TSTP Solution File: SCT161+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SCT161+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 : Tue Apr 30 20:38:24 EDT 2024
% Result : Theorem 15.49s 2.42s
% Output : CNFRefutation 16.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SCT161+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.36 % Computer : n009.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Apr 29 20:07:41 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.21/0.42 % Drodi V3.6.0
% 15.49/2.42 % Refutation found
% 15.49/2.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 15.49/2.42 % SZS output start CNFRefutation for theBenchmark
% 15.49/2.42 fof(f10,axiom,(
% 15.49/2.42 (! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f18,axiom,(
% 15.49/2.42 (! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f48,axiom,(
% 15.49/2.42 (! [V_P_2,V_n_2,V_m_2] :( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )=> ( ( V_m_2 = V_n_2=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f50,axiom,(
% 15.49/2.42 ~ (! [B_h] :( c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))=> c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) ) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f52,axiom,(
% 15.49/2.42 (! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f68,axiom,(
% 15.49/2.42 (! [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)) ) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f69,axiom,(
% 15.49/2.42 (! [V_A_2,V_f_2,T_b,T_a] :( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)<=> (! [B_x] :( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))=> (! [B_xa] :( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))=> ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)=> B_x = B_xa ) ) )) )) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f72,axiom,(
% 15.49/2.42 (! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f147,axiom,(
% 15.49/2.42 (! [V_u_2,V_l_2] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2,V_u_2)) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f158,axiom,(
% 15.49/2.42 (! [V_A_2,T_a] :( class_Finite__Set_Ofinite(T_a)=> c_Finite__Set_Ofinite(T_a,V_A_2) ) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f211,axiom,(
% 15.49/2.42 (! [V_A_2,T_a] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f223,axiom,(
% 15.49/2.42 (! [V_B_2,V_A_2,T_a] :( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))& V_A_2 != V_B_2 ) ) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f229,axiom,(
% 15.49/2.42 (! [V_A_2,V_f_2,T_b,T_a] :( c_Finite__Set_Ofinite(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))=> ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2)=> c_Finite__Set_Ofinite(T_b,V_A_2) ) ) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f247,axiom,(
% 15.49/2.42 (! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f250,axiom,(
% 15.49/2.42 (! [V_n,V_m] :( V_m = V_n=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f254,axiom,(
% 15.49/2.42 ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f286,axiom,(
% 15.49/2.42 (! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f304,axiom,(
% 15.49/2.42 (! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f307,axiom,(
% 15.49/2.42 (! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f336,axiom,(
% 15.49/2.42 (! [V_aa_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f493,axiom,(
% 15.49/2.42 (! [T_2,T_1] :( class_Orderings_Opreorder(T_1)=> class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f495,axiom,(
% 15.49/2.42 (! [T_2,T_1] :( class_Orderings_Oorder(T_1)=> class_Orderings_Oorder(tc_fun(T_2,T_1)) ) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f499,axiom,(
% 15.49/2.42 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f508,axiom,(
% 15.49/2.42 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f509,axiom,(
% 15.49/2.42 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f511,axiom,(
% 15.49/2.42 class_Orderings_Olinorder(tc_Nat_Onat) ),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f512,axiom,(
% 15.49/2.42 class_Groups_Omonoid__add(tc_Nat_Onat) ),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f515,axiom,(
% 15.49/2.42 class_Orderings_Obot(tc_Nat_Onat) ),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f517,axiom,(
% 15.49/2.42 class_Orderings_Opreorder(tc_HOL_Obool) ),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f518,axiom,(
% 15.49/2.42 class_Finite__Set_Ofinite(tc_HOL_Obool) ),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f519,axiom,(
% 15.49/2.42 class_Orderings_Oorder(tc_HOL_Obool) ),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f532,axiom,(
% 15.49/2.42 (! [V_y_2,V_x_2] :( V_x_2 != V_y_2| hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) )),
% 15.49/2.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 15.49/2.42 fof(f550,plain,(
% 15.49/2.42 ![X0]: (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)))),
% 15.49/2.42 inference(cnf_transformation,[status(esa)],[f10])).
% 15.49/2.42 fof(f564,plain,(
% 15.49/2.42 ![X0]: (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 15.49/2.42 inference(cnf_transformation,[status(esa)],[f18])).
% 15.49/2.42 fof(f657,plain,(
% 15.49/2.42 ![V_P_2,V_n_2,V_m_2]: ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))&~hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))|((V_m_2=V_n_2&~hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))|((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))&~hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))|hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))))),
% 15.49/2.42 inference(pre_NNF_transformation,[status(esa)],[f48])).
% 15.49/2.42 fof(f658,plain,(
% 15.49/2.42 ![V_P_2,V_n_2,V_m_2]: (pd0_0(V_m_2,V_n_2,V_P_2)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))&~hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))))),
% 15.49/2.42 introduced(predicate_definition,[f657])).
% 15.49/2.42 fof(f659,plain,(
% 15.49/2.42 ![V_P_2,V_n_2,V_m_2]: (pd0_0(V_m_2,V_n_2,V_P_2)|((V_m_2=V_n_2&~hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))|((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))&~hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))|hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))))),
% 15.49/2.42 inference(formula_renaming,[status(thm)],[f657,f658])).
% 15.49/2.42 fof(f660,plain,(
% 15.49/2.42 ![V_P_2,V_n_2,V_m_2]: (pd0_1(V_m_2,V_n_2,V_P_2)=>(V_m_2=V_n_2&~hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))))),
% 15.49/2.42 introduced(predicate_definition,[f659])).
% 15.49/2.42 fof(f666,plain,(
% 15.49/2.42 (?[B_h]: (c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))&c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))=c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))))),
% 15.49/2.42 inference(pre_NNF_transformation,[status(esa)],[f50])).
% 15.49/2.42 fof(f667,plain,(
% 15.49/2.42 (c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,sk0_1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))&c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,sk0_1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))=c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))),
% 15.49/2.42 inference(skolemization,[status(esa)],[f666])).
% 15.49/2.42 fof(f668,plain,(
% 15.49/2.42 c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,sk0_1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
% 15.49/2.42 inference(cnf_transformation,[status(esa)],[f667])).
% 15.49/2.42 fof(f673,plain,(
% 15.49/2.42 ![X0,X1]: (hBOOL(hAPP(hAPP(c_member(X0),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))))),
% 15.49/2.42 inference(cnf_transformation,[status(esa)],[f52])).
