f29173,plain,(
% 9.35/1.94 spl0_59|~spl0_44|~spl0_26),
% 9.35/1.94 inference(split_clause,[status(thm)],[f29172,f29169,f29082,f28591])).
% 9.35/1.94 fof(f29182,plain,(
% 9.35/1.94 spl0_61 <=> hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29183,plain,(
% 9.35/1.94 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))|~spl0_61),
% 9.35/1.94 inference(component_clause,[status(thm)],[f29182])).
% 9.35/1.94 fof(f29184,plain,(
% 9.35/1.94 ~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))|spl0_61),
% 9.35/1.94 inference(component_clause,[status(thm)],[f29182])).
% 9.35/1.94 fof(f29271,plain,(
% 9.35/1.94 spl0_73 <=> hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),c_Map_Odom(X3,tc_Com_Ocom,c_Com_Obody)),c_SetInterval_Oord_OatLeast(X1,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29274,plain,(
% 9.35/1.94 ![X0,X1,X2,X3]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),c_Map_Odom(X3,tc_Com_Ocom,c_Com_Obody)),c_SetInterval_Oord_OatLeast(X1,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))|hAPP(c_Com_Obody,sk0_322)=c_Option_Ooption_ONone(tc_Com_Ocom)|~spl0_13)),
% 9.35/1.94 inference(resolution,[status(thm)],[f26854,f28570])).
% 9.35/1.94 fof(f29275,plain,(
% 9.35/1.94 spl0_73|spl0_26|~spl0_13),
% 9.35/1.94 inference(split_clause,[status(thm)],[f29274,f29271,f28591,f20270])).
% 9.35/1.94 fof(f29277,plain,(
% 9.35/1.94 spl0_74 <=> hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),c_Com_Obody),c_SetInterval_Oord_OatLeast(X1,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29280,plain,(
% 9.35/1.94 ![X0,X1,X2]: (hBOOL(hAPP(hAPP(c_member(X0),sk0_322),c_SetInterval_Oord_OgreaterThanAtMost(X0,c_member(X1),c_Option_Othe(X2),hAPP(c_Option_Ooption_OSome(X2),c_Com_Obody),c_SetInterval_Oord_OatLeast(X1,c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)))))|~hBOOL(c_Option_Ooption_ONone(tc_Com_Ocom))|~spl0_13|~spl0_26)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f28592,f26854])).
% 9.35/1.94 fof(f29281,plain,(
% 9.35/1.94 spl0_74|~spl0_44|~spl0_13|~spl0_26),
% 9.35/1.94 inference(split_clause,[status(thm)],[f29280,f29277,f29082,f20270,f28591])).
% 9.35/1.94 fof(f29282,plain,(
% 9.35/1.94 hAPP(c_Com_Obody,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sk0_4(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|~spl0_61),
% 9.35/1.94 inference(resolution,[status(thm)],[f29183,f5335])).
% 9.35/1.94 fof(f29283,plain,(
% 9.35/1.94 c_Option_Ooption_ONone(tc_Com_Ocom)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sk0_4(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|~spl0_22|~spl0_61),
% 9.35/1.94 inference(forward_demodulation,[status(thm)],[f28573,f29282])).
% 9.35/1.94 fof(f29292,plain,(
% 9.35/1.94 hAPP(c_Com_Obody,v_pn)=c_Option_Ooption_ONone(tc_Com_Ocom)|~spl0_1|spl0_17),
% 9.35/1.94 inference(resolution,[status(thm)],[f28370,f28405])).
% 9.35/1.94 fof(f29388,plain,(
% 9.35/1.94 spl0_86 <=> c_Option_Ooption_ONone(tc_Com_Ocom)=c_Option_Ooption_ONone(tc_Com_Ocom)),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29390,plain,(
% 9.35/1.94 ~c_Option_Ooption_ONone(tc_Com_Ocom)=c_Option_Ooption_ONone(tc_Com_Ocom)|spl0_86),
% 9.35/1.94 inference(component_clause,[status(thm)],[f29388])).
% 9.35/1.94 fof(f29396,plain,(
% 9.35/1.94 spl0_88 <=> ~hAPP(c_Com_Obody,X0)=c_Option_Ooption_ONone(tc_Com_Ocom)),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29397,plain,(
% 9.35/1.94 ![X0]: (~hAPP(c_Com_Obody,X0)=c_Option_Ooption_ONone(tc_Com_Ocom)|~spl0_88)),
% 9.35/1.94 inference(component_clause,[status(thm)],[f29396])).
% 9.35/1.94 fof(f29401,plain,(
% 9.35/1.94 ![X0]: (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X0)))|~hAPP(c_Com_Obody,X0)=c_Option_Ooption_ONone(tc_Com_Ocom)|~spl0_22|~spl0_61)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f29283,f5336])).
% 9.35/1.94 fof(f29402,plain,(
% 9.35/1.94 ![X0]: (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X0)))|~spl0_22|~spl0_61)),
% 9.35/1.94 inference(forward_subsumption_resolution,[status(thm)],[f29401,f5381])).
% 9.35/1.94 fof(f29477,plain,(
% 9.35/1.94 $false|spl0_86),
% 9.35/1.94 inference(trivial_equality_resolution,[status(esa)],[f29390])).
% 9.35/1.94 fof(f29478,plain,(
% 9.35/1.94 spl0_86),
% 9.35/1.94 inference(contradiction_clause,[status(thm)],[f29477])).
% 9.35/1.94 fof(f29479,plain,(
% 9.35/1.94 ![X0]: (hAPP(c_Com_Obody,X0)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sk0_4(X0))|~spl0_22|~spl0_61)),
% 9.35/1.94 inference(backward_subsumption_resolution,[status(thm)],[f5335,f29402])).
% 9.35/1.94 fof(f29497,plain,(
% 9.35/1.94 ![X0]: (hBOOL(hAPP(c_Com_OWT,sk0_4(X0)))|~spl0_22|~spl0_61|~spl0_1)),
% 9.35/1.94 inference(resolution,[status(thm)],[f29479,f20226])).
% 9.35/1.94 fof(f29511,plain,(
% 9.35/1.94 ![X0]: (hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X0))=sk0_4(X0)|~spl0_22|~spl0_61)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f29479,f5331])).
% 9.35/1.94 fof(f29799,plain,(
% 9.35/1.94 ~hBOOL(hAPP(c_Com_OWT,sk0_4(v_pn)))|~spl0_22|~spl0_61),
% 9.35/1.94 inference(forward_demodulation,[status(thm)],[f29511,f19981])).
% 9.35/1.94 fof(f29800,plain,(
% 9.35/1.94 $false|~spl0_1|~spl0_22|~spl0_61),
% 9.35/1.94 inference(forward_subsumption_resolution,[status(thm)],[f29799,f29497])).
% 9.35/1.94 fof(f29801,plain,(
% 9.35/1.94 ~spl0_1|~spl0_22|~spl0_61),
% 9.35/1.94 inference(contradiction_clause,[status(thm)],[f29800])).
% 9.35/1.94 fof(f29802,plain,(
% 9.35/1.94 ~hBOOL(hAPP(c_Com_OWT,hAPP(c_Option_Othe(tc_Com_Ocom),c_Option_Ooption_ONone(tc_Com_Ocom))))|~spl0_18),
% 9.35/1.94 inference(forward_demodulation,[status(thm)],[f28407,f19981])).
% 9.35/1.94 fof(f29948,plain,(
% 9.35/1.94 hAPP(c_Com_Obody,v_pn)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sk0_5(v_pn,tc_Com_Ocom,c_Com_Obody))),
% 9.35/1.94 inference(resolution,[status(thm)],[f5354,f21006])).
% 9.35/1.94 fof(f29949,plain,(
% 9.35/1.94 c_Option_Ooption_ONone(tc_Com_Ocom)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sk0_5(v_pn,tc_Com_Ocom,c_Com_Obody))|~spl0_18),
% 9.35/1.94 inference(forward_demodulation,[status(thm)],[f28407,f29948])).
% 9.35/1.94 fof(f29953,plain,(
% 9.35/1.94 ![X0]: (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X0)))|~hAPP(c_Com_Obody,X0)=c_Option_Ooption_ONone(tc_Com_Ocom)|~spl0_18)),
% 9.35/1.94 inference(paramodulation,[status(thm)],[f29949,f5336])).
% 9.35/1.94 fof(f29954,plain,(
% 9.35/1.94 ![X0]: (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X0)))|~spl0_18)),
% 9.35/1.94 inference(forward_subsumption_resolution,[status(thm)],[f29953,f5381])).
% 9.35/1.94 fof(f29955,plain,(
% 9.35/1.94 spl0_112 <=> hBOOL(hAPP(c_Com_OWT,sk0_5(v_pn,tc_Com_Ocom,c_Com_Obody)))),
% 9.35/1.94 introduced(split_symbol_definition)).