% 15.49/2.42 fof(f738,plain,(
% 15.49/2.42 ![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))))),
% 15.49/2.42 inference(NNF_transformation,[status(esa)],[f68])).
% 15.49/2.42 fof(f739,plain,(
% 15.49/2.42 (![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))))),
% 15.49/2.42 inference(miniscoping,[status(esa)],[f738])).
% 15.49/2.42 fof(f740,plain,(
% 15.49/2.42 ![X0,X1,X2]: (~hBOOL(hAPP(hAPP(c_member(X0),X1),X2))|hBOOL(hAPP(X2,X1)))),
% 15.49/2.42 inference(cnf_transformation,[status(esa)],[f739])).
% 15.49/2.42 fof(f741,plain,(
% 15.49/2.42 ![X0,X1,X2]: (hBOOL(hAPP(hAPP(c_member(X0),X1),X2))|~hBOOL(hAPP(X2,X1)))),
% 15.49/2.42 inference(cnf_transformation,[status(esa)],[f739])).
% 15.49/2.42 fof(f742,plain,(
% 15.49/2.42 ![V_A_2,V_f_2,T_b,T_a]: (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)<=>(![B_x]: (~hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))|(![B_xa]: (~hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))|(~hAPP(V_f_2,B_x)=hAPP(V_f_2,B_xa)|B_x=B_xa))))))),
% 15.49/2.42 inference(pre_NNF_transformation,[status(esa)],[f69])).
% 15.49/2.42 fof(f743,plain,(
% 15.49/2.42 ![V_A_2,V_f_2,T_b,T_a]: ((~c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)|(![B_x]: (~hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))|(![B_xa]: (~hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))|(~hAPP(V_f_2,B_x)=hAPP(V_f_2,B_xa)|B_x=B_xa))))))&(c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)|(?[B_x]: (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))&(?[B_xa]: (hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))&(hAPP(V_f_2,B_x)=hAPP(V_f_2,B_xa)&~B_x=B_xa)))))))),
% 15.49/2.42 inference(NNF_transformation,[status(esa)],[f742])).
% 15.49/2.42 fof(f744,plain,(
% 15.49/2.42 (![V_A_2,V_f_2,T_a]: ((![T_b]: ~c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2))|(![B_x]: (~hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))|(![B_xa]: (~hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))|(~hAPP(V_f_2,B_x)=hAPP(V_f_2,B_xa)|B_x=B_xa)))))))&(![V_A_2,V_f_2,T_a]: ((![T_b]: c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2))|(?[B_x]: (hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))&(?[B_xa]: (hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))&(hAPP(V_f_2,B_x)=hAPP(V_f_2,B_xa)&~B_x=B_xa)))))))),
% 15.49/2.42 inference(miniscoping,[status(esa)],[f743])).
% 15.49/2.42 fof(f745,plain,(
% 15.49/2.42 (![V_A_2,V_f_2,T_a]: ((![T_b]: ~c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2))|(![B_x]: (~hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))|(![B_xa]: (~hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))|(~hAPP(V_f_2,B_x)=hAPP(V_f_2,B_xa)|B_x=B_xa)))))))&(![V_A_2,V_f_2,T_a]: ((![T_b]: c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2))|(hBOOL(hAPP(hAPP(c_member(T_a),sk0_8(T_a,V_f_2,V_A_2)),V_A_2))&(hBOOL(hAPP(hAPP(c_member(T_a),sk0_9(T_a,V_f_2,V_A_2)),V_A_2))&(hAPP(V_f_2,sk0_8(T_a,V_f_2,V_A_2))=hAPP(V_f_2,sk0_9(T_a,V_f_2,V_A_2))&~sk0_8(T_a,V_f_2,V_A_2)=sk0_9(T_a,V_f_2,V_A_2))))))),
% 15.49/2.42 inference(skolemization,[status(esa)],[f744])).
% 15.49/2.42 fof(f746,plain,(
% 15.49/2.42 ![X0,X1,X2,X3,X4,X5]: (~c_Fun_Oinj__on(X0,X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(X0),X4),X3))|~hBOOL(hAPP(hAPP(c_member(X0),X5),X3))|~hAPP(X2,X4)=hAPP(X2,X5)|X4=X5)),
% 15.49/2.42 inference(cnf_transformation,[status(esa)],[f745])).
% 15.49/2.42 fof(f747,plain,(
% 15.49/2.42 ![X0,X1,X2,X3]: (c_Fun_Oinj__on(X0,X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X0),sk0_8(X0,X2,X3)),X3)))),
% 15.49/2.42 inference(cnf_transformation,[status(esa)],[f745])).
% 15.49/2.42 fof(f749,plain,(
% 15.49/2.42 ![X0,X1,X2,X3]: (c_Fun_Oinj__on(X0,X1,X2,X3)|hAPP(X2,sk0_8(X0,X2,X3))=hAPP(X2,sk0_9(X0,X2,X3)))),
% 15.49/2.42 inference(cnf_transformation,[status(esa)],[f745])).
% 15.49/2.42 fof(f750,plain,(
% 15.49/2.42 ![X0,X1,X2,X3]: (c_Fun_Oinj__on(X0,X1,X2,X3)|~sk0_8(X0,X2,X3)=sk0_9(X0,X2,X3))),
% 15.49/2.42 inference(cnf_transformation,[status(esa)],[f745])).
% 15.49/2.42 fof(f753,plain,(
% 15.49/2.42 ![X0,X1]: (c_Fun_Oinj__on(X0,X0,c_COMBI(X0),X1))),
% 15.49/2.42 inference(cnf_transformation,[status(esa)],[f72])).
% 15.49/2.42 fof(f1080,plain,(
% 15.49/2.42 ![X0,X1]: (c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0,X1)))),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f147])).
% 15.49/2.43 fof(f1113,plain,(
% 15.49/2.43 ![V_A_2,T_a]: (~class_Finite__Set_Ofinite(T_a)|c_Finite__Set_Ofinite(T_a,V_A_2))),
% 15.49/2.43 inference(pre_NNF_transformation,[status(esa)],[f158])).
% 15.49/2.43 fof(f1114,plain,(
% 15.49/2.43 ![T_a]: (~class_Finite__Set_Ofinite(T_a)|(![V_A_2]: c_Finite__Set_Ofinite(T_a,V_A_2)))),
% 15.49/2.43 inference(miniscoping,[status(esa)],[f1113])).