% 9.35/1.94 fof(f29956,plain,(
% 9.35/1.94 hBOOL(hAPP(c_Com_OWT,sk0_5(v_pn,tc_Com_Ocom,c_Com_Obody)))|~spl0_112),
% 9.89/1.99 inference(component_clause,[status(thm)],[f29955])).
% 9.89/1.99 fof(f29958,plain,(
% 9.89/1.99 ![X0]: (~hAPP(c_Com_Obody,X0)=c_Option_Ooption_ONone(tc_Com_Ocom)|hBOOL(hAPP(c_Com_OWT,sk0_5(v_pn,tc_Com_Ocom,c_Com_Obody)))|~spl0_1|~spl0_18)),
% 9.89/1.99 inference(paramodulation,[status(thm)],[f29949,f20226])).
% 9.89/1.99 fof(f29959,plain,(
% 9.89/1.99 spl0_88|spl0_112|~spl0_1|~spl0_18),
% 9.89/1.99 inference(split_clause,[status(thm)],[f29958,f29396,f29955,f20225,f28406])).
% 9.89/1.99 fof(f29968,plain,(
% 9.89/1.99 hAPP(c_Option_Othe(tc_Com_Ocom),c_Option_Ooption_ONone(tc_Com_Ocom))=sk0_5(v_pn,tc_Com_Ocom,c_Com_Obody)|~spl0_18),
% 9.89/1.99 inference(paramodulation,[status(thm)],[f29949,f5331])).
% 9.89/1.99 fof(f30111,plain,(
% 9.89/1.99 $false|~spl0_88|~spl0_18),
% 9.89/1.99 inference(backward_subsumption_resolution,[status(thm)],[f28407,f29397])).
% 9.89/1.99 fof(f30112,plain,(
% 9.89/1.99 ~spl0_88|~spl0_18),
% 9.89/1.99 inference(contradiction_clause,[status(thm)],[f30111])).
% 9.89/1.99 fof(f30113,plain,(
% 9.89/1.99 spl0_18|~spl0_1|spl0_17),
% 9.89/1.99 inference(split_clause,[status(thm)],[f29292,f28406,f20225,f28403])).
% 9.89/1.99 fof(f30271,plain,(
% 9.89/1.99 $false|~spl0_18|spl0_61),
% 9.89/1.99 inference(forward_subsumption_resolution,[status(thm)],[f29184,f29954])).
% 9.89/1.99 fof(f30272,plain,(
% 9.89/1.99 ~spl0_18|spl0_61),
% 9.89/1.99 inference(contradiction_clause,[status(thm)],[f30271])).
% 9.89/1.99 fof(f30356,plain,(
% 9.89/1.99 ~hBOOL(hAPP(c_Com_OWT,sk0_5(v_pn,tc_Com_Ocom,c_Com_Obody)))|~spl0_18),
% 9.89/1.99 inference(backward_demodulation,[status(thm)],[f29968,f29802])).
% 9.89/1.99 fof(f30357,plain,(
% 9.89/1.99 $false|~spl0_112|~spl0_18),
% 9.89/1.99 inference(forward_subsumption_resolution,[status(thm)],[f30356,f29956])).
% 9.89/1.99 fof(f30358,plain,(
% 9.89/1.99 ~spl0_112|~spl0_18),
% 9.89/1.99 inference(contradiction_clause,[status(thm)],[f30357])).
% 9.89/1.99 fof(f30359,plain,(
% 9.89/1.99 $false),
% 9.89/1.99 inference(sat_refutation,[status(thm)],[f20228,f20235,f20239,f20265,f20396,f20398,f20400,f28410,f28560,f28565,f28579,f28584,f28590,f28598,f28623,f28628,f28633,f28638,f28643,f28648,f28653,f28666,f28671,f28682,f28687,f28693,f28698,f29086,f29091,f29096,f29101,f29107,f29115,f29121,f29128,f29133,f29140,f29149,f29158,f29163,f29173,f29275,f29281,f29478,f29801,f29959,f30112,f30113,f30272,f30358])).
% 9.89/1.99 % SZS output end CNFRefutation for theBenchmark.p
% 9.89/2.01 % Elapsed time: 1.653485 seconds
% 9.89/2.01 % CPU time: 9.759691 seconds
% 9.89/2.01 % Memory used: 673.792 MB
%------------------------------------------------------------------------------