% 15.49/2.43 fof(f1115,plain,(
% 15.49/2.43 ![X0,X1]: (~class_Finite__Set_Ofinite(X0)|c_Finite__Set_Ofinite(X0,X1))),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f1114])).
% 15.49/2.43 fof(f1299,plain,(
% 15.49/2.43 ![X0,X1]: (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))))),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f211])).
% 15.49/2.43 fof(f1343,plain,(
% 15.49/2.43 ![V_B_2,V_A_2,T_a]: ((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))|(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))&~V_A_2=V_B_2))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))|(~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))|V_A_2=V_B_2)))),
% 15.49/2.43 inference(NNF_transformation,[status(esa)],[f223])).
% 15.49/2.43 fof(f1344,plain,(
% 15.49/2.43 (![V_B_2,V_A_2,T_a]: (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))|(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))&~V_A_2=V_B_2)))&(![V_B_2,V_A_2,T_a]: (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))|(~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))|V_A_2=V_B_2)))),
% 15.49/2.43 inference(miniscoping,[status(esa)],[f1343])).
% 15.49/2.43 fof(f1346,plain,(
% 15.49/2.43 ![X0,X1,X2]: (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X0,tc_HOL_Obool)),X1),X2))|~X1=X2)),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f1344])).
% 15.49/2.43 fof(f1361,plain,(
% 15.49/2.43 ![V_A_2,V_f_2,T_b,T_a]: (~c_Finite__Set_Ofinite(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))|(~c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2)|c_Finite__Set_Ofinite(T_b,V_A_2)))),
% 15.49/2.43 inference(pre_NNF_transformation,[status(esa)],[f229])).
% 15.49/2.43 fof(f1362,plain,(
% 15.49/2.43 ![X0,X1,X2,X3]: (~c_Finite__Set_Ofinite(X0,c_Set_Oimage(X1,X0,X2,X3))|~c_Fun_Oinj__on(X1,X0,X2,X3)|c_Finite__Set_Ofinite(X1,X3))),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f1361])).
% 15.49/2.43 fof(f1423,plain,(
% 15.49/2.43 ![X0]: (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)))),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f247])).
% 15.49/2.43 fof(f1429,plain,(
% 15.49/2.43 ![V_n,V_m]: (~V_m=V_n|hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)))),
% 15.49/2.43 inference(pre_NNF_transformation,[status(esa)],[f250])).
% 15.49/2.43 fof(f1430,plain,(
% 15.49/2.43 ![X0,X1]: (~X0=X1|hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X1)))),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f1429])).
% 15.49/2.43 fof(f1440,plain,(
% 15.49/2.43 ~c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f254])).
% 15.49/2.43 fof(f1523,plain,(
% 15.49/2.43 ![X0]: (~hAPP(c_Nat_OSuc,X0)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f286])).
% 15.49/2.43 fof(f1566,plain,(
% 15.49/2.43 ![X0]: (~hAPP(c_Nat_OSuc,X0)=X0)),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f304])).
% 15.49/2.43 fof(f1571,plain,(
% 15.49/2.43 ![X0]: (c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X0))),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f307])).
% 15.49/2.43 fof(f1666,plain,(
% 15.49/2.43 ![X0,X1]: (~hBOOL(hAPP(hAPP(c_member(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))))),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f336])).
% 15.49/2.43 fof(f2167,plain,(
% 15.49/2.43 ![T_2,T_1]: (~class_Orderings_Opreorder(T_1)|class_Orderings_Opreorder(tc_fun(T_2,T_1)))),
% 15.49/2.43 inference(pre_NNF_transformation,[status(esa)],[f493])).
% 15.49/2.43 fof(f2168,plain,(
% 15.49/2.43 ![T_1]: (~class_Orderings_Opreorder(T_1)|(![T_2]: class_Orderings_Opreorder(tc_fun(T_2,T_1))))),
% 15.49/2.43 inference(miniscoping,[status(esa)],[f2167])).
% 15.49/2.43 fof(f2169,plain,(
% 15.49/2.43 ![X0,X1]: (~class_Orderings_Opreorder(X0)|class_Orderings_Opreorder(tc_fun(X1,X0)))),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f2168])).
% 15.49/2.43 fof(f2172,plain,(
% 15.49/2.43 ![T_2,T_1]: (~class_Orderings_Oorder(T_1)|class_Orderings_Oorder(tc_fun(T_2,T_1)))),
% 15.49/2.43 inference(pre_NNF_transformation,[status(esa)],[f495])).
% 15.49/2.43 fof(f2173,plain,(
% 15.49/2.43 ![T_1]: (~class_Orderings_Oorder(T_1)|(![T_2]: class_Orderings_Oorder(tc_fun(T_2,T_1))))),
% 15.49/2.43 inference(miniscoping,[status(esa)],[f2172])).
% 15.49/2.43 fof(f2174,plain,(
% 15.49/2.43 ![X0,X1]: (~class_Orderings_Oorder(X0)|class_Orderings_Oorder(tc_fun(X1,X0)))),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f2173])).
% 15.49/2.43 fof(f2184,plain,(
% 15.49/2.43 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat)),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f499])).
% 15.49/2.43 fof(f2193,plain,(
% 15.49/2.43 class_Groups_Ocomm__monoid__add(tc_Nat_Onat)),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f508])).
% 15.49/2.43 fof(f2194,plain,(
% 15.49/2.43 class_Rings_Ocomm__semiring__1(tc_Nat_Onat)),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f509])).
% 15.49/2.43 fof(f2196,plain,(
% 15.49/2.43 class_Orderings_Olinorder(tc_Nat_Onat)),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f511])).
% 15.49/2.43 fof(f2197,plain,(
% 15.49/2.43 class_Groups_Omonoid__add(tc_Nat_Onat)),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f512])).
% 15.49/2.43 fof(f2200,plain,(
% 15.49/2.43 class_Orderings_Obot(tc_Nat_Onat)),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f515])).
% 15.49/2.43 fof(f2202,plain,(
% 15.49/2.43 class_Orderings_Opreorder(tc_HOL_Obool)),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f517])).
% 15.49/2.43 fof(f2203,plain,(
% 15.49/2.43 class_Finite__Set_Ofinite(tc_HOL_Obool)),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f518])).
% 15.49/2.43 fof(f2204,plain,(
% 15.49/2.43 class_Orderings_Oorder(tc_HOL_Obool)),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f519])).
% 15.49/2.43 fof(f2220,plain,(
% 15.49/2.43 ![X0,X1]: (~X0=X1|hBOOL(hAPP(hAPP(c_fequal,X0),X1)))),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f532])).
% 15.49/2.43 fof(f2226,plain,(
% 15.49/2.43 ![V_P_2,V_n_2,V_m_2]: (~pd0_0(V_m_2,V_n_2,V_P_2)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))&~hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))))),
% 15.49/2.43 inference(pre_NNF_transformation,[status(esa)],[f658])).
% 15.49/2.43 fof(f2227,plain,(
% 15.49/2.43 ![X0,X1,X2]: (~pd0_0(X0,X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1)))),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f2226])).
% 15.49/2.43 fof(f2228,plain,(
% 15.49/2.43 ![X0,X1,X2]: (~pd0_0(X0,X1,X2)|~hBOOL(hAPP(hAPP(X2,X1),X0)))),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f2226])).
% 15.49/2.43 fof(f2229,plain,(
% 15.49/2.43 ![V_P_2,V_n_2,V_m_2]: (~pd0_1(V_m_2,V_n_2,V_P_2)|(V_m_2=V_n_2&~hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))))),
% 15.49/2.43 inference(pre_NNF_transformation,[status(esa)],[f660])).
% 15.49/2.43 fof(f2231,plain,(
% 15.49/2.43 ![X0,X1,X2]: (~pd0_1(X0,X1,X2)|~hBOOL(hAPP(hAPP(X2,X1),X0)))),
% 15.49/2.43 inference(cnf_transformation,[status(esa)],[f2229])).
% 15.49/2.43 fof(f2327,plain,(
% 15.49/2.43 ![X0,X1]: (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X0,tc_HOL_Obool)),X1),X1)))),
% 15.49/2.43 inference(destructive_equality_resolution,[status(esa)],[f1346])).
% 15.49/2.43 fof(f2329,plain,(
% 15.49/2.43 ![X0]: (hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),X0)))),
% 15.49/2.43 inference(destructive_equality_resolution,[status(esa)],[f1430])).
% 15.49/2.43 fof(f2368,plain,(
% 15.49/2.43 ![X0]: (hBOOL(hAPP(hAPP(c_fequal,X0),X0)))),
% 15.49/2.43 inference(destructive_equality_resolution,[status(esa)],[f2220])).
% 15.49/2.43 fof(f2559,plain,(
% 15.49/2.43 spl0_23 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f2561,plain,(
% 15.49/2.43 ~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|spl0_23),
% 15.49/2.43 inference(component_clause,[status(thm)],[f2559])).
% 15.49/2.43 fof(f3445,plain,(
% 15.49/2.43 spl0_169 <=> c_Finite__Set_Ofinite(X0,X1)),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f3446,plain,(
% 15.49/2.43 ![X0,X1]: (c_Finite__Set_Ofinite(X0,X1)|~spl0_169)),
% 15.49/2.43 inference(component_clause,[status(thm)],[f3445])).
% 15.49/2.43 fof(f3485,plain,(
% 15.49/2.43 $false|~spl0_169),
% 15.49/2.43 inference(backward_subsumption_resolution,[status(thm)],[f1440,f3446])).
% 15.49/2.43 fof(f3486,plain,(
% 15.49/2.43 ~spl0_169),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f3485])).
% 15.49/2.43 fof(f4177,plain,(
% 15.49/2.43 spl0_232 <=> ~class_Finite__Set_Ofinite(X0)),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f4178,plain,(
% 15.49/2.43 ![X0]: (~class_Finite__Set_Ofinite(X0)|~spl0_232)),
% 15.49/2.43 inference(component_clause,[status(thm)],[f4177])).
% 15.49/2.43 fof(f4311,plain,(
% 15.49/2.43 $false|~spl0_232),
% 15.49/2.43 inference(backward_subsumption_resolution,[status(thm)],[f2203,f4178])).
% 15.49/2.43 fof(f4312,plain,(
% 15.49/2.43 ~spl0_232),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f4311])).
% 15.49/2.43 fof(f4722,plain,(
% 15.49/2.43 spl0_280 <=> ~c_Fun_Oinj__on(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oindi,X0,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f4723,plain,(
% 15.49/2.43 ![X0]: (~c_Fun_Oinj__on(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oindi,X0,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))|~spl0_280)),
% 15.49/2.43 inference(component_clause,[status(thm)],[f4722])).
% 15.49/2.43 fof(f4733,plain,(
% 15.49/2.43 spl0_283 <=> ~c_Fun_Oinj__on(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oindi,X0,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2)))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f4734,plain,(
% 15.49/2.43 ![X0]: (~c_Fun_Oinj__on(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oindi,X0,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2)))|~spl0_283)),
% 15.49/2.43 inference(component_clause,[status(thm)],[f4733])).
% 15.49/2.43 fof(f4741,plain,(
% 15.49/2.43 spl0_285 <=> class_Orderings_Oorder(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f4743,plain,(
% 15.49/2.43 ~class_Orderings_Oorder(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|spl0_285),
% 15.49/2.43 inference(component_clause,[status(thm)],[f4741])).
% 15.49/2.43 fof(f4746,plain,(
% 15.49/2.43 spl0_286 <=> class_Orderings_Opreorder(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f4748,plain,(
% 15.49/2.43 ~class_Orderings_Opreorder(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|spl0_286),
% 15.49/2.43 inference(component_clause,[status(thm)],[f4746])).
% 15.49/2.43 fof(f4782,plain,(
% 15.49/2.43 spl0_288 <=> c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2))=c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f4783,plain,(
% 15.49/2.43 c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2))=c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|~spl0_288),
% 15.49/2.43 inference(component_clause,[status(thm)],[f4782])).
% 15.49/2.43 fof(f4828,plain,(
% 15.49/2.43 spl0_294 <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f4829,plain,(
% 15.49/2.43 c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~spl0_294),
% 15.49/2.43 inference(component_clause,[status(thm)],[f4828])).
% 15.49/2.43 fof(f4833,plain,(
% 15.49/2.43 $false|~spl0_294),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f4829,f1523])).
% 15.49/2.43 fof(f4834,plain,(
% 15.49/2.43 ~spl0_294),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f4833])).
% 15.49/2.43 fof(f4837,plain,(
% 15.49/2.43 spl0_295 <=> ~class_Orderings_Olinorder(X0)),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f4838,plain,(
% 15.49/2.43 ![X0]: (~class_Orderings_Olinorder(X0)|~spl0_295)),
% 15.49/2.43 inference(component_clause,[status(thm)],[f4837])).
% 15.49/2.43 fof(f4854,plain,(
% 15.49/2.43 spl0_299 <=> hAPP(X3,X3)=X3),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f4855,plain,(
% 15.49/2.43 ![X0]: (hAPP(X0,X0)=X0|~spl0_299)),
% 15.49/2.43 inference(component_clause,[status(thm)],[f4854])).
% 15.49/2.43 fof(f5035,plain,(
% 15.49/2.43 c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))|~spl0_288),
% 15.49/2.43 inference(paramodulation,[status(thm)],[f4783,f1080])).
% 15.49/2.43 fof(f5036,plain,(
% 15.49/2.43 $false|~spl0_288),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f5035,f1440])).
% 15.49/2.43 fof(f5037,plain,(
% 15.49/2.43 ~spl0_288),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f5036])).
% 15.49/2.43 fof(f5083,plain,(
% 15.49/2.43 $false|~spl0_295),
% 15.49/2.43 inference(backward_subsumption_resolution,[status(thm)],[f2196,f4838])).
% 15.49/2.43 fof(f5084,plain,(
% 15.49/2.43 ~spl0_295),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f5083])).
% 15.49/2.43 fof(f5085,plain,(
% 15.49/2.43 $false|~spl0_299),
% 15.49/2.43 inference(resolution,[status(thm)],[f4855,f1566])).
% 15.49/2.43 fof(f5086,plain,(
% 15.49/2.43 ~spl0_299),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f5085])).
% 15.49/2.43 fof(f5233,plain,(
% 15.49/2.43 spl0_323 <=> class_Orderings_Obot(tc_Nat_Onat)),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f5235,plain,(
% 15.49/2.43 ~class_Orderings_Obot(tc_Nat_Onat)|spl0_323),
% 15.49/2.43 inference(component_clause,[status(thm)],[f5233])).
% 15.49/2.43 fof(f5241,plain,(
% 15.49/2.43 $false|spl0_323),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f5235,f2200])).
% 15.49/2.43 fof(f5242,plain,(
% 15.49/2.43 spl0_323),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f5241])).
% 15.49/2.43 fof(f5256,plain,(
% 15.49/2.43 ![X0]: (~pd0_0(X0,X0,c_fequal))),
% 15.49/2.43 inference(resolution,[status(thm)],[f2228,f2368])).
% 15.49/2.43 fof(f5291,plain,(
% 15.49/2.43 ![X0]: (~pd0_1(X0,X0,c_fequal))),
% 15.49/2.43 inference(resolution,[status(thm)],[f2231,f2368])).
% 15.49/2.43 fof(f5442,plain,(
% 15.49/2.43 spl0_330 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_h____,v_Sledgehammer_058p__2)),hAPP(v_h____,v_Sledgehammer_058p__2)))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f5444,plain,(
% 15.49/2.43 ~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_h____,v_Sledgehammer_058p__2)),hAPP(v_h____,v_Sledgehammer_058p__2)))|spl0_330),
% 15.49/2.43 inference(component_clause,[status(thm)],[f5442])).
% 15.49/2.43 fof(f5451,plain,(
% 15.49/2.43 $false|spl0_330),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f5444,f2329])).
% 15.49/2.43 fof(f5452,plain,(
% 15.49/2.43 spl0_330),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f5451])).
% 15.49/2.43 fof(f5591,plain,(
% 15.49/2.43 spl0_342 <=> pd0_0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Orderings_Oord__class_Oless(tc_Nat_Onat))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f5592,plain,(
% 15.49/2.43 pd0_0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Orderings_Oord__class_Oless(tc_Nat_Onat))|~spl0_342),
% 15.49/2.43 inference(component_clause,[status(thm)],[f5591])).
% 15.49/2.43 fof(f5641,plain,(
% 15.49/2.43 spl0_345 <=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat)),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f5643,plain,(
% 15.49/2.43 ~class_Groups_Ocomm__monoid__add(tc_Nat_Onat)|spl0_345),
% 15.49/2.43 inference(component_clause,[status(thm)],[f5641])).
% 15.49/2.43 fof(f5648,plain,(
% 15.49/2.43 $false|spl0_345),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f5643,f2193])).
% 15.49/2.43 fof(f5649,plain,(
% 15.49/2.43 spl0_345),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f5648])).
% 15.49/2.43 fof(f5650,plain,(
% 15.49/2.43 spl0_346 <=> class_Groups_Omonoid__add(tc_Nat_Onat)),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f5652,plain,(
% 15.49/2.43 ~class_Groups_Omonoid__add(tc_Nat_Onat)|spl0_346),
% 15.49/2.43 inference(component_clause,[status(thm)],[f5650])).
% 15.49/2.43 fof(f5657,plain,(
% 15.49/2.43 $false|spl0_346),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f5652,f2197])).
% 15.49/2.43 fof(f5658,plain,(
% 15.49/2.43 spl0_346),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f5657])).
% 15.49/2.43 fof(f5667,plain,(
% 15.49/2.43 spl0_347 <=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat)),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f5669,plain,(
% 15.49/2.43 ~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat)|spl0_347),
% 15.49/2.43 inference(component_clause,[status(thm)],[f5667])).
% 15.49/2.43 fof(f5674,plain,(
% 15.49/2.43 $false|spl0_347),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f5669,f2184])).
% 15.49/2.43 fof(f5675,plain,(
% 15.49/2.43 spl0_347),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f5674])).
% 15.49/2.43 fof(f5755,plain,(
% 15.49/2.43 spl0_354 <=> c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi,c_COMBI(tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f5757,plain,(
% 15.49/2.43 ~c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi,c_COMBI(tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))|spl0_354),
% 15.49/2.43 inference(component_clause,[status(thm)],[f5755])).
% 15.49/2.43 fof(f5760,plain,(
% 15.49/2.43 $false|spl0_354),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f5757,f753])).
% 15.49/2.43 fof(f5761,plain,(
% 15.49/2.43 spl0_354),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f5760])).
% 15.49/2.43 fof(f6011,plain,(
% 15.49/2.43 spl0_374 <=> pd0_0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f6012,plain,(
% 15.49/2.43 pd0_0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))|~spl0_374),
% 15.49/2.43 inference(component_clause,[status(thm)],[f6011])).
% 15.49/2.43 fof(f6025,plain,(
% 15.49/2.43 spl0_377 <=> pd0_0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f6026,plain,(
% 15.49/2.43 pd0_0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~spl0_377),
% 15.49/2.43 inference(component_clause,[status(thm)],[f6025])).
% 15.49/2.43 fof(f6270,plain,(
% 15.49/2.43 spl0_394 <=> class_Rings_Ocomm__semiring__1(tc_Nat_Onat)),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f6272,plain,(
% 15.49/2.43 ~class_Rings_Ocomm__semiring__1(tc_Nat_Onat)|spl0_394),
% 15.49/2.43 inference(component_clause,[status(thm)],[f6270])).
% 15.49/2.43 fof(f6277,plain,(
% 15.49/2.43 $false|spl0_394),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f6272,f2194])).
% 15.49/2.43 fof(f6278,plain,(
% 15.49/2.43 spl0_394),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f6277])).
% 15.49/2.43 fof(f6398,plain,(
% 15.49/2.43 spl0_406 <=> pd0_0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc)),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f6399,plain,(
% 15.49/2.43 pd0_0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc)|~spl0_406),
% 15.49/2.43 inference(component_clause,[status(thm)],[f6398])).
% 15.49/2.43 fof(f7124,plain,(
% 15.49/2.43 spl0_438 <=> pd0_0(c_Orderings_Otop__class_Otop(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f7125,plain,(
% 15.49/2.43 pd0_0(c_Orderings_Otop__class_Otop(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))|~spl0_438),
% 15.49/2.43 inference(component_clause,[status(thm)],[f7124])).
% 15.49/2.43 fof(f7363,plain,(
% 15.49/2.43 spl0_458 <=> c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f7365,plain,(
% 15.49/2.43 ~c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))|spl0_458),
% 15.49/2.43 inference(component_clause,[status(thm)],[f7363])).
% 15.49/2.43 fof(f7386,plain,(
% 15.49/2.43 $false|spl0_458),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f7365,f1571])).
% 15.49/2.43 fof(f7387,plain,(
% 15.49/2.43 spl0_458),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f7386])).
% 15.49/2.43 fof(f7424,plain,(
% 15.49/2.43 spl0_460 <=> ~X0=X0),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f7425,plain,(
% 15.49/2.43 ![X0]: (~X0=X0|~spl0_460)),
% 15.49/2.43 inference(component_clause,[status(thm)],[f7424])).
% 15.49/2.43 fof(f7429,plain,(
% 15.49/2.43 $false|~spl0_460),
% 15.49/2.43 inference(trivial_equality_resolution,[status(esa)],[f7425])).
% 15.49/2.43 fof(f7430,plain,(
% 15.49/2.43 ~spl0_460),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f7429])).
% 15.49/2.43 fof(f7487,plain,(
% 15.49/2.43 ![X0,X1]: (~hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X1)))),
% 15.49/2.43 inference(resolution,[status(thm)],[f1666,f741])).
% 15.49/2.43 fof(f7553,plain,(
% 15.49/2.43 spl0_464 <=> pd0_0(v_Sledgehammer_058p__2,v_Sledgehammer_058p__2,v_h____)),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f7554,plain,(
% 15.49/2.43 pd0_0(v_Sledgehammer_058p__2,v_Sledgehammer_058p__2,v_h____)|~spl0_464),
% 15.49/2.43 inference(component_clause,[status(thm)],[f7553])).
% 15.49/2.43 fof(f7677,plain,(
% 15.49/2.43 spl0_473 <=> pd0_0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_fequal)),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f7678,plain,(
% 15.49/2.43 pd0_0(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_fequal)|~spl0_473),
% 15.49/2.43 inference(component_clause,[status(thm)],[f7677])).
% 15.49/2.43 fof(f7680,plain,(
% 15.49/2.43 spl0_474 <=> pd0_1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_fequal)),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f7681,plain,(
% 15.49/2.43 pd0_1(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_fequal)|~spl0_474),
% 15.49/2.43 inference(component_clause,[status(thm)],[f7680])).
% 15.49/2.43 fof(f7685,plain,(
% 15.49/2.43 $false|~spl0_474),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f7681,f5291])).
% 15.49/2.43 fof(f7686,plain,(
% 15.49/2.43 ~spl0_474),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f7685])).
% 15.49/2.43 fof(f7687,plain,(
% 15.49/2.43 $false|~spl0_473),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f7678,f5256])).
% 15.49/2.43 fof(f7688,plain,(
% 15.49/2.43 ~spl0_473),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f7687])).
% 15.49/2.43 fof(f7692,plain,(
% 15.49/2.43 spl0_476 <=> hBOOL(hAPP(hAPP(c_fequal,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f7694,plain,(
% 15.49/2.43 ~hBOOL(hAPP(hAPP(c_fequal,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|spl0_476),
% 15.49/2.43 inference(component_clause,[status(thm)],[f7692])).
% 15.49/2.43 fof(f7738,plain,(
% 15.49/2.43 ![X0,X1]: (~pd0_0(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))),
% 15.49/2.43 inference(resolution,[status(thm)],[f2227,f564])).
% 15.49/2.43 fof(f7743,plain,(
% 15.49/2.43 ![X0,X1]: (~pd0_0(X0,X0,X1))),
% 15.49/2.43 inference(resolution,[status(thm)],[f2227,f550])).
% 15.49/2.43 fof(f7781,plain,(
% 15.49/2.43 $false|~spl0_464),
% 15.49/2.43 inference(backward_subsumption_resolution,[status(thm)],[f7554,f7743])).
% 15.49/2.43 fof(f7782,plain,(
% 15.49/2.43 ~spl0_464),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f7781])).
% 15.49/2.43 fof(f7783,plain,(
% 15.49/2.43 $false|~spl0_438),
% 15.49/2.43 inference(backward_subsumption_resolution,[status(thm)],[f7125,f7743])).
% 15.49/2.43 fof(f7784,plain,(
% 15.49/2.43 ~spl0_438),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f7783])).
% 15.49/2.43 fof(f7785,plain,(
% 15.49/2.43 $false|~spl0_377),
% 15.49/2.43 inference(backward_subsumption_resolution,[status(thm)],[f6026,f7743])).
% 15.49/2.43 fof(f7786,plain,(
% 15.49/2.43 ~spl0_377),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f7785])).
% 15.49/2.43 fof(f7787,plain,(
% 15.49/2.43 $false|~spl0_374),
% 15.49/2.43 inference(backward_subsumption_resolution,[status(thm)],[f6012,f7743])).
% 15.49/2.43 fof(f7788,plain,(
% 15.49/2.43 ~spl0_374),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f7787])).
% 15.49/2.43 fof(f7789,plain,(
% 15.49/2.43 $false|~spl0_406),
% 15.49/2.43 inference(backward_subsumption_resolution,[status(thm)],[f6399,f7743])).
% 15.49/2.43 fof(f7790,plain,(
% 15.49/2.43 ~spl0_406),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f7789])).
% 15.49/2.43 fof(f7864,plain,(
% 15.49/2.43 spl0_488 <=> ~class_Orderings_Oorder(X0)),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f7865,plain,(
% 15.49/2.43 ![X0]: (~class_Orderings_Oorder(X0)|~spl0_488)),
% 15.49/2.43 inference(component_clause,[status(thm)],[f7864])).
% 15.49/2.43 fof(f7869,plain,(
% 15.49/2.43 $false|~spl0_488),
% 15.49/2.43 inference(backward_subsumption_resolution,[status(thm)],[f2204,f7865])).
% 15.49/2.43 fof(f7870,plain,(
% 15.49/2.43 ~spl0_488),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f7869])).
% 15.49/2.43 fof(f7875,plain,(
% 15.49/2.43 spl0_489 <=> ~class_Orderings_Opreorder(X0)),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f7876,plain,(
% 15.49/2.43 ![X0]: (~class_Orderings_Opreorder(X0)|~spl0_489)),
% 15.49/2.43 inference(component_clause,[status(thm)],[f7875])).
% 15.49/2.43 fof(f7880,plain,(
% 15.49/2.43 $false|~spl0_489),
% 15.49/2.43 inference(backward_subsumption_resolution,[status(thm)],[f2202,f7876])).
% 15.49/2.43 fof(f7881,plain,(
% 15.49/2.43 ~spl0_489),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f7880])).
% 15.49/2.43 fof(f8165,plain,(
% 15.49/2.43 $false|spl0_23),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f2561,f1423])).
% 15.49/2.43 fof(f8166,plain,(
% 15.49/2.43 spl0_23),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f8165])).
% 15.49/2.43 fof(f8379,plain,(
% 15.49/2.43 ~class_Orderings_Oorder(tc_HOL_Obool)|spl0_285),
% 15.49/2.43 inference(resolution,[status(thm)],[f4743,f2174])).
% 15.49/2.43 fof(f8380,plain,(
% 15.49/2.43 $false|spl0_285),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f8379,f2204])).
% 15.49/2.43 fof(f8381,plain,(
% 15.49/2.43 spl0_285),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f8380])).
% 15.49/2.43 fof(f8382,plain,(
% 15.49/2.43 ~class_Orderings_Opreorder(tc_HOL_Obool)|spl0_286),
% 15.49/2.43 inference(resolution,[status(thm)],[f4748,f2169])).
% 15.49/2.43 fof(f8383,plain,(
% 15.49/2.43 $false|spl0_286),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f8382,f2202])).
% 15.49/2.43 fof(f8384,plain,(
% 15.49/2.43 spl0_286),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f8383])).
% 15.49/2.43 fof(f8388,plain,(
% 15.49/2.43 $false|spl0_476),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f7694,f2368])).
% 15.49/2.43 fof(f8389,plain,(
% 15.49/2.43 spl0_476),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f8388])).
% 15.49/2.43 fof(f8527,plain,(
% 15.49/2.43 spl0_515 <=> ~c_Fun_Oinj__on(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oindi,X0,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2)))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f8528,plain,(
% 15.49/2.43 ![X0]: (~c_Fun_Oinj__on(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oindi,X0,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2)))|~spl0_515)),
% 15.49/2.43 inference(component_clause,[status(thm)],[f8527])).
% 15.49/2.43 fof(f9053,plain,(
% 15.49/2.43 spl0_529 <=> ~c_Fun_Oinj__on(X0,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f9054,plain,(
% 15.49/2.43 ![X0,X1,X2]: (~c_Fun_Oinj__on(X0,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))|~spl0_529)),
% 15.49/2.43 inference(component_clause,[status(thm)],[f9053])).
% 15.49/2.43 fof(f9139,plain,(
% 15.49/2.43 $false|~spl0_529),
% 15.49/2.43 inference(backward_subsumption_resolution,[status(thm)],[f668,f9054])).
% 15.49/2.43 fof(f9140,plain,(
% 15.49/2.43 ~spl0_529),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f9139])).
% 15.49/2.43 fof(f9444,plain,(
% 15.49/2.43 spl0_551 <=> c_Finite__Set_Ofinite(tc_Nat_Onat,X0)),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f9445,plain,(
% 15.49/2.43 ![X0]: (c_Finite__Set_Ofinite(tc_Nat_Onat,X0)|~spl0_551)),
% 15.49/2.43 inference(component_clause,[status(thm)],[f9444])).
% 15.49/2.43 fof(f9474,plain,(
% 15.49/2.43 ![X0,X1,X2,X3]: (~c_Fun_Oinj__on(X0,X1,X2,X3)|c_Finite__Set_Ofinite(X0,X3)|~class_Finite__Set_Ofinite(X1))),
% 15.49/2.43 inference(resolution,[status(thm)],[f1362,f1115])).
% 15.49/2.43 fof(f9548,plain,(
% 15.49/2.43 ![X0,X1,X2,X3,X4]: (~c_Fun_Oinj__on(X0,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))|~hBOOL(hAPP(hAPP(c_member(X0),X3),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))))|~hAPP(X2,X3)=hAPP(X2,X4)|X3=X4)),
% 15.49/2.43 inference(resolution,[status(thm)],[f746,f673])).
% 15.49/2.43 fof(f9549,plain,(
% 15.49/2.43 ![X0,X1,X2,X3,X4]: (~c_Fun_Oinj__on(X0,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))|~hAPP(X2,X3)=hAPP(X2,X4)|X3=X4)),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f9548,f673])).
% 15.49/2.43 fof(f9567,plain,(
% 15.49/2.43 ![X0,X1,X2,X3]: (c_Fun_Oinj__on(X0,X1,X2,X3)|hBOOL(hAPP(X3,sk0_8(X0,X2,X3))))),
% 15.49/2.43 inference(resolution,[status(thm)],[f747,f740])).
% 15.49/2.43 fof(f9702,plain,(
% 15.49/2.43 $false|~spl0_551),
% 15.49/2.43 inference(backward_subsumption_resolution,[status(thm)],[f1440,f9445])).
% 15.49/2.43 fof(f9703,plain,(
% 15.49/2.43 ~spl0_551),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f9702])).
% 15.49/2.43 fof(f9919,plain,(
% 15.49/2.43 $false|~spl0_342),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f5592,f7738])).
% 15.49/2.43 fof(f9920,plain,(
% 15.49/2.43 ~spl0_342),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f9919])).
% 15.49/2.43 fof(f9921,plain,(
% 15.49/2.43 ![X0,X1]: (~hAPP(sk0_1,X0)=hAPP(sk0_1,X1)|X0=X1)),
% 15.49/2.43 inference(resolution,[status(thm)],[f9549,f668])).
% 15.49/2.43 fof(f10127,plain,(
% 15.49/2.43 ![X0,X1,X2,X3]: (c_Fun_Oinj__on(X0,X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))),
% 15.49/2.43 inference(resolution,[status(thm)],[f9567,f7487])).
% 15.49/2.43 fof(f10212,plain,(
% 15.49/2.43 ![X0,X1,X2]: (c_Fun_Oinj__on(X0,X1,sk0_1,X2)|sk0_8(X0,sk0_1,X2)=sk0_9(X0,sk0_1,X2))),
% 15.49/2.43 inference(resolution,[status(thm)],[f749,f9921])).
% 15.49/2.43 fof(f10213,plain,(
% 15.49/2.43 ![X0,X1,X2]: (c_Fun_Oinj__on(X0,X1,sk0_1,X2))),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f10212,f750])).
% 15.49/2.43 fof(f10535,plain,(
% 15.49/2.43 spl0_586 <=> ~c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi,X1,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f10536,plain,(
% 15.49/2.43 ![X0]: (~c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))|~spl0_586)),
% 15.49/2.43 inference(component_clause,[status(thm)],[f10535])).
% 15.49/2.43 fof(f10549,plain,(
% 15.49/2.43 spl0_588 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f10551,plain,(
% 15.49/2.43 ~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))|spl0_588),
% 15.49/2.43 inference(component_clause,[status(thm)],[f10549])).
% 15.49/2.43 fof(f10598,plain,(
% 15.49/2.43 $false|spl0_588),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f10551,f1299])).
% 15.49/2.43 fof(f10599,plain,(
% 15.49/2.43 spl0_588),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f10598])).
% 15.49/2.43 fof(f10600,plain,(
% 15.49/2.43 $false|~spl0_586),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f10536,f10127])).
% 15.49/2.43 fof(f10601,plain,(
% 15.49/2.43 ~spl0_586),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f10600])).
% 15.49/2.43 fof(f10612,plain,(
% 15.49/2.43 spl0_593 <=> c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2))=c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f10614,plain,(
% 15.49/2.43 ~c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2))=c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2))|spl0_593),
% 15.49/2.43 inference(component_clause,[status(thm)],[f10612])).
% 15.49/2.43 fof(f10617,plain,(
% 15.49/2.43 $false|spl0_593),
% 15.49/2.43 inference(trivial_equality_resolution,[status(esa)],[f10614])).
% 15.49/2.43 fof(f10618,plain,(
% 15.49/2.43 spl0_593),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f10617])).
% 15.49/2.43 fof(f10649,plain,(
% 15.49/2.43 spl0_598 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2))))),
% 15.49/2.43 introduced(split_symbol_definition)).
% 15.49/2.43 fof(f10650,plain,(
% 15.49/2.43 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2))))|~spl0_598),
% 15.49/2.43 inference(component_clause,[status(thm)],[f10649])).
% 15.49/2.43 fof(f10654,plain,(
% 15.49/2.43 $false|~spl0_598),
% 15.49/2.43 inference(forward_subsumption_resolution,[status(thm)],[f10650,f2327])).
% 15.49/2.43 fof(f10655,plain,(
% 15.49/2.43 ~spl0_598),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f10654])).
% 15.49/2.43 fof(f10722,plain,(
% 15.49/2.43 $false|~spl0_515),
% 15.49/2.43 inference(resolution,[status(thm)],[f10213,f8528])).
% 15.49/2.43 fof(f10723,plain,(
% 15.49/2.43 ~spl0_515),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f10722])).
% 15.49/2.43 fof(f10724,plain,(
% 15.49/2.43 $false|~spl0_283),
% 15.49/2.43 inference(resolution,[status(thm)],[f10213,f4734])).
% 15.49/2.43 fof(f10725,plain,(
% 15.49/2.43 ~spl0_283),
% 15.49/2.43 inference(contradiction_clause,[status(thm)],[f10724])).
% 15.49/2.43 fof(f10726,plain,(
% 15.49/2.43 $false|~spl0_280),
% 16.19/2.48 inference(resolution,[status(thm)],[f10213,f4723])).
% 16.19/2.48 fof(f10727,plain,(
% 16.19/2.48 ~spl0_280),
% 16.19/2.48 inference(contradiction_clause,[status(thm)],[f10726])).
% 16.19/2.48 fof(f10732,plain,(
% 16.19/2.48 ![X0,X1,X2]: (c_Finite__Set_Ofinite(X0,X1)|~class_Finite__Set_Ofinite(X2))),
% 16.19/2.48 inference(resolution,[status(thm)],[f10213,f9474])).
% 16.19/2.48 fof(f10733,plain,(
% 16.19/2.48 spl0_169|spl0_232),
% 16.19/2.48 inference(split_clause,[status(thm)],[f10732,f3445,f4177])).
% 16.19/2.48 fof(f10734,plain,(
% 16.19/2.48 $false),
% 16.19/2.48 inference(sat_refutation,[status(thm)],[f3486,f4312,f4834,f5037,f5084,f5086,f5242,f5452,f5649,f5658,f5675,f5761,f6278,f7387,f7430,f7686,f7688,f7782,f7784,f7786,f7788,f7790,f7870,f7881,f8166,f8381,f8384,f8389,f9140,f9703,f9920,f10599,f10601,f10618,f10655,f10723,f10725,f10727,f10733])).
% 16.19/2.48 % SZS output end CNFRefutation for theBenchmark.p
% 16.19/2.49 % Elapsed time: 2.130380 seconds
% 16.19/2.49 % CPU time: 16.225957 seconds
% 16.19/2.49 % Total memory used: 319.799 MB
% 16.19/2.49 % Net memory used: 315.771 MB
%------------------------------------------------------------------------